Модуль:Math

--[[

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:

]] 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 ''
   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:

]] 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 ''
   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:

OR

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:

OR

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:

--]] 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 ''
   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 Шаблон:Rnd. Output is a string.

Usage: ]]

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 '' 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 .. '×10^{' .. order .. '}' 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{'',roman(N),''} or )..roman(R) else return ''; -- вывод ошибки end end

--[[

 Выводит числа прописью на русском

]] 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