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Flocq
flocq
Commits
3aac99c3
Commit
3aac99c3
authored
Sep 09, 2016
by
BOLDO Sylvie
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FTS, TS, presque tout underflow ErrFMA
parent
603d5937
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2
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-95
src/Translate/Ftranslate_flocq2Pff.v
src/Translate/Ftranslate_flocq2Pff.v
+61
-0
src/Translate/Missing_theos.v
src/Translate/Missing_theos.v
+416
-95
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src/Translate/Ftranslate_flocq2Pff.v
View file @
3aac99c3
...
...
@@ -367,6 +367,67 @@ rewrite inj_abs; simpl; omega.
apply
pff_round_NE_is_round
.
Qed
.
Lemma
FloatFexp_gt
:
forall
e
f
,
Fbounded
b
f
->
(
bpow
beta
(
e
+
p
)
<=
Rabs
(
FtoR
beta
f
))
%
R
->
(
e
<
Float
.
Fexp
f
)
%
Z
.
Proof
.
intros
e
f
Ff
H1
.
apply
lt_bpow
with
beta
.
apply
Rmult_lt_reg_r
with
(
bpow
beta
p
).
apply
bpow_gt_0
.
rewrite
<-
bpow_plus
.
apply
Rle_lt_trans
with
(
1
:=
H1
).
rewrite
<-
Fabs_correct
.
2
:
apply
radix_gt_0
.
unfold
Fabs
,
FtoR
;
simpl
;
rewrite
Rmult_comm
.
rewrite
bpow_powerRZ
,
Z2R_IZR
.
apply
Rmult_lt_compat_l
.
apply
powerRZ_lt
.
replace
0
%
R
with
(
IZR
0
)
by
reflexivity
.
apply
IZR_lt
,
radix_gt_0
.
destruct
Ff
as
(
T1
,
T2
).
rewrite
bpow_powerRZ
.
rewrite
Z2R_IZR
.
replace
p
with
(
Z
.
of_nat
(
Zabs_nat
p
)).
rewrite
<-
Zpower_nat_Z_powerRZ
.
apply
IZR_lt
.
now
rewrite
<-
pGivesBound
.
rewrite
inj_abs
;
omega
.
Qed
.
Lemma
CanonicGeNormal
:
forall
f
,
Fcanonic
beta
b
f
->
(
bpow
beta
(
-
dExp
b
+
p
-
1
)
<=
Rabs
(
FtoR
beta
f
))
%
R
->
(
Fnormal
beta
b
f
)
%
Z
.
Proof
.
intros
f
Cf
H1
.
case
Cf
;
trivial
.
intros
(
H2
,(
H3
,
H4
)).
contradict
H1
;
apply
Rlt_not_le
.
rewrite
<-
Fabs_correct
.
2
:
apply
radix_gt_0
.
unfold
FtoR
,
Fabs
;
simpl
.
rewrite
H3
,
<-
(
Z2R_IZR
beta
),
<-
bpow_powerRZ
.
apply
Rlt_le_trans
with
(
bpow
beta
(
p
-
1
)
*
bpow
beta
(
-
dExp
b
))
%
R
.
2
:
rewrite
<-
bpow_plus
.
2
:
right
;
f_equal
;
ring
.
apply
Rmult_lt_compat_r
.
apply
bpow_gt_0
.
apply
Rmult_lt_reg_l
with
(
Z2R
beta
).
change
0
%
R
with
(
Z2R
0
);
apply
Z2R_lt
,
radix_gt_0
.
rewrite
Z2R_IZR
,
<-
mult_IZR
.
apply
Rlt_le_trans
with
(
IZR
(
Z
.
pos
(
vNum
b
))).
apply
IZR_lt
.
rewrite
<-
(
Zabs_eq
beta
).
now
rewrite
<-
Zabs_Zmult
.
apply
Zlt_le_weak
,
radix_gt_0
.
rewrite
pGivesBound
.
rewrite
<-
Z2R_IZR
,
Z2R_Zpower_nat
.
rewrite
<-
Z2R_IZR
,
<-
bpow_1
.
rewrite
<-
bpow_plus
.
apply
bpow_le
.
rewrite
inj_abs
;
omega
.
Qed
.
End
Equiv
.
Section
Equiv_instanc
.
...
...
src/Translate/Missing_theos.v
View file @
3aac99c3
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