Module type `Int_intf.S_unbounded`

S_unbounded is a generic interface for unbounded integers, e.g. Bignum.Bigint. S_unbounded is a restriction of S (below) that omits values that depend on fixed-size integers.

type t

val hash_fold_t : Base.Hash.state -> t -> Base.Hash.state
val hash : t -> Base.Hash.hash_value

include Base.Sexpable.S with type t := t

type t

val t_of_sexp : Base.Sexp.t -> t
val sexp_of_t : t -> Base.Sexp.t

include Base.Floatable.S with type t := t

type t

val of_float : float -> t
val to_float : t -> float

include Base.Intable.S with type t := t

type t

val of_int_exn : int -> t
val to_int_exn : t -> int

include Base.Identifiable.S with type t := t

type t

val hash_fold_t : Base.Hash.state -> t -> Base.Hash.state
val hash : t -> Base.Hash.hash_value

include Base.Sexpable.S with type t := t

type t

val t_of_sexp : Base.Sexp.t -> t
val sexp_of_t : t -> Base.Sexp.t

include Base.Stringable.S with type t := t

type t

val of_string : string -> t
val to_string : t -> string

include Base.Comparable.S with type t := t

include Base__.Comparable_intf.Polymorphic_compare

include Base.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 Base.Or_error.t

include Base.Comparator.S with type t := t

type t
type comparator_witness

val comparator : (t, comparator_witness) Base.Comparator.comparator

include Base__.Comparable_intf.Validate with type t := t

type t

val validate_lbound : min:t Base.Maybe_bound.t -> t Base.Validate.check
val validate_ubound : max:t Base.Maybe_bound.t -> t Base.Validate.check
val validate_bound : min:t Base.Maybe_bound.t -> max:t Base.Maybe_bound.t -> t Base.Validate.check

include Base.Pretty_printer.S with type t := t

type t

val pp : Base.Formatter.t -> t -> unit

include Base.Comparable.With_zero with type t := t

type t

val validate_positive : t Base.Validate.check
val validate_non_negative : t Base.Validate.check
val validate_negative : t Base.Validate.check
val validate_non_positive : t Base.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.Invariant.S with type t := t

type t

val invariant : t Base__.Invariant_intf.inv

include 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

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.

Other common functions

include 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. If the result overflows (too far positive or too far negative), round returns an incorrect result.

       | `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.

Successor and predecessor functions

val succ : t -> t
val pred : t -> t

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

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.

module O : Operators_unbounded with type t := t: A sub-module designed to be opened to make working with ints more convenient.