Module `Bigint`

type t

gen produces integers representable within Quickcheck.size bytes, with a random sign.

include Core_kernel.Int_intf.S_unbounded with type t := t

include Core_kernel.Int_intf.Extension

type t

include Bin_prot.Binable.S with type t := t

type t

include Bin_prot.Binable.S_only_functions with type t := t

type t

val bin_size_t : t Bin_prot.Size.sizer
val bin_write_t : t Bin_prot.Write.writer
val bin_read_t : t Bin_prot.Read.reader
val __bin_read_t__ : (int -> t) Bin_prot.Read.reader: This function only needs implementation if t exposed to be a polymorphic variant. Despite what the type reads, this does *not* produce a function after reading; instead it takes the constructor tag (int) before reading and reads the rest of the variant t afterwards.

val bin_shape_t : Bin_prot.Shape.t
val bin_writer_t : t Bin_prot.Type_class.writer
val bin_reader_t : t Bin_prot.Type_class.reader
val bin_t : t Bin_prot.Type_class.t

include Typerep_lib.Typerepable.S with type t := t

type t

val typerep_of_t : t Typerep_lib.Std_internal.Typerep.t
val typename_of_t : t Typerep_lib.Typename.t

include Core_kernel.Int_intf.Hexable with type t := t

type t

module Hex : sig ... end

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

type t

include Bin_prot.Binable.S with type t := t

type t

include Bin_prot.Binable.S_only_functions with type t := t

type t

val bin_size_t : t Bin_prot.Size.sizer
val bin_write_t : t Bin_prot.Write.writer
val bin_read_t : t Bin_prot.Read.reader
val __bin_read_t__ : (int -> t) Bin_prot.Read.reader: This function only needs implementation if t exposed to be a polymorphic variant. Despite what the type reads, this does *not* produce a function after reading; instead it takes the constructor tag (int) before reading and reads the rest of the variant t afterwards.

val bin_shape_t : Bin_prot.Shape.t
val bin_writer_t : t Bin_prot.Type_class.writer
val bin_reader_t : t Bin_prot.Type_class.reader
val bin_t : t Bin_prot.Type_class.t

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

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

type t

val t_of_sexp : Sexplib0.Sexp.t -> t
val sexp_of_t : t -> Sexplib0.Sexp.t

include Core_kernel.Identifiable.S_common with type t := t

type t

val compare : t -> t -> Core_kernel__.Import.int
val hash_fold_t : Base.Hash.state -> t -> Base.Hash.state
val hash : t -> Base.Hash.hash_value
val sexp_of_t : t -> Ppx_sexp_conv_lib.Sexp.t

include Core_kernel__.Import.Stringable.S with type t := t

type t

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

include Core_kernel__.Import.Pretty_printer.S with type t := t

type t

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

include Core_kernel.Comparable.S_binable with type t := t

include Core_kernel__.Comparable_intf.S_common

include Base.Comparable.S

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

module Replace_polymorphic_compare : Core_kernel__.Comparable_intf.Polymorphic_compare with type t := t

include Core_kernel__.Comparable_intf.Map_and_set_binable with type t := t with type comparator_witness := comparator_witness

type t

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

type t
type comparator_witness

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

module Map : Core_kernel.Map.S_binable with type Key.t = t with type Key.comparator_witness = comparator_witness

module Set : Core_kernel.Set.S_binable with type Elt.t = t with type Elt.comparator_witness = comparator_witness

include Core_kernel.Hashable.S_binable with type t := t

type t

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

val hashable : t Core_kernel.Hashtbl.Hashable.t

module Table : Core_kernel.Hashtbl.S_binable with type key = t

module Hash_set : Core_kernel.Hash_set.S_binable with type elt = t

module Hash_queue : Core_kernel.Hash_queue.S with type Key.t = t

include Core_kernel.Quickcheckable.S_int with type t := t

include Core_kernel.Quickcheck_intf.S

type t

val quickcheck_generator : t Base_quickcheck.Generator.t
val quickcheck_observer : t Base_quickcheck.Observer.t
val quickcheck_shrinker : t Base_quickcheck.Shrinker.t

val gen_incl : t -> t -> t Base_quickcheck.Generator.t: gen_incl lower_bound upper_bound produces values between lower_bound and upper_bound, inclusive. It uses an ad hoc distribution that stresses boundary conditions more often than a uniform distribution, while still able to produce any value in the range. Raises if lower_bound > upper_bound.

val gen_uniform_incl : t -> t -> t Base_quickcheck.Generator.t: gen_uniform_incl lower_bound upper_bound produces a generator for values uniformly distributed between lower_bound and upper_bound, inclusive. Raises if lower_bound > upper_bound.

val gen_log_uniform_incl : t -> t -> t Base_quickcheck.Generator.t: gen_log_uniform_incl lower_bound upper_bound produces a generator for values between lower_bound and upper_bound, inclusive, where the number of bits used to represent the value is uniformly distributed. Raises if (lower_bound < 0) || (lower_bound > upper_bound).

val gen_log_incl : t -> t -> t Base_quickcheck.Generator.t: gen_log_incl lower_bound upper_bound is like gen_log_uniform_incl, but weighted slightly more in favor of generating lower_bound and upper_bound specifically.

include Base.Int.S_unbounded with type t := t with type comparator_witness := comparator_witness with module Hex := Hex

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__.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

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 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.

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

val to_int64_exn : t -> Core_kernel.Int64.t
val to_int : t -> int option
val to_int32 : t -> Core_kernel.Int32.t option
val to_int64 : t -> Core_kernel.Int64.t option
val to_nativeint : t -> nativeint option
val of_int : int -> t
val of_int32 : Core_kernel.Int32.t -> t
val of_int64 : Core_kernel.Int64.t -> t
val of_nativeint : nativeint -> t
val to_zarith_bigint : t -> Bigint__.Zarith.Z.t
val of_zarith_bigint : Bigint__.Zarith.Z.t -> t
val random : ?⁠state:Core_kernel.Random.State.t -> t -> t: random t produces a value uniformly distributed between zero (inclusive) and t (exclusive), or raises if t <= zero.

val gen_positive : t Core_kernel.Quickcheck.Generator.t
val gen_negative : t Core_kernel.Quickcheck.Generator.t

module Stable : sig ... end