Editing Module:Math

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]]
]]
local z = {}


local yesno, getArgs -- lazily initialized
-- 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])


local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
    if first then -- if NaN or nil, will skip down to final return
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
        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
Helper functions used to avoid redundant code.
        return math.random(first)
]]
    end 
 
    return math.random()
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
end


Line 110: Line 26:


Usage:
Usage:
{{#invoke: Math | order | value }}
    {{#invoke: Math | order | value }}
]]
]]
 
function z.order(frame)
function wrap.order(args)
    local input_string = (frame.args[1] or frame.args.x or '0');
local input_string = (args[1] or args.x or '0');
    local input_number;
local input_number = p._cleanNumber(input_string);
   
if input_number == nil then
    input_number = z._cleanNumber( frame, input_string );
return err('order of magnitude input appears non-numeric')
    if input_number == nil then
else
        return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
return p._order(input_number)
    else
end     
        return z._order( input_number )
    end     
end
end
 
function z._order(x)
function p._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


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Usage:
Usage:
{{ #invoke: Math | precision | value }}
    {{ #invoke: Math | precision | value }}
]]
]]
 
function z.precision( frame )
function wrap.precision(args)
    local input_string = (frame.args[1] or frame.args.x or '0');
local input_string = (args[1] or args.x or '0');
    local trap_fraction = frame.args.check_fraction or false;
local trap_fraction = args.check_fraction;
    local input_number;
local input_number;
   
 
    if type( trap_fraction ) == 'string' then
if not yesno then
        trap_fraction = trap_fraction:lower();
yesno = require('Module:Yesno')
        if trap_fraction == 'false' or trap_fraction == '0' or
end
                trap_fraction == 'no' or trap_fraction == '' then
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
            trap_fraction = false;
local pos = string.find(input_string, '/', 1, true);
        else
if pos ~= nil then
            trap_fraction = true;
if string.find(input_string, '/', pos + 1, true) == nil then
        end
local denominator = string.sub(input_string, pos+1, -1);
    end
local denom_value = tonumber(denominator);
   
if denom_value ~= nil then
    if trap_fraction then
return math.log10(denom_value);
        local pos = string.find( input_string, '/', 1, true );
end
        if pos ~= nil then
end                         
            if string.find( input_string, '/', pos + 1, true ) == nil then
end
                local denominator = string.sub( input_string, pos+1, -1 );
end     
                local denom_value = tonumber( denominator );
 
                if denom_value ~= nil then
input_number, input_string = p._cleanNumber(input_string);
                    return math.log10(denom_value);
if input_string == nil then
                end
return err('precision input appears non-numeric')
            end                         
else
        end
return p._precision(input_string)
    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
end
function z._precision( x )   
    x = string.upper( x )


function p._precision(x)
    local decimal = string.find( x, '.', 1, true )
if type(x) == 'number' then
    local exponent_pos = string.find( x, 'E', 1, true )
x = tostring(x)
    local result = 0;
end
   
x = string.upper(x)
    if exponent_pos ~= nil then
 
        local exponent = string.sub( x, exponent_pos + 1 )
local decimal = x:find('%.')
        x = string.sub( x, 1, exponent_pos - 1 )
local exponent_pos = x:find('E')
        result = result - tonumber( exponent )
local result = 0;
    end     
 
   
if exponent_pos ~= nil then
    if decimal ~= nil then
local exponent = string.sub(x, exponent_pos + 1)
        result = result + string.len( x ) - decimal
x = string.sub(x, 1, exponent_pos - 1)
        return result
result = result - tonumber(exponent)
    end
end     
       
 
    local pos = string.len( x );
if decimal ~= nil then
    while x:byte(pos) == string.byte('0') do
result = result + string.len(x) - decimal
        pos = pos - 1
return result
        result = result - 1
end
        if pos <= 0 then
 
            return 0
local pos = string.len(x);
        end
while x:byte(pos) == string.byte('0') do
    end
pos = pos - 1
   
result = result - 1
    return result
if pos <= 0 then
return 0
end
end
 
return result
end
end


--[[
--[[
Line 206: Line 123:


Usage:
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
    {{#invoke:Math| max | value1 | value2 | ... }}
OR
    {{#invoke:Math| max }}


