math

--[[  This module provides a number of basic mathematical operations.  ]] local z = {}  -- Generate random number function z.random( frame )     local first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil     local 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 'Formatting error: Order of magnitude input appears non-numeric'     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 'Formatting error: Precision input appears non-numeric'     else         return z._precision( input_string )     end     end function z._precision( x )         x = string.upper( x )      local decimal = string.find( x, '.', 1, true )     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 'Formatting error: Round input appears non-numeric'     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( frame )     -- For access to Mediawiki built-in formatter.     local lang = mw.getContentLanguage();          local value_string, value, precision;     value, value_string = z._cleanNumber( frame, frame.args[1] or 0 );     precision = z._cleanNumber( frame, frame.args[2] or 0 );          -- Check for non-numeric input     if value == nil or precision == nil then         return 'Formatting error: invalid input when rounding'     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:preprocess( '{{#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 = number_string:match( "^%s*(.-)%s*$" );     end          return number, number_string; end  return z