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<TITLE>APRON 0.9.10: Linear expressions of level 1</TITLE>
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<H2> Linear expressions of level 1 (<TT>`ap_linexpr1.h'</TT>) </H2>
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<P>
We manipulate here expressions of the form
<BLOCKQUOTE>
<EM>a_0.x_0 + ... + a_n.x_n + b</EM>
</BLOCKQUOTE>
where the coefficients <EM>a_0, ..., a_n, b</EM> are of
<CODE>ap_coeff_t</CODE> type (either scalars or intervals) and the variables
<EM>x_0, ... , x_n</EM> are of type <CODE>ap_var_t</CODE>.
<P>
The semantics of linear expressions is exact, in the sense that the
arithmetic operations are interpreted in the real (or rational)
numbers. However, abstract domains are free to overapproximate this
exact semantics (this may occur when converting rational scalars to
<CODE>double</CODE> type for instance).
</P><P>
A special remark concerns integer variables. Abstract domains are
assumed to perform the operations involving linear expressions using a
real/rational semantics, and then possibly to reduce the result using
the knowledge that integer variables may only take integer
values.
<BLOCKQUOTE>
This semantics <EM>coincides</EM> with the natural integer semantics of
expressions involving only integer variables <EM>only if</EM> the
involved coefficients are all integers.
</BLOCKQUOTE>
<BLOCKQUOTE>
A typical counter-example to this is an assignement <EM>y := 1/3 x</EM> where
<EM>x</EM> and <EM>y</EM> are integer variables. If this assignement is
applied to the BOX abstract domain value <EM>x in [1;1]</EM>, it
may lead to the bottom value, because one will first obtain <EM>y in
[1/3;1/3]</EM> by real/rational computations, and this may be reduced to
the empty interval because <EM>y</EM> is integer and the interval
contains no integer values.
</BLOCKQUOTE>
<P>
If you need expressions with a less simple semantics (mixing integer,
real/rational and floating-point semantics with casts), you should use
tree expressions (see section <A HREF="apron_77.html#SEC113">Tree expressions of level 1 (<TT>`ap_texpr1.h'</TT>)</A>).
</P><P>
<A NAME="IDX129"></A>
<DL>
<DT><U>datatype:</U> <B>ap_linexpr1_t</B>
<DD>(Internal) type of interval linear expressions.
</P><P>
Linear expressions of level 1 are created as objects of type
<CODE>ap_linexpr1_t</CODE>, not as pointers of type <CODE>ap_linexpr1_t*</CODE>.
</P><P>
For information:
<TABLE><tr><td> </td><td class=example><pre>typedef struct ap_linexpr1_t {
ap_linexpr0_t* linexpr0;
ap_environment_t* env;
} ap_linexpr1_t;
</pre></td></tr></table></DL>
</P><P>
<BLOCKQUOTE><TABLE BORDER=0 CELLSPACING=0>
<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="apron_58.html#SEC94">Allocating linear expressions of level 1</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR>
<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="apron_59.html#SEC95">Tests on linear expressions of level 1</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR>
<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="apron_60.html#SEC96">Access to linear expressions of level 1</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR>
<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="apron_65.html#SEC101">Change of dimensions and permutations of linear expressions of level 1</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR>
</TABLE></BLOCKQUOTE>
<P>
<A NAME="Allocating linear expressions of level 1"></A>
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