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Charles Southerland
framac
Commits
9176cd9e
Commit
9176cd9e
authored
Nov 04, 2020
by
Allan Blanchard
Browse files
[wp/doc] Document tactic: BitTest Range
parent
bc4a7baa
Changes
1
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Sidebyside
src/plugins/wp/doc/manual/wp_plugin.tex
View file @
9176cd9e
...
...
@@ 405,6 +405,30 @@ to apply the theorems. Such a strategy is \emph{not} complete in general.
Typically,
$
\mathtt
{
land
}
(
x,y
)
<
38
$
is true whenever both
$
x
$
and
$
y
$
are in range
$
0
\ldots
31
$
, but this is also true
in other cases.
\paragraph
{
BitTest Range
}
Tighten Bounds with respect to bits
\\
The
\lstinline
{
bit
_
test(a,b)
}
function is predefined in
\textsf
{
WP
}
and is equivalent
to the
\textsf
{
ACSL
}
expression
\lstinline
{
(a
&
(1 << k)) != 0
}
. The
\textsf
{
Qed
}
engine has many simplification rules that applies to
such patterns.
The user selects an expression
$
\mathtt
{
bit
\_
test
}
(
n,k
)
$
with
$
k
$
a
\emph
{
constant
}
integer value greater or equal to 0 and lower than
128. The tactic uses this test to thighten the bounds of
$
n
$
.
$$
\TACTIC
{
\Delta\models\,
G
}{
%
\begin
{
array
}
[
t
]
{
ll
}
\Delta
,T
&
\models
G
\\
\Delta
,F
&
\models
G
\end
{
array
}}
$$
with
$$
\begin
{
array
}
[
t
]
{
rlcll
}
T
\equiv
&
\mathtt
{
bit
\_
test
}
(
n,k
)
&
\wedge
&
(
0
\leq
n
&
\Rightarrow
2
^{
k
}
\leq
n
)
\\
F
\equiv
&
\neg
\mathtt
{
bit
\_
test
}
(
n,k
)
&
\wedge
&
(
0
\leq
n <
2
^{
k
+
1
}
&
\Rightarrow
n <
2
^{
k
}
)
\end
{
array
}
$$
\paragraph
{
Bitwise
}
Decompose equalities over
$
N
$
bits
\\
The use selects an integer equality and a number of bits.
Providing the two members of the equality are in range
$
0
..
2
^
N

1
$
,
...
...
@@ 422,11 +446,6 @@ where $\sigma$ is the following subsitution:
\right
]
\]
The
\lstinline
{
bit
_
test(a,b)
}
function is predefined in
\textsf
{
WP
}
and is equivalent
to the
\textsf
{
ACSL
}
expression
\lstinline
{
(a
&
(1 << k)) != 0
}
. The
\textsf
{
Qed
}
engine has many simplification rules that applies to
such patterns, and the a tactic is good way to reason over bits.
\paragraph
{
Congruence
}
Simplify Divisions and Products
\\
This tactic rewrites integer comparisons involving products and divisions.
The tactic applies one of the following theorems to the current goal.
...
...
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