Module BatFloat.Safe_float

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

The operations implemented in this module are the same as the operations implemented in module Float, with the exception that no operation returns nan, infinity or neg_infinity. In case of overflow, instead of returning infinity or neg_infinity, operations raise exception Number.Overflow. In case of nan, operations raise exception Number.NaN.

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.

@documents Safe_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
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 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 operations : t BatNumber.numeric
include BatNumber.Bounded with type bounded = t
type bounded = t
val min_num : bounded
val max_num : bounded
Operations specific to floating-point numbers
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 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.

val is_nan : float -> bool

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

val epsilon : float

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

val pi : float

The constant pi (3.14159...)

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 =
| FP_normal(*

Normal number, none of the below

*)
| FP_subnormal(*

Number very close to 0.0, has reduced precision

*)
| FP_zero(*

Number is 0.0 or -0.0

*)
| FP_infinite(*

Number is positive or negative infinity

*)
| 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.

Boilerplate code
val print : 'a BatInnerIO.output -> t -> unit

Printing