Difference between revisions of "Module:Math/sandbox"

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blackwiki>Mr. Stradivarius
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--[[
 
--[[
+
 
 
This module provides a number of basic mathematical operations.
 
This module provides a number of basic mathematical operations.
+
 
 
]]
 
]]
 
local z = {}
 
local z = {}
+
 
 
-- Generate random number
 
-- Generate random number
 
function z.random( frame )
 
function z.random( frame )
 
     first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil
 
     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])
 
     second = tonumber(frame.args[2])
+
 
 
     if first then -- if NaN or nil, will skip down to final return
 
     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
 
         if first <= second then -- could match if both nil, but already checked that first is a number in last line
Line 19: Line 19:
 
     return math.random()
 
     return math.random()
 
end
 
end
+
 
 
--[[
 
--[[
 
order
 
order
+
 
 
Determine order of magnitude of a number
 
Determine order of magnitude of a number
+
 
 
Usage:
 
Usage:
 
     {{#invoke: Math | order | value }}
 
     {{#invoke: Math | order | value }}
Line 31: Line 31:
 
     local input_string = (frame.args[1] or frame.args.x or '0');
 
     local input_string = (frame.args[1] or frame.args.x or '0');
 
     local input_number;
 
     local input_number;
+
   
 
     input_number = z._cleanNumber( frame, input_string );
 
     input_number = z._cleanNumber( frame, input_string );
 
     if input_number == nil then
 
     if input_number == nil then
Line 43: Line 43:
 
     return math.floor(math.log10(math.abs(x)))
 
     return math.floor(math.log10(math.abs(x)))
 
end
 
end
+
 
 
--[[
 
--[[
 
precision
 
precision
+
 
 
Detemines the precision of a number using the string representation
 
Detemines the precision of a number using the string representation
+
 
 
Usage:
 
Usage:
 
     {{ #invoke: Math | precision | value }}
 
     {{ #invoke: Math | precision | value }}
Line 56: Line 56:
 
     local trap_fraction = frame.args.check_fraction or false;
 
     local trap_fraction = frame.args.check_fraction or false;
 
     local input_number;
 
     local input_number;
+
   
 
     if type( trap_fraction ) == 'string' then
 
     if type( trap_fraction ) == 'string' then
 
         trap_fraction = trap_fraction:lower();
 
         trap_fraction = trap_fraction:lower();
Line 66: Line 66:
 
         end
 
         end
 
     end
 
     end
+
   
 
     if trap_fraction then
 
     if trap_fraction then
 
         local pos = string.find( input_string, '/', 1, true );
 
         local pos = string.find( input_string, '/', 1, true );
Line 79: Line 79:
 
         end
 
         end
 
     end     
 
     end     
+
   
 
     input_number, input_string = z._cleanNumber( frame, input_string );
 
     input_number, input_string = z._cleanNumber( frame, input_string );
 
     if input_string == nil then
 
     if input_string == nil then
Line 89: Line 89:
 
function z._precision( x )     
 
function z._precision( x )     
 
     x = string.upper( x )
 
     x = string.upper( x )
+
 
 
     local decimal = string.find( x, '.', 1, true )
 
     local decimal = string.find( x, '.', 1, true )
 
     local exponent_pos = string.find( x, 'E', 1, true )
 
     local exponent_pos = string.find( x, 'E', 1, true )
 
     local result = 0;
 
     local result = 0;
+
   
 
     if exponent_pos ~= nil then
 
     if exponent_pos ~= nil then
 
         local exponent = string.sub( x, exponent_pos + 1 )
 
         local exponent = string.sub( x, exponent_pos + 1 )
Line 99: Line 99:
 
         result = result - tonumber( exponent )
 
         result = result - tonumber( exponent )
 
     end     
 
     end     
+
   
 
     if decimal ~= nil then
 
     if decimal ~= nil then
 
         result = result + string.len( x ) - decimal
 
         result = result + string.len( x ) - decimal
 
         return result
 
         return result
 
     end
 
     end
+
       
 
     local pos = string.len( x );
 
     local pos = string.len( x );
 
     while x:byte(pos) == string.byte('0') do
 
     while x:byte(pos) == string.byte('0') do
Line 113: Line 113:
 
         end
 
         end
 
     end
 
     end
+
   
 
     return result
 
     return result
 
end
 
end
+
 
 
--[[
 
--[[
 
max
 
max
+
 
 
Finds the maximum argument
 
Finds the maximum argument
+
 
 
Usage:
 
Usage:
 
     {{#invoke:Math| max | value1 | value2 | ... }}
 
     {{#invoke:Math| max | value1 | value2 | ... }}
 
OR
 
OR
 
     {{#invoke:Math| max }}
 
     {{#invoke:Math| max }}
+
 
 
When used with no arguments, it takes its input from the parent
 
When used with no arguments, it takes its input from the parent
 
frame.  Note, any values that do not evaluate to numbers are ignored.
 
