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Flocq
flocq
Commits
3ab57ca8
Commit
3ab57ca8
authored
Apr 10, 2009
by
Guillaume Melquiond
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Added generic_UP_pt_*.
parent
d17abc9f
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src/Flocq_rnd_generic.v
src/Flocq_rnd_generic.v
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src/Flocq_rnd_generic.v
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3ab57ca8
Require
Import
Flocq_Raux
.
Require
Import
Flocq_defs
.
Require
Import
Flocq_rnd_ex
.
Require
Import
Flocq_rnd_prop
.
Require
Import
Flocq_float_prop
.
Section
RND_generic
.
...
...
@@ -625,4 +626,35 @@ apply Zlt_succ.
apply
epow_ge_0
.
Qed
.
Theorem
generic_UP_pt_pos
:
forall
x
ex
,
(
bpow
(
ex
-
1
)
%
Z
<=
x
<
bpow
ex
)
%
R
->
Rnd_UP_pt
generic_format
x
(
F2R
(
Float
beta
(
Zceil
(
x
*
bpow
(
Zopp
(
fexp
ex
))))
(
fexp
ex
))).
Proof
.
intros
x
ex
Hx1
.
apply
Rnd_DN_UP_pt_sym
.
apply
generic_format_satisfies_any
.
unfold
Zceil
.
rewrite
<-
Ropp_mult_distr_l_reverse
.
rewrite
opp_F2R
.
rewrite
Zopp_involutive
.
apply
generic_DN_pt_neg
.
now
rewrite
Ropp_involutive
.
Qed
.
Theorem
generic_UP_pt_neg
:
forall
x
ex
,
(
bpow
(
ex
-
1
)
%
Z
<=
-
x
<
bpow
ex
)
%
R
->
Rnd_UP_pt
generic_format
x
(
F2R
(
Float
beta
(
Zceil
(
x
*
bpow
(
Zopp
(
fexp
ex
))))
(
fexp
ex
))).
Proof
.
intros
x
ex
Hx1
.
apply
Rnd_DN_UP_pt_sym
.
apply
generic_format_satisfies_any
.
unfold
Zceil
.
rewrite
<-
Ropp_mult_distr_l_reverse
.
rewrite
opp_F2R
.
rewrite
Zopp_involutive
.
now
apply
generic_DN_pt_pos
.
Qed
.
End
RND_generic
.
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