bignum

Core-flavoured wrapper around zarith's arbitrary-precision rationals.
IN THIS PACKAGE
Module Bignum
include module type of Bignum0 with module Stable := Bignum0.Stable

Arbitrary-precision rational numbers.

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

Sexp conversions represent values as decimals if possible, or defaults to (x + y/z) where x is decimal and y and z are integers. So for example, 1/3 <-> (0.333333333 + 1/3000000000). In string and sexp conversions, values with denominator of zero are special-cased: 0/0 <-> "nan", 1/0 <-> "inf", and -1/0 <-> "-inf".

include Core_kernel.Sexpable with type t := t
val t_of_sexp : Base.Sexp.t -> t
val sexp_of_t : t -> Base.Sexp.t
include Core_kernel.Comparable 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
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 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 comparator_witness
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.Hashable with type t := t
include Core_kernel.Hashable.Common with type t := t
val compare : t -> t -> Base.Int.t
val hash_fold_t : Base.Hash.state -> t -> Base.Hash.state
val hash : t -> Base.Hash.hash_value
module Table : Core_kernel.Hashtbl.S with type key = t
module Hash_set : Core_kernel.Hash_set.S with type elt = t
include Core_kernel.Binable with type t := 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

gen produces values with an order of magnitude (roughly the number of digits) in the numerator and denominator proportional to Quickcheck.Generator.size. Also includes values with zero in the denominator.

include Core_kernel.Quickcheckable with type t := t
val zero : t
val one : t
val ten : t
val hundred : t
val thousand : t
val million : t
val billion : t
val trillion : t
val tenth : t
val hundredth : t
val thousandth : t
val millionth : t
val billionth : t
val trillionth : t
val (+) : t -> t -> t
val (-) : t -> t -> t
val (/) : t -> t -> t

Note that division by zero will not raise, but will return inf, -inf, or nan.

val (//) : int -> int -> t

m // n is equivalent to of_int m / of_int n. Example: Bigint.O.(2 // 3).

val (*) : t -> t -> t
val (**) : t -> int -> t

Beware: 2 ** 8_000_000 will take at least a megabyte to store the result, and multiplying numbers a megabyte long is slow no matter how clever your algorithm. Be careful to ensure the second argument is reasonably-sized.

val abs : t -> t
val neg : t -> t
val inverse : t -> t

Note that inverse zero is infinity, not an error.

val sum : t list -> t
val round : ?dir:[ `Down | `Up | `Nearest | `Zero ] -> ?to_multiple_of:t -> t -> t

Default rounding direction is `Nearest. to_multiple_of defaults to one and must not be zero.

val iround : ?dir:[ `Down | `Up | `Nearest | `Zero ] -> ?to_multiple_of:int -> t -> int option

None if the result would overflow or to_multiple_of is zero.

val round_as_bigint : ?dir:[ `Down | `Up | `Nearest | `Zero ] -> ?to_multiple_of:Bigint.t -> t -> Bigint.t option
val iround_exn : ?dir:[ `Down | `Up | `Nearest | `Zero ] -> ?to_multiple_of:int -> t -> int

Exception if the result would overflow or to_multiple_of is zero.

val round_as_bigint_exn : ?dir:[ `Down | `Up | `Nearest | `Zero ] -> ?to_multiple_of:Bigint.t -> t -> Bigint.t
val round_decimal : ?dir:[ `Down | `Up | `Nearest | `Zero ] -> digits:int -> t -> t

Convenience wrapper around round to round to the specified number of decimal digits. This raises if the number is infinite or undefined.

val round_decimal_to_nearest_half_to_even : digits:int -> t -> t
val to_float : t -> float
val to_string_decimal_accurate_exn : t -> string

Accurate if possible. If this number is not representable as a finite decimal fraction, it raises instead.

val to_string_decimal_accurate : t -> string Core_kernel.Or_error.t

As above, returns Or_error.t instead of raising

val is_representable_as_decimal : t -> bool

true if and only if to_string_decimal_accurate_exn doesn't raise.

