Editing Module:Math

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--[[
local z = {}


This module provides a number of basic mathematical operations.
-- 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
local yesno, getArgs -- lazily initialized
            return math.random(first, second)
 
        end
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
        return math.random(first)
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
    end 
 
    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
 
local function makeArgArray(...)
-- Makes an array of arguments from a list of arguments that might include nils.
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
 
local function fold(func, ...)
-- 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
 
--[[
Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value).
]]
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
 
--[[
random
 
Generate a random number
 
Usage:
{{#invoke: Math | random }}
{{#invoke: Math | random | maximum value }}
{{#invoke: Math | random | minimum value | maximum value }}
]]
 
function wrap.random(args)
local first = p._cleanNumber(args[1])
local second = p._cleanNumber(args[2])
return p._random(first, second)
end
 
function p._random(first, second)
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
-- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params.
if first and second then
if first <= second then -- math.random doesn't allow the first number to be greater than the second.
return math.random(first, second)
end
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 wrap.order(args)
local input_string = (args[1] or args.x or '0');
local input_number = p._cleanNumber(input_string);
if input_number == nil then
return err('order of magnitude input appears non-numeric')
else
return p._order(input_number)
end   
end
 
function p._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 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
 
function p._precision(x)
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
 
 
--[[
max
 
Finds the maximum argument
 
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
 
Note, any values that do not evaluate to numbers are ignored.
]]
 
function wrap.max(args)
return p._max(unpackNumberArgs(args))
end
 
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
end


--[[
-- Determine order of magnitude
round
function z.order(frame)
 
    return z._order(tonumber(frame.args[1] or frame.args.x or 0))
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
end
 
function z._order(x)
--[[
    if x == 0 then return 0 end
mod
    return math.floor(math.log10(math.abs(x)))
 
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
end


function p._mod(x, y)
-- Determines precision of a number using the string representation
local ret = x % y
function z.precision( frame )
if not (0 <= ret and ret < y) then
    return z._precision( frame.args[1] or frame.args.x or '0' )
ret = 0
end
return ret
end
end
function z._precision( x )
    x = string.upper( x )


--[[
    -- Remove leading / trailing whitespace
gcd
    x = x:match "^%s*(.-)%s*$";
 
Calculates the greatest common divisor of multiple numbers


Usage:
    local decimal = string.find( x, '.', 1, true )
{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
    local exponent_pos = string.find( x, 'E', 1, true )
--]]
    local result = 0;
 
   
function wrap.gcd(args)
    if exponent_pos ~= nil then
return p._gcd(unpackNumberArgs(args))
        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


function p._gcd(...)
-- Finds maximum argument
local function findGcd(a, b)
function z.max( frame )
local r = b
    if frame.args[1] == nil then
local oldr = a
        return ''
while r ~= 0 do
    end
local quotient = math.floor(oldr / r)
    local max_value = tonumber( frame.args[1] )
oldr, r = r, oldr - quotient * r
   
end
    local i = 2;
if oldr < 0 then
    while frame.args[i] ~= nil do
oldr = oldr * -1
        local val = tonumber( frame.args[i] );
end
        if val ~= nil then
return oldr
            if val > max_value then
end
                max_value = val;
local result, count = fold(findGcd, ...)
            end
return result
        end      
        i = i + 1;
    end
 
    return max_value
end
end


--[[
-- Finds minimum argument
precision_format
function z.min( frame )
 
    if frame.args[1] == nil then
Rounds a number to the specified precision and formats according to rules
        return ''
originally used for {{template:Rnd}}.  Output is a string.
    end
 
    local min_value = tonumber( frame.args[1] )
Usage:
   
{{#invoke: Math | precision_format | number | precision }}
    local i = 2;
]]
    while frame.args[i] ~= nil do
 
        local val = tonumber( frame.args[i] );
function wrap.precision_format(args)
        if val ~= nil then
local value_string = args[1] or 0
            if val < min_value then
local precision = args[2] or 0
                min_value = val;
return p._precision_format(value_string, precision)
            end
end
        end      
 
        i = i + 1;
function p._precision_format(value_string, precision)
    end
-- For access to Mediawiki built-in formatter.
 
local lang = mw.getContentLanguage();
    return min_value
 
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
end


--[[
-- Rounds a number to the specified precision and formats according to rules
Helper function that interprets the input numerically. If the
-- originally used for {{template:Rnd}}
input does not appear to be a number, attempts evaluating it as
function z.round( frame )
a parser functions expression.
    -- For access to Mediawiki built-in formatter.
]]
    local lang = mw.getContentLanguage();
   
    local value_string = ( frame.args[1] or '0' )
    local value = tonumber( value_string );
    local precision = tonumber( frame.args[2] or 0 );
    local current_precision = z._precision( value );


function p._cleanNumber(number_string)
    local order = z._order( value );
if type(number_string) == 'number' then
   
-- We were passed a number, so we don't need to do any processing.
    -- Due to round-off effects it is neccesary to limit the returned precision under
return number_string, tostring(number_string)
    -- some circumstances because the terminal digits will be inaccurately reported.
elseif type(number_string) ~= 'string' or not number_string:find('%S') then
    if order + precision >= 14 then
-- We were passed a non-string or a blank string, so exit.
        local orig_precision = z._precision( value_string );
return nil, nil;
        if order + orig_precision >= 14 then
end
            precision = 13 - order;
        end
    end


-- Attempt basic conversion
    -- If rounding off, truncate extra digits
local number = tonumber(number_string)
    if precision < current_precision then
        local rescale = math.pow( 10, precision );
        value = math.floor( value * rescale + 0.5 ) / rescale;
        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


-- If failed, attempt to evaluate input as an expression
    -- Add exponential notation, if necessary.
if number == nil then
    if order ~= 0 then
local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
        -- Use proper unary minus sign rather than ASCII default
if success then
        if order < 0 then
number = tonumber(result)
            order = '−' .. lang:formatNum( math.abs(order) );
number_string = tostring(number)
        else
else
            order = lang:formatNum( order );
number = nil
        end  
number_string = nil
       
end
        formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
else
    end
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.
    return formatted_num;
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
end


--[[
return z
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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