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Flocq
flocq
Commits
1d9e2f52
Commit
1d9e2f52
authored
Sep 16, 2009
by
Guillaume Melquiond
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Completed proofs on flush to zero.
parent
07f4d40c
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src/Flocq_rnd_FTZ.v
src/Flocq_rnd_FTZ.v
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src/Flocq_rnd_FTZ.v
View file @
1d9e2f52
...
...
@@ -154,4 +154,65 @@ now eexists.
now
rewrite
<-
Hx1
.
Qed
.
End
RND_FTZ
.
\ No newline at end of file
Theorem
FTZ_format_satisfies_any
:
satisfies_any
FTZ_format
.
Proof
.
refine
(
satisfies_any_eq
_
_
_
(
generic_format_satisfies_any
beta
FTZ_exp
_
)).
exact
FTZ_format_generic
.
exact
FTZ_exp_correct
.
Qed
.
Theorem
FTZ_format_FLXN
:
forall
x
:
R
,
(
bpow
(
emin
+
prec
-
1
)
<=
Rabs
x
)
%
R
->
(
FTZ_format
x
<->
FLXN_format
beta
prec
x
).
Proof
.
intros
x
Hx
.
split
.
(
*
.
*
)
destruct
(
Req_dec
x
0
)
as
[
H4
|
H4
].
intros
_.
rewrite
H4
.
apply
->
FLX_format_FLXN
.
apply
->
FLX_format_generic
.
apply
generic_format_0
.
exact
Hp
.
exact
Hp
.
intros
((
xm
,
xe
),(
H1
,(
H2
,
H3
))).
specialize
(
H2
H4
).
rewrite
H1
.
eexists
.
split
.
split
.
now
intros
_.
(
*
.
*
)
intros
((
xm
,
xe
),(
H1
,
H2
)).
rewrite
H1
.
eexists
.
split
.
split
.
split
.
now
rewrite
<-
H1
at
1.
rewrite
(
Zsucc_pred
emin
).
apply
Zlt_le_succ
.
apply
<-
(
epow_lt
beta
).
apply
Rmult_lt_reg_l
with
(
Z2R
(
Zabs
xm
)).
apply
Rmult_lt_reg_r
with
(
bpow
xe
).
apply
epow_gt_0
.
rewrite
Rmult_0_l
.
rewrite
H1
,
abs_F2R
in
Hx
.
apply
Rlt_le_trans
with
(
2
:=
Hx
).
apply
epow_gt_0
.
rewrite
H1
,
abs_F2R
in
Hx
.
apply
Rlt_le_trans
with
(
2
:=
Hx
).
replace
(
emin
+
prec
-
1
)
%
Z
with
(
prec
+
(
emin
-
1
))
%
Z
by
ring
.
rewrite
epow_add
.
apply
Rmult_lt_compat_r
.
apply
epow_gt_0
.
rewrite
<-
Z2R_Zpower
.
apply
Z2R_lt
.
apply
H2
.
intros
H
.
rewrite
<-
abs_F2R
,
<-
H1
,
H
,
Rabs_right
in
Hx
.
apply
Rle_not_lt
with
(
1
:=
Hx
).
apply
epow_gt_0
.
apply
Rle_refl
.
now
apply
Zlt_le_weak
.
Qed
.
End
RND_FTZ
.
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