모듈:Math

--[[

This module provides a number of basic mathematical operations.

]]

local yesno, getArgs -- lazily initialized

local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.

Helper functions used to avoid redundant code.
]]

local function err(msg)
-- Generates wikitext error messages.
return mw.ustring.format('', 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:
0.38965002651776
0.67332277990567
0.14610954567143
]]

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:

]]

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:

]]

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:
0

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

min

Finds the minimum argument

Usage:
0
OR

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

average

Finds the average

Usage:
0
OR
0

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:

--]]

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

mod

Implements the modulo operator

Usage:

--]]

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:
0
--]]

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 틀:Rnd. Output is a string.

Usage:

]]

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 .. '×10^{' .. order .. '}'
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)