package coq

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package coq
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type t

t is currently implemented by OCaml's float type.

Beware: NaNs have a sign and a payload, while they should be indistinguishable from Coq's perspective.

val is_nan : t -> bool

Test functions for special values to avoid calling classify

val is_infinity : t -> bool
val is_neg_infinity : t -> bool
val of_string : string -> t
val to_hex_string : t -> string

Print a float exactly as an hexadecimal value (exact decimal * printing would be possible but sometimes requires more than 700 * digits).

val to_string : t -> string

Print a float as a decimal value. The printing is not exact (the * real value printed is not always the given floating-point value), * however printing is precise enough that forall float f, * of_string (to_decimal_string f) = f.

val compile : t -> string
val of_float : float -> t
val sign : t -> bool

Return true for "-", false for "+".

val opp : t -> t
val abs : t -> t
type float_comparison =
  1. | FEq
  2. | FLt
  3. | FGt
  4. | FNotComparable
val eq : t -> t -> bool
val lt : t -> t -> bool
val le : t -> t -> bool
val compare : t -> t -> float_comparison

The IEEE 754 float comparison. * NotComparable is returned if there is a NaN in the arguments

type float_class =
  1. | PNormal
  2. | NNormal
  3. | PSubn
  4. | NSubn
  5. | PZero
  6. | NZero
  7. | PInf
  8. | NInf
  9. | NaN
val classify : t -> float_class
val mul : t -> t -> t
val add : t -> t -> t
val sub : t -> t -> t
val div : t -> t -> t
val sqrt : t -> t
val of_uint63 : Uint63.t -> t

Link with integers

val normfr_mantissa : t -> Uint63.t
val eshift : int

Shifted exponent extraction

val frshiftexp : t -> t * Uint63.t
val ldshiftexp : t -> Uint63.t -> t
val next_up : t -> t
val next_down : t -> t
val equal : t -> t -> bool

Return true if two floats are equal. * All NaN values are considered equal.

val hash : t -> int
val total_compare : t -> t -> int

Total order relation over float values. Behaves like Pervasives.compare.

val is_float64 : Stdlib.Obj.t -> bool
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