@spec digits(integer(), pos_integer()) :: [integer(), ...]

Returns the ordered digits for the given integer.

An optional base value may be provided representing the radix for the returned digits. This one must be an integer >= 2.

Examples

iex> Integer.digits(123)
[1, 2, 3]

iex> Integer.digits(170, 2)
[1, 0, 1, 0, 1, 0, 1, 0]

iex> Integer.digits(-170, 2)
[-1, 0, -1, 0, -1, 0, -1, 0]

@spec extended_gcd(integer(), integer()) :: {non_neg_integer(), integer(), integer()}

Returns the extended greatest common divisor of the two given integers.

It uses the Extended Euclidean algorithm to return a three-element tuple with the gcd and the coefficients m and n of Bézout's identity such that:

gcd(a, b) = m*a + n*b

By convention, extended_gcd(0, 0) returns {0, 0, 0}.

Examples

iex> Integer.extended_gcd(240, 46)
{2, -9, 47}
iex> Integer.extended_gcd(46, 240)
{2, 47, -9}
iex> Integer.extended_gcd(-46, 240)
{2, -47, -9}
iex> Integer.extended_gcd(-46, -240)
{2, -47, 9}

iex> Integer.extended_gcd(14, 21)
{7, -1, 1}

iex> Integer.extended_gcd(10, 0)
{10, 1, 0}
iex> Integer.extended_gcd(0, 10)
{10, 0, 1}
iex> Integer.extended_gcd(0, 0)
{0, 0, 0}

@spec floor_div(integer(), neg_integer() | pos_integer()) :: integer()

Performs a floored integer division.

Raises an ArithmeticError exception if one of the arguments is not an integer, or when the divisor is 0.

Integer.floor_div/2 performs floored integer division. This means that the result is always rounded towards negative infinity.

If you want to perform truncated integer division (rounding towards zero), use Kernel.div/2 instead.

Examples

iex> Integer.floor_div(5, 2)
2
iex> Integer.floor_div(6, -4)
-2
iex> Integer.floor_div(-99, 2)
-50

@spec gcd(integer(), integer()) :: non_neg_integer()

Returns the greatest common divisor of the two given integers.

The greatest common divisor (GCD) of integer1 and integer2 is the largest positive integer that divides both integer1 and integer2 without leaving a remainder.

By convention, gcd(0, 0) returns 0.

Examples

iex> Integer.gcd(2, 3)
1

iex> Integer.gcd(8, 12)
4

iex> Integer.gcd(8, -12)
4

iex> Integer.gcd(10, 0)
10

iex> Integer.gcd(7, 7)
7

iex> Integer.gcd(0, 0)
0

@spec mod(integer(), neg_integer() | pos_integer()) :: integer()

Computes the modulo remainder of an integer division.

Integer.mod/2 uses floored division, which means that the result will always have the sign of the divisor.

Raises an ArithmeticError exception if one of the arguments is not an integer, or when the divisor is 0.

Examples

iex> Integer.mod(5, 2)
1
iex> Integer.mod(6, -4)
-2

@spec parse(binary(), 2..36) :: {integer(), remainder_of_binary :: binary()} | :error

Parses a text representation of an integer.

An optional base to the corresponding integer can be provided. If base is not given, 10 will be used.

If successful, returns a tuple in the form of {integer, remainder_of_binary}. Otherwise :error.

Raises an error if base is less than 2 or more than 36.

If you want to convert a string-formatted integer directly to an integer, String.to_integer/1 or String.to_integer/2 can be used instead.

Examples

iex> Integer.parse("34")
{34, ""}

iex> Integer.parse("34.5")
{34, ".5"}

iex> Integer.parse("three")
:error

iex> Integer.parse("34", 10)
{34, ""}

iex> Integer.parse("f4", 16)
{244, ""}

iex> Integer.parse("Awww++", 36)
{509216, "++"}

iex> Integer.parse("fab", 10)
:error

iex> Integer.parse("a2", 38)
** (ArgumentError) invalid base 38

@spec pow(integer(), non_neg_integer()) :: integer()

Computes base raised to power of exponent.

Both base and exponent must be integers. The exponent must be zero or positive.

See Float.pow/2 for exponentiation of negative exponents as well as floats.

Examples

iex> Integer.pow(2, 0)
1
iex> Integer.pow(2, 1)
2
iex> Integer.pow(2, 10)
1024
iex> Integer.pow(2, 11)
2048
iex> Integer.pow(2, 64)
0x10000000000000000

iex> Integer.pow(3, 4)
81
iex> Integer.pow(4, 3)
64

iex> Integer.pow(-2, 3)
-8
iex> Integer.pow(-2, 4)
16

iex> Integer.pow(2, -2)
** (ArithmeticError) bad argument in arithmetic expression

@spec to_charlist(integer(), 2..36) :: charlist()

Returns a charlist which corresponds to the text representation of integer in the given base.

base can be an integer between 2 and 36. If no base is given, it defaults to 10.

Inlined by the compiler.

Examples

iex> Integer.to_charlist(123)
'123'

iex> Integer.to_charlist(+456)
'456'

iex> Integer.to_charlist(-789)
'-789'

iex> Integer.to_charlist(0123)
'123'

iex> Integer.to_charlist(100, 16)
'64'

iex> Integer.to_charlist(-100, 16)
'-64'

iex> Integer.to_charlist(882_681_651, 36)
'ELIXIR'

@spec to_string(integer(), 2..36) :: String.t()

Returns a binary which corresponds to the text representation of integer in the given base.

base can be an integer between 2 and 36. If no base is given, it defaults to 10.

Inlined by the compiler.

Examples

iex> Integer.to_string(123)
"123"

iex> Integer.to_string(+456)
"456"

iex> Integer.to_string(-789)
"-789"

iex> Integer.to_string(0123)
"123"

iex> Integer.to_string(100, 16)
"64"

iex> Integer.to_string(-100, 16)
"-64"

iex> Integer.to_string(882_681_651, 36)
"ELIXIR"

@spec undigits([integer()], pos_integer()) :: integer()

Returns the integer represented by the ordered digits.

An optional base value may be provided representing the radix for the digits. Base has to be an integer greater than or equal to 2.

Examples

iex> Integer.undigits([1, 2, 3])
123

iex> Integer.undigits([1, 4], 16)
20

iex> Integer.undigits([])
0