Note, any values that do not evaluate to numbers are ignored.
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.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 z.max( frame )
function wrap.median(args)
    local args = frame.args;
return p._median(unpackNumberArgs(args))
   
end
    if args[1] == nil then
 
        local parent = frame:getParent();
function p._median(...)
        args = parent.args;
local vals = makeArgArray(...)
    end
local count = #vals
    local max_value = nil;
table.sort(vals)
   
    local i = 1;
if count == 0 then
    while args[i] ~= nil do
return 0
        local val = z._cleanNumber( frame, args[i] );
end
        if val ~= nil then
            if max_value == nil or val > max_value then
if p._mod(count, 2) == 0 then
                max_value = val;
return (vals[count/2] + vals[count/2+1])/2
            end
else
        end       
return vals[math.ceil(count/2)]
        i = i + 1;
end
    end
 
    return max_value
end
end


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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 z.min( frame )
function wrap.min(args)
    local args = frame.args;
return p._min(unpackNumberArgs(args))
   
end
    if args[1] == nil then
 
        local parent = frame:getParent();
function p._min(...)
        args = parent.args;
local min_value = binary_fold((function(a, b) return a < b end), ...)
    end
if min_value then
    local min_value = nil;
return min_value
   
end
    local i = 1;
end
    while args[i] ~= nil do
 
        local val = z._cleanNumber( frame, args[i] );
--[[
        if val ~= nil then
sum
            if min_value == nil or val < min_value then
 
                min_value = val;
Finds the sum
            end
 
        end       
Usage:
        i = i + 1;
{{#invoke:Math| sum | value1 | value2 | ... }}
    end
OR
 
{{#invoke:Math| sum }}
    return min_value
 
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
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 }}
 
Note, any values that do not evaluate to numbers are ignored.
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 )
function wrap.average(args)
    local args = frame.args;
return p._average(unpackNumberArgs(args))
    if args[1] == nil then
end
        local parent = frame:getParent();
 
        args = parent.args;
function p._average(...)
    end
local sum, count = fold((function(a, b) return a + b end), ...)
    local sum = 0;
if not sum then
    local count = 0;
return 0
else
    local i = 1;
return sum / count
    while args[i] ~= nil do
end
        local val = z._cleanNumber( frame, args[i] );
        if val ~= nil then
            sum = sum + val
            count = count + 1
        end      
        i = i + 1;
    end
    return (count == 0 and 0 or sum/count)
end
end


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Usage:
Usage:
{{#invoke:Math | round | value | precision }}
    {{#invoke:Math | round | value | precision }}
 
   
--]]
--]]
 
function z.round(frame)
function wrap.round(args)
    local value, precision;
local value = p._cleanNumber(args[1] or args.value or 0)
   
local precision = p._cleanNumber(args[2] or args.precision or 0)
    value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
if value == nil or precision == nil then
    precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );
return err('round input appears non-numeric')
   
else
    if value == nil or precision == nil then
return p._round(value, precision)
        return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
end     
    else
end
        return z._round( value, precision );
 
    end     
function p._round(value, precision)
local rescale = math.pow(10, precision or 0);
return math.floor(value * rescale + 0.5) / rescale;
end
end
 
function z._round( value, precision )
--[[
    local rescale = math.pow( 10, precision );
log10
    return math.floor( value * rescale + 0.5 ) / rescale;
 
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
end


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Usage:
Usage:
{{#invoke: Math | precision_format | number | precision }}
    {{#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 );


function wrap.precision_format(args)
    local order = z._order( value );
local value_string = args[1] or 0
   
local precision = args[2] or 0
    -- Due to round-off effects it is neccesary to limit the returned precision under
return p._precision_format(value_string, precision)
    -- some circumstances because the terminal digits will be inaccurately reported.
end
    if order + precision >= 14 then
 
        orig_precision = z._precision( value_string );
function p._precision_format(value_string, precision)
        if order + orig_precision >= 14 then
-- For access to Mediawiki built-in formatter.
            precision = 13 - order;       
local lang = mw.getContentLanguage();
        end       
 
    end
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)
    -- If rounding off, truncate extra digits
local order = p._order(value)
    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 541: Line 357:
]]
]]


function p._cleanNumber(number_string)
function z._cleanNumber( frame, number_string )
if type(number_string) == 'number' then
    if number_string == nil or number_string:len() == 0 then
-- We were passed a number, so we don't need to do any processing.
        return nil, nil;
return number_string, tostring(number_string)
    end  
elseif type(number_string) ~= 'string' or not number_string:find('%S') then
   
-- We were passed a non-string or a blank string, so exit.
    -- Attempt basic conversion
return nil, nil;
    local number = tonumber( number_string )
end
   
 
    -- If failed, attempt to evaluate input as an expression
-- Attempt basic conversion
    if number == nil then      
local number = tonumber(number_string)
        local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
 
        attempt = tonumber( attempt );
-- If failed, attempt to evaluate input as an expression
        if attempt ~= nil then
if number == nil then
            number = attempt;
local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
            number_string = tostring( number );
if success then
        else
number = tonumber(result)
            number = nil;
number_string = tostring(number)
            number_string = nil;
else
        end
number = nil
    else
number_string = nil
    -- String is valid but may contain padding, clean it.
end
        number_string = number_string:match( "^%s*(.-)%s*$" );
else
    end
number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
   
number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs.
    return number, number_string;
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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