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 unary operations are shown in \autoref{t:iscc:unary},
  40 while the binary operations are shown in \autoref{t:iscc:binary}.
  41 Here are some examples:
  42 \begin{verbatim}
  43 P := [n, m] -> { [i,j] : 0 <= i <= n and i <= j <= m };
  44 card P;
  45
  46 f := [n,m] -> { [i,j] -> i*j + n*i*i*j : i,j >= 0 and 5i + 27j <= n+m };
  47 sum f;
  48 s := sum f;
  49 s @ [n,m] -> { [] : 0 <= n,m <= 20 };
  50
  51 f := [n] -> { [i] -> 2*n*i - n*n + 3*n - 1/2*i*i - 3/2*i-1 :
  52                 (exists j : 0 <= i < 4*n-1 and 0 <= j < n and
  53                             2*n-1 <= i+j <= 4*n-2 and i <= 2*n-1 ) };
  54 ub f;
  55 u := ub f;
  56 u @ [n] -> { [] : 0 <= n <= 10 };
  57 \end{verbatim}
  58
  59 \begin{table}
  60 \begin{tabular}{lllp{0.5\textwidth}}
  61 Name & Argument type & Result type & Meaning
  62 \\
  63 \hline
  64 \ai[\tt]{card} & set & pw quasipolynomial &
  65 number of elements in the set
  66 \\
  67 \ai[\tt]{card} & map & pw quasipolynomial &
  68 number of elements in the image of a domain element
  69 \\
  70 \ai[\tt]{dom} & map & set &
  71 domain of map
  72 \\
  73 \ai[\tt]{ran} & map & set &
  74 range of map
  75 \\
  76 \ai[\tt]{lexmin} & set & set &
  77 lexicographically minimal element of a set
  78 \\
  79 \ai[\tt]{lexmin} & map & map &
  80 lexicographically minimal image element
  81 \\
  82 \ai[\tt]{lexmax} & set & set &
  83 lexicographically maximal element of a set
  84 \\
  85 \ai[\tt]{lexmax} & map & map &
  86 lexicographically maximal image element
  87 \\
  88 \ai[\tt]{sample} & set & set &
  89 a sample element of the set
  90 \\
  91 \ai[\tt]{sample} & map & map &
  92 a sample element of the map
  93 \\
  94 \ai[\tt]{sum} & pw qp & pw qp &
  95 sum over all integer points in the domain
  96 \\
  97 \ai[\tt]{ub} & pw qp & pw qp fold &
  98 upper bound on the quasipolynomial over
  99 all integer points in the domain.
 100 This operation is only available if
 101 \ai[\tt]{GiNaC} support was compiled in.
 102 \\
 103 \end{tabular}
 104 \caption{\protect\ai[\tt]{iscc} unary operations}
 105 \label{t:iscc:unary}
 106 \end{table}
 107
 108 \begin{table}
 109 \begin{tabular}{llllp{0.5\textwidth}}
 110 LHS type & Name & RHS type & Result type & Meaning
 111 \\
 112 \hline
 113 set & \ai{$+$} & set & set & union
 114 \\
 115 map & \ai{$+$} & map & map & union
 116 \\
 117 pwqp & \ai{$+$} & pwqp & pwqp & sum
 118 \\
 119 set & \ai{$-$} & set & set & set difference
 120 \\
 121 map & \ai{$-$} & map & map & set difference
 122 \\
 123 pwqp & \ai{$-$} & pwqp & pwqp & difference
 124 \\
 125 set & \ai{$*$} & set & set & intersection
 126 \\
 127 map & \ai{$*$} & map & map & intersection
 128 \\
 129 pwqp & \ai{$*$} & pwqp & pwqp & product
 130 \\
 131 pwqp & \ai{@} & set & pwqp &
 132 evaluate the piecewise quasipolynomial in each element
 133 of the set and return a piecewise quasipolynomial
 134 mapping each of the individual elements to the resulting
 135 constant
 136 \\
 137 pw qp fold & \ai{@} & set & pwqp &
 138 evaluate the piecewise quasipolynomial fold in each element
 139 of the set and return a piecewise quasipolynomial
 140 mapping each of the individual elements to the resulting
 141 constant
 142 \\
 143 \end{tabular}
 144 \caption{\protect\ai[\tt]{iscc} binary operations}
 145 \label{t:iscc:binary}
 146 \end{table}