ocaml-base-compiler
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package ocaml-base-compiler
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Floating-point arithmetic

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 arithmetic operation with nan as argument returns nan as result.

  • since 4.07.0
val zero : float

The floating point 0.

  • since 4.08.0
val one : float

The floating-point 1.

  • since 4.08.0
val minus_one : float

The floating-point -1.

  • since 4.08.0
val neg : float -> float

Unary negation.

val add : float -> float -> float

Floating-point addition.

val sub : float -> float -> float

Floating-point subtraction.

val mul : float -> float -> float

Floating-point multiplication.

val div : float -> float -> float

Floating-point division.

val fma : float -> float -> float -> float

fma x y z returns x * y + z, with a best effort for computing this expression with a single rounding, using either hardware instructions (providing full IEEE compliance) or a software emulation. Note: since software emulation of the fma is costly, make sure that you are using hardware fma support if performance matters.

  • since 4.08.0
val rem : float -> float -> float

rem a b returns the remainder of a with respect to b. The returned value is a -. n *. b, where n is the quotient a /. b rounded towards zero to an integer.

val succ : float -> float

succ x returns the floating point number right after x i.e., the smallest floating-point number greater than x. See also next_after.

  • since 4.08.0
val pred : float -> float

pred x returns the floating-point number right before x i.e., the greatest floating-point number smaller than x. See also next_after.

  • since 4.08.0
val abs : float -> float

abs f returns the absolute value of 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 pi : float

The constant pi.

val max_float : float

The largest positive finite value of type float.

val min_float : float

The smallest positive, non-zero, non-denormalized value of type float.

val epsilon : float

The difference between 1.0 and the smallest exactly representable floating-point number greater than 1.0.

val is_finite : float -> bool

is_finite x is true iff x is finite i.e., not infinite and not nan.

  • since 4.08.0
val is_infinite : float -> bool

is_infinite x is true iff x is infinity or neg_infinity.

  • since 4.08.0
val is_nan : float -> bool

is_nan x is true iff x is not a number (see nan).

  • since 4.08.0
val is_integer : float -> bool

is_integer x is true iff x is an integer.

  • since 4.08.0
val of_int : int -> float

Convert an integer to floating-point.

val to_int : float -> int

Truncate the given floating-point number to an integer. The result is unspecified if the argument is nan or falls outside the range of representable integers.

val of_string : string -> float

Convert the given string to a float. The string is read in decimal (by default) or in hexadecimal (marked by 0x or 0X). The format of decimal floating-point numbers is [-] dd.ddd (e|E) [+|-] dd , where d stands for a decimal digit. The format of hexadecimal floating-point numbers is [-] 0(x|X) hh.hhh (p|P) [+|-] dd , where h stands for an hexadecimal digit and d for a decimal digit. In both cases, at least one of the integer and fractional parts must be given; the exponent part is optional. The _ (underscore) character can appear anywhere in the string and is ignored. Depending on the execution platforms, other representations of floating-point numbers can be accepted, but should not be relied upon.

  • raises Failure

    if the given string is not a valid representation of a float.

val of_string_opt : string -> float option

Same as of_string, but returns None instead of raising.

val to_string : float -> string

Return the string representation of a floating-point number.

type fpclass = 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

    *)

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

val classify_float : float -> fpclass

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

val pow : float -> float -> float

Exponentiation.

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 expm1 : float -> float

expm1 x computes exp x -. 1.0, giving numerically-accurate results even if x is close to 0.0.

val log1p : float -> float

log1p x computes log(1.0 +. x) (natural logarithm), giving numerically-accurate results even if x is close to 0.0.

val cos : float -> float

Cosine. Argument is in radians.

val sin : float -> float

Sine. Argument is in radians.

val tan : float -> float

Tangent. Argument is in radians.

val acos : float -> float

Arc cosine. The argument must fall within the range [-1.0, 1.0]. Result is in radians and is between 0.0 and pi.

val asin : float -> float

Arc sine. The argument must fall within the range [-1.0, 1.0]. Result is in radians and is between -pi/2 and pi/2.

val atan : float -> float

Arc tangent. Result is in radians and is between -pi/2 and pi/2.

val atan2 : float -> float -> float

atan2 y x returns the arc tangent of y /. x. The signs of x and y are used to determine the quadrant of the result. Result is in radians and is between -pi and pi.

val hypot : float -> float -> float

hypot x y returns sqrt(x *. x + y *. y), that is, the length of the hypotenuse of a right-angled triangle with sides of length x and y, or, equivalently, the distance of the point (x,y) to origin. If one of x or y is infinite, returns infinity even if the other is nan.

val cosh : float -> float

Hyperbolic cosine. Argument is in radians.

val sinh : float -> float

Hyperbolic sine. Argument is in radians.

val tanh : float -> float

Hyperbolic tangent. Argument is in radians.

val trunc : float -> float

trunc x rounds x to the nearest integer whose absolute value is less than or equal to x.

  • since 4.08.0
val round : float -> float

round x rounds x to the nearest integer with ties (fractional values of 0.5) rounded away from zero, regardless of the current rounding direction. If x is an integer, +0., -0., <