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Flocq
flocq
Commits
96436d36
Commit
96436d36
authored
Jul 22, 2013
by
BOLDO Sylvie
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End of the definition and first props of of Rnd_odd
parent
e58683ac
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1
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src/Appli/Fappli_rnd_odd.v
src/Appli/Fappli_rnd_odd.v
+44
-29
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src/Appli/Fappli_rnd_odd.v
View file @
96436d36
...
...
@@ -294,9 +294,7 @@ reflexivity.
apply
round_generic
...
intros
Y
.
replace
(
Fnum
{|
Fnum
:=
Zfloor
(
scaled_mantissa
beta
fexp
x
);
Fexp
:=
cexp
x
|}
)
with
(
Fnum
(
Float
beta
0
(
fexp
(
ln_beta
beta
0
)))).
generalize
(
DN_UP_parity_generic
beta
fexp
)...
unfold
DN_UP_parity_prop
.
intros
T
;
apply
T
with
x
;
clear
T
.
...
...
@@ -310,30 +308,25 @@ assumption.
apply
Rmult_le_pos
.
now
left
.
apply
bpow_ge_0
.
unfold
Fcore_generic_fmt
.
canonic
.
simpl
.
apply
sym_eq
,
canonic_exp_DN
...
apply
canonic_0
.
unfold
Fcore_generic_fmt
.
canonic
.
rewrite
<-
H0
;
reflexivity
.
re
flexivity
.
re
write
<-
Y
;
unfold
F2R
;
simpl
;
ring
.
apply
trans_eq
with
(
round
beta
fexp
Ztrunc
(
round
beta
fexp
Zceil
x
)).
reflexivity
.
apply
round_generic
...
intros
Y
.
simpl
.
replace
(
scaled_mantissa
beta
fexp
x
)
with
(
Z2R
0
).
rewrite
Zfloor_Z2R
;
simpl
.
SearchAbout
Fnum
.
apply
eq_Z2R
,
Rmult_eq_reg_r
with
(
bpow
(
cexp
x
)).
unfold
round
,
F2R
in
Y
;
simpl
in
Y
;
rewrite
<-
Y
.
simpl
;
ring
.
apply
Rgt_not_eq
,
bpow_gt_0
.
(
*
.
*
)
intros
Y
.
case
(
Rle_lt_or_eq_dec
0
(
round
beta
fexp
Zfloor
x
)).
rewrite
<-
round_0
with
beta
fexp
Zfloor
...
apply
round_le
...
now
left
.
intros
Hrx
.
set
(
ef
:=
canonic_exp
beta
fexp
x
).
set
(
mf
:=
Zfloor
(
scaled_mantissa
beta
fexp
x
)).
exists
(
Float
beta
mf
ef
).
...
...
@@ -342,21 +335,43 @@ repeat split; try assumption.
simpl
.
apply
trans_eq
with
(
cexp
(
round
beta
fexp
Zfloor
x
)).
apply
sym_eq
,
canonic_exp_DN
...
reflexivity
.
intros
Hrx
;
contradict
Y
.
replace
(
Zfloor
(
scaled_mantissa
beta
fexp
x
))
with
0
%
Z
.
simpl
;
discriminate
.
apply
eq_Z2R
,
Rmult_eq_reg_r
with
(
bpow
(
cexp
x
)).
unfold
round
,
F2R
in
Hrx
;
simpl
in
Hrx
;
rewrite
<-
Hrx
.
simpl
;
ring
.
apply
Rgt_not_eq
,
bpow_gt_0
.
Qed
.
End
Fcore_rnd_odd
.
Section
Odd_prop
.
admit
.
(
*
dur
mais
ok
*
)
Variable
beta
:
radix
.
reflexivity
.
Qed
.
Notation
bpow
e
:=
(
bpow
beta
e
).
Variable
fexp
:
Z
->
Z
.
Variable
fexpe
:
Z
->
Z
.
Context
{
valid_exp
:
Valid_exp
fexp
}
.
Context
{
exists_NE_
:
Exists_NE
beta
fexp
}
.
assert
(
0
<
round
beta
fexp
Zfloor
x
)
%
R
.
case
(
Rle_lt_or_eq_dec
0
(
round
beta
fexp
Zfloor
x
)).
rewrite
<-
round_0
with
beta
fexp
Zfloor
...
apply
round_le
...
now
left
.
trivial
.
Context
{
valid_expe
:
Valid_exp
fexpe
}
.
Context
{
exists_NE_e
:
Exists_NE
beta
fexpe
}
.
Hypothesis
fexpe_fexp
:
forall
e
,
(
fexpe
e
<=
fexp
e
-
2
)
%
Z
.
(
*
???
*
)
Theorem
rnd_opp
:
forall
x
,
round
beta
fexp
ZnearestE
(
round
beta
fexpe
Zrnd_odd
x
)
=
round
beta
fexp
ZnearestE
x
.
Proof
with
auto
with
typeclass_instances
.
intros
x
.
apply
round_unicity
with
(
Rnd_NE_pt
beta
fexp
)
x
...
apply
Rnd_NE_pt_monotone
...
2
:
apply
round_NE_pt
...
TOTO
.
...
...
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