Module Float

module Float: sig .. end

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 4.07.0

let zero: float;

The floating point 0.

Since 4.08.0

let one: float;

The floating-point 1.

Since 4.08.0

let minus_one: float;

The floating-point -1.

Since 4.08.0

let neg: float => float;

Unary negation.

let add: (float, float) => float;

Floating-point addition.

let sub: (float, float) => float;

Floating-point subtraction.

let mul: (float, float) => float;

Floating-point multiplication.

let div: (float, float) => float;

Floating-point division.

let 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

let 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.

let 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 Float.next_after.

Since 4.08.0

let 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 Float.next_after.

Since 4.08.0

let abs: float => float;

abs f returns the absolute value of f.

let infinity: float;

Positive infinity.

let neg_infinity: float;

Negative infinity.

let 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.

let pi: float;

The constant pi.

let max_float: float;

The largest positive finite value of type float.

let min_float: float;

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

let epsilon: float;

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

let is_finite: float => bool;

is_finite x is true if and only if x is finite i.e., not infinite and not Float.nan.

Since 4.08.0

let is_infinite: float => bool;

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

Since 4.08.0

let is_nan: float => bool;

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

Since 4.08.0

let is_integer: float => bool;

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

Since 4.08.0

let of_int: int => float;

Convert an integer to floating-point.

let 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.

let 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.

let of_string_opt: string => option(float);

Same as of_string, but returns None instead of raising.

let to_string: float => string;

Return the string representation of a floating-point number.

type fpclass = 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	`*)`

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

let classify_float: float => fpclass;

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

let pow: (float, float) => float;

Exponentiation.

let sqrt: float => float;

Square root.

let exp: float => float;

Exponential.

let log: float => float;

Natural logarithm.

let log10: float => float;

Base 10 logarithm.

let expm1: float => float;

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

let log1p: float => float;

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

let cos: float => float;

Cosine. Argument is in radians.

let sin: float => float;

Sine. Argument is in radians.

let tan: float => float;

Tangent. Argument is in radians.

let 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.

let 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.

let atan: float => float;

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

let 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.

let 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.

let cosh: float => float;

Hyperbolic cosine. Argument is in radians.

let sinh: float => float;

Hyperbolic sine. Argument is in radians.

let tanh: float => float;

Hyperbolic tangent. Argument is in radians.

let 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

let 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.

Since 4.08.0

let 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.

let 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.

let 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 4.08.0

let 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.

let 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 4.08.0

let 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.

let ldexp: (float, int) => float;

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

let 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.

let 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.

let equal: (t, t) => bool;

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

let 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 4.08.0

let 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 4.08.0

let min_max: (float, float) => (float, float);

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

Since 4.08.0

let 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 4.08.0

let 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 4.08.0

let 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 4.08.0

let hash: t => int;

The hash function for floating-point numbers.

module Array: sig .. end

Float arrays with packed representation.

module ArrayLabels: sig .. end

Float arrays with packed representation (labeled functions).