モジュール:Utilsのソースを表示

local get_args = require("Module:Arguments").getArgs
local p = {}

-- check if a table contains x
function p.table_contains(tbl, x)
	for i = 1, #tbl do
		if x == tbl[i] then
			return true
		end
	end
	return false
end

-- return the first index with the given value (or nil if not found)
function p.index_of(array, value)
	for i, v in ipairs(array) do
		if v == value then
			return i
		end
	end
	return nil
end

-- check whether the input is a non-empty string
function p.value_provided(s)
	return type(s) == "string" and #s > 0
end

-- evaluate input on error use default; cannot be used with {{#invoke:}}
function p.eval_num_arg(input, def_value)
	local result = input
	if type(input) ~= "number" then
		result = def_value
		if type(input) == "string" then
			-- check for fraction notation
			if input:match("/") == "/" then
				local numerator, denominator = input:match("^%s*([0-9]+)[/?]([0-9]+)%s*$")
				result = (tonumber(numerator) or def_value) / (tonumber(denominator) or 1)
			else
				input = input:match("^%s*(.-)%s*$")
				result = tonumber(input)
			end
		end
	end
	return result
end

-- return logarithm base b of x
function p.log(frame)
	local args = get_args(frame)
	return p._log(args[1], args[2])
end

local LN_2 = math.log(2)
-- return logarithm base 2 of x
function p.log2(x)
	return math.log(x) / LN_2
end

function p._log(x, b)
	-- x defaults to 0
	x = p.eval_num_arg(x, 0)
	-- b defaults to 2 ("octave")
	b = p.eval_num_arg(b, 2)
	return math.log(x) / math.log(b)
end

-- return greatest common divisor of a and b
function p.gcd(frame)
	local args = get_args(frame)
	return p._gcd(args[1], args[2])
end

function p._gcd(a, b)
	if b ~= 0 then
		return p._gcd(b, a % b)
	else
		return math.abs(a)
	end
end

-- return x rounded to places decimal places
function p.round_dec(frame)
	local args = get_args(frame)
	return p._round_dec(args[1], args[2])
end

function p._round_dec(x, places)
	-- x defaults to 0
	x = p.eval_num_arg(x, 0)
	-- places defaults to 0
	places = p.eval_num_arg(places, 0)
	return math.floor(x * 10 ^ places + 0.5) / 10 ^ places
end

-- return x rounded to a precision of prec significant figures
function p.round(frame)
	local args = get_args(frame)
	return p._round(args[1], args[2])
end

function p._round(x, prec)
	-- x defaults to 0
	x = p.eval_num_arg(x, 0)
	-- prec defaults to 6
	prec = p.eval_num_arg(prec, 6)
	if x == 0 then
		return 0
	else
		return p._round_dec(x, prec - math.floor(p._log(math.abs(x), 10)) - 1)
	end
end

-- cached list of primes for is_prime
local primes_cache = {
	[0] = false,
	[1] = false,
}

-- returns true if integer n is prime; cannot be used with {{#invoke:}}
function p.is_prime(n)
	local cached = primes_cache[n]
	if cached ~= nil then
		return cached
	end
	for i = 2, math.sqrt(n) do
		if n % i == 0 then
			primes_cache[n] = false
			return false
		end
	end
	primes_cache[n] = true
	return true
end

-- returns prime factorization of integer n > 1; cannot be used with {{#invoke:}}
-- note: the order of keys is not specified for Lua tables
function p.prime_factorization_raw(n)
	local factors = {}
	local m = n
	for i = 2, math.sqrt(n) + 1 do
		while m % i == 0 do
			factors[i] = factors[i] or 0
			factors[i] = factors[i] + 1
			m = m / i
		end
		if m == 1 then
			break
		end
	end
	if m > 1 then
		factors[m] = factors[m] or 1
	end
	return factors
end

-- returns prime factorization of integer n > 2 (with wiki markup for exponents)
function p.prime_factorization(frame)
	local args = get_args(frame)
	return p._prime_factorization(p.eval_num_arg(args[1], 12)) -- default to 12
end

function p._prime_factorization(n)
	if n <= 1 then
		return "n/a"
	end
	local factors, powers = {}, {}
	local new_number = n
	for i = 2, n do
		if p.is_prime(i) then
			if new_number % i == 0 then
				factors[#factors + 1] = i
				powers[#factors] = 0
				while new_number % i == 0 do
					powers[#factors] = powers[#factors] + 1
					new_number = new_number / i
				end
				if powers[#factors] > 1 then
					powers[#factors] = factors[#factors] .. "<sup>" .. powers[#factors] .. "</sup>"
				else
					powers[#factors] = factors[#factors]
				end
			end
		end
		if new_number == 1 then
			break
		end
	end
	return table.concat(powers, " × ")
end

-- returns signum(x); cannot be used with {{#invoke:}}
function p.signum(x)
	if type(x) ~= "number" then
		return 0
	end
	if x > 0 then
		return 1
	end
	if x < 0 then
		return -1
	end
	return 0
end

-- returns the next Young diagram of the same size or nil; cannot be used with {{#invoke:}}
-- modifies the input table
function p.next_young_diagram(d)
	if #d == 0 then
		return nil
	end
	local i_from = nil
	local size = 0
	for i = #d, 1, -1 do
		if d[i] > 1 then
			i_from = i
			break
		end
		size = size + d[i]
	end
	if i_from == nil then
		return nil
	end
	d[i_from] = d[i_from] - 1
	size = size + 1
	-- repacking the tail
	local max_d = d[i_from]
	for i = i_from + 1, #d + 1 do
		if size >= max_d then
			d[i] = max_d
			size = size - max_d
		elseif size > 0 then
			d[i] = size
			size = 0
		else
			d[i] = nil
		end
	end
	return d
end

-- stylua: ignore
p.primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
			   101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
			   211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271}

return p