The Coq Proof Assistant

# 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.
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)
else
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
end.
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
end.