모듈:Math: 두 판 사이의 차이

Revi HQ
내용 추가됨 내용 삭제됨
(add a gcd function per edit request by User:Mxn, add a mod function, alter existing functions to allow access from Lua without calling a frame object, use Module:Arguments to process arguments, p._cleanNumber improvements)
(Undid revision 586573269 by Mr. Stradivarius (talk) the code refactor broke some existing modules - revert for now while I work out the extent of the problem)
4번째 줄: 4번째 줄:


]]
]]
local z = {}


-- Generate random number
local yesno = require('Module:Yesno')
function z.random( frame )
local getArgs = require('Module:Arguments').getArgs
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
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
if first <= second then -- could match if both nil, but already checked that first is a number in last line
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(first, second)

end
--[[
return math.random(first)
Helper functions used to avoid redundant code.
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 applyFuncToArgs(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

--[[
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


103번째 줄: 26번째 줄:


Usage:
Usage:
{{#invoke: Math | order | value }}
{{#invoke: Math | order | value }}
]]
]]
function z.order(frame)

local input_string = (frame.args[1] or frame.args.x or '0');
function wrap.order(args)
local input_number;
local input_string = (args[1] or args.x or '0');
local input_number = p._cleanNumber(input_string);
if input_number == nil then
input_number = z._cleanNumber( frame, input_string );
if input_number == nil then
return err('order of magnitude input appears non-numeric')
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 z._order(x)

if x == 0 then return 0 end
function p._order(x)
return math.floor(math.log10(math.abs(x)))
if x == 0 then return 0 end
return math.floor(math.log10(math.abs(x)))
end
end


127번째 줄: 50번째 줄:


Usage:
Usage:
{{ #invoke: Math | precision | value }}
{{ #invoke: Math | precision | value }}
]]
]]
function z.precision( frame )

local input_string = (frame.args[1] or frame.args.x or '0');
function wrap.precision(args)
local trap_fraction = frame.args.check_fraction or false;
local input_string = (args[1] or args.x or '0');
local input_number;
local trap_fraction = args.check_fraction;
local input_number;
if type( trap_fraction ) == 'string' then

trap_fraction = trap_fraction:lower();
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
if trap_fraction == 'false' or trap_fraction == '0' or
local pos = string.find(input_string, '/', 1, true);
trap_fraction == 'no' or trap_fraction == '' then
if pos ~= nil then
trap_fraction = false;
if string.find(input_string, '/', pos + 1, true) == nil then
else
local denominator = string.sub(input_string, pos+1, -1);
trap_fraction = true;
local denom_value = tonumber(denominator);
end
if denom_value ~= nil then
end
return math.log10(denom_value);
end
if trap_fraction then
end
local pos = string.find( input_string, '/', 1, true );
end
if pos ~= nil then
end
if string.find( input_string, '/', pos + 1, true ) == nil then

input_number, input_string = p._cleanNumber(input_string);
local denominator = string.sub( input_string, pos+1, -1 );
local denom_value = tonumber( denominator );
if input_string == nil then
if denom_value ~= nil then
return err('precision input appears non-numeric')
return math.log10(denom_value);
else
end
return p._precision(input_string)
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
end
function z._precision( x )
x = string.upper( x )


local decimal = string.find( x, '.', 1, true )
function p._precision(x)
local exponent_pos = string.find( x, 'E', 1, true )
if type(x) == 'number' then
local result = 0;
x = tostring(x)
end
if exponent_pos ~= nil then
x = string.upper(x)
local exponent = string.sub( x, exponent_pos + 1 )

x = string.sub( x, 1, exponent_pos - 1 )
local decimal = x:find('%.')
result = result - tonumber( exponent )
local exponent_pos = x:find('E')
end
local result = 0;

if exponent_pos ~= nil then
if decimal ~= nil then
local exponent = string.sub(x, exponent_pos + 1)
result = result + string.len( x ) - decimal
return result
x = string.sub(x, 1, exponent_pos - 1)
end
result = result - tonumber(exponent)
end
local pos = string.len( x );

while x:byte(pos) == string.byte('0') do
if decimal ~= nil then
pos = pos - 1
result = result + string.len(x) - decimal
return result
result = result - 1
if pos <= 0 then
end
return 0

end
local pos = string.len(x);
end
while x:byte(pos) == string.byte('0') do
pos = pos - 1
return result
result = result - 1
if pos <= 0 then
return 0
end
end

return result
end
end


195번째 줄: 123번째 줄:


