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Flocq
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Commits
ef1c2fb4
Commit
ef1c2fb4
authored
Sep 08, 2015
by
BOLDO Sylvie
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Still WIP renaming
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2ecd88e3
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src/Core/Fcore_ulp.v
src/Core/Fcore_ulp.v
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src/Core/Fcore_ulp.v
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ef1c2fb4
...
...
@@ -2012,13 +2012,14 @@ apply generic_format_round...
Qed
.
Theorem
betw_eq_DN
:
forall
x
d
,
F
d
(
*
TODO
round_DN_eq_betw
+
changer
sens
*
)
(
*
was
betw_eq_DN
*
)
Theorem
round_DN_eq_betw
:
forall
x
d
,
F
d
->
(
d
<=
x
<
succ
d
)
%
R
->
d
=
round
beta
fexp
Zfloor
x
.
->
round
beta
fexp
Zfloor
x
=
d
.
Proof
with
auto
with
typeclass_instances
.
intros
x
d
Fd
(
Hxd1
,
Hxd2
).
generalize
(
round_DN_pt
beta
fexp
x
);
intros
(
T1
,(
T2
,
T3
)).
apply
Rle_antisym
.
apply
sym_eq
,
Rle_antisym
.
now
apply
T3
.
destruct
(
generic_format_EM
beta
fexp
x
)
as
[
Fx
|
NFx
].
rewrite
round_generic
...
...
...
@@ -2032,16 +2033,17 @@ apply generic_format_succ...
now
left
.
Qed
.
Theorem
betw_eq_UP
:
forall
x
u
,
F
u
(
*
TODO
round_UP_eq_betw
+
changer
sens
*
)
(
*
was
betw_eq_UP
*
)
Theorem
round_UP_eq_betw
:
forall
x
u
,
F
u
->
(
pred
u
<
x
<=
u
)
%
R
->
u
=
round
beta
fexp
Zceil
x
.
->
round
beta
fexp
Zceil
x
=
u
.
Proof
with
auto
with
typeclass_instances
.
intros
x
u
Fu
Hux
.
rewrite
<-
(
Ropp_involutive
(
round
beta
fexp
Zceil
x
)).
rewrite
<-
round_DN_opp
.
rewrite
<-
(
Ropp_involutive
u
).
apply
f_equal
.
apply
betw_eq_DN
;
try
assumption
.
apply
round_DN_eq_betw
;
try
assumption
.
now
apply
generic_format_opp
.
split
;[
now
apply
Ropp_le_contravar
|
idtac
].
rewrite
succ_opp
.
...
...
@@ -2094,11 +2096,11 @@ apply round_N_pt...
apply
Rnd_DN_pt_N
with
(
succ
u
)
%
R
.
pattern
u
at
3
;
replace
u
with
(
round
beta
fexp
Zfloor
((
u
+
succ
u
)
/
2
)).
apply
round_DN_pt
...
apply
sym
_eq
,
betw
_eq_DN
;
trivial
.
apply
round_DN
_eq
_
betw
;
trivial
.
split
;
try
left
;
assumption
.
pattern
(
succ
u
)
at
2
;
replace
(
succ
u
)
with
(
round
beta
fexp
Zceil
((
u
+
succ
u
)
/
2
)).
apply
round_UP_pt
...
apply
sym
_eq
,
betw
_eq_UP
;
trivial
.
apply
round_UP
_eq
_
betw
;
trivial
.
apply
generic_format_succ
...
rewrite
pred_succ
;
trivial
.
split
;
try
left
;
assumption
.
...
...
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