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Operations on floating-point numbers.

OCaml's floating-point numbers follow the IEEE 754 standard, using double precision (64 bits) numbers. Floating-point operations never raise an exception on overflow, underflow, division by zero, etc. Instead, special IEEE numbers are returned as appropriate, such as infinity for 1.0 /. 0.0, neg_infinity for -1.0 /. 0.0, and nan (``not a number'') for 0.0 /. 0.0. These special numbers then propagate through floating-point computations as expected: for instance, 1.0 /. infinity is 0.0, and any operation with nan as argument returns nan as result.

For more precision, see The Wikipedia entry on standard IEEE 754.

  • author Gabriel Scherer
  • author David Teller
  • author Edgar Friendly

@documents Float

type t = float

The type of floating-point numbers.

Floating-point numbers are the default representation of real numbers by OCaml.

Usual operations
val zero : float

Floating number zero. This is the same thing as 0.

val one : float

Floating number one. This is the same thing as 1.

val neg : float -> float

Returns the negation of the input, i.e. (fun x -> ~-. x)

val succ : float -> float

Add 1. to a floating number. Note that, as per IEEE 754, if x is a large enough float number, succ x might be equal to x, due to rounding.

val pred : float -> float

Subtract 1. from a floating number. Note that, as per IEEE 754, if x is a large enough float number, pred x might be equal to x, due to rounding.

val abs : float -> float

The absolute value of a floating point number.

val add : float -> float -> float
val sub : float -> float -> float
val mul : float -> float -> float
val div : float -> float -> float
val modulo : float -> float -> float
val pow : float -> float -> float
val compare : float -> float -> int
val equal : float -> float -> bool
val ord : float -> float -> BatOrd.order
val of_int : int -> float
val to_int : float -> int
val of_float : float -> float
val to_float : float -> float
val of_string : string -> float
val to_string : float -> string
val (+) : t -> t -> t
val (-) : t -> t -> t
val (*) : t -> t -> t
val (/) : t -> t -> t
val (**) : t -> t -> t
val min : float -> float -> float
val max : float -> float -> float
val (--) : t -> t -> t BatEnum.t
val (---) : t -> t -> t BatEnum.t
val operations : t BatNumber.numeric
Operations specific to floating-point numbers
val sqrt : float -> float

Square root.

val exp : float -> float

Exponential.

val log : float -> float

Natural logarithm.

val log10 : float -> float

Base 10 logarithm.

val cos : float -> float

See atan2.

val sin : float -> float

See atan2.

val tan : float -> float

See atan2.

val acos : float -> float

See atan2.

val asin : float -> float

See atan2.

val atan : float -> float

See atan2.

val atan2 : float -> float -> float

The usual trigonometric functions.

val cosh : float -> float

See tanh.

val sinh : float -> float

See tanh.

val tanh : float -> float

The usual hyperbolic trigonometric functions.

val ceil : float -> float

See floor.

val floor : float -> float

Round the given float to an integer value. floor f returns the greatest integer value less than or equal to f. ceil f returns the least integer value greater than or equal to f.

val round : float -> float

round x rounds x to the nearest integral floating-point (the nearest of floor x and ceil x). In case the fraction of x is exactly 0.5, we round away from 0. : round 1.5 is 2. but round (-3.5) is -4..

val round_to_int : float -> int

round_to_int x is int_of_float (round x).

  • since 2.0
val round_to_string : ?digits:int -> float -> string

round_to_string ~digits:d x will return a string representation of x -- in base 10 -- rounded to d digits after the decimal point. By default, digits is 0, we round to the nearest integer.

  • raises Invalid_argument

    if the ~digits argument is negative.

    This is strictly a convenience function for simple end-user printing and you should not rely on its behavior. One possible implementation is to rely on C `sprintf` internally, which means:

    • no guarantee is given on the round-at-half behavior; it may not be consistent with round or round_to_int
    • round_to_string ~digits:0 3. may return "3" instead of "3." as string_of_float would
    • no guarantee is given on the behavior for abusively high number of digits precision; for example round_to_string ~digits:max_int x may return the empty string.
  • since 2.0
val root : float -> int -> float

root x n calculates the nth root of x.

