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Operations on floating-point numbers.
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 operation with nan as argument returns nan as result.
Round the given float to an integer value. floor f returns the greatest integer value less than or equal to f. ceil f returns the least integer value greater than or equal to f.
val round : float -> float
round x rounds x to the nearest integral floating-point (the nearest of floor x and ceil x). In case the fraction of x is exactly 0.5, we round away from 0. : round 1.5 is 2. but round (-3.5) is -4..
val round_to_int : float -> int
round_to_int x is int_of_float (round x).
since 2.0
val round_to_string : ?digits:int ->float -> string
round_to_string ~digits:d x will return a string representation of x -- in base 10 -- rounded to d digits after the decimal point. By default, digits is 0, we round to the nearest integer.
This is strictly a convenience function for simple end-user printing and you should not rely on its behavior. One possible implementation is to rely on C `sprintf` internally, which means:
no guarantee is given on the round-at-half behavior; it may not be consistent with round or round_to_int
round_to_string ~digits:0 3. may return "3" instead of "3." as string_of_float would
no guarantee is given on the behavior for abusively high number of digits precision; for example round_to_string
~digits:max_int x may return the empty string.
if n is negative or if the result would be imaginary
val signbit : float -> bool
returns
True if the sign bit of x is set. This usually indicates thet x is negative.
@since 2.0
val copysign : float ->float -> float
copysign x y returns a copy of x with the same sign as y.
since 2.0
val is_nan : float -> bool
is_nan f returns true if f is nan, false otherwise.
val is_special : float -> bool
is_special f returns true if f is nan or +/- infinity, false otherwise.
since 2.0
val is_finite : float -> bool
is_finite f returns true if f is not nan or +/- infinity, false otherwise.
since 2.0
Constants
Special float constants. It may not be safe to compare directly with these, as they have multiple internal representations. Instead use the is_special, is_nan, etc. tests
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.
Numeric constants
val epsilon : float
The smallest positive float x such that 1.0 +. x <> 1.0.
val e : float
Euler? ... Euler? ... Euler?
since 2.0
val log2e : float
Math.log2 e
since 2.0
val log10e : float
log10 e
since 2.0
val ln2 : float
log 2
since 2.0
val ln10 : float
log 10
since 2.0
val pi : float
The constant pi (3.14159...)
val pi2 : float
pi /. 2.
since 2.0
val pi4 : float
pi /. 4.
since 2.0
val invpi : float
1. /. pi
since 2.0
val invpi2 : float
2. /. pi
since 2.0
val sqrtpi2 : float
2. *. sqrt pi
since 2.0
val sqrt2 : float
sqrt 2.
since 2.0
val invsqrt2 : float
1. /. sqrt 2.
since 2.0
Operations on the internal representation of floating-point numbers
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.