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Module:Math (edit)

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local z = {}
--[[


-- Generate random number
This module provides a number of basic mathematical operations.
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)
local yesno, getArgs -- lazily initialized
        end
 
        return math.random(first)
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
    end  
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
    return math.random()
 
--[[
Helper functions used to avoid redundant code.
]]
 
local function err(msg)
-- Generates wikitext error messages.
return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
end
 
local function unpackNumberArgs(args)
-- Returns an unpacked list of arguments specified with numerical keys.
local ret = {}
for k, v in pairs(args) do
if type(k) == 'number' then
table.insert(ret, v)
end
end
return unpack(ret)
end
end


-- Determine order of magnitude
local function makeArgArray(...)
function z.order(frame)
-- Makes an array of arguments from a list of arguments that might include nils.
    return z._order(tonumber(frame.args[1] or frame.args.x or 0))
local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs.
local nums = {} -- Stores the numbers of valid numerical arguments.
local ret = {}
for k, v in pairs(args) do
v = p._cleanNumber(v)
if v then
nums[#nums + 1] = k
args[k] = v
end
end
table.sort(nums)
for i, num in ipairs(nums) do
ret[#ret + 1] = args[num]
end
return ret
end
end
function z._order(x)
 
    if x == 0 then return 0 end
local function fold(func, ...)
    return math.floor(math.log10(math.abs(x)))
-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
-- and must return a number as an output. This number is then supplied as input to the next function call.
local vals = makeArgArray(...)
local count = #vals -- The number of valid arguments
if count == 0 then return
-- Exit if we have no valid args, otherwise removing the first arg would cause an error.
nil, 0
end  
local ret = table.remove(vals, 1)
for _, val in ipairs(vals) do
ret = func(ret, val)
end
return ret, count
end
end


-- Determines precision of a number using the string representation
--[[
function z.precision( frame )
Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value).
    return z._precision( frame.args[1] or frame.args.x or '0' )
]]
local function binary_fold(func, ...)
local value = fold((function(a, b) if func(a, b) then return a else return b end end), ...)
return value
end
end
function z._precision( x )
    x = string.upper( x )


    -- Remove leading / trailing whitespace
--[[
    x = x:match "^%s*(.-)%s*$";
random


    local decimal = string.find( x, '.', 1, true )
Generate a random number
    local exponent_pos = string.find( x, 'E', 1, true )
 
    local result = 0;
Usage:
   
{{#invoke: Math | random }}
    if exponent_pos ~= nil then
{{#invoke: Math | random | maximum value }}
        local exponent = string.sub( x, exponent_pos + 1 )
{{#invoke: Math | random | minimum value | maximum value }}
        x = string.sub( x, 1, exponent_pos - 1 )
]]
        result = result - tonumber( exponent )
 
    end   
function wrap.random(args)
   
local first = p._cleanNumber(args[1])
    if decimal ~= nil then
local second = p._cleanNumber(args[2])
        result = result + string.len( x ) - decimal
return p._random(first, second)
        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
end


-- Finds maximum argument
function p._random(first, second)
function z.max( frame )
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
    if frame.args[1] == nil then
-- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params.
        return ''
if first and second then
    end
if first <= second then -- math.random doesn't allow the first number to be greater than the second.
    local max_value = tonumber( frame.args[1] )
return math.random(first, second)
   
end
    local i = 2;
elseif first then
    while frame.args[i] ~= nil do
return math.random(first)
        local val = tonumber( frame.args[i] );
else
        if val ~= nil then
return math.random()
            if val > max_value then
end
                max_value = val;
            end
        end      
        i = i + 1;
    end
 
    return max_value
end
end


-- Finds minimum argument
--[[
function z.min( frame )
order
    if frame.args[1] == nil then
 
        return ''
Determine order of magnitude of a number
    end
 
    local min_value = tonumber( frame.args[1] )
Usage:
   
