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NAME

       Stdlib.Float - no description

Module

       Module   Stdlib.Float

Documentation

       Module Float
        : (module Stdlib__Float)

       val zero : float

       The floating point 0.

       Since 4.08.0

       val one : float

       The floating-point 1.

       Since 4.08.0

       val minus_one : float

       The floating-point -1.

       Since 4.08.0

       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 4.08.0

       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 .

       Since 4.08.0

       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 .

       Since 4.08.0

       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 .

       Since 4.08.0

       val 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

       val 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

       val is_integer : float -> bool

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

       Since 4.08.0

       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 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.

       Since 4.13.0

       val exp : float -> float

       Exponential.

       val exp2 : float -> float

       Base 2 exponential function.

       Since 4.13.0

       val log : float -> float

       Natural logarithm.

       val log10 : float -> float

       Base 10 logarithm.

       val log2 : float -> float

       Base 2 logarithm.

       Since 4.13.0

       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 4.13.0

       val asinh : float -> float

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

       Since 4.13.0

       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 4.13.0

       val erf : float -> float

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

       Since 4.13.0

       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] .

       Since 4.13.0

       val trunc : float -> float

       trunc x rounds x to the nearest integer whose absolute value is less than or equal to x .

       Since 4.08.0

       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 4.08.0

       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 4.08.0

       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 .

       Since 4.08.0

       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.

       Since 4.08.0

       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.

       Since 4.08.0

       val min_max : float -> float -> float * float

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

       Since 4.08.0

       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 4.08.0

       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.

       Since 4.08.0

       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) .

       Since 4.08.0

       val 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).