Module Base.Int

include Base__.Int_intf.Int_without_module_types
include Base__.Int_intf.S with type t = int
type t
include sig ... end
val hash_fold_t : Hash.state ‑> t ‑> Hash.state
val hash : t ‑> Hash.hash_value
val t_of_sexp : Sexp.t ‑> t
val sexp_of_t : t ‑> Sexp.t
include Floatable.S with type t := t
type t
val of_float : float ‑> t
val to_float : t ‑> float
include Intable.S with type t := t
type t
val of_int_exn : int ‑> t
val to_int_exn : t ‑> int
include Identifiable.S with type t := t
type t
include sig ... end
val hash_fold_t : Hash.state ‑> t ‑> Hash.state
val hash : t ‑> Hash.hash_value
val t_of_sexp : Sexp.t ‑> t
val sexp_of_t : t ‑> Sexp.t
include Stringable.S with type t := t
type t
val of_string : string ‑> t
val to_string : t ‑> string
include Comparable.S with type t := t
include Base__.Comparable_intf.Polymorphic_compare
include Comparisons.Infix
type t
val (>=) : t ‑> t ‑> bool
val (<=) : t ‑> t ‑> bool
val (=) : t ‑> t ‑> bool
val (>) : t ‑> t ‑> bool
val (<) : t ‑> t ‑> bool
val (<>) : t ‑> t ‑> bool
val equal : t ‑> t ‑> bool
val compare : t ‑> t ‑> int

compare t1 t2 returns 0 if t1 is equal to t2, a negative integer if t1 is less than t2, and a positive integer if t1 is greater than t2.

val min : t ‑> t ‑> t
val max : t ‑> t ‑> t
val ascending : t ‑> t ‑> int

ascending is identical to compare. descending x y = ascending y x. These are intended to be mnemonic when used like List.sort ~compare:ascending and List.sort ~cmp:descending, since they cause the list to be sorted in ascending or descending order, respectively.

val descending : t ‑> t ‑> int
val between : t ‑> low:t ‑> high:t ‑> bool

between t ~low ~high means low <= t <= high

val clamp_exn : t ‑> min:t ‑> max:t ‑> t

clamp_exn t ~min ~max returns t', the closest value to t such that between t' ~low:min ~high:max is true.

Raises if not (min <= max).

val clamp : t ‑> min:t ‑> max:t ‑> t Or_error.t
include Comparator.S with type t := t
type t
type comparator_witness
include Base__.Comparable_intf.Validate with type t := t
type t
val validate_lbound : min:t Maybe_bound.t ‑> t Validate.check
val validate_ubound : max:t Maybe_bound.t ‑> t Validate.check
val validate_bound : min:t Maybe_bound.t ‑> max:t Maybe_bound.t ‑> t Validate.check
include Pretty_printer.S with type t := t
type t
val pp : Formatter.t ‑> t ‑> unit
include Comparable.With_zero with type t := t
type t
val validate_positive : t Validate.check
val validate_non_negative : t Validate.check
val validate_negative : t Validate.check
val validate_non_positive : t Validate.check
val is_positive : t ‑> bool
val is_non_negative : t ‑> bool
val is_negative : t ‑> bool
val is_non_positive : t ‑> bool
val sign : t ‑> Base__.Sign0.t

Returns Neg, Zero, or Pos in a way consistent with the above functions.

include Base__.Int_intf.Hexable with type t := t
type t
module Hex : sig ... end
val to_string_hum : ?⁠delimiter:char ‑> t ‑> string

delimiter is an underscore by default.

Infix operators and constants

val zero : t
val one : t
val minus_one : t
val (+) : t ‑> t ‑> t
val (-) : t ‑> t ‑> t
val (*) : t ‑> t ‑> t
val (**) : t ‑> t ‑> t

Integer exponentiation

Negation

val neg : t ‑> t
val (~-) : t ‑> t

There are two pairs of integer division and remainder functions, /% and %, and / and rem. They both satisfy the same equation relating the quotient and the remainder:

        x = (x /% y) * y + (x % y);
        x = (x /  y) * y + (rem x y);

The functions return the same values if x and y are positive. They all raise if y = 0.

The functions differ if x < 0 or y < 0.

If y < 0, then % and /% raise, whereas / and rem do not.

x % y always returns a value between 0 and y - 1, even when x < 0. On the other hand, rem x y returns a negative value if and only if x < 0; that value satisfies abs (rem x y) <= abs y - 1.

val (/%) : t ‑> t ‑> t
val (%) : t ‑> t ‑> t
val (/) : t ‑> t ‑> t
val rem : t ‑> t ‑> t
val (//) : t ‑> t ‑> float

Float division of integers.

val (land) : t ‑> t ‑> t

Same as bit_and.

val (lor) : t ‑> t ‑> t

Same as bit_or.

val (lxor) : t ‑> t ‑> t

Same as bit_xor.

val (lnot) : t ‑> t

Same as bit_not.

val (lsl) : t ‑> int ‑> t

Same as shift_left.

val (asr) : t ‑> int ‑> t

Same as shift_right.