{{#invoke: Math | order | value }}
    local i = 2;
]]
    while frame.args[i] ~= nil do
 
        local val = tonumber( frame.args[i] );
function wrap.order(args)
        if val ~= nil then
local input_string = (args[1] or args.x or '0');
            if val < min_value then
local input_number = p._cleanNumber(input_string);
                min_value = val;
if input_number == nil then
            end
return err('order of magnitude input appears non-numeric')
        end      
else
        i = i + 1;
return p._order(input_number)
    end
end  
 
    return min_value
end
end


-- Rounds a number to specified precision
function p._order(x)
function z.round(frame)
if x == 0 then return 0 end
    local value = tonumber(frame.args[1] or frame.args.value or 0);
return math.floor(math.log10(math.abs(x)))
    local precision = tonumber(frame.args[2] or frame.args.precision or 0);
end
    return z._round( value, precision );
 
--[[
precision
 
Detemines the precision of a number using the string representation
 
Usage:
{{ #invoke: Math | precision | value }}
]]
 
function wrap.precision(args)
local input_string = (args[1] or args.x or '0');
local trap_fraction = args.check_fraction;
local input_number;
 
if not yesno then
yesno = require('Module:Yesno')
end
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
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 = p._cleanNumber(input_string);
if input_string == nil then
return err('precision input appears non-numeric')
else
return p._precision(input_string)
end   
end
end
function z._round( value, precision )
 
    local rescale = math.pow( 10, precision );
function p._precision(x)
    return math.floor( value * rescale + 0.5 ) / rescale;
if type(x) == 'number' then
x = tostring(x)
end
x = string.upper(x)
 
local decimal = x:find('%.')
local exponent_pos = x:find('E')
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
end


-- Rounds a number to the specified precision and formats according to rules
-- originally used for {{template:Rnd}}.  Output is a string.
function z.precision_format( frame )
    -- For access to Mediawiki built-in formatter.
    local lang = mw.getContentLanguage();
   
    local value = tonumber( frame.args[1] or 0 );
    local precision = tonumber( 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 );
--[[
   
max
    -- Due to round-off effects it is neccesary to limit the returned precision under
 
    -- some circumstances because the terminal digits will be inaccurately reported.
Finds the maximum argument
    if order + precision >= 14 then
        precision = 13 - order;       
    end


    -- If rounding off, truncate extra digits
Usage:
    if precision < current_precision then
{{#invoke:Math| max | value1 | value2 | ... }}
        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
        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);
                formatted_num = formatted_num .. string.rep( '0', precision );
            end           
        else     
            formatted_num = formatted_num .. string.rep( '0', precision - current_precision );
        end
    end


    -- Add exponential notation, if necessary.
Note, any values that do not evaluate to numbers are ignored.
    if order ~= 0 then
]]
        -- Use proper unary minus sign rather than ASCII default
 
        if order < 0 then
function wrap.max(args)
            order = '−' .. lang:formatNum( math.abs(order) );
return p._max(unpackNumberArgs(args))
        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


return z
function p._max(...)
local max_value = binary_fold((function(a, b) return a > b end), ...)
if max_value then
return max_value
end
end
 
--[[
median
 
Find the median of set of numbers
 
Usage:
{{#invoke:Math | median | number1 | number2 | ...}}
OR
{{#invoke:Math | median }}
]]
 
function wrap.median(args)
return p._median(unpackNumberArgs(args))
end
 
function p._median(...)
local vals = makeArgArray(...)
local count = #vals
table.sort(vals)
if count == 0 then
return 0
end
if p._mod(count, 2) == 0 then
return (vals[count/2] + vals[count/2+1])/2
else
return vals[math.ceil(count/2)]
end
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 wrap.min(args)
return p._min(unpackNumberArgs(args))
end
 
function p._min(...)
local min_value = binary_fold((function(a, b) return a < b end), ...)
if min_value then
return min_value
end
end
 
