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`include module type of struct include Float 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`

, and any arithmetic operation with `nan`

as argument returns `nan`

as result.

`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.

`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.

`succ x`

returns the floating point number right after `x`

i.e., the smallest floating-point number greater than `x`

. See also `next_after`

.

`pred x`

returns the floating-point number right before `x`

i.e., the greatest floating-point number smaller than `x`

. See also `next_after`

.

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`

.

The difference between `1.0`

and the smallest exactly representable floating-point number greater than `1.0`

.

`is_finite x`

is `true`

iff `x`

is finite i.e., not infinite and not `nan`

.

`is_infinite x`

is `true`

iff `x`

is `infinity`

or `neg_infinity`

.

`is_nan x`

is `true`

iff `x`

is not a number (see `nan`

).

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.

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.

`type fpclass = fpclass = `

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.

`expm1 x`

computes `exp x -. 1.0`

, giving numerically-accurate results even if `x`

is close to `0.0`

.

`log1p x`

computes `log(1.0 +. x)`

(natural logarithm), giving numerically-accurate results even if `x`

is close to `0.0`

.

Arc cosine. The argument must fall within the range `[-1.0, 1.0]`

. Result is in radians and is between `0.0`

and `pi`

.

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`

.

`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`

.

`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`

.

`trunc x`

rounds `x`

to the nearest integer whose absolute value is less than or equal to `x`

.

`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.

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.

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.

`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.`

`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.

`sign_bit x`

is `true`

iff 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`

.

`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`

.

`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.

`min x y`

returns the minimum of `x`

and `y`

. It returns `nan`

when `x`

or `y`

is `nan`

. Moreover `min (-0.) (+0.) = -0.`

`max x y`

returns the maximum of `x`

and `y`

. It returns `nan`

when `x`

or `y`

is `nan`

. Moreover `max (-0.) (+0.) = +0.`

`min_max x y`

is `(min x y, max x y)`

, just more efficient.

`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.`

`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.`

`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)`

.

`val hash : t -> int`

The hash function for floating-point numbers.

`module Array = Float.Array`

`module ArrayLabels = Float.ArrayLabels`