Module Bignum.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 sig ... end
val bin_read_t : t Bin_prot.Read.reader
val __bin_read_t__ : (int ‑> t) Bin_prot.Read.reader
val bin_reader_t : t Bin_prot.Type_class.reader
val bin_size_t : t Bin_prot.Size.sizer
val bin_write_t : t Bin_prot.Write.writer
val bin_writer_t : t Bin_prot.Type_class.writer
val bin_shape_t : Bin_prot.Shape.t
val typerep_of_t : t Typerep_lib.Std.Typerep.t
val typename_of_t : t Typerep_lib.Std.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 sig ... end
val bin_read_t : t Bin_prot.Read.reader
val __bin_read_t__ : (Core_kernel__.Import.int ‑> t) Bin_prot.Read.reader
val bin_reader_t : t Bin_prot.Type_class.reader
val bin_size_t : t Bin_prot.Size.sizer
val bin_write_t : t Bin_prot.Write.writer
val bin_writer_t : t Bin_prot.Type_class.writer
val bin_shape_t : Bin_prot.Shape.t
val hash_fold_t : Base.Hash.state ‑> t ‑> Base.Hash.state
val hash : t ‑> Base.Hash.hash_value
val t_of_sexp : Sexplib.Sexp.t ‑> t
val sexp_of_t : t ‑> Sexplib.Sexp.t
include Core_kernel.Identifiable.S_common with type t := t
type t
include sig ... end
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 ‑> Sexplib.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 : Caml.Format.formatter ‑> t ‑> unit
include Core_kernel.Comparable.S_binable with type t := t
include Core_kernel__.Comparable_intf.S_common
include Base.Comparable_intf.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 ~cmp: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
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
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 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
include Core_kernel.Hashable.S_binable with type t := t
type t
include sig ... end
val hash_fold_t : Base.Hash.state ‑> t ‑> Base.Hash.state
val hash : t ‑> Base.Hash.hash_value
include Core_kernel.Quickcheckable.S_int with type t := t
include Core_kernel.Quickcheck_intf.S
type 'a gen
type 'a obs
type 'a shr
type t
val gen : t gen
val obs : t obs
val shrinker : t shr
val gen_incl : t ‑> t ‑> t gen

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 gen

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 gen

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 gen

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_intf.S_unbounded with type t := t with type comparator_witness := comparator_witness with module Hex := Hex
include Base.Int_intf.S_common
type t
include sig ... end
val hash_fold_t : Base.Hash.state ‑> t ‑> Base.Hash.state
val hash : t ‑> Base.Hash.hash_value
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
include sig ... end
val hash_fold_t : Base.Hash.state ‑> t ‑> Base.Hash.state
val hash : t ‑> Base.Hash.hash_value
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 ~cmp: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
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
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 : Caml.Format.formatter ‑> 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 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 neg : t ‑> t

Negation

val (~-) : t ‑> t
val (/%) : t ‑> 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 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
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.

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 ‑> Bignum.Zarith.Z.t
val of_zarith_bigint : Bignum.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