(** Correctness of Bparse *)

Theorem Bparse_correct:
forall b m e (BASE: 2 <= Zpos b),
let base := {| radix_val := Zpos b; radix_prop := Zle_imp_le_bool _ _ BASE |} in
let r := round radix2 fexp (round_mode mode_NE) (Z2R (Zpos m) * bpow base e) in
if Rlt_bool (Rabs r) (bpow radix2 emax) then
B2R _ _ (Bparse b m e) = r
/\ is_finite _ _ (Bparse b m e) = true
/\ Bsign _ _ (Bparse b m e) = false
else
B2FF _ _ (Bparse b m e) = F754_infinity false.