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Flocq
flocq
Commits
c2005beb
Commit
c2005beb
authored
Jan 23, 2009
by
Guillaume Melquiond
Browse files
Cleaned some obsolete comments.
parent
4614156a
Changes
1
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Side-by-side
src/Flocq_rnd_ex.v
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c2005beb
...
...
@@ -774,53 +774,6 @@ Qed.
(
*
(
*
symmetric
sets
are
simpler
*
)
Theorem
satisfies_DN_imp_UP
:
forall
is_float
:
R
->
Prop
,
(
forall
x
:
R
,
is_float
x
->
is_float
(
-
x
)
%
R
)
->
satisfies_DN
is_float
->
satisfies_DN_UP
is_float
.
Proof
.
intros
is_float
Hneg
Hdn
.
split
.
apply
Hdn
.
intros
x
.
destruct
(
Hdn
(
-
x
)
%
R
)
as
(
yn
,(
H1
,(
H2
,
H3
))).
exists
(
-
yn
)
%
R
.
repeat
split
.
now
apply
Hneg
.
rewrite
<-
(
Ropp_idempotent
x
).
now
apply
Ropp_le_contravar
.
intros
z
Hz
Hxz
.
rewrite
<-
(
Ropp_idempotent
z
).
apply
Ropp_le_contravar
.
apply
H3
.
now
apply
Hneg
.
now
apply
Ropp_le_contravar
.
Qed
.
Theorem
Rnd_DN_is_rounding
:
forall
is_float
:
R
->
Prop
,
satisfies_DN
is_float
->
RoundedModeP
(
Rnd_DN
is_float
)
/
\
Compatible_With_Format
is_float
(
Rnd_DN
is_float
).
Proof
.
intros
is_float
K
.
repeat
split
;
try
apply
Rle_refl
;
trivial
.
(
*
monotone
*
)
intros
x
y
f
g
Hx
Hy
Hxy
.
eapply
Hy
.
eapply
Hx
.
apply
Rle_trans
with
(
2
:=
Hxy
).
eapply
Hx
.
(
*
.
*
)
eapply
H
.
intros
Hx
.
eapply
Hx
.
Qed
.
Theorem
exp_ln_powerRZ
:
forall
u
v
:
Z
,
(
0
<
u
)
%
Z
->
exp
(
ln
(
IZR
u
)
*
(
IZR
v
))
=
powerRZ
(
IZR
u
)
v
.
admit
.
...
...
@@ -1129,22 +1082,4 @@ rewrite Z2R_IZR.
eapply
archimed
.
Qed
.
(
*
Theorem
Rnd_DN_is_FLT_rounding
:
FLT_RoundedModeP
radix
emin
prec
(
Rnd_DN
(
FLT_format
radix
emin
prec
)).
Proof
.
intros
.
apply
Rnd_DN_is_rounding
.
eapply
FLT_format_satisfies_DN_UP
.
Qed
.
Theorem
Rnd_DN_is_FIX_rounding
:
FIX_RoundedModeP
radix
emin
(
Rnd_DN
(
FIX_format
radix
emin
)).
Proof
.
intros
.
apply
Rnd_DN_is_rounding
.
eapply
FIX_format_satisfies_DN_UP
.
Qed
.
*
)
End
RND_ex
.
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