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Flocq
flocq
Commits
a29eed78
Commit
a29eed78
authored
Feb 24, 2010
by
Guillaume Melquiond
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Generalized lemma.
parent
6f68b82d
Changes
2
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2 changed files
with
33 additions
and
14 deletions
+33
-14
src/Core/Fcore_generic_fmt.v
src/Core/Fcore_generic_fmt.v
+31
-2
src/Core/Fcore_ulp.v
src/Core/Fcore_ulp.v
+2
-12
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src/Core/Fcore_generic_fmt.v
View file @
a29eed78
...
...
@@ -51,7 +51,7 @@ apply sym_eq.
apply
ln_beta_bpow
.
Qed
.
Theorem
generic_DN_pt_large_pos_ge_pow
:
Theorem
generic_DN_pt_large_pos_ge_pow
_aux
:
forall
x
ex
,
(
fexp
ex
<
ex
)
%
Z
->
(
bpow
(
ex
-
1
)
<=
x
)
%
R
->
...
...
@@ -87,7 +87,7 @@ intros x ex (Hx1, Hx2).
destruct
(
Z_lt_le_dec
(
fexp
ex
)
ex
)
as
[
He1
|
He1
].
(
*
-
positive
big
enough
*
)
assert
(
Hbl
:
(
bpow
(
ex
-
1
)
<=
F2R
(
Float
beta
(
Zfloor
(
x
*
bpow
(
-
fexp
ex
)))
(
fexp
ex
)))
%
R
).
now
apply
generic_DN_pt_large_pos_ge_pow
.
now
apply
generic_DN_pt_large_pos_ge_pow
_aux
.
(
*
-
.
smaller
*
)
assert
(
Hrx
:
(
F2R
(
Float
beta
(
Zfloor
(
x
*
bpow
(
-
fexp
ex
)))
(
fexp
ex
))
<=
x
)
%
R
).
unfold
F2R
.
simpl
.
...
...
@@ -762,6 +762,35 @@ rewrite <- Hxd.
apply
Hd
.
Qed
.
Theorem
generic_DN_pt_large_pos_ge_pow
:
forall
x
d
e
,
(
0
<
d
)
%
R
->
Rnd_DN_pt
generic_format
x
d
->
(
bpow
e
<=
x
)
%
R
->
(
bpow
e
<=
d
)
%
R
.
Proof
.
intros
x
d
e
Hd
Hxd
Hex
.
destruct
(
ln_beta
beta
x
)
as
(
ex
,
He
).
assert
(
Hx
:
(
0
<
x
)
%
R
).
apply
Rlt_le_trans
with
(
1
:=
Hd
).
apply
Hxd
.
specialize
(
He
(
Rgt_not_eq
_
_
Hx
)).
rewrite
Rabs_pos_eq
in
He
.
2
:
now
apply
Rlt_le
.
apply
Rle_trans
with
(
bpow
(
ex
-
1
)).
apply
->
bpow_le
.
cut
(
e
<
ex
)
%
Z
.
omega
.
apply
<-
bpow_lt
.
now
apply
Rle_lt_trans
with
(
2
:=
proj2
He
).
apply
Hxd
with
(
2
:=
proj1
He
).
apply
generic_format_bpow
.
destruct
(
Zle_or_lt
ex
(
fexp
ex
)).
elim
Rgt_not_eq
with
(
1
:=
Hd
).
apply
Rnd_DN_pt_unicity
with
(
1
:=
Hxd
).
now
apply
generic_DN_pt_small_pos
with
(
1
:=
He
).
ring_simplify
(
ex
-
1
+
1
)
%
Z
.
omega
.
Qed
.
End
RND_generic
.
Theorem
canonic_fun_eq
:
...
...
src/Core/Fcore_ulp.v
View file @
a29eed78
...
...
@@ -257,7 +257,7 @@ intros x d Hd Hxd.
unfold
ulp
.
apply
(
f_equal
(
fun
e
=>
bpow
(
fexp
e
))).
apply
ln_beta_unique
.
rewrite
(
Rabs_pos_eq
d
).
rewrite
(
Rabs_pos_eq
d
).
2
:
now
apply
Rlt_le
.
destruct
(
ln_beta
beta
x
)
as
(
ex
,
He
).
simpl
.
assert
(
Hx
:
(
0
<
x
)
%
R
).
...
...
@@ -266,19 +266,9 @@ apply Hxd.
specialize
(
He
(
Rgt_not_eq
_
_
Hx
)).
rewrite
Rabs_pos_eq
in
He
.
2
:
now
apply
Rlt_le
.
split
.
assert
(
Rnd_DN_pt
F
(
bpow
(
ex
-
1
))
(
bpow
(
ex
-
1
))).
apply
Rnd_DN_pt_refl
.
apply
generic_format_bpow
.
destruct
(
Zle_or_lt
ex
(
fexp
ex
)).
elim
Rgt_not_eq
with
(
1
:=
Hd
).
apply
Rnd_DN_pt_unicity
with
(
1
:=
Hxd
).
now
apply
generic_DN_pt_small_pos
with
(
2
:=
He
).
ring_simplify
(
ex
-
1
+
1
)
%
Z
.
omega
.
apply
(
Rnd_DN_pt_monotone
_
_
_
_
_
H
Hxd
(
proj1
He
)).
now
apply
generic_DN_pt_large_pos_ge_pow
with
(
3
:=
Hxd
).
apply
Rle_lt_trans
with
(
2
:=
proj2
He
).
apply
Hxd
.
now
apply
Rlt_le
.
Qed
.
End
Fcore_ulp
.
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