doc/isl.tex

   1 \section{\protect\isl/ interface}
   2
   3 \subsection{Library}
   4
   5 The \barvinok/ library currently supports just two
   6 functions that interface with the \isl/ library.
   7 In time, this interface will grow and is set to replace
   8 the \PolyLib/ interface.
   9 For more information on the \isl/ data structures, see
  10 the \isl/ user manual.
  11
  12 \begin{verbatim}
  13 __isl_give isl_pw_qpolynomial *isl_set_card(__isl_take isl_set *set);
  14 \end{verbatim}
  15 Compute the number of elements in an \ai[\tt]{isl\_set}.
  16 The resulting \ai[\tt]{isl\_pw\_qpolynomial} has purely parametric cells.
  17
  18 \begin{verbatim}
  19 __isl_give isl_pw_qpolynomial *isl_map_card(__isl_take isl_map *map);
  20 \end{verbatim}
  21 Compute a closed form expression for the number of image elements
  22 associated to any element in the domain of the given \ai[\tt]{isl\_map}.
  23 The union of the cells in the resulting \ai[\tt]{isl\_pw\_qpolynomial}
  24 is equal to the domain of the input \ai[\tt]{isl\_map}.
  25
  26 \begin{verbatim}
  27 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sum(
  28         __isl_take isl_pw_qpolynomial *pwqp);
  29 \end{verbatim}
  30 Compute the sum of the given piecewise quasipolynomial over
  31 all integer points in the domain.  The result is a piecewise
  32 quasipolynomial that only involves the parameters.
  33
  34 \subsection{Calculator}
  35
  36 The \ai[\tt]{iscc} calculator offers an interface to some
  37 of the functionality provided by the \isl/ and \barvinok/
  38 libraries.
  39 The supported operations are shown in \autoref{t:iscc}.
  40 Here are some examples:
  41 \begin{verbatim}
  42 P := [n, m] -> { [i,j] : 0 <= i <= n and i <= j <= m };
  43 card P;
  44
  45 f := [n,m] -> { [i,j] -> i*j + n*i*i*j : i,j >= 0 and 5i + 27j <= n+m };
  46 sum f;
  47 s := sum f;
  48 s @ [n,m] -> { [] : 0 <= n,m <= 20 };
  49
  50 f := [n] -> { [i] -> 2*n*i - n*n + 3*n - 1/2*i*i - 3/2*i-1 :
  51                 (exists j : 0 <= i < 4*n-1 and 0 <= j < n and
  52                             2*n-1 <= i+j <= 4*n-2 and i <= 2*n-1 ) };
  53 ub f;
  54 u := ub f;
  55 u @ [n] -> { [] : 0 <= n <= 10 };
  56
  57 m := [n] -> { [i,j] -> [i+1,j+1] : 1 <= i,j < n;
  58               [i,j] -> [i+1,j-1] : 1 <= i < n and 2 <= j <= n };
  59 m^+;
  60 (m^+)[0];
  61 \end{verbatim}
  62
  63 \bottomcaption{{\tt iscc} operations.  The variables
  64 have the following types,
  65 $s$: set,
  66 $m$: map,
  67 $q$: piecewise quasipolynomial,
  68 $f$: piecewise quasipolynomial fold,
  69 $l$: list,
  70 $i$: integer
  71 }
  72 \label{t:iscc}
  73 \tablehead{
  74 Syntax & Meaning
  75 \\
  76 \hline
  77 }
  78 \tabletail{
  79 \multicolumn{2}{r}{\small\sl continued on next page}
  80 \\
  81 }
  82 \tablelasttail{}
  83 \begin{supertabular}{lp{0.7\textwidth}}
  84 $s_2$ := \ai[\tt]{aff} $s_1$ & affine hull of $s_1$
  85 \\
  86 $m_2$ := \ai[\tt]{aff} $m_1$ & affine hull of $m_1$
  87 \\
  88 $q$ := \ai[\tt]{card} $s$ &
