Вікіпедія

Модуль:Math: відмінності між версіями

Інтерактивний перегляд історії
[перевірена версія][перевірена версія]
← Попереднє редагуванняНаступне редагування →
Вилучено вміст Додано вміст
а якщо російську взяти?
ні
Рядок 4:
 
]]
local z = {}
 
local yesno, getArgs -- lazily initialized
-- Generate random number
function z.random( frame )
first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil
second = tonumber(frame.args[2])
 
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
if first then -- if NaN or nil, will skip down to final return
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
if first <= second then -- could match if both nil, but already checked that first is a number in last line
 
return math.random(first, second)
--[[
end
Helper functions used to avoid redundant code.
return math.random(first)
]]
end
 
return math.random()
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
 
Рядок 26 ⟶ 110:
 
Usage:
{{#invoke: Math | order | value }}
]]
 
function z.order(frame)
function wrap.order(args)
local input_string = (frame.args[1] or frame.args.x or '0');
local input_string = (args[1] or args.x or '0');
local input_number;
local input_number = p._cleanNumber(input_string);
if input_number == z._cleanNumber( frame, input_stringnil );then
return err('order of magnitude input appears non-numeric')
if input_number == nil then
else
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при определении десятичной степени</strong>'
return p._order(input_number)
else
end
return z._order( input_number )
end
end
 
function z._order(x)
function p._order(x)
if x == 0 then return 0 end
if x == 0 then return 0 end
return math.floor(math.log10(math.abs(x)))
end
 
Рядок 50 ⟶ 134:
 
Usage:
{{ #invoke: Math | precision | value }}
]]
 
function z.precision( frame )
function wrap.precision(args)
local input_string = (frame.args[1] or frame.args.x or '0');
local input_string = (args[1] or args.x or '0');
local trap_fraction = frame.args.check_fraction or false;
local trap_fraction = args.check_fraction;
local input_number;
local input_number;
 
if type( trap_fraction ) == 'string' then
if not yesno then
trap_fraction = trap_fraction:lower();
yesno = require('Module:Yesno')
if trap_fraction == 'false' or trap_fraction == '0' or
end
trap_fraction == 'no' or trap_fraction == '' then
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
trap_fraction = false;
local pos = string.find(input_string, '/', 1, true);
else
if pos ~= nil then
trap_fraction = true;
if string.find(input_string, '/', pos + 1, true) == nil then
end
local denominator = string.sub(input_string, pos+1, -1);
end
local denom_value = tonumber(denominator);
if denom_value ~= nil then
if trap_fraction then
return math.log10(denom_value);
local pos = string.find( input_string, '/', 1, true );
end
if pos ~= nil then
end if string.find( input_string, '/', pos + 1, true ) == nil then
end
local denominator = string.sub( input_string, pos+1, -1 );
end
local denom_value = tonumber( denominator );
 
if denom_value ~= nil then
input_number, input_string = p._cleanNumber(input_string);
return math.log10(denom_value);
if input_string == nil then
end
return err('precision input appears non-numeric')
end
else
end
return p._precision(input_string)
end
end
input_number, input_string = z._cleanNumber( frame, input_string );
if input_string == nil then
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при определении дробной части</strong>'
else
return z._precision( input_string )
end
end
function z._precision( x )
x = string.upper( x )
 
function p._precision(x)
local decimal = string.find( x, '[.,]', 1 )
if type(x) == 'number' then
local exponent_pos = string.find( x, 'E', 1, true )
x = tostring(x)
local result = 0;
end
x = string.upper(x)
if exponent_pos ~= nil then
 
local exponent = string.sub( x, exponent_pos + 1 )
local decimal = x:find('%.')
x = string.sub( x, 1, exponent_pos - 1 )
local exponent_pos = x:find('E')
result = result - tonumber( exponent )
local result = 0;
end
 
if decimalexponent_pos ~= nil then
local resultexponent = result + string.lensub( x, )exponent_pos -+ decimal1)
x = string.sub(x, 1, exponent_pos - 1)
return result
result = result - tonumber(exponent)
end
end
 
local pos = string.len( x );
if decimal ~= nil then
while x:byte(pos) == string.byte('0') do
result = result + string.len(x) - decimal
pos = pos - 1
return result = result - 1
end
if pos <= 0 then
 
return 0
local pos = string.len(x);
end
while x:byte(pos) == string.byte('0') do
end
pos = pos - 1
result = result - 1
return result
if pos <= 0 then
return 0
end
end
 
return result
end
 
 
--[[
Рядок 123 ⟶ 206:
 