  • raises Invalid_argument

    if n is negative or if the result would be imaginary

val signbit : float -> bool
  • returns

    True if the sign bit of x is set. This usually indicates thet x is negative.

    @since 2.0

val copysign : float -> float -> float

copysign x y returns a copy of x with the same sign as y.

  • since 2.0
val is_nan : float -> bool

is_nan f returns true if f is nan, false otherwise.

val is_special : float -> bool

is_special f returns true if f is nan or +/- infinity, false otherwise.

  • since 2.0
val is_finite : float -> bool

is_finite f returns true if f is not nan or +/- infinity, false otherwise.

  • since 2.0
Constants

Special float constants. It may not be safe to compare directly with these, as they have multiple internal representations. Instead use the is_special, is_nan, etc. tests

val infinity : float

Positive infinity.

val neg_infinity : float

Negative infinity.

val nan : float

A special floating-point value denoting the result of an undefined operation such as 0.0 /. 0.0. Stands for ``not a number''. Any floating-point operation with nan as argument returns nan as result. As for floating-point comparisons, =, <, <=, > and >= return false and <> returns true if one or both of their arguments is nan.

Numeric constants

val epsilon : float

The smallest positive float x such that 1.0 +. x <> 1.0.

val e : float

Euler? ... Euler? ... Euler?

  • since 2.0
val log2e : float

Math.log2 e

  • since 2.0
val log10e : float

log10 e

  • since 2.0
val ln2 : float

log 2

  • since 2.0
val ln10 : float

log 10

  • since 2.0
val pi : float

The constant pi (3.14159...)

val pi2 : float

pi /. 2.

  • since 2.0
val pi4 : float

pi /. 4.

  • since 2.0
val invpi : float

1. /. pi

  • since 2.0
val invpi2 : float

2. /. pi

  • since 2.0
val sqrtpi2 : float

2. *. sqrt pi

  • since 2.0
val sqrt2 : float

sqrt 2.

  • since 2.0
val invsqrt2 : float

1. /. sqrt 2.

  • since 2.0
Operations on the internal representation of floating-point numbers
val frexp : float -> float * int

frexp f returns the pair of the significant and the exponent of f. When f is zero, the significant x and the exponent n of f are equal to zero. When f is non-zero, they are defined by f = x *. 2 ** n and 0.5 <= x < 1.0.

val ldexp : float -> int -> float

ldexp x n returns x *. 2 ** n.

val modf : float -> float * float

modf f returns the pair of the fractional and integral part of f.

type fpkind = Pervasives.fpclass =
  1. | FP_normal
    (*

    Normal number, none of the below

    *)
  2. | FP_subnormal
    (*

    Number very close to 0.0, has reduced precision

    *)
  3. | FP_zero
    (*

    Number is 0.0 or -0.0

    *)
  4. | FP_infinite
    (*

    Number is positive or negative infinity

    *)
  5. | FP_nan
    (*

    Not a number: result of an undefined operation

    *)

Classes of floating point numbers

The five classes of floating-point numbers, as determined by the classify function.

val classify : float -> fpkind

Return the class of the given floating-point number: normal, subnormal, zero, infinite, or not a number.

val approx_equal : ?epsilon:float -> float -> float -> bool

Test whether two floats are approximately equal (i.e. within epsilon of each other). epsilon defaults to 1e-5.

Submodules grouping all infix operators
module Infix : sig ... end
include BatNumber.RefOps with type bat__refops_t = t
type bat__refops_t = t
include BatNumber.Bounded with type bounded = t
type bounded = t
val min_num : bounded
val max_num : bounded
Boilerplate code
val print : (t, _) BatIO.printer

Printing

module Safe_float : sig ... end

Operations on floating-point numbers, with exceptions raised in case of error.

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