package base

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package base
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63-bit integers.

The size of Int63 is always 63 bits. On a 64-bit platform it is just an int (63-bits), and on a 32-bit platform it is an int64 wrapped to respect the semantics of 63-bit integers.

Because Int63 has different representations on 32-bit and 64-bit platforms, marshalling Int63 will not work between 32-bit and 64-bit platforms -- unmarshal will segfault.

type t

The @@immediate64 attribute is to indicate that t is implemented by a type that is immediate only on 64 bit platforms. It is currently ignored by the compiler, however we are hoping that one day it will be taken into account so that the compiler can omit caml_modify when dealing with mutable data structures holding Int63.t values.

include Sexplib0.Sexpable.S with type t := t
val t_sexp_grammar : t Sexplib0.Sexp_grammar.t
include Floatable.S with type t := t
val of_float : float -> t
val to_float : t -> float
include Intable.S with type t := t
val of_int_exn : int -> t
val to_int_exn : t -> int
include Identifiable.S with type t := t
val hash_fold_t : Hash.state -> t -> Hash.state
val hash : t -> Hash.hash_value
include Sexplib0.Sexpable.S with type t := t
val t_of_sexp : Sexplib0.Sexp.t -> t
val sexp_of_t : t -> Sexplib0.Sexp.t
include Stringable.S with type t := t
val of_string : string -> t
val to_string : t -> string
include Comparable.S with type t := t
include Comparisons.S with type t := t
include Comparisons.Infix with type t := 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 comparator_witness
include Pretty_printer.S with type t := t
val pp : Formatter.t -> t -> unit
val hashable : t Hashable.t
include Comparable.With_zero with type t := t
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 -> Sign.t

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

include Invariant.S with type t := t
val invariant : t -> unit
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.

Other common functions

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 Caml.ref -> unit
val incr : t Caml.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.

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.

val ceil_pow2 : t -> t

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 : t -> t

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 : t -> int

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

val is_pow2 : t -> bool

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

val clz : t -> int

Returns the number of leading zeros in the binary representation of the input, as an integer between 0 and one less than num_bits.

The results are unspecified for t = 0.

val ctz : t -> int

Returns the number of trailing zeros in the binary representation of the input, as an integer between 0 and one less than num_bits.

The results are unspecified for t = 0.

module O : sig ... end

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

Arithmetic with overflow

Unlike the usual operations, these never overflow, preferring instead to raise.

module Overflow_exn : sig ... end

Conversion functions

val of_int : int -> t
val to_int : t -> int option
val of_int32 : Int32.t -> t
val to_int32 : t -> Int32.t option
val of_int64 : Int64.t -> t option
val of_nativeint : nativeint -> t option
val to_nativeint : t -> nativeint option

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 to_int_trunc : t -> int
val to_int32_trunc : t -> Int32.t
val of_int64_trunc : Int64.t -> t
val of_nativeint_trunc : nativeint -> t
val to_nativeint_trunc : t -> nativeint

Byteswap functions

See Int's byte swap section for a description of Base's approach to exposing byte swap primitives.

val bswap16 : t -> t
val bswap32 : t -> t
val bswap48 : t -> t

Random generation

val random : ?state:Random.State.t -> t -> t

random ~state bound returns a random integer between 0 (inclusive) and bound (exclusive). bound must be greater than 0.

The default ~state is Random.State.default.

val random_incl : ?state:Random.State.t -> t -> t -> t

random_incl ~state lo hi returns a random integer between lo (inclusive) and hi (inclusive). Raises if lo > hi.

The default ~state is Random.State.default.

val floor_log2 : t -> int

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

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