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