val is_real : t -> bool

true if and only if the number is non-infinity and non-undefined.

val is_nan : t -> bool

true if and only if the number is undefined.

val to_string_hum : ?delimiter:char -> ?decimals:int -> ?strip_zero:bool -> t -> string

Pretty print bignum in an approximate decimal form or print inf, -inf, nan. For example to_string_hum ~delimiter:',' ~decimals:3 ~strip_zero:false 1234.1999 = "1,234.200". No delimiters are inserted to the right of the decimal.

val to_string_accurate : t -> string

Always accurate. If the number is representable as a finite decimal, it will return this decimal string. If the denomiator is zero, it would return "nan", "inf" or "-inf". Finally, if the bignum is a rational non representable as a decimal, to_string_accurate t returns an expression that evaluates to the right value. Example: to_string_accurate (Bignum.of_string "1/3") = "(0.333333333 + 1/3000000000)".

Since the introduction of that function in the API, of_string is able to read any value returned by this function, and would yield the original bignum. That is:

fun bignum -> bignum |> to_string_accurate |> of_string

is the identity in Bignum.

val of_float_decimal : float -> t

Transforming a float into a Bignum.t needs to be done with care. Most rationals and decimals are not exactly representable as floats, thus their float representation includes some small imprecision at the end of their decimal form (typically after the 17th digits). It is very likely that when transforming a float into a Bignum.t, it is best to try to determine which was the original value and retrieve it instead of honoring the noise coming from its imprecise float representation.

Given that the original value is not available in the context of a function whose type is float -> Bignum.t, it is not possible to solve that problem in a principled way. However, a very reasonable approximation is to build the Bignum from a short string-representation of the float that guarantees the round-trip float |> to_string |> of_string. In particular, if the float was obtained from a short decimal string, this heuristic in practice succeeds at retrieving the original value.

In the context where it is assumed that a float is a perfect representative of the value meant to be modelled, the actual Bignum.t value for it may be built using of_float_dyadic.

For example:

3.14 is not a representable decimal, thus:

of_float_dyadic (Float.of_string "3.14") = (3.14 + 7/56294995342131200)
of_float_decimal (Float.of_string "3.14") = 3.14

of_float_dyadic used to be called of_float but we think it is not the right default choice, thus of_float was deprecated, and we introduced different names for this operation to force some explicit decision at call site.

After some time has passed, of_float_decimal will be renamed to of_float, thus re-introducing of_float in the API.

val of_float_dyadic : float -> t
val of_float : float -> t
val to_int : t -> int option

Rounds toward zero. None if the conversion would overflow

val to_int_exn : t -> int
val is_zero : t -> bool
val sign : t -> int
val of_string : string -> t
val of_int : int -> t
val num : t -> t

num t returns the numerator of the numeric

val den : t -> t

den t returns the denominator of the numeric

val of_bigint : Bigint.t -> t
val num_as_bigint : t -> Bigint.t
val den_as_bigint : t -> Bigint.t
val pp_hum : Format.formatter -> t -> unit
val pp_accurate : Format.formatter -> t -> unit

gen_finite is like gen but excludes values with zero in the denominator.

val gen_uniform_excl : t -> t -> t Core_kernel.Quickcheck.Generator.t

gen_uniform_excl lower_bound upper_bound produces a uniform distribution between lower_bound and upper_bound, exclusive, in units based on the fractional parts of the bounds plus a number of decimal places proportional to Quickcheck.Generator.size.

gen_incl lower_bound upper_bound produces a distribution of values between lower_bound and upper_bound, inclusive, that is approximately uniform with extra weight given to producing the endpoints lower_bound and upper_bound.

module O : sig ... end
val to_string : t -> string
val pp : Format.formatter -> t -> unit
module Stable : sig ... end
module Bignum0 : sig ... end
module Std : sig ... end