Module `Core_kernel.Float`

Floating-point numbers.

include module type of sig ... end

type t = float

val of_float : float -> t
val to_float : t -> float
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
val of_string : string -> 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
val min : t -> t -> t
val max : t -> t -> t
val ascending : t -> t -> int
val descending : t -> t -> int
val between : t -> low:t -> high:t -> bool
val clamp_exn : t -> min:t -> max:t -> t
val clamp : t -> min:t -> max:t -> t Base.Or_error.t

type comparator_witness = Base__Float.comparator_witness

val comparator : (t, comparator_witness) Base.Comparator.comparator
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
val pp : Base.Formatter.t -> t -> unit
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 invariant : t Base__.Invariant_intf.inv
val validate_ordinary : t Base.Validate.check
val nan : t
val infinity : t
val neg_infinity : t
val max_value : t
val min_value : t
val zero : t
val one : t
val minus_one : t
val pi : t
val sqrt_pi : t
val sqrt_2pi : t
val euler : t
val epsilon_float : t
val max_finite_value : t
val min_positive_subnormal_value : t
val min_positive_normal_value : t
val to_int64_preserve_order : t -> int64 option
val to_int64_preserve_order_exn : t -> int64
val of_int64_preserve_order : int64 -> t
val one_ulp : [ `Down | `Up ] -> t -> t
val of_int : int -> t
val to_int : t -> int
val of_int63 : Base.Int63.t -> t
val of_int64 : int64 -> t
val to_int64 : t -> int64
val round : ?⁠dir:[ `Down | `Nearest | `Up | `Zero ] -> t -> t
val iround : ?⁠dir:[ `Down | `Nearest | `Up | `Zero ] -> t -> int option
val iround_exn : ?⁠dir:[ `Down | `Nearest | `Up | `Zero ] -> t -> int
val round_towards_zero : t -> t
val round_down : t -> t
val round_up : t -> t
val round_nearest : t -> t
val round_nearest_half_to_even : t -> t
val iround_towards_zero : t -> int option
val iround_down : t -> int option
val iround_up : t -> int option
val iround_nearest : t -> int option
val iround_towards_zero_exn : t -> int
val iround_down_exn : t -> int
val iround_up_exn : t -> int
val iround_nearest_exn : t -> int
val int63_round_down_exn : t -> Base.Int63.t
val int63_round_up_exn : t -> Base.Int63.t
val int63_round_nearest_exn : t -> Base.Int63.t
val iround_lbound : t
val iround_ubound : t
val round_significant : float -> significant_digits:int -> float
val round_decimal : float -> decimal_digits:int -> float
val is_nan : t -> bool
val is_inf : t -> bool
val min_inan : t -> t -> t
val max_inan : t -> t -> t
val (+) : t -> t -> t
val (-) : t -> t -> t
val (/) : t -> t -> t
val (*) : t -> t -> t
val (**) : t -> t -> t
val (~-) : t -> t

module Parts = Base__Float.Parts

val modf : t -> Parts.t
val mod_float : t -> t -> t
val add : t -> t -> t
val sub : t -> t -> t
val neg : t -> t
val scale : t -> t -> t
val abs : t -> t

module O = Base__Float.O

module O_dot = Base__Float.O_dot

val to_string : t -> string
val to_string_hum : ?⁠delimiter:char -> ?⁠decimals:int -> ?⁠strip_zero:bool -> t -> string
val to_padded_compact_string : t -> string
val to_padded_compact_string_custom : t -> ?⁠prefix:string -> kilo:string -> mega:string -> giga:string -> tera:string -> ?⁠peta:string -> unit -> string
val int_pow : t -> int -> t
val square : t -> t
val ldexp : t -> int -> t
val frexp : t -> t * int

val log10 : t -> t
val expm1 : t -> t
val log1p : t -> t
val copysign : t -> t -> t
val cos : t -> t
val sin : t -> t
val tan : t -> t
val acos : t -> t
val asin : t -> t
val atan : t -> t
val atan2 : t -> t -> t
val hypot : t -> t -> t
val cosh : t -> t
val sinh : t -> t
val tanh : t -> t
val sqrt : t -> t
val exp : t -> t
val log : t -> t

module Class = Base__Float.Class

val classify : t -> Class.t
val is_finite : t -> bool
val sign : t -> Base.Sign.t
val sign_exn : t -> Base.Sign.t
val sign_or_nan : t -> Base.Sign_or_nan.t
val create_ieee : negative:bool -> exponent:int -> mantissa:Base.Int63.t -> t Base.Or_error.t
val create_ieee_exn : negative:bool -> exponent:int -> mantissa:Base.Int63.t -> t
val ieee_negative : t -> bool
val ieee_exponent : t -> int
val ieee_mantissa : t -> Base.Int63.t

module Terse = Base__Float.Terse

module Private = Base__Float.Private

type t = Core_kernel__.Import.float

include Typerep_lib.Typerepable.S with type t := t

type t

val typerep_of_t : t Typerep_lib.Std_internal.Typerep.t
val typename_of_t : t Typerep_lib.Typename.t

module Robust_compare : sig ... end

The results of robust comparisons on nan should be considered undefined.

