Library Coq.Floats.FloatOps

Require Import ZArith Uint63 SpecFloat PrimFloat.

Derived operations and mapping between primitive floats and spec_floats

Definition prec := 53%Z.
Definition emax := 1024%Z.
Notation emin := (emin prec emax).

Definition shift := 2101%Z.
= 2*emax + prec

Module Z.
  Definition frexp f :=
    let (m, se) := frshiftexp f in
    (m, (φ se - shift)%Z%uint63).

  Definition ldexp f e :=
    let e' := Z.max (Z.min e (emax - emin)) (emin - emax - 1) in
    ldshiftexp f (of_Z (e' + shift)).
End Z.

#[deprecated(since = "8.15.0", note = "Use Z.frexp instead.")]
Notation frexp := Z.frexp (only parsing).

#[deprecated(since = "8.15.0", note = "Use Z.ldexp instead.")]
Notation ldexp := Z.ldexp (only parsing).

Definition ulp f := Z.ldexp one (fexp prec emax (snd (Z.frexp f))).

Prim2SF is an injective function that will be useful to express the properties of the implemented Binary64 format (see FloatAxioms).
Definition Prim2SF f :=
  if is_nan f then S754_nan
  else if is_zero f then S754_zero (get_sign f)
       else if is_infinity f then S754_infinity (get_sign f)
              let (r, exp) := Z.frexp f in
              let e := (exp - prec)%Z in
              let (shr, e') := shr_fexp prec emax (φ (normfr_mantissa r))%uint63 e loc_Exact in
              match shr_m shr with
              | Zpos p => S754_finite (get_sign f) p e'
              | Zneg _ | Z0 => S754_zero false

Definition SF2Prim ef :=
  match ef with
  | S754_nan => nan
  | S754_zero false => zero
  | S754_zero true => neg_zero
  | S754_infinity false => infinity
  | S754_infinity true => neg_infinity
  | S754_finite s m e =>
    let pm := of_uint63 (of_Z (Zpos m)) in
    let f := Z.ldexp pm e in
    if s then (-f)%float else f