Successor and predecessor functions

val succ : t ‑> t
val pred : t ‑> t
include Base__.Int_intf.Round with type t := t
type t

round rounds an int to a multiple of a given to_multiple_of argument, according to a direction dir, with default dir being `Nearest. round will raise if to_multiple_of <= 0.

       | `Down    | rounds toward Int.neg_infinity                          |
       | `Up      | rounds toward Int.infinity                              |
       | `Nearest | rounds to the nearest multiple, or `Up in case of a tie |
       | `Zero    | rounds toward zero                                      |

Here are some examples for round ~to_multiple_of:10 for each direction:

       | `Down    | {10 .. 19} --> 10 | { 0 ... 9} --> 0 | {-10 ... -1} --> -10 |
       | `Up      | { 1 .. 10} --> 10 | {-9 ... 0} --> 0 | {-19 .. -10} --> -10 |
       | `Zero    | {10 .. 19} --> 10 | {-9 ... 9} --> 0 | {-19 .. -10} --> -10 |
       | `Nearest | { 5 .. 14} --> 10 | {-5 ... 4} --> 0 | {-15 ... -6} --> -10 |

For convenience and performance, there are variants of round with dir hard-coded. If you are writing performance-critical code you should use these.

val round : ?⁠dir:[ `Zero | `Nearest | `Up | `Down ] ‑> t ‑> to_multiple_of:t ‑> t
val round_towards_zero : t ‑> to_multiple_of:t ‑> t
val round_down : t ‑> to_multiple_of:t ‑> t
val round_up : t ‑> to_multiple_of:t ‑> t
val round_nearest : t ‑> to_multiple_of:t ‑> t
val abs : t ‑> t

Returns the absolute value of the argument. May be negative if the input is min_value.

Exponentiation

val pow : t ‑> t ‑> t

pow base exponent returns base raised to the power of exponent. It is OK if base <= 0. pow raises if exponent < 0, or an integer overflow would occur.

Bit-wise logical operations

val bit_and : t ‑> t ‑> t

These are identical to land, lor, etc. except they're not infix and have different names.

val bit_or : t ‑> t ‑> t
val bit_xor : t ‑> t ‑> t
val bit_not : t ‑> t
val popcount : t ‑> int

Returns the number of 1 bits in the binary representation of the input.

Bit-shifting operations

The results are unspecified for negative shifts and shifts >= num_bits.

val shift_left : t ‑> int ‑> t

Shifts left, filling in with zeroes.

val shift_right : t ‑> int ‑> t

Shifts right, preserving the sign of the input.

Increment and decrement functions for integer references

val decr : t Base__.Import.ref ‑> unit
val incr : t Base__.Import.ref ‑> unit

Conversion functions to related integer types

val of_int32_exn : int32 ‑> t
val to_int32_exn : t ‑> int32
val of_int64_exn : int64 ‑> t
val to_int64 : t ‑> int64
val of_nativeint_exn : nativeint ‑> t
val to_nativeint_exn : t ‑> nativeint
val of_float_unchecked : float ‑> t

of_float_unchecked truncates the given floating point number to an integer, rounding towards zero. The result is unspecified if the argument is nan or falls outside the range of representable integers.

val num_bits : int

The number of bits available in this integer type. Note that the integer representations are signed.

val max_value : t

The largest representable integer.

val min_value : t

The smallest representable integer.

val (lsr) : t ‑> int ‑> t

Same as shift_right_logical.

val shift_right_logical : t ‑> int ‑> t

Shifts right, filling in with zeroes, which will not preserve the sign of the input.

module O : Base__.Int_intf.Operators with type t := t

A sub-module designed to be opened to make working with ints more convenient.

val max_value_30_bits : t

max_value_30_bits = 2^30 - 1. It is useful for writing tests that work on both 64-bit and 32-bit platforms.

val ceil_pow2 : int ‑> int

ceil_pow2 x returns the smallest power of 2 that is greater than or equal to x. The implementation may only be called for x > 0. Example: ceil_pow2 17 = 32

val floor_pow2 : int ‑> int

floor_pow2 x returns the largest power of 2 that is less than or equal to x. The implementation may only be called for x > 0. Example: floor_pow2 17 = 16

val ceil_log2 : int ‑> int

ceil_log2 x returns the ceiling of log-base-2 of x, and raises if x <= 0.

val floor_log2 : int ‑> int

floor_log2 x returns the floor of log-base-2 of x, and raises if x <= 0.

val is_pow2 : int ‑> bool

is_pow2 x returns true iff x is a power of 2. is_pow2 raises if x <= 0.

Conversion functions

val of_int : int ‑> t
val to_int : t ‑> int
val of_int32 : int32 ‑> t option
val to_int32 : t ‑> int32 option
val of_int64 : int64 ‑> t option
val of_nativeint : nativeint ‑> t option
val to_nativeint : t ‑> nativeint

Truncating conversions

These functions return the least-significant bits of the input. In cases where optional conversions return Some x, truncating conversions return x.

val of_int32_trunc : int32 ‑> t
val to_int32_trunc : t ‑> int32
val of_int64_trunc : int64 ‑> t
val of_nativeint_trunc : nativeint ‑> t
module type Hexable = Base__.Int_intf.Hexable

Module types specifying integer operations.

module type Int_without_module_types = Base__.Int_intf.Int_without_module_types
module type Operators = Base__.Int_intf.Operators
module type Operators_unbounded = Base__.Int_intf.Operators_unbounded
module type Round = Base__.Int_intf.Round
module type S = Base__.Int_intf.S
module type S_common = Base__.Int_intf.S_common
module type S_unbounded = Base__.Int_intf.S_unbounded