Module: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 ''
   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 ''
   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

--[[ average

Finds the average

Usage:

   {{#invoke:Math| average | value1 | value2 | ... }}

OR

   {{#invoke:Math| average }}

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.average( frame )

   local args = frame.args;
   if args[1] == nil then
       local parent = frame:getParent();
       args = parent.args;
   end
   local sum = 0;
   local count = 0;

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

   return (count == 0 and 0 or sum/count)

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 ''
   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 {{#invoke:Math|precision_format| {{{1}}} | 0}}. 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 ''
   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:preprocess( '' );
       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