frame.  Note, any values that do not evaluate to numbers are ignored.
Line 132: Line 132:
 
function z.max( frame )
 
function z.max( frame )
 
     local args = frame.args;
 
     local args = frame.args;
+
   
 
     if args[1] == nil then
 
     if args[1] == nil then
 
         local parent = frame:getParent();
 
         local parent = frame:getParent();
Line 138: Line 138:
 
     end
 
     end
 
     local max_value = nil;
 
     local max_value = nil;
+
   
 
     local i = 1;
 
     local i = 1;
 
     while args[i] ~= nil do
 
     while args[i] ~= nil do
Line 149: Line 149:
 
         i = i + 1;
 
         i = i + 1;
 
     end
 
     end
+
 
 
     return max_value
 
     return max_value
 
end
 
end
+
 
 
--[[
 
--[[
 
min  
 
min  
+
 
 
Finds the minimum argument
 
Finds the minimum argument
+
 
 
Usage:
 
Usage:
 
     {{#invoke:Math| min | value1 | value2 | ... }}
 
     {{#invoke:Math| min | value1 | value2 | ... }}
 
OR
 
OR
 
     {{#invoke:Math| min }}
 
     {{#invoke:Math| min }}
+
 
 
When used with no arguments, it takes its input from the parent
 
When used with no arguments, it takes its input from the parent
 
frame.  Note, any values that do not evaluate to numbers are ignored.
 
frame.  Note, any values that do not evaluate to numbers are ignored.
Line 168: Line 168:
 
function z.min( frame )
 
function z.min( frame )
 
     local args = frame.args;
 
     local args = frame.args;
+
   
 
     if args[1] == nil then
 
     if args[1] == nil then
 
         local parent = frame:getParent();
 
         local parent = frame:getParent();
Line 174: Line 174:
 
     end
 
     end
 
     local min_value = nil;
 
     local min_value = nil;
+
   
 
     local i = 1;
 
     local i = 1;
 
     while args[i] ~= nil do
 
     while args[i] ~= nil do
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         i = i + 1;
 
         i = i + 1;
 
     end
 
     end
+
 
 
     return min_value
 
     return min_value
 
end
 
end
+
 
 
--[[
 
--[[
 
average  
 
average  
Line 223: Line 223:
 
     return (count == 0 and 0 or sum/count)
 
     return (count == 0 and 0 or sum/count)
 
end
 
end
+
 
 
--[[
 
--[[
 
round
 
round
+
 
 
Rounds a number to specified precision
 
Rounds a number to specified precision
+
 
 
Usage:
 
Usage:
 
     {{#invoke:Math | round | value | precision }}
 
     {{#invoke:Math | round | value | precision }}
+
   
 
--]]
 
--]]
 
function z.round(frame)
 
function z.round(frame)
 
     local value, precision;
 
     local value, precision;
+
   
 
     value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
 
     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 );
 
     precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );
+
   
 
     if value == nil or precision == nil then
 
     if value == nil or precision == nil then
 
         return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
 
         return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
Line 249: Line 249:
 
     return math.floor( value * rescale + 0.5 ) / rescale;
 
     return math.floor( value * rescale + 0.5 ) / rescale;
 
end
 
end
+
 
 
--[[
 
--[[
 
precision_format
 
precision_format
+
 
 
Rounds a number to the specified precision and formats according to rules  
 
Rounds a number to the specified precision and formats according to rules  
 
originally used for {{template:Rnd}}.  Output is a string.
 
originally used for {{template:Rnd}}.  Output is a string.
+
 
 
Usage:
 
Usage:
 
     {{#invoke: Math | precision_format | number | precision }}
 
     {{#invoke: Math | precision_format | number | precision }}
Line 262: Line 262:
 
     -- For access to Mediawiki built-in formatter.
 
     -- For access to Mediawiki built-in formatter.
 
     local lang = mw.getContentLanguage();
 
     local lang = mw.getContentLanguage();
+
   
 
     local value_string, value, precision;
 
     local value_string, value, precision;
 
     value, value_string = z._cleanNumber( frame, frame.args[1] or 0 );
 
     value, value_string = z._cleanNumber( frame, frame.args[1] or 0 );
 
     precision = z._cleanNumber( frame, frame.args[2] or 0 );
 
     precision = z._cleanNumber( frame, frame.args[2] or 0 );
+
   
 
     -- Check for non-numeric input
 
     -- Check for non-numeric input
 
     if value == nil or precision == nil then
 
     if value == nil or precision == nil then
 
         return '<strong class="error">Formatting error: invalid input when rounding</strong>'
 
         return '<strong class="error">Formatting error: invalid input when rounding</strong>'
 
     end
 
     end
+
   
 
     local current_precision = z._precision( value );
 
     local current_precision = z._precision( value );
+
 
 
     local order = z._order( value );
 
     local order = z._order( value );
+
   
 
     -- Due to round-off effects it is neccesary to limit the returned precision under
 
     -- Due to round-off effects it is neccesary to limit the returned precision under
 
     -- some circumstances because the terminal digits will be inaccurately reported.
 