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


When used with no arguments, it takes its input from the parent
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.max( frame )

local args = frame.args;
function wrap.max(args)
return p._max(unpackNumberArgs(args))
if args[1] == nil then
end
local parent = frame:getParent();

args = parent.args;
function p._max(...)
end
local function maxOfTwo(a, b)
local max_value = nil;
if a > b then
return a
local i = 1;
else
while args[i] ~= nil do
return b
local val = z._cleanNumber( frame, args[i] );
end
if val ~= nil then
end
local max_value = applyFuncToArgs(maxOfTwo, ...)
if max_value == nil or val > max_value then
if max_value then
max_value = val;
end
return max_value
end
end
i = i + 1;
end
return max_value
end
end


224번째 줄: 159번째 줄:


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 )

local args = frame.args;
function wrap.min(args)
return p._min(unpackNumberArgs(args))
if args[1] == nil then
end
local parent = frame:getParent();

args = parent.args;
function p._min(...)
end
local function minOfTwo(a, b)
local min_value = nil;
if a < b then
return a
local i = 1;
else
while args[i] ~= nil do
return b
local val = z._cleanNumber( frame, args[i] );
end
if val ~= nil then
end
local min_value = applyFuncToArgs(minOfTwo, ...)
if min_value == nil or val < min_value then
if min_value then
min_value = val;
end
return min_value
end
end
i = i + 1;
end
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
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.average( frame )

local args = frame.args;
function wrap.average(args)
if args[1] == nil then
return p._average(unpackNumberArgs(args))
local parent = frame:getParent();
end
args = parent.args;

end
function p._average(...)
local function getSum(a, b)
local sum = 0;
local count = 0;
return a + b
end
local i = 1;
local sum, count = applyFuncToArgs(getSum, ...)
while args[i] ~= nil do
if not sum then
local val = z._cleanNumber( frame, args[i] );
return 0
if val ~= nil then
else
return sum / count
sum = sum + val
count = count + 1
end
end
i = i + 1;
end
return (count == 0 and 0 or sum/count)
end
end


285번째 줄: 230번째 줄:


Usage:
Usage:
{{#invoke:Math | round | value | precision }}
{{#invoke:Math | round | value | precision }}

--]]
--]]
function z.round(frame)

local 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)
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')
if value == nil or precision == nil then
else
return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
return p._round(value, precision)
end
else
return z._round( value, precision );
end
end
end
function z._round( value, precision )

function p._round(value, precision)
local rescale = math.pow( 10, precision );
return math.floor( value * rescale + 0.5 ) / rescale;
local rescale = math.pow(10, precision or 0);
return math.floor(value * rescale + 0.5) / rescale;
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 = applyFuncToArgs(findGcd, ...)
return result
end
end


371번째 줄: 257번째 줄:


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 );


local order = z._order( value );
function wrap.precision_format(args)
local value_string = args[1] or 0
-- Due to round-off effects it is neccesary to limit the returned precision under
local precision = args[2] or 0
-- some circumstances because the terminal digits will be inaccurately reported.
return p._precision_format(value_string, precision)
if order + precision >= 14 then
end
orig_precision = z._precision( value_string );
if order + orig_precision >= 14 then
precision = 13 - order;
end
end


-- If rounding off, truncate extra digits
function p._precision_format(value_string, precision)
if precision < current_precision then
-- For access to Mediawiki built-in formatter.
value = z._round( value, precision );
local lang = mw.getContentLanguage();
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;
local value
if padding > 20 then
value, value_string = p._cleanNumber(value_string)
padding = 20;
precision = p._cleanNumber(precision)
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.
-- Check for non-numeric input
if value == nil or precision == nil then
if order ~= 0 then
-- Use proper unary minus sign rather than ASCII default
return err('invalid input when rounding')
if order < 0 then
end
order = '−' .. lang:formatNum( math.abs(order) );

else
local current_precision = p._precision(value)
local order = p._order(value)
order = lang:formatNum( order );
end

-- Due to round-off effects it is neccesary to limit the returned precision under
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
-- some circumstances because the terminal digits will be inaccurately reported.
end
if order + precision >= 14 then
orig_precision = p._precision(value_string)
return formatted_num;
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


477번째 줄: 357번째 줄:
]]
]]


