Module:Math: Difference between revisions

    From Nonbinary Wiki
    m>Dragons flight
    (Adds comments, slight reordering of functions.)
    m>Dragons flight
    (add average)
    Line 187: Line 187:
        
        
         return min_value
         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
    end



    Revision as of 14:36, 18 April 2013

    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">Formatting error: Order of magnitude input appears non-numeric</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">Formatting error: Precision input appears non-numeric</strong>'
        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 '<strong class="error">Formatting error: Round input appears non-numeric</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( 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 '<strong class="error">Formatting error: invalid input when rounding</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: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