     -- some circumstances because the terminal digits will be inaccurately reported.
Line 284: Line 284:
 
         end         
 
         end         
 
     end
 
     end
+
 
 
     -- If rounding off, truncate extra digits
 
     -- If rounding off, truncate extra digits
 
     if precision < current_precision then
 
     if precision < current_precision then
Line 290: Line 290:
 
         current_precision = z._precision( value );
 
         current_precision = z._precision( value );
 
     end     
 
     end     
+
   
 
     local formatted_num = lang:formatNum( math.abs(value) );
 
     local formatted_num = lang:formatNum( math.abs(value) );
 
     local sign;
 
     local sign;
+
   
 
     -- Use proper unary minus sign rather than ASCII default
 
     -- Use proper unary minus sign rather than ASCII default
 
     if value < 0 then
 
     if value < 0 then
Line 300: Line 300:
 
         sign = '';
 
         sign = '';
 
     end     
 
     end     
+
       
 
     -- Handle cases requiring scientific notation
 
     -- Handle cases requiring scientific notation
 
     if string.find( formatted_num, 'E', 1, true ) ~= nil or math.abs(order) >= 9 then
 
     if string.find( formatted_num, 'E', 1, true ) ~= nil or math.abs(order) >= 9 then
Line 311: Line 311:
 
     end
 
     end
 
     formatted_num = sign .. formatted_num;
 
     formatted_num = sign .. formatted_num;
+
   
 
     -- Pad with zeros, if needed     
 
     -- Pad with zeros, if needed     
 
     if current_precision < precision then
 
     if current_precision < precision then
Line 319: Line 319:
 
                 local zero_sep = lang:formatNum( 1.1 );
 
                 local zero_sep = lang:formatNum( 1.1 );
 
                 formatted_num = formatted_num .. zero_sep:sub(2,2);
 
                 formatted_num = formatted_num .. zero_sep:sub(2,2);
+
 
 
                 padding = precision;
 
                 padding = precision;
 
                 if padding > 20 then
 
                 if padding > 20 then
 
                     padding = 20;
 
                     padding = 20;
 
                 end
 
                 end
+
               
 
                 formatted_num = formatted_num .. string.rep( '0', padding );
 
                 formatted_num = formatted_num .. string.rep( '0', padding );
 
             end             
 
             end             
Line 335: Line 335:
 
         end
 
         end
 
     end
 
     end
+
 
 
     -- Add exponential notation, if necessary.
 
     -- Add exponential notation, if necessary.
 
     if order ~= 0 then
 
     if order ~= 0 then
Line 344: Line 344:
 
             order = lang:formatNum( order );
 
             order = lang:formatNum( order );
 
         end     
 
         end     
+
       
 
         formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
 
         formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
 
     end
 
     end
+
   
 
     return formatted_num;
 
     return formatted_num;
 
end
 
end
+
 
 
--[[
 
--[[
 
Helper function that interprets the input numerically.  If the  
 
Helper function that interprets the input numerically.  If the  
Line 356: Line 356:
 
a parser functions expression.
 
a parser functions expression.
 
]]
 
]]
+
 
 
function z._cleanNumber( frame, number_string )
 
function z._cleanNumber( frame, number_string )
 
     if number_string == nil or number_string:len() == 0 then
 
     if number_string == nil or number_string:len() == 0 then
 
         return nil, nil;
 
         return nil, nil;
 
     end     
 
     end     
+
   
 
     -- Attempt basic conversion
 
     -- Attempt basic conversion
 
     local number = tonumber( number_string )
 
     local number = tonumber( number_string )
+
   
 
     -- If failed, attempt to evaluate input as an expression
 
     -- If failed, attempt to evaluate input as an expression
 
     if number == nil then         
 
     if number == nil then         
Line 380: Line 380:
 
         number_string = number_string:match( "^%s*(.-)%s*$" );
 
         number_string = number_string:match( "^%s*(.-)%s*$" );
 
     end
 
     end
+
   
 
     return number, number_string;
 
     return number, number_string;
 
end
 
end
+
 
 
return z
 
return z

Revision as of 10:20, 2 December 2013

Documentation for this module may be created at Module:Math/sandbox/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