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Flocq
flocq
Commits
3d44b057
Commit
3d44b057
authored
14 years ago
by
BOLDO Sylvie
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src/Appli/Fappli_Axpy.v
+21
-22
21 additions, 22 deletions
src/Appli/Fappli_Axpy.v
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src/Appli/Fappli_Axpy.v
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3d44b057
...
...
@@ -33,32 +33,31 @@ now apply H.
Qed
.
Theorem
implies_
MinOrMax_le
:
Theorem
implies_
DN_lt_ulp_f
:
forall
x
f
,
format
f
->
(
f
<=
x
)
%
R
->
(
Rabs
(
f
-
x
)
<
ulp
x
)
%
R
->
MinOrMax
x
f
.
(
0
<
f
<=
x
)
%
R
->
(
Rabs
(
f
-
x
)
<
ulp
f
)
%
R
->
(
f
=
rounding
beta
(
FLX_exp
prec
)
ZrndDN
x
)
%
R
.
intros
x
f
Hf
Hxf1
Hxf2
.
left
;
apply
sym_eq
.
apply
Rnd_DN_pt_unicity
with
format
x
.
apply
generic_DN_pt
.
now
apply
FLX_exp_correct
.
split
;[
assumption
|
idtac
].
split
;[
assumption
|
idtac
].
intros
g
Hg
Hxg
.
case
(
Rle_or_lt
g
f
);
trivial
;
intros
Hfg
.
contradict
Hxf2
.
apply
Rle_not_lt
.
rewrite
Rabs_left1
.
2
:
apply
Rle_minus
;
assumption
.
replace
(
-
(
f
-
x
))
%
R
with
((
x
-
g
)
+
(
g
-
f
))
%
R
by
ring
.
rewrite
<-
(
Rplus_0_l
(
ulp
x
)).
apply
Rplus_le_compat
.
apply
Rle_0_minus
;
assumption
.
(
*
succ_lt_le
:*
)
Admitted
.
apply
sym_eq
.
replace
x
with
(
f
+-
(
f
-
x
))
%
R
by
ring
.
apply
rounding_DN_succ
;
trivial
.
apply
Hxf1
.
replace
(
-
(
f
-
x
))
%
R
with
(
Rabs
(
f
-
x
)).
split
;
trivial
;
apply
Rabs_pos
.
rewrite
Rabs_left1
;
trivial
.
now
apply
Rle_minus
.
Qed
.
Theorem
implies_DN_lt_ulp
:
forall
x
f
,
format
f
->
(
0
<
f
<=
x
)
%
R
->
(
Rabs
(
f
-
x
)
<
ulp
x
)
%
R
->
(
f
=
rounding
beta
(
FLX_exp
prec
)
ZrndDN
x
)
%
R
.
intros
x
f
Hf
Hxf1
Hxf2
.
apply
implies_DN_lt_ulp_f
;
trivial
.
Admitted
.
Theorem
implies_MinOrMax_quarter
:
...
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