Difference between revisions of "Module:Math"

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Revision as of 16:52, 24 August 2016

Documentation for this module may be created at Module:Math/doc 

--[[

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

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

--[[
  Выводит числа прописью russian
]]
function z.Russian(frame)
	local str = frame.args[1] or '';
	if str == '' then
		return '';
	end
	local number = tonumber( str, 10 )

	local lang = mw.getLanguage( 'ru' )
	
	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
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