(** ** Decidable equality *)
Definition Beq_dec: forall (f1 f2: binary_float), {f1 = f2} + {f1 <> f2}.

(* Specifications: *)
Lemma integer_representable_n2p:
forall n p,
-2^prec < n < 2^prec -> 0 <= p -> p <= emax - prec ->
integer_representable (n * 2^p).
Lemma integer_representable_2p:
forall p,
0 <= p <= emax - 1 ->
integer_representable (2^p).
Lemma integer_representable_opp:
forall n, integer_representable n -> integer_representable (-n).
Lemma integer_representable_n2p_wide:
forall n p,
-2^prec <= n <= 2^prec -> 0 <= p -> p < emax - prec ->
integer_representable (n * 2^p).
Lemma integer_representable_n:
forall n, -2^prec <= n <= 2^prec -> integer_representable n.
Lemma round_int_no_overflow:
forall n,
Z.abs n <= 2^emax - 2^(emax-prec) ->
(Rabs (round radix2 fexp (round_mode mode_NE) (Z2R n)) < bpow radix2 emax)%R.
Lemma integer_representable_n2p:
forall n p,
-2^prec < n < 2^prec -> 0 <= p -> p <= emax - prec ->
integer_representable (n * 2^p).
Lemma integer_representable_2p:
forall p,
0 <= p <= emax - 1 ->
integer_representable (2^p).
Lemma integer_representable_opp:
forall n, integer_representable n -> integer_representable (-n).
Lemma integer_representable_n2p_wide:
forall n p,
-2^prec <= n <= 2^prec -> 0 <= p -> p < emax - prec ->
integer_representable (n * 2^p).
Lemma integer_representable_n:
forall n, -2^prec <= n <= 2^prec -> integer_representable n.
Lemma round_int_no_overflow:
forall n,
Z.abs n <= 2^emax - 2^(emax-prec) ->
(Rabs (round radix2 fexp (round_mode mode_NE) (Z2R n)) < bpow radix2 emax)%R.