module Float: sig .. endFloating-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, ...
val zero : float
The floating point 0.
val one : float
The floating-point 1.
val minus_one : float
The floating-point -1.
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.
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
Float.next_after.
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
Float.next_after.
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 if and only if x is finite i.e., not infinite and
not Float.nan.
val is_infinite : float -> bool
is_infinite x is true if and only if x is Float.infinity or
Float.neg_infinity.
val is_nan : float -> bool
is_nan x is true if and only if x is not a number (see Float.nan).
val is_integer : float -> bool
is_integer x is true if and only if x is an integer.
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.
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 string_of_float.
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.
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.
val exp : float -> float
Exponential.
val exp2 : float -> float
Base 2 exponential function.
val log : float -> float
Natural logarithm.
val log10 : float -> float
Base 10 logarithm.
val log2 : float -> float
Base 2 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 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.
val asinh : float -> float
Hyperbolic arc sine. The argument and result range over the entire real line. Result is in radians.
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.
val erf : float -> float
Error function. The argument ranges over the entire real line.
The result is always within [-1.0, 1.0].
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].
val trunc : float -> float
trunc x rounds x to the nearest integer whose absolute value is
less than or equal to x.
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.
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.
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.
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 Float.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.
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.
val min_max : float -> float -> float * float
min_max x y is (min x y, max x y), just more efficient.
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.
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.
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).
val hash : t -> int
The hash function for floating-point numbers.
module Array: sig .. endFloat arrays with packed representation.
module ArrayLabels: sig .. endFloat arrays with packed representation (labeled functions).