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
return nil, nil;
-- We were passed a number, so we don't need to do any processing.
end
return number_string, tostring(number_string)
elseif type(number_string) ~= 'string' or not number_string:find('%S') then
-- Attempt basic conversion
-- We were passed a non-string or a blank string, so exit.
local number = tonumber( number_string )
return nil, nil;
end
-- If failed, attempt to evaluate input as an expression

if number == nil then
-- Attempt basic conversion
local number = tonumber(number_string)
local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
attempt = tonumber( attempt );

if attempt ~= nil then
-- If failed, attempt to evaluate input as an expression
if number == nil then
number = attempt;
number_string = tostring( number );
local frame = mw.getCurrentFrame()
else
local attempt = frame:preprocess('{{#expr: ' .. number_string .. '}}')
number = nil;
attempt = tonumber(attempt)
number_string = nil;
if attempt ~= nil then
end
number = attempt
else
number_string = tostring(number)
-- String is valid but may contain padding, clean it.
else
number_string = number_string:match( "^%s*(.-)%s*$" );
number = nil
end
number_string = nil
end
return number, number_string;
else
number_string = number_string:match("^%s*(.-)%s*$") -- 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 function makeWrapper(funcName)
return function (frame)
local args = getArgs(frame) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
return wrap[funcName](args)
end
end

for funcName in pairs(wrap) do
p[funcName] = makeWrapper(funcName)
end
end


return p
return z

2013년 12월 18일 (수) 13:06 판

이 모듈에 대한 설명문서는 모듈:Math/설명문서에서 만들 수 있습니다 

--[[

This module provides a number of basic mathematical operations.

]]
local z = {}

-- Generate random number
function z.random( frame )
    first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil
    second = tonumber(frame.args[2])

    if first then -- if NaN or nil, will skip down to final return
        if first <= second then -- could match if both nil, but already checked that first is a number in last line
            return math.random(first, second)
        end
        return math.random(first)
    end   
    return math.random()
end

--[[
order

Determine order of magnitude of a number

Usage:
    {{#invoke: Math | order | value }}
]]
function z.order(frame)
    local input_string = (frame.args[1] or frame.args.x or '0');
    local input_number;
    
    input_number = z._cleanNumber( frame, input_string );
    if input_number == nil then
        return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
    else
        return z._order( input_number )
    end    
end
function z._order(x)
    if x == 0 then return 0 end
    return math.floor(math.log10(math.abs(x)))
end

--[[
precision

Detemines the precision of a number using the string representation

Usage:
    {{ #invoke: Math | precision | value }}
]]
function z.precision( frame )
    local input_string = (frame.args[1] or frame.args.x or '0');
    local trap_fraction = frame.args.check_fraction or false;
    local input_number;
    
    if type( trap_fraction ) == 'string' then
        trap_fraction = trap_fraction:lower();
        if trap_fraction == 'false' or trap_fraction == '0' or
                trap_fraction == 'no' or trap_fraction == '' then
            trap_fraction = false;
        else
            trap_fraction = true;
        end
    end
    
    if trap_fraction then
        local pos = string.find( input_string, '/', 1, true );
        if pos ~= nil then
            if string.find( input_string, '/', pos + 1, true ) == nil then
                local denominator = string.sub( input_string, pos+1, -1 );
                local denom_value = tonumber( denominator );
                if denom_value ~= nil then
                    return math.log10(denom_value);
                end
            end                        
        end
    end    
    
    input_number, input_string = z._cleanNumber( frame, input_string );
    if input_string == nil then
        return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
    else
        return z._precision( input_string )
    end    
end
function z._precision( x )    
    x = string.upper( x )

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

--[[
max

Finds the maximum argument

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

When used with no arguments, it takes its input from the parent
frame.  Note, any values that do not evaluate to numbers are ignored.
]]
function z.max( frame )
    local args = frame.args;
    
    if args[1] == nil then
        local parent = frame:getParent();
        args = parent.args;
    end
    local max_value = nil;
    
    local i = 1;
    while args[i] ~= nil do
        local val = z._cleanNumber( frame, args[i] );
        if val ~= nil then
            if max_value == nil or val > max_value then
                max_value = val;
            end
        end        
        i = i + 1;
    end
  
    return max_value
end

--[[
min 

Finds the minimum argument

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

When used with no arguments, it takes its input from the parent
frame.  Note, any values that do not evaluate to numbers are ignored.
]]
function z.min( frame )
    local args = frame.args;
    
    if args[1] == nil then
        local parent = frame:getParent();
        args = parent.args;
    end
    local min_value = nil;
    
    local i = 1;
    while args[i] ~= nil do
        local val = z._cleanNumber( frame, args[i] );
        if val ~= nil then
            if min_value == nil or val < min_value then
                min_value = val;
            end
        end        
        i = i + 1;
    end
  
    return min_value
end

--[[
average 
 
Finds the average
 
Usage:
    {{#invoke:Math| average | value1 | value2 | ... }}
OR
    {{#invoke:Math| average }}
 