  89 number of elements in the set $s$
  90 \\
  91 $q$ := \ai[\tt]{card} $m$ &
  92 number of elements in the image of a domain element
  93 \\
  94 $s$ := \ai[\tt]{dom} $m$ &
  95 domain of map $m$
  96 \\
  97 $s$ := \ai[\tt]{dom} $q$ &
  98 domain of piecewise quasipolynomial $q$
  99 \\
 100 $s$ := \ai[\tt]{dom} $f$ &
 101 domain of piecewise quasipolynomial fold $f$
 102 \\
 103 $s$ := \ai[\tt]{ran} $m$ &
 104 range of map $m$
 105 \\
 106 $s_2$ := \ai[\tt]{lexmin} $s_1$ &
 107 lexicographically minimal element of $s_1$
 108 \\
 109 $m_2$ := \ai[\tt]{lexmin} $m_1$ &
 110 lexicographically minimal image element
 111 \\
 112 $s_2$ := \ai[\tt]{lexmax} $s_1$ &
 113 lexicographically maximal element of $s_1$
 114 \\
 115 $m_2$ := \ai[\tt]{lexmax} $m_1$ &
 116 lexicographically maximal image element
 117 \\
 118 $s_2$ := \ai[\tt]{sample} $s_1$ &
 119 a sample element of the set $s_1$
 120 \\
 121 $m_2$ := \ai[\tt]{sample} $m_1$ &
 122 a sample element of the map $m_1$
 123 \\
 124 $q_2$ := \ai[\tt]{sum} $q_1$ &
 125 sum $q_1$ over all integer points in the domain of $q_1$
 126 \\
 127 $f$ := \ai[\tt]{ub} $q$ &
 128 upper bound on the piecewise quasipolynomial $q$ over
 129 all integer points in the domain of $q$.
 130 This operation is only available if
 131 \ai[\tt]{GiNaC} support was compiled in.
 132 \\
 133 $s_3$ := $s_1$ \ai{$+$} $s_2$ & union
 134 \\
 135 $m_3$ := $m_1$ \ai{$+$} $m_2$ & union
 136 \\
 137 $q_3$ := $q_1$ \ai{$+$} $q_2$ & sum
 138 \\
 139 $s_3$ := $s_1$ \ai{$-$} $s_2$ & set difference
 140 \\
 141 $m_3$ := $m_1$ \ai{$-$} $m_2$ & set difference
 142 \\
 143 $q_3$ := $q_1$ \ai{$-$} $q_2$ & difference
 144 \\
 145 $s_3$ := $s_1$ \ai{$*$} $s_2$ & intersection
 146 \\
 147 $m_3$ := $m_1$ \ai{$*$} $m_2$ & intersection
 148 \\
 149 $q_3$ := $q_1$ \ai{$*$} $q_2$ & product
 150 \\
 151 $m_2$ := $m_1$ \ai{$*$} $s$ & intersect domain of $m_1$ with $s$
 152 \\
 153 $q_2$ := $q_1$ \ai{$*$} $s$ & intersect domain of $q_1$ with $s$
 154 \\
 155 $f_2$ := $f_1$ \ai{$*$} $s$ & intersect domain of $f_1$ with $s$
 156 \\
 157 $m_3$ := $m_1$ \ai[\tt]{.} $m_2$ & join of $m_1$ and $m_2$
 158 \\
 159 $m$ := $s_1$ \ai[\tt]{->} $s_2$ & universal map with domain $s_1$
 160 and range $s_2$
 161 \\
 162 $q_2$ := $q_1$ \ai{@} $s$ &
 163 evaluate the piecewise quasipolynomial $q_1$ in each element
 164 of the set $s$ and return a piecewise quasipolynomial
 165 mapping each of the individual elements to the resulting
 166 constant
 167 \\
 168 $q$ := $f$ \ai{@} $s$ &
 169 evaluate the piecewise quasipolynomial fold $f$ in each element
 170 of the set $s$ and return a piecewise quasipolynomial
 171 mapping each of the individual elements to the resulting
 172 constant
 173 \\
 174 $l$ := $m$\ai[\tt]{\^{}+} &
 175 compute an overapproximation of the transitive closure
 176 of $m$ and return a list containing the overapproximation
 177 and a boolean that is true if the overapproximation
 178 is known to be exact
 179 \\
 180 $l$[$i$] &
 181 the element at position $i$ in the list $l$
 182 \\
 183 \end{supertabular}