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
OR
{{#invoke:Math| max }}
 
Note, any values that do not evaluate to numbers are ignored.
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 z.max( frame )
function wrap.max(args)
local args = frame.args;
return p._max(unpackNumberArgs(args))
end
if args[1] == nil then
 
local parent = frame:getParent();
function p._max(...)
args = parent.args;
local max_value = binary_fold((function(a, b) return a > b end), ...)
end
local if max_value = nil;then
return max_value
end
local i = 1;
while args[i] ~= nil do
local val = z._cleanNumber( frame, args[i] );
if val ~= nil then
if max_value == nil or val > max_value then
max_value = val;
end
end
i = i + 1;
end
return max_value
end
 
Рядок 159 ⟶ 228:
 
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 z.min( frame )
function wrap.min(args)
local args = frame.args;
return p._min(unpackNumberArgs(args))
end
if args[1] == nil then
 
local parent = frame:getParent();
function p._min(...)
args = parent.args;
local min_value = binary_fold((function(a, b) return a < b end), ...)
end
local if min_value = nil;then
return min_value
end
local i = 1;
end
while args[i] ~= nil do
 
local val = z._cleanNumber( frame, args[i] );
--[[
if val ~= nil then
average
if min_value == nil or val < min_value then
 
min_value = val;
Finds the average
end
 
end
Usage:
i = i + 1;
{{#invoke:Math| average | value1 | value2 | ... }}
end
OR
{{#invoke:Math| average }}
return min_value
 
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
 
Рядок 195 ⟶ 279:
 
Usage:
{{#invoke:Math | round | value | precision }}
 
--]]
 
function z.round(frame)
function wrap.round(args)
local value, precision;
local value = p._cleanNumber(args[1] or args.value or 0)
local valueprecision = zp._cleanNumber( frame, frame.args[12] or frame.args.valueprecision or 0 );
if value precision == z._cleanNumber( frame, frame.args[2]nil or frame.args.precision or== 0nil );then
return err('round input appears non-numeric')
else
if value == nil or precision == nil then
return p._round(value, precision)
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при округлении до целого</strong>'
end else
return z._round( value, precision );
end
end
 
function z._round( value, precision )
function local rescale = mathp.pow_round( 10value, precision );
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 = fold(findGcd, ...)
return result
end
 
Рядок 225 ⟶ 368:
]]
 
function zwrap.precision_format(args)
local value_string = args[1] or 0
local precision = args[2] or 0
return zp._precision_format(value_string, precision)
end
 
function zp._precision_format(value_string, precision)
-- For access to Mediawiki built-in formatter.
local lang = mw.getContentLanguage();
 
local value
value, value_string = zp._cleanNumber(value_string)
precision = zp._cleanNumber(precision)
 
-- Check for non-numeric input
if value == nil or precision == nil then
return err('invalid input when rounding')
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при округлении с заданной точностью</strong>'
end
 
local current_precision = zp._precision(value)
local order = p._order(value)
local order = z._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 = zp._precision(value_string)
if order + orig_precision >= 14 then
precision = 13 - order;
Рядок 259 ⟶ 401:
-- If rounding off, truncate extra digits
if precision < current_precision then
value = zp._round(value, precision)
current_precision = zp._precision(value)
end
 
Рядок 329 ⟶ 471:
]]
 
function zp._cleanNumber( frame, number_string )
if type(number_string == nil or number_string:len() == 0'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 )
-- If failed, attempt to evaluate input as an expression
if number == nil then
local attempt = frame:callParserFunction( '#expr', number_string );
attempt = tonumber( attempt );
if attempt ~= nil then
number = attempt;
number_string = tostring( number );
else
number = nil;
number_string = nil;
end
else
-- String is valid but may contain padding, clean it.
number_string = mw.text.trim(number_string)
end
return number, number_string;
end
 
