# Module `Extraction_plugin.Big`

`type big_int`` = Z.t`

The type of big integers.

`val zero : Z.t`

The big integer `0`.

`val one : Z.t`

The big integer `1`.

`val two : Z.t`

The big integer `2`.

###### Arithmetic operations
`val opp : Z.t -> Z.t`

Unary negation.

`val abs : Z.t -> Z.t`

Absolute value.

`val add : Z.t -> Z.t -> Z.t`

`val succ : Z.t -> Z.t`

`val add_int : Z.t -> Z.t -> Z.t`

Addition of a small integer to a big integer.

`val sub : Z.t -> Z.t -> Z.t`

Subtraction.

`val pred : Z.t -> Z.t`

Predecessor (subtract 1).

`val mult : Z.t -> Z.t -> Z.t`

Multiplication of two big integers.

`val mult_int : int -> Z.t -> Z.t`

Multiplication of a big integer by a small integer

`val square : Z.t -> Z.t`

Return the square of the given big integer

`val sqrt : Z.t -> Z.t`

`sqrt_big_int a` returns the integer square root of `a`, that is, the largest big integer `r` such that `r * r <= a`. Raise `Invalid_argument` if `a` is negative.

`val quomod : Z.t -> Z.t -> Z.t * Z.t`

Euclidean division of two big integers. The first part of the result is the quotient, the second part is the remainder. Writing `(q,r) = quomod_big_int a b`, we have `a = q * b + r` and `0 <= r < |b|`. Raise `Division_by_zero` if the divisor is zero.

`val div : Z.t -> Z.t -> Z.t`

Euclidean quotient of two big integers. This is the first result `q` of `quomod_big_int` (see above).

`val modulo : Z.t -> Z.t -> Z.t`

Euclidean modulus of two big integers. This is the second result `r` of `quomod_big_int` (see above).

`val gcd : Z.t -> Z.t -> Z.t`

Greatest common divisor of two big integers.

`val power : Z.t -> int -> Z.t`

Exponentiation functions. Return the big integer representing the first argument `a` raised to the power `b` (the second argument). Depending on the function, `a` and `b` can be either small integers or big integers. Raise `Invalid_argument` if `b` is negative.

###### Comparisons and tests
`val sign : Z.t -> int`

Return `0` if the given big integer is zero, `1` if it is positive, and `-1` if it is negative.

`val compare : Z.t -> Z.t -> int`

`compare_big_int a b` returns `0` if `a` and `b` are equal, `1` if `a` is greater than `b`, and `-1` if `a` is smaller than `b`.

`val eq : Z.t -> Z.t -> bool`
`val le : Z.t -> Z.t -> bool`
`val ge : Z.t -> Z.t -> bool`
`val lt : Z.t -> Z.t -> bool`
`val gt : Z.t -> Z.t -> bool`

Usual boolean comparisons between two big integers.

`val max : Z.t -> Z.t -> Z.t`

Return the greater of its two arguments.

`val min : Z.t -> Z.t -> Z.t`

Return the smaller of its two arguments.

###### Conversions to and from strings
`val to_string : Z.t -> string`

Return the string representation of the given big integer, in decimal (base 10).

`val of_string : string -> Z.t`

Convert a string to a big integer, in decimal. The string consists of an optional `-` or `+` sign, followed by one or several decimal digits.

###### Conversions to and from other numerical types
`val of_int : int -> Z.t`

Convert a small integer to a big integer.

`val is_int : Z.t -> bool`

Test whether the given big integer is small enough to be representable as a small integer (type `int`) without loss of precision. On a 32-bit platform, `is_int_big_int a` returns `true` if and only if `a` is between 230 and 230-1. On a 64-bit platform, `is_int_big_int a` returns `true` if and only if `a` is between -262 and 262-1.

`val to_int : Z.t -> int`

Convert a big integer to a small integer (type `int`). Raises `Failure "int_of_big_int"` if the big integer is not representable as a small integer.

`val double : Z.t -> Z.t`
`val doubleplusone : Z.t -> Z.t`
`val nat_case : (unit -> 'a) -> (Z.t -> 'a) -> Z.t -> 'a`
`val positive_case : (Z.t -> 'a) -> (Z.t -> 'a) -> (unit -> 'a) -> Z.t -> 'a`
`val n_case : (unit -> 'a) -> (Z.t -> 'a) -> Z.t -> 'a`
`val z_case : (unit -> 'a) -> (Z.t -> 'a) -> (Z.t -> 'a) -> Z.t -> 'a`
`val compare_case : 'a -> 'a -> 'a -> Z.t -> Z.t -> 'a`
`val nat_rec : 'a -> ('a -> 'a) -> Z.t -> 'a`
`val positive_rec : ('a -> 'a) -> ('a -> 'a) -> 'a -> Z.t -> 'a`
`val z_rec : 'a -> (Z.t -> 'a) -> (Z.t -> 'a) -> Z.t -> 'a`