Модуль:Math

ХӀокху модулах лаьцна хааман Модуль:Math/doc агӀо кхолла мега

--[[

This module provides a number of basic mathematical operations.

]]
local z = {}

-- 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])

	if first then -- if NaN or nil, will skip down to final return
		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
		return math.random(first)
	end
	return math.random()
end

--[[
order

Determine order of magnitude of a number

Usage:
	{{#invoke: Math | order | value }}
]]
function z.order(frame)
	local input_string = (frame.args[1] or frame.args.x or '0');
	local input_number;

	input_number = z._cleanNumber( frame, input_string );
	if input_number == nil then
		return '<strong class="error">Ошибка формата данных: нечисловое входное значение при определении десятичной степени</strong>'
	else
		return z._order( input_number )
	end
end
function z._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 z.precision( frame )
	local input_string = (frame.args[1] or frame.args.x or '0');
	local trap_fraction = frame.args.check_fraction or false;
	local input_number;

	if type( trap_fraction ) == 'string' then
		trap_fraction = trap_fraction:lower();
		if trap_fraction == 'false' or trap_fraction == '0' or
				trap_fraction == 'no' or trap_fraction == '' then
			trap_fraction = false;
		else
			trap_fraction = true;
		end
	end

	if trap_fraction then
		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 = 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 )

	local decimal = string.find( x, '[.,]', 1 )
	local exponent_pos = string.find( x, 'E', 1, true )
	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 | ... }}
OR
	{{#invoke:Math| max }}

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 )
	local args = frame.args;

	if args[1] == nil then
		local parent = frame:getParent();
		args = parent.args;
	end
	local max_value = nil;

	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

--[[
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 z.min( frame )
	local args = frame.args;

	if args[1] == nil then
		local parent = frame:getParent();
		args = parent.args;
	end
	local min_value = nil;

	local i = 1;
	while args[i] ~= nil do
		local val = z._cleanNumber( frame, args[i] );
		if val ~= nil then
			if min_value == nil or val < min_value then
				min_value = val;
			end
		end
		i = i + 1;
	end

	return min_value
end

--[[
round

Rounds a number to specified precision

Usage:
	{{#invoke:Math | round | value | precision }}

--]]
function z.round(frame)
	local value, precision;

	value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
	precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );

	if value == nil or precision == nil then
		return '<strong class="error">Ошибка формата данных: нечисловое входное значение при округлении до целого</strong>'
	else
		return z._round( value, precision );
	end
end
function z._round( value, precision )
	local rescale = math.pow( 10, precision );
	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 z.precision_format(args)
	local value_string = args[1] or 0
	local precision = args[2] or 0
	return z._precision_format(value_string, precision)
end

function z._cleanNumberNew( 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

function z._precision_format(value_string, precision)
	-- For access to Mediawiki built-in formatter.
	local lang = mw.getContentLanguage();

	local r = "before: v = " .. tostring(value_string) .. "; p= " .. tostring(precision) .. '\n'

	local value
	value, value_string = z._cleanNumberNew(value_string)
	precision = z._cleanNumberNew(precision)

	-- Check for non-numeric input
	if value == nil or precision == nil then
		return '<strong class="error">Ошибка формата данных: нечисловое входное значение при округлении с заданной точностью</strong>'
	end

	local current_precision = z._precision(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
		local orig_precision = z._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 = z._round(value, precision)
		current_precision = z._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 z._cleanNumber( frame, number_string )
	if number_string == nil or number_string:len() == 0 then
		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 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 '';
	if str == '' then -- пустой параметр
		return str;
	end
	local r, N = pcall(try_tonumber, str); -- попытка преобразовать в число
	if r then
		if N<1 or N>=5e6 then
			return frame.args[2] or 'N/A'
		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
		return '<strong class="error">' .. N .. '</strong>'; -- вывод ошибки
	end
end

function z.RussianFem(frame)
	local result = z.Russian(frame)
	return string.gsub(string.gsub(result, 'два$', 'две'), 'один$', 'одна')
end

--[[
  Выводит числа прописью на русском
]]
function z.Russian(frame)
	local str = frame.args[1] or '';
	if str == '' then
		return '';
	end
	local lang = mw.getLanguage( 'ru' )
	if string.find(str, '%.') or string.find(str, ',') then
		a, b = string.match(str, '(%d+).(%d+)')
		local basic = { 'десят', 'сот'}
		local prefixes = {'', 'десяти', 'сто'}
		local orders = {'тысячн', 'миллионн', 'миллиардн',
						'триллионн', 'квадриллионн'}
		local ed = {'ая', 'ые', 'ых'}
		a = #a and a or '0'
		b = #b and b or '0'
		local order = math.floor(#b / #prefixes)
		if order > #orders then
			order = #orders
			b = string.sub(b, 0, #prefixes * #orders)
		end
		mw.log(order)
		local ia = z.RussianFem({args={a}})
		local ib = z.RussianFem({args={b}})
		local intgr = 'цел'
		local fract = ''
		if order == 0 then
			fract = basic[#b]
		else
			fract = prefixes[#b % #prefixes + 1] .. orders[order]
		end
		intgr = lang:plural(tonumber(a, 10) % 1000, intgr .. ed[1],
													intgr .. ed[2],
													intgr .. ed[3])
		fract = lang:plural(tonumber(b, 10) % 1000, fract .. ed[1],
													fract .. ed[2],
													fract .. ed[3])
		return ia .. ' ' .. intgr .. ', ' .. ib .. ' ' .. fract
	end
	local number = tonumber( str, 10 )
	
	local zero = 'ноль'
	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

		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

	if ( out == '' ) then
		out = zero
	end

	out = outMinus .. out
	out = mw.ustring.gsub( out, ' +', ' ' )
	out = mw.text.trim ( out )
	return out
end

return z