include Robust_compare.S

val robust_comparison_tolerance : Core_kernel__.Import.float: intended to be a tolerance on human-entered floats

include Robustly_comparable.S with type t := Core_kernel__.Import.float

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 robustly_compare : t -> t -> int

module O : sig ... end

module Robustly_comparable : Robust_compare.S

module Terse : sig ... end

include Identifiable.S with type t := t and type comparator_witness := Base.Float.comparator_witness

type t

include Bin_prot.Binable.S with type t := t

type t

include Bin_prot.Binable.S_only_functions with type t := t

type 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
val bin_t : t Bin_prot.Type_class.t

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

include Ppx_sexp_conv_lib.Sexpable.S with type t := t

type t

val t_of_sexp : Sexplib0.Sexp.t -> t
val sexp_of_t : t -> Sexplib0.Sexp.t

include Identifiable.S_common with type t := t

type t

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 -> Ppx_sexp_conv_lib.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 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

val comparator : (t, comparator_witness) Base.Comparator.comparator

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

module Replace_polymorphic_compare : Core_kernel__.Comparable_intf.Polymorphic_compare with type t := t

include Core_kernel__.Comparable_intf.Map_and_set_binable with type t := t with type comparator_witness := comparator_witness

type t

include Comparator.S with type t := t

type t
type comparator_witness

val comparator : (t, comparator_witness) Comparator.comparator

module Map : Map.S_binable with type Key.t = t with type Key.comparator_witness = comparator_witness

module Set : Set.S_binable with type Elt.t = t with type Elt.comparator_witness = comparator_witness

include Hashable.S_binable with type t := t

type t

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

val hashable : t Hashtbl.Hashable.t

module Table : Hashtbl.S_binable with type key = t

module Hash_set : Hash_set.S_binable with type elt = t

module Hash_queue : Hash_queue.S with type key = t

val to_string_12 : t -> Core_kernel__.Import.string: to_string_12 x builds a string representing x using up to 12 significant digits. It loses precision. You can use "%{Float#12}" in formats, but consider "%.12g", "%{Float#hum}", or "%{Float}" as alternatives.

val to_string : t -> Core_kernel__.Import.string

to_string x builds a string s representing the float x that guarantees the round trip, i.e., Float.equal x (Float.of_string s).

It usually yields as few significant digits as possible. That is, it won't print 3.14 as 3.1400000000000001243. The only exception is that occasionally it will output 17 significant digits when the number can be represented with just 16 (but not 15 or fewer) of them.

include Quickcheckable.S with type t := t

type t

val quickcheck_generator : t Base_quickcheck.Generator.t
val quickcheck_observer : t Base_quickcheck.Observer.t
val quickcheck_shrinker : t Base_quickcheck.Shrinker.t

val sign : t -> Sign.t
val robust_sign : t -> Sign.t: (Formerly sign) Uses robust comparison (so sufficiently small numbers are mapped to Zero). Also maps NaN to Zero. Using this function is weakly discouraged.

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

gen_uniform_excl lo hi creates a Quickcheck generator producing finite t values between lo and hi, exclusive. The generator approximates a uniform distribution over the interval (lo, hi). Raises an exception if lo is not finite, hi is not finite, or the requested range is empty.

The implementation chooses values uniformly distributed between 0 (inclusive) and 1 (exclusive) up to 52 bits of precision, then scales that interval to the requested range. Due to rounding errors and non-uniform floating point precision, the resulting distribution may not be precisely uniform and may not include all values between lo and hi.

val gen_incl : t -> t -> t Quickcheck.Generator.t: gen_incl lo hi creates a Quickcheck generator that produces values between lo and hi, inclusive, approximately uniformly distributed, with extra weight given to generating the endpoints lo and hi. Raises an exception if lo is not finite, hi is not finite, or the requested range is empty.

val gen_finite : t Quickcheck.Generator.t: gen_finite produces all finite t values, excluding infinities and all NaN values.

val gen_positive : t Quickcheck.Generator.t: gen_positive produces all (strictly) positive finite t values.

val gen_negative : t Quickcheck.Generator.t: gen_negative produces all (strictly) negative finite t values.

val gen_without_nan : t Quickcheck.Generator.t: gen_without_nan produces all finite and infinite t values, excluding all NaN values.

val gen_infinite : t Quickcheck.Generator.t: gen_infinite produces both infinite values

val gen_nan : t Quickcheck.Generator.t: gen_nan produces all NaN values.

val gen_normal : t Quickcheck.Generator.t: gen_normal produces all normal values

val gen_subnormal : t Quickcheck.Generator.t: gen_subnormal produces all subnormal values

val gen_zero : t Quickcheck.Generator.t: gen_zero produces both zero values