package bignum

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Core-flavoured wrapper around zarith's arbitrary-precision rationals

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Dune Dependency

github.com Changelog MIT License Edit opam file Versions (6)

Authors

  1. J
    Jane Street Group, LLC

Maintainers

  1. J
    Jane Street developers

Sources

v0.17.0.tar.gz
sha256=7acc936acbaaf71b2c1518e09b7651bec20d8dc72a990c871c40a74b63b1a8ed

doc/bignum.bigint/Bigint/index.html

Module BigintSource

Sourcetype t

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

include Core.Int_intf.S_unbounded with type t := t
include Base.Int.S_unbounded with type t := t
include Sexplib0.Sexpable.S with type t := t
Sourceval t_sexp_grammar : t Sexplib0.Sexp_grammar.t
include Base.Floatable.S with type t := t
Sourceval of_float : float -> t
Sourceval to_float : t -> float
include Base.Intable.S with type t := t
Sourceval of_int_exn : int -> t
Sourceval to_int_exn : t -> int
include Base.Identifiable.S with type t := t
include Sexplib0.Sexpable.S with type t := t
include Base.Stringable.S with type t := t
include Base.Comparable.S with type t := t
include Base.Comparisons.S with type t := t
include Base.Comparisons.Infix with type t := t
include Base.Comparator.S with type t := t
Sourcetype comparator_witness
include Base.Pretty_printer.S with type t := t
include Base.Comparable.With_zero with type t := t
Sourceval is_positive : t -> bool
Sourceval is_non_negative : t -> bool
Sourceval is_negative : t -> bool
Sourceval is_non_positive : t -> bool
Sourceval sign : t -> Base.Sign.t

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

Sourceval compare__local : t -> t -> int
Sourceval equal__local : t -> t -> bool
include Base.Invariant.S with type t := t
Sourceval invariant : t -> unit
Sourceval of_string_opt : string -> t option
Sourceval to_string_hum : ?delimiter:char -> t -> string

delimiter is an underscore by default.

Infix operators and constants

Sourceval zero : t
Sourceval one : t
Sourceval minus_one : t
Sourceval (+) : t -> t -> t
Sourceval (-) : t -> t -> t
Sourceval (*) : t -> t -> t
Sourceval (**) : t -> t -> t

Integer exponentiation

Negation

Sourceval neg : t -> t
Sourceval (~-) : 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.

Sourceval (/%) : t -> t -> t
Sourceval (%) : t -> t -> t
Sourceval (/) : t -> t -> t
Sourceval rem : t -> t -> t
Sourceval (//) : t -> t -> float

Float division of integers.

Sourceval (land) : t -> t -> t

Same as bit_and.

Sourceval (lor) : t -> t -> t

Same as bit_or.

Sourceval (lxor) : t -> t -> t

Same as bit_xor.

Sourceval lnot : t -> t

Same as bit_not.

Sourceval (lsl) : t -> int -> t

Same as shift_left.

Sourceval (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.

Sourceval round : ?dir:[ `Zero | `Nearest | `Up | `Down ] -> t -> to_multiple_of:t -> t
Sourceval round_towards_zero : t -> to_multiple_of:t -> t
Sourceval round_down : t -> to_multiple_of:t -> t
Sourceval round_up : t -> to_multiple_of:t -> t
Sourceval round_nearest : t -> to_multiple_of:t -> t
Sourceval abs : t -> t

Returns the absolute value of the argument. May be negative if the input is min_value.

Successor and predecessor functions

Sourceval succ : t -> t
Sourceval pred : t -> t

Exponentiation

Sourceval 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

Sourceval bit_and : t -> t -> t

These are identical to land, lor, etc. except they're not infix and have different names.

Sourceval bit_or : t -> t -> t
Sourceval bit_xor : t -> t -> t
Sourceval bit_not : t -> t
Sourceval 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.

Sourceval shift_left : t -> int -> t

Shifts left, filling in with zeroes.

Sourceval shift_right : t -> int -> t

Shifts right, preserving the sign of the input.

Increment and decrement functions for integer references

Sourceval decr : t ref -> unit
Sourceval incr : t ref -> unit
Sourceval of_int32_exn : int32 -> t
Sourceval to_int32_exn : t -> int32
Sourceval of_int64_exn : int64 -> t
Sourceval of_nativeint_exn : nativeint -> t
Sourceval to_nativeint_exn : t -> nativeint
Sourceval 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.

