Difference between revisions of "Module:Math/sandbox"

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blackwiki>Mr. Stradivarius
(improve the comment for the random function)
blackwiki>Mr. Stradivarius
(temporarily add the Commons version from commons:Module:Math)
Line 4: Line 4:
  
 
]]
 
]]
local p = {}
+
local z = {}
  
--[[
+
--[[Generate random number
random
 
  
Generate a random number
+
    With no arguments, returns a real number in the range [0,1)
 
+
    With one argument, returns an integer in the range [1,m]
Usage:
+
    With two arguments, returns an integer in the range [m,n]
{{#invoke: Math | random }}
 
{{#invoke: Math | random | maximum value }}
 
{{#invoke: Math | random | minimum value | maximum value }}
 
 
]]
 
]]
function p.random( frame )
+
function z.random( frame )
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
+
first = tonumber(frame.args[1])
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 second and first and (first <= second) then
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)
return math.random(first, second)
+
elseif first then
end
+
  return math.random(first)
return math.random(first)
+
else
end 
+
return math.random()  
return math.random()
+
end
 
end
 
end
  
Line 36: Line 31:
  
 
Usage:
 
Usage:
{{#invoke: Math | order | value }}
+
    {{#invoke: Math | order | value }}
 
]]
 
]]
function p.order(frame)
+
function z.order(frame)
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 = p._cleanNumber( frame, input_string );
+
    input_number = z._cleanNumber( frame, input_string );
if input_number == nil then
+
    if input_number == nil then
return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
+
        return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
else
+
    else
return p._order( input_number )
+
        return z._order( input_number )
end     
+
    end     
 
end
 
end
function p._order(x)
+
function z._order(x)
if x == 0 then return 0 end
+
    if x == 0 then return 0 end
return math.floor(math.log10(math.abs(x)))
+
    return math.floor(math.log10(math.abs(x)))
 
end
 
end
  
Line 60: Line 55:
  
 
Usage:
 
Usage:
{{ #invoke: Math | precision | value }}
+
    {{ #invoke: Math | precision | value }}
 
]]
 
]]
function p.precision( frame )
+
function z.precision( frame )
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 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();
if trap_fraction == 'false' or trap_fraction == '0' or
+
        if trap_fraction == 'false' or trap_fraction == '0' or
trap_fraction == 'no' or trap_fraction == '' then
+
                trap_fraction == 'no' or trap_fraction == '' then
trap_fraction = false;
+
            trap_fraction = false;
else
+
        else
trap_fraction = true;
+
            trap_fraction = true;
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 );
if pos ~= nil then
+
        if pos ~= nil then
if string.find( input_string, '/', pos + 1, true ) == nil then
+
            if string.find( input_string, '/', pos + 1, true ) == nil then
local denominator = string.sub( input_string, pos+1, -1 );
+
                local denominator = string.sub( input_string, pos+1, -1 );
local denom_value = tonumber( denominator );
+
                local denom_value = tonumber( denominator );
if denom_value ~= nil then
+
                if denom_value ~= nil then
return math.log10(denom_value);
+
                    return math.log10(denom_value);
end
+
                end
end                         
+
            end                         
end
+
        end
end     
+
    end     
 
+
   
input_number, input_string = p._cleanNumber( frame, input_string );
+
    input_number, input_string = z._cleanNumber( frame, input_string );
if input_string == nil then
+
    if input_string == nil then
return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
+
        return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
else
+
    else
return p._precision( input_string )
+
        return z._precision( input_string )
end     
+
    end     
 
end
 
end
function p._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 )
x = string.sub( x, 1, exponent_pos - 1 )
+
        x = string.sub( x, 1, exponent_pos - 1 )
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
pos = pos - 1
+
        pos = pos - 1
result = result - 1
+
        result = result - 1
if pos <= 0 then
+
        if pos <= 0 then
return 0
+
            return 0
end
+
        end
end
+
    end
 
+
   
return result
+
    return result
 
end
 
end
  
Line 133: Line 128:
  
 
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.
 
]]
 
]]
function p.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();
args = parent.args;
+
        args = parent.args;
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
local val = p._cleanNumber( frame, args[i] );
+
        local val = z._cleanNumber( frame, args[i] );
if val ~= nil then
+
        if val ~= nil then
if max_value == nil or val > max_value then
+
            if max_value == nil or val > max_value then
max_value = val;
+
                max_value = val;
end
+
            end
end         
+
        end         
i = i + 1;
+
        i = i + 1;
end
+
    end
 
+
 
return max_value
+
    return max_value
 
end
 
end
  
Line 169: Line 164:
  
 
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.
 
]]
 
]]
function p.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();
args = parent.args;
+
        args = parent.args;
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
local val = p._cleanNumber( frame, args[i] );
+
        local val = z._cleanNumber( frame, args[i] );
if val ~= nil then
+
        if val ~= nil then
if min_value == nil or val < min_value then
+
            if min_value == nil or val < min_value then
min_value = val;
+
                min_value = val;
end
+
            end
end         
+
        end         
i = i + 1;
+
        i = i + 1;
end
+
    end
 
+
 
return min_value
+
    return min_value
 
end
 
end
  
 
--[[
 
--[[
 
average  
 
average  
 
+
 
Finds the average
 
Finds the average
 
+
 
Usage:
 
Usage:
{{#invoke:Math| average | value1 | value2 | ... }}
+
    {{#invoke:Math| average | value1 | value2 | ... }}
 
OR
 
OR
{{#invoke:Math| average }}
+
    {{#invoke:Math| average }}
 
+
 
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.
 