local function roman(i)
local w, t, val, let = {}, {
{1000, "M"},
{900, "CM"},
{500, "D"},
{400, "CD"},
{100, "C"},
{90, "XC"},
{50, "L"},
{40, "XL"},
{10, "X"},
{9, "IX"},
{5, "V"},
{4, "IV"},
{1, "I"}
}
for n, v in ipairs(t) do
val, let = unpack(v)
w[n]=string.rep(let,i/val)
i=i % val
end
return table.concat(w)
end
function z.Roman(frame) -- Преобразует числа от 1 до 4999999 в римские
local function try_tonumber(a)
return math.floor(tonumber(a) or error('\''.. a ..'\' не является числом.'));
end
 
local str = frame.args[1] or '';
-- Attempt basic conversion
if str == '' then -- пустой параметр
local number = tonumber(number_string)
return str;
 
end
-- If failed, attempt to evaluate input as an expression
local r, N = pcall(try_tonumber, str); -- попытка преобразовать в число
if rnumber == nil then
local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
if N<1 or N>=5e6 then
if success then
return frame.args[2] or 'N/A'
number = tonumber(result)
number_string = tostring(number)
else
number = nil
number_string = nil
end
local R=N%5000
N=(N-R)/1000
return (N>0 and table.concat{'<span style="text-decoration:overline;">',roman(N),'</span>'} or '')..roman(R)
else
number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
return '<strong class="error">' .. N .. '</strong>'; -- вывод ошибки
number_string = number_string:match("^%+(.*)$") 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
Выводит числа прописью на русском
frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
]]
function z.Russian(frame)
local str = frame.args[1] or '';
if str == '' then
return '';
end
local number = tonumber( str, 10 )
 
local langmt = mw.getLanguage({ 'ru'__index = function(t, k)
return function(frame)
if not getArgs then
local zero = 'ноль'
getArgs = require('Module:Arguments').getArgs
local ones = { 'один', 'два', 'три', 'четыре', 'пять', 'шесть',
'семь', 'восемь', 'девять', 'десять', 'одиннадцать', 'двенадцать',
'тринадцать', 'четырнадцать', 'пятнадцать', 'шестнадцать', 'семнадцать',
'восемнадцать', 'девятнадцать' }
local tens = { '', 'двадцать', 'тридцать', 'сорок', 'пятьдесят',
'шестьдесят', 'семьдесят', 'восемьдесят', 'девяносто' }
local hundreds = { 'сто', 'двести', 'триста', 'четыреста', 'пятьсот',
'шестьсот', 'семьсот', 'восемьсот', 'девятьсот' }
 
local unitsPlural = {
{ '', '', '' },
{ 'тысяча', 'тысячи', 'тысяч' },
{ 'миллион', 'миллиона', 'миллионов' },
{ 'миллиард', 'миллиарда', 'миллиардов' },
{ 'триллион', 'триллиона', 'триллионов' },
}
 
local out = ''
local outMinus = ''
if ( number < 0 ) then
outMinus = 'минус '
number = math.abs( number )
end
local tripletPos = 0
while ( number > 0 ) do
local triplet = number % 1000
number = math.floor( number / 1000 )
 
tripletPos = tripletPos + 1
if ( tripletPos > 5 ) then
return ''
end
return wrap[k](getArgs(frame)) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
 
local tripletStr = ''
local tripletUnit = ''
if ( triplet > 0 ) then
local unitPlural = unitsPlural[ tripletPos ]
tripletUnit = lang:plural( triplet, unitPlural[1], unitPlural[2], unitPlural[3] )
end
 
if ( triplet >= 100 ) then
tripletStr = hundreds[ math.floor( triplet / 100 ) ]
triplet = triplet % 100
end
 
if ( triplet >= 20 ) then
tripletStr = tripletStr .. ' ' .. tens[ math.floor( triplet / 10 ) ]
triplet = triplet % 10
end
 
if ( triplet >= 1 ) then
tripletStr = tripletStr .. ' ' .. ones[ triplet ]
end
-- две тысячи
if ( tripletPos == 2 ) then
tripletStr = mw.ustring.gsub( tripletStr, 'один$', 'одна' )
tripletStr = mw.ustring.gsub( tripletStr, 'два$', 'две' )
end
out = tripletStr .. ' ' .. tripletUnit .. ' ' .. out
end
end }
 
return setmetatable(p, mt)
if ( out == '' ) then
out = zero
end
 
out = outMinus .. out
out = mw.ustring.gsub( out, ' +', ' ' )
out = mw.text.trim ( out )
return out
end
 
return z
Отримано з https://uk.wikipedia.org/wiki/Модуль:Math