Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
F
flocq
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
1
Issues
1
List
Boards
Labels
Service Desk
Milestones
Merge Requests
1
Merge Requests
1
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Packages & Registries
Packages & Registries
Container Registry
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Flocq
flocq
Commits
aa2517ea
Commit
aa2517ea
authored
Sep 21, 2010
by
Guillaume Melquiond
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Added theorem rounding_up_succ.
parent
16c12aa9
Changes
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
26 additions
and
0 deletions
+26
-0
src/Core/Fcore_ulp.v
src/Core/Fcore_ulp.v
+26
-0
No files found.
src/Core/Fcore_ulp.v
View file @
aa2517ea
...
...
@@ -194,6 +194,32 @@ admit.
now
apply
Rlt_le
.
Qed
.
Theorem
rounding_UP_succ
:
forall
x
,
(
0
<
x
)
%
R
->
F
x
->
forall
eps
,
(
0
<
eps
<=
ulp
x
)
%
R
->
rounding
beta
fexp
ZrndUP
(
x
+
eps
)
=
(
x
+
ulp
x
)
%
R
.
Proof
.
intros
x
Zx
Fx
eps
(
Heps1
,[
Heps2
|
Heps2
]).
assert
(
Heps
:
(
0
<=
eps
<
ulp
x
)
%
R
).
split
.
now
apply
Rlt_le
.
exact
Heps2
.
assert
(
Hd
:=
rounding_DN_succ
x
Zx
Fx
eps
Heps
).
rewrite
ulp_DN_UP
.
rewrite
Hd
.
unfold
ulp
,
canonic_exponent
.
now
rewrite
ln_beta_succ
.
intros
Fs
.
rewrite
rounding_generic
in
Hd
.
apply
Rgt_not_eq
with
(
2
:=
Hd
).
pattern
x
at
2
;
rewrite
<-
Rplus_0_r
.
now
apply
Rplus_lt_compat_l
.
exact
Fs
.
rewrite
Heps2
.
apply
rounding_generic
.
now
apply
generic_format_succ
.
Qed
.
Theorem
ulp_error
:
forall
Zrnd
x
,
(
Rabs
(
rounding
beta
fexp
Zrnd
x
-
x
)
<
ulp
x
)
%
R
.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment