package melange

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package melange
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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, basic arithmetic operations (+., -., *., /.) with nan as an argument return nan, ...

  • since 4.07
val zero : float

The floating point 0.

  • since 4.08
val one : float

The floating-point 1.

  • since 4.08
val minus_one : float

The floating-point -1.

  • since 4.08
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.

On 64-bit Cygwin, 64-bit mingw-w64 and MSVC 2017 and earlier, this function may be emulated owing to known bugs on limitations on these platforms. Note: since software emulation of the fma is costly, make sure that you are using hardware fma support if performance matters.

  • since 4.08
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
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
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, unless otherwise specified in IEEE 754 standard. As for floating-point comparisons, =, <, <=, > and >= return false and <> returns true if one or both of their arguments is nan.

nan is quiet_nan since 5.1; it was a signaling NaN before.

val signaling_nan : float

Signaling NaN. The corresponding signals do not raise OCaml exception, but the value can be useful for interoperability with C libraries.

  • since 5.1
val quiet_nan : float

Quiet NaN.

  • since 5.1
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 if and only if x is finite i.e., not infinite and not nan.

  • since 4.08
val is_infinite : float -> bool

is_infinite x is true if and only if x is infinity or neg_infinity.

  • since 4.08
val is_nan : float -> bool

is_nan x is true if and only if x is not a number (see nan).

  • since 4.08
val is_integer : float -> bool

is_integer x is true if and only if x is an integer.

  • since 4.08
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 a string representation of a floating-point number.

This conversion can involve a loss of precision. For greater control over the manner in which the number is printed, see Printf.

This function is an alias for Stdlib.string_of_float.

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 cbrt : float -> float

Cube root.

  • since 4.13
val exp : float -> float

Exponential.

val exp2 : float -> float

Base 2 exponential function.

  • since 4.13
val log : float -> float

Natural logarithm.

val log10 : float -> float

Base 10 logarithm.

val log2 : float -> float

Base 2 logarithm.

  • since 4.13
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 acosh : float -> float

Hyperbolic arc cosine. The argument must fall within the range [1.0, inf]. Result is in radians and is between 0.0 and inf.

  • since 4.13
val asinh : float -> float

Hyperbolic arc sine. The argument and result range over the entire real line. Result is in radians.

  • since 4.13
val atanh : float -> float

Hyperbolic arc tangent. The argument must fall within the range [-1.0, 1.0]. Result is in radians and ranges over the entire real line.

  • since 4.13
val erf : float -> float

Error function. The argument ranges over the entire real line. The result is always within [-1.0, 1.0].

  • since 4.13
val erfc : float -> float

Complementary error function (erfc x = 1 - erf x). The argument ranges over the entire real line. The result is always within [-1.0, 1.0].

  • since 4.13
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
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., nan, or infinite, x itself is returned.

On 64-bit mingw-w64, this function may be emulated owing to a bug in the C runtime library (CRT) on this platform.

  • since 4.08
val ceil : float -> float

Round above to an integer value. ceil f returns the least integer value greater than or equal to f. The result is returned as a float.

val floor : float -> float

Round below to an integer value. floor f returns the greatest integer value less than or equal to f. The result is returned as a float.

val next_after : float -> float -> float

next_after x y returns the next representable floating-point value following x in the direction of y. More precisely, if y is greater (resp. less) than x, it returns the smallest (resp. largest) representable number greater (resp. less) than x. If x equals y, the function returns y. If x or y is nan, a nan is returned. Note that next_after max_float infinity = infinity and that next_after 0. infinity is the smallest denormalized positive number. If x is the smallest denormalized positive number, next_after x 0. = 0.

  • since 4.08
val copy_sign : float -> float -> float

copy_sign x y returns a float whose absolute value is that of x and whose sign is that of y. If x is nan, returns nan. If y is nan, returns either x or -. x, but it is not specified which.

val sign_bit : float -> bool

sign_bit x is true if and only if the sign bit of x is set. For example sign_bit 1. and signbit 0. are false while sign_bit (-1.) and sign_bit (-0.) are true.

  • since 4.08
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 t = float

An alias for the type of floating-point numbers.

val compare : t -> t -> int

compare x y returns 0 if x is equal to y, a negative integer if x is less than y, and a positive integer if x is greater than y. compare treats nan as equal to itself and less than any other float value. This treatment of nan ensures that compare defines a total ordering relation.

val equal : t -> t -> bool

The equal function for floating-point numbers, compared using compare.

val min : t -> t -> t

min x y returns the minimum of x and y. It returns nan when x or y is nan. Moreover min (-0.) (+0.) = -0.

  • since 4.08
val max : float -> float -> float

max x y returns the maximum of x and y. It returns nan when x or y is nan. Moreover max (-0.) (+0.) = +0.

  • since 4.08
val min_max : float -> float -> float * float

min_max x y is (min x y, max x y), just more efficient.

  • since 4.08
val min_num : t -> t -> t

min_num x y returns the minimum of x and y treating nan as missing values. If both x and y are nan, nan is returned. Moreover min_num (-0.) (+0.) = -0.

  • since 4.08
val max_num : t -> t -> t

max_num x y returns the maximum of x and y treating nan as missing values. If both x and y are nan nan is returned. Moreover max_num (-0.) (+0.) = +0.

  • since 4.08
val min_max_num : float -> float -> float * float

min_max_num x y is (min_num x y, max_num x y), just more efficient. Note that in particular min_max_num x nan = (x, x) and min_max_num nan y = (y, y).

  • since 4.08
val seeded_hash : int -> t -> int

A seeded hash function for floats, with the same output value as Hashtbl.seeded_hash. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded.

  • since 5.1
val hash : t -> int

An unseeded hash function for floats, with the same output value as Hashtbl.hash. This function allows this module to be passed as argument to the functor Hashtbl.Make.

module Array : sig ... end

Float arrays with packed representation.

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