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: {{#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 'Ошибка формата данных: нечисловое входное значение при определении десятичной степени' 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 'Ошибка формата данных: нечисловое входное значение при определении дробной части' 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 'Ошибка формата данных: нечисловое входное значение при округлении до целого' 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 'Ошибка формата данных: нечисловое входное значение при округлении с заданной точностью' 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 .. '×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 '' .. N .. ''; -- 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 .. ' и ' .. 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