Sourcemodule O : sig ... end

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

include Core.Int_intf.Extension with type t := t with type comparator_witness := comparator_witness
include Bin_prot.Binable.S with type t := t
include Bin_prot.Binable.S_only_functions with type t := t
include Typerep_lib.Typerepable.S with type t := t
Sourceval typename_of_t : t Typerep_lib.Typename.t
include Core.Int_intf.Binaryable with type t := t
Sourcemodule Binary : sig ... end
include Base.Int.Binaryable with type t := t and module Binary := Binary
include Core.Int_intf.Hexable with type t := t
Sourcemodule Hex : sig ... end
include Base.Int.Hexable with type t := t and module Hex := Hex
include Core.Identifiable.S with type t := t with type comparator_witness := comparator_witness
include Bin_prot.Binable.S with type t := t
include Bin_prot.Binable.S_only_functions with type t := t
Sourceval bin_shape_t : Bin_prot.Shape.t
include Ppx_hash_lib.Hashable.S with type t := t
include Sexplib0.Sexpable.S with type t := t
Sourceval t_of_sexp : Sexplib0.Sexp.t -> t
include Ppx_compare_lib.Comparable.S with type t := t
include Ppx_hash_lib.Hashable.S with type t := t
Sourceval sexp_of_t : t -> Sexplib0.Sexp.t
include Base.Stringable.S with type t := t
Sourceval of_string : string -> t
Sourceval to_string : t -> string
include Base.Pretty_printer.S with type t := t
Sourceval pp : Base.Formatter.t -> t -> unit
include Core.Comparable.S_binable with type t := t with type comparator_witness := comparator_witness
include Base.Comparable.S with type t := t with type comparator_witness := comparator_witness
include Base.Comparisons.S with type t := t
include Base.Comparisons.Infix with type t := t
Sourceval (>=) : t -> t -> bool
Sourceval (<=) : t -> t -> bool
Sourceval (=) : t -> t -> bool
Sourceval (>) : t -> t -> bool
Sourceval (<) : t -> t -> bool
Sourceval (<>) : t -> t -> bool
Sourceval equal : t -> t -> bool
Sourceval 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.

Sourceval min : t -> t -> t
Sourceval max : t -> t -> t
Sourceval 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.

Sourceval descending : t -> t -> int
Sourceval between : t -> low:t -> high:t -> bool

between t ~low ~high means low <= t <= high

Sourceval 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).

Sourceval clamp : t -> min:t -> max:t -> t Base.Or_error.t
include Base.Comparator.S with type t := t with type comparator_witness := comparator_witness
include Core.Comparator.S with type t := t with type comparator_witness := comparator_witness
include Core.Hashable.S_binable with type t := t
include Ppx_hash_lib.Hashable.S with type t := t
Sourceval hash_fold_t : Base.Hash.state -> t -> Base.Hash.state
Sourceval hashable : t Base.Hashable.t
include Core.Comparable.Validate_with_zero with type t := t
Sourceval validate_lbound : min:t Core.Maybe_bound.t -> t Validate.check
Sourceval validate_ubound : max:t Core.Maybe_bound.t -> t Validate.check
Sourceval validate_bound : min:t Core.Maybe_bound.t -> max:t Core.Maybe_bound.t -> t Validate.check
Sourceval validate_positive : t Validate.check
Sourceval validate_non_negative : t Validate.check
Sourceval validate_negative : t Validate.check
Sourceval validate_non_positive : t Validate.check
include Core.Quickcheckable.S_int with type t := t
include Core.Quickcheck_intf.S_range with type t := t
include Core.Quickcheck_intf.S with type t := t
Sourceval quickcheck_generator : t Base_quickcheck.Generator.t
Sourceval quickcheck_observer : t Base_quickcheck.Observer.t
Sourceval quickcheck_shrinker : t Base_quickcheck.Shrinker.t
Sourceval 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.

Sourceval 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.

Sourceval 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).

Sourceval 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.

Sourceval to_int64_exn : t -> Core.Int64.t
Sourceval to_int : t -> int option
Sourceval to_int32 : t -> Core.Int32.t option
Sourceval to_int64 : t -> Core.Int64.t option
Sourceval to_nativeint : t -> nativeint option
Sourceval of_int : int -> t
Sourceval of_int32 : Core.Int32.t -> t
Sourceval of_int64 : Core.Int64.t -> t
Sourceval of_nativeint : nativeint -> t
Sourceval to_zarith_bigint : t -> Z.t
Sourceval of_zarith_bigint : Z.t -> t
Sourceval random : ?state:Core.Random.State.t -> t -> t

random t produces a value uniformly distributed between zero (inclusive) and t (exclusive), or raises if t <= zero.

Sourcemodule Stable : sig ... end
Sourcemodule Unstable : sig ... end
  • deprecated [since 2019-10] use module V1 or Unstable instead
  • deprecated [since 2019-10] use module V1 or Unstable instead
  • deprecated [since 2019-10] use module V1 or Unstable instead
Sourceval __bin_read_t__ : (int -> t) Core.Bin_prot.Read.reader
  • deprecated [since 2019-10] use module V1 or Unstable instead
  • deprecated [since 2019-10] use module V1 or Unstable instead
  • deprecated [since 2019-10] use module V1 or Unstable instead
  • deprecated [since 2019-10] use module V1 or Unstable instead
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