When used with no arguments, it takes its input from the parent
frame.  Note, any values that do not evaluate to numbers are ignored.
]]
function z.average( frame )
    local args = frame.args;
    if args[1] == nil then
        local parent = frame:getParent();
        args = parent.args;
    end
    local sum = 0;
    local count = 0;
 
    local i = 1;
    while args[i] ~= nil do
        local val = z._cleanNumber( frame, args[i] );
        if val ~= nil then
            sum = sum + val
            count = count + 1
        end        
        i = i + 1;
    end
 
    return (count == 0 and 0 or sum/count)
end

--[[
round

Rounds a number to specified precision

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

--[[
precision_format

Rounds a number to the specified precision and formats according to rules 
originally used for {{template:Rnd}}.  Output is a string.

Usage:
    {{#invoke: Math | precision_format | number | precision }}
]]
function z.precision_format( frame )
    -- For access to Mediawiki built-in formatter.
    local lang = mw.getContentLanguage();
    
    local value_string, value, precision;
    value, value_string = z._cleanNumber( frame, frame.args[1] or 0 );
    precision = z._cleanNumber( frame, frame.args[2] or 0 );
    
    -- Check for non-numeric input
    if value == nil or precision == nil then
        return '<strong class="error">Formatting error: invalid input when rounding</strong>'
    end
    
    local current_precision = z._precision( value );

    local order = z._order( value );
    
    -- Due to round-off effects it is neccesary to limit the returned precision under
    -- some circumstances because the terminal digits will be inaccurately reported.
    if order + precision >= 14 then
        orig_precision = z._precision( value_string );
        if order + orig_precision >= 14 then
            precision = 13 - order;        
        end        
    end

    -- If rounding off, truncate extra digits
    if precision < current_precision then
        value = z._round( value, precision );
        current_precision = z._precision( value );
    end    
    
    local formatted_num = lang:formatNum( math.abs(value) );
    local sign;
    
    -- Use proper unary minus sign rather than ASCII default
    if value < 0 then
        sign = '−';
    else
        sign = '';
    end    
        
    -- Handle cases requiring scientific notation
    if string.find( formatted_num, 'E', 1, true ) ~= nil or math.abs(order) >= 9 then
        value = value * math.pow( 10, -order );
        current_precision = current_precision + order;
        precision = precision + order;
        formatted_num = lang:formatNum( math.abs(value) );
    else
        order = 0;        
    end
    formatted_num = sign .. formatted_num;
    
    -- Pad with zeros, if needed    
    if current_precision < precision then
        local padding;
        if current_precision <= 0 then
            if precision > 0 then
                local zero_sep = lang:formatNum( 1.1 );
                formatted_num = formatted_num .. zero_sep:sub(2,2);

                padding = precision;
                if padding > 20 then
                    padding = 20;
                end
                
                formatted_num = formatted_num .. string.rep( '0', padding );
            end            
        else                   
            padding = precision - current_precision
            if padding > 20 then
                padding = 20;
            end
            formatted_num = formatted_num .. string.rep( '0', padding );
        end
    end

    -- Add exponential notation, if necessary.
    if order ~= 0 then
        -- Use proper unary minus sign rather than ASCII default
        if order < 0 then
            order = '−' .. lang:formatNum( math.abs(order) );
        else
            order = lang:formatNum( order );
        end    
        
        formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
    end
    
    return formatted_num;
end

--[[
Helper function that interprets the input numerically.  If the 
input does not appear to be a number, attempts evaluating it as
a parser functions expression.
]]

function z._cleanNumber( frame, number_string )
    if number_string == nil or number_string:len() == 0 then
        return nil, nil;
    end    
    
    -- Attempt basic conversion
    local number = tonumber( number_string )
    
    -- If failed, attempt to evaluate input as an expression
    if number == nil then        
        local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
        attempt = tonumber( attempt );
        if attempt ~= nil then
            number = attempt;
            number_string = tostring( number );
        else
            number = nil;
            number_string = nil;
        end
    else
    -- String is valid but may contain padding, clean it.
        number_string = number_string:match( "^%s*(.-)%s*$" );
    end
    
    return number, number_string;
end

return z
원본 주소 "https://revi.wiki/wiki/모듈:Math?oldid=2231"