Int(3) OCaml library Int(3) NAME Int - Integer values. Module Module Int Documentation Module Int : sig end Integer values. Integers are Sys.int_size bits wide and use two's complement representation. All operations are taken modulo 2^ Sys.int_size . They do not fail on overflow. Since 4.08 Integers type t = int The type for integer values. val zero : int zero is the integer 0 . val one : int one is the integer 1 . val minus_one : int minus_one is the integer -1 . val neg : int -> int neg x is ~-x . val add : int -> int -> int add x y is the addition x + y . val sub : int -> int -> int sub x y is the subtraction x - y . val mul : int -> int -> int mul x y is the multiplication x * y . val div : int -> int -> int Rounding division. div x y is the real quotient x / y rounded towards zero to an integer. See (/) for details. Raises Division_by_zero if the second argument is 0. val rem : int -> int -> int rem x y is the remainder of the rounding division div x y . We have rem x y = x - div x y * y . See (mod) for details. Raises Division_by_zero if the second argument is 0. val fdiv : int -> int -> int Floor division. fdiv x y is the real quotient x / y rounded down to an integer. We have fdiv x y <= div x y <= cdiv x y and cdiv x y - fdiv x y <= 1 . Since 5.5 Raises Division_by_zero if the second argument is 0. val cdiv : int -> int -> int Ceil division. cdiv x y is the real quotient x / y rounded up to an integer. We have fdiv x y <= div x y <= cdiv x y and cdiv x y - fdiv x y <= 1 . Since 5.5 Raises Division_by_zero if the second argument is 0. val ediv : int -> int -> int Euclidean division. ediv x y is the real quotient x / y rounded down to an integer if y > 0 and rounded up to an integer if y < 0 . The remainder erem x y = x - ediv x y * y is always non-negative. Moreover, ediv x (-y) = - ediv x y . Since 5.5 Raises Division_by_zero if the second argument is 0. val erem : int -> int -> int Euclidean remainder. If y is not zero, we have x = ediv x y * y + erem x y and 0 <= erem x y <= abs y - 1 . The result of erem x y is always non-negative, unlike the result of rem x y , which has the sign of x . Since 5.5 Raises Division_by_zero if the second argument is 0. val succ : int -> int succ x is add x 1 . val pred : int -> int pred x is sub x 1 . val abs : int -> int abs x is the absolute value of x . That is x if x is positive and neg x if x is negative. Warning. This may be negative if the argument is Int.min_int . val max_int : int max_int is the greatest representable integer, 2 ^ Sys.int_size - 1 -1 . val min_int : int min_int is the smallest representable integer, -2 ^ Sys.int_size - 1 . val logand : int -> int -> int logand x y is the bitwise logical and of x and y . val logor : int -> int -> int logor x y is the bitwise logical or of x and y . val logxor : int -> int -> int logxor x y is the bitwise logical exclusive or of x and y . val lognot : int -> int lognot x is the bitwise logical negation of x . val shift_left : int -> int -> int shift_left x n shifts x to the left by n bits. The result is unspecified if n < 0 or n > Sys.int_size . val shift_right : int -> int -> int shift_right x n shifts x to the right by n bits. This is an arithmetic shift: the sign bit of x is replicated and inserted in the vacated bits. The result is unspecified if n < 0 or n > Sys.int_size . val shift_right_logical : int -> int -> int shift_right_logical x n shifts x to the right by n bits. This is a logical shift: zeroes are inserted in the vacated bits regardless of the sign of x . The result is unspecified if n < 0 or n > Sys.int_size . Predicates and comparisons val equal : int -> int -> bool equal x y is true if and only if x = y . val compare : int -> int -> int compare x y is compare x y but more efficient. val min : int -> int -> int Return the smaller of the two arguments. Since 4.13 val max : int -> int -> int Return the greater of the two arguments. Since 4.13 Bit counting val popcount : t -> int Population count, also known as Hamming weight. popcount n is the number of 1 bits in the binary representation of n . Negative n are represented in two's complement. Since 5.5 val unsigned_bitsize : t -> int unsigned_bitsize n is the minimal number of bits needed to represent n as an unsigned binary number. It is the smallest integer i between 0 and Sys.int_size inclusive such that 0 <= n < 2{^i} (unsigned). Since 5.5 val signed_bitsize : t -> int signed_bitsize n is the minimal number of bits needed to represent n as a signed, two's complement binary number. It is the smallest integer i between 1 and Sys.int_size inclusive such that -2{^i-1} <= n < 2{^i-1} (signed). Since 5.5 val leading_zeros : t -> int leading_zeros n is the number of leading (most significant) 0 bits in the binary representation of n . It is an integer between 0 and Sys.int_size inclusive. If n is negative, leading_zeros n = 0 since the most significant bit of n is 1. leading_zeros n = {!Sys.int_size} if and only if n = zero . Note that leading_zeros n + unsigned_bitsize n = {!Sys.int_size} . Since 5.5 val leading_sign_bits : t -> int leading_sign_bits n is the number of leading (most significant) sign bits in the binary representation of n , excluding the sign bit itself. It is an integer between 0 and {!Sys.int_size} - 1 inclusive. For positive n , it is the number of leading zero bits minus one. For negative n , it is the number of leading one bits minus one. Note that leading_sign_bits n + signed_bitsize n = {!Sys.int_size} . Since 5.5 val trailing_zeros : t -> int trailing_zeros n is the number of trailing (least significant) 0 bits in the binary representation of n . It is an integer between 0 and Sys.int_size inclusive. It is the largest integer i <= {!Sys.int_size} such that 2{^i} divides n evenly. For example, trailing_zeros n = 0 if and only if n is odd, and trailing_zeros n = {!Sys.int_size} if and only if n = zero . Since 5.5 Converting val to_float : int -> float to_float x is x as a floating point number. val of_float : float -> int of_float x truncates x to an integer. The result is unspecified if the argument is nan or falls outside the range of representable integers. val to_string : int -> string to_string x is the written representation of x in decimal. val seeded_hash : int -> int -> int A seeded hash function for ints, with the same output value as Hashtbl.seeded_hash . This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded . Since 5.1 val hash : int -> int An unseeded hash function for ints, with the same output value as Hashtbl.hash . This function allows this module to be passed as argument to the functor Hashtbl.Make . Since 5.1 OCamldoc 2026-06-22 Int(3)