--[[
sum
 
Finds the sum
 
Usage:
{{#invoke:Math| sum | value1 | value2 | ... }}
OR
{{#invoke:Math| sum }}
 
Note, any values that do not evaluate to numbers are ignored.
]]
 
function wrap.sum(args)
return p._sum(unpackNumberArgs(args))
end
 
function p._sum(...)
local sums, count = fold((function(a, b) return a + b end), ...)
if not sums then
return 0
else
return sums
end
end
 
--[[
average
 
Finds the average
 
Usage:
{{#invoke:Math| average | value1 | value2 | ... }}
OR
{{#invoke:Math| average }}
 
Note, any values that do not evaluate to numbers are ignored.
]]
 
function wrap.average(args)
return p._average(unpackNumberArgs(args))
end
 
function p._average(...)
local sum, count = fold((function(a, b) return a + b end), ...)
if not sum then
return 0
else
return sum / count
end
end
 
--[[
round
 
Rounds a number to specified precision
 
Usage:
{{#invoke:Math | round | value | precision }}
 
--]]
 
function wrap.round(args)
local value = p._cleanNumber(args[1] or args.value or 0)
local precision = p._cleanNumber(args[2] or args.precision or 0)
if value == nil or precision == nil then
return err('round input appears non-numeric')
else
return p._round(value, precision)
end   
end
 
function p._round(value, precision)
local rescale = math.pow(10, precision or 0);
return math.floor(value * rescale + 0.5) / rescale;
end
 
--[[
log10
 
returns the log (base 10) of a number
 
Usage:
{{#invoke:Math | log10 | x }}
]]
 
function wrap.log10(args)
return math.log10(args[1])
end
 
--[[
mod
 
Implements the modulo operator
 
Usage:
{{#invoke:Math | mod | x | y }}
 
--]]
 
function wrap.mod(args)
local x = p._cleanNumber(args[1])
local y = p._cleanNumber(args[2])
if not x then
return err('first argument to mod appears non-numeric')
elseif not y then
return err('second argument to mod appears non-numeric')
else
return p._mod(x, y)
end   
end
 
function p._mod(x, y)
local ret = x % y
if not (0 <= ret and ret < y) then
ret = 0
end
return ret
end
 
--[[
gcd
 
Calculates the greatest common divisor of multiple numbers
 
Usage:
{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
--]]
 
function wrap.gcd(args)
return p._gcd(unpackNumberArgs(args))
end
 
function p._gcd(...)
local function findGcd(a, b)
local r = b
local oldr = a
while r ~= 0 do
local quotient = math.floor(oldr / r)
oldr, r = r, oldr - quotient * r
end
if oldr < 0 then
oldr = oldr * -1
end
return oldr
end
local result, count = fold(findGcd, ...)
return result
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 wrap.precision_format(args)
local value_string = args[1] or 0
local precision = args[2] or 0
return p._precision_format(value_string, precision)
end
 
function p._precision_format(value_string, precision)
-- For access to Mediawiki built-in formatter.
local lang = mw.getContentLanguage();
 
local value
value, value_string = p._cleanNumber(value_string)
precision = p._cleanNumber(precision)
 
-- Check for non-numeric input
if value == nil or precision == nil then
return err('invalid input when rounding')
end
 
local current_precision = p._precision(value)
local order = p._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 = p._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 = p._round(value, precision)
current_precision = p._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 p._cleanNumber(number_string)
if type(number_string) == 'number' then
-- We were passed a number, so we don't need to do any processing.
return number_string, tostring(number_string)
elseif type(number_string) ~= 'string' or not number_string:find('%S') then
-- We were passed a non-string or a blank string, so exit.
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 success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
if success then
number = tonumber(result)
number_string = tostring(number)
else
number = nil
number_string = nil
end
else
number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs.
if number_string:find('^%-?0[xX]') then
-- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead.
number_string = tostring(number)
end
end
 
return number, number_string
end
 
--[[
Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current
frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
]]
 
local mt = { __index = function(t, k)
return function(frame)
if not getArgs then
getArgs = require('Module:Arguments').getArgs
end
return wrap[k](getArgs(frame))  -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
end
end }
 
return setmetatable(p, mt)
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