]]
 
]]
function p.average( frame )
+
function z.average( 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();
args = parent.args;
+
        args = parent.args;
end
+
    end
local sum = 0;
+
    local sum = 0;
local count = 0;
+
    local count = 0;
 
+
local i = 1;
+
    local i = 1;
while args[i] ~= nil do
+
    while args[i] ~= nil do
local val = p._cleanNumber( frame, args[i] );
+
        local val = z._cleanNumber( frame, args[i] );
if val ~= nil then
+
        if val ~= nil then
sum = sum + val
+
            sum = sum + val
count = count + 1
+
            count = count + 1
end         
+
        end         
i = i + 1;
+
        i = i + 1;
end
+
    end
 
+
return (count == 0 and 0 or sum/count)
+
    return (count == 0 and 0 or sum/count)
 
end
 
end
  
Line 240: Line 235:
  
 
Usage:
 
Usage:
{{#invoke:Math | round | value | precision }}
+
    {{#invoke:Math | round | value | precision }}
 
+
   
 
--]]
 
--]]
function p.round(frame)
+
function z.round(frame)
local value, precision;
+
    local value, precision;
 
+
   
value = p._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 = p._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>'
else
+
    else
return p._round( value, precision );
+
        return z._round( value, precision );
end     
+
    end     
 
end
 
end
function p._round( value, precision )
+
function z._round( value, precision )
local rescale = math.pow( 10, precision );
+
    local rescale = math.pow( 10, precision );
return math.floor( value * rescale + 0.5 ) / rescale;
+
    return math.floor( value * rescale + 0.5 ) / rescale;
end
 
 
 
--[=[
 
gcd
 
 
 
Calculates the [[greatest common divisor]] of two numbers according to the [[extended Euclidean algorithm]].
 
 
 
Usage:
 
{{#invoke:Math | gcd | value 1 | value 2 }}
 
]=]
 
function p.gcd(frame)
 
local args = frame.args
 
 
 
if args[1] == nil then
 
local parent = frame:getParent()
 
args = parent.args
 
end
 
 
 
local a = p._cleanNumber(frame, args[1])
 
local b = p._cleanNumber(frame, args[2])
 
if not a or not b then return end
 
 
 
local r = b
 
local oldr = a
 
while r ~= 0 do
 
local quotient = math.floor(oldr / r)
 
oldr, r = r, oldr - quotient * r
 
end
 
 
 
if a == 0 and b < 0 or b == 0 and a < 0 then oldr = oldr * -1 end
 
 
 
return oldr
 
 
end
 
end
  
Line 299: Line 262:
  
 
Usage:
 
Usage:
{{#invoke: Math | precision_format | number | precision }}
+
    {{#invoke: Math | precision_format | number | precision }}
 
]]
 
]]
function p.precision_format( frame )
+
function z.precision_format( frame )
-- 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 = p._cleanNumber( frame, frame.args[1] or 0 );
+
    value, value_string = z._cleanNumber( frame, frame.args[1] or '0' );
precision = p._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 = p._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
  
local order = p._order( value );
+
    -- 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);
  
-- Due to round-off effects it is neccesary to limit the returned precision under
+
                padding = precision;
-- some circumstances because the terminal digits will be inaccurately reported.
+
                if padding > 20 then
if order + precision >= 14 then
+
                    padding = 20;
orig_precision = p._precision( value_string );
+
                end
if order + orig_precision >= 14 then
+
               
precision = 13 - order;      
+
                formatted_num = formatted_num .. string.rep( '0', padding );
end      
+
            end           
end
+
        else                 
 +
            padding = precision - current_precision
 +
            if padding > 20 then
 +
                padding = 20;
 +
            end
 +
            formatted_num = formatted_num .. string.rep( '0', padding );
 +
        end
 +
    end
  
-- If rounding off, truncate extra digits
+
    -- Add exponential notation, if necessary.
if precision < current_precision then
+
    if order ~= 0 then
value = p._round( value, precision );
+
        -- Use proper unary minus sign rather than ASCII default
current_precision = p._precision( value );
+
        if order < 0 then
end   
+
            order = '−' .. lang:formatNum( math.abs(order) );
 
+
        else
local formatted_num = lang:formatNum( math.abs(value) );
+
            order = lang:formatNum( order );
local sign;
+
        end     
 
+
       
-- Use proper unary minus sign rather than ASCII default
+
        formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
if value < 0 then
+
    end
sign = '−';
+
   
else
+
    return formatted_num;
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
 
end
  
Line 399: Line 362:
 
]]
 
]]
  
function p._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         
local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
+
        local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
attempt = tonumber( attempt );
+
        attempt = tonumber( attempt );
if attempt ~= nil then
+
        if attempt ~= nil then
number = attempt;
+
            number = attempt;
number_string = tostring( number );
+
            number_string = tostring( number );
else
+
        else
number = nil;
+
            number = nil;
number_string = nil;
+
            number_string = nil;
end
+
        end
else
+
    else
-- String is valid but may contain padding, clean it.
+
    -- String is valid but may contain padding, clean it.
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 p
+
return z

Revision as of 03:27, 5 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

    With no arguments, returns a real number in the range [0,1)
    With one argument, returns an integer in the range [1,m]
    With two arguments, returns an integer in the range [m,n]
]]
function z.random( frame )
	first  = tonumber(frame.args[1])
	second = tonumber(frame.args[2])

	if second and first and (first <= second) then
  		return math.random(first, second)
	elseif first then
  		return math.random(first)
	else 
		return math.random() 
	end
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