Module Core_extended.Std.Int

include Core.Int

This module extends Base.Int.

Note that int is already stable by itself, since as a primitive type it is an integral part of the sexp / bin_io protocol. Int.Stable exists only to introduce Int.Stable.Set and Int.Stable.Map, and provide interface uniformity with other stable types.

include Base.Int.Int_without_module_types with module Hex := Base.Int.Hex
include Base__.Int_intf.S with type t = int
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 ~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
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

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
include Core_kernel.Int_intf.Extension_with_stable with type t := t and type comparator_witness := comparator_witness
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 : Base.Sexp.t ‑> t
val sexp_of_t : t ‑> Base.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 ‑> Base.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
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 Extended_int
include Number.Verified_std with type repr = Core.Int.t
type repr = Core.Int.t
module type S : Number.S with type repr = repr

Abbreviations

module type S0 : Number.S0 with type repr = repr
module Pos : S with type t = private repr

Positive and negative numbers with and without zero.

module Pos0 : S0 with type t = private repr
module Neg : S with type t = private repr
module Neg0 : S0 with type t = private repr
module type Bounded_spec : sig ... end

Specification of bounded numbers

module type Bounded : sig ... end

Signature of bounded numbers

module Make_bounded : functor (Spec : Bounded_spec) -> Bounded with type t = private repr

Functor of creating bounded numbers

Unsafe modules and functors that still fully expose the representation for extensibility.

module Pos_unsafe : S with type t = repr
module Pos0_unsafe : S0 with type t = repr
module Neg_unsafe : S with type t = repr
module Neg0_unsafe : S0 with type t = repr
module Make_bounded_unsafe : functor (Spec : Bounded_spec) -> Bounded with type t = repr
val gcd : int ‑> int ‑> int

Computes greatest common divisor for the given two integers, with convention that gcd 0 0 = 0.

Returns a nonnegative value unless one of the arguments is Int.min_value and the other is Int.min_value or 0, in which case Int.min_value is returned.