forked from OSchip/llvm-project
404 lines
10 KiB
C
404 lines
10 KiB
C
/*
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* Copyright 2010 INRIA Saclay
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*
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* Use of this software is governed by the MIT license
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*
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* Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
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* Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
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* 91893 Orsay, France
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*/
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#include <isl_map_private.h>
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#include <isl/set.h>
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#include <isl_space_private.h>
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#include <isl_seq.h>
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/*
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* Let C be a cone and define
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*
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* C' := { y | forall x in C : y x >= 0 }
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*
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* C' contains the coefficients of all linear constraints
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* that are valid for C.
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* Furthermore, C'' = C.
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*
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* If C is defined as { x | A x >= 0 }
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* then any element in C' must be a non-negative combination
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* of the rows of A, i.e., y = t A with t >= 0. That is,
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*
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* C' = { y | exists t >= 0 : y = t A }
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*
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* If any of the rows in A actually represents an equality, then
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* also negative combinations of this row are allowed and so the
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* non-negativity constraint on the corresponding element of t
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* can be dropped.
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*
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* A polyhedron P = { x | b + A x >= 0 } can be represented
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* in homogeneous coordinates by the cone
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* C = { [z,x] | b z + A x >= and z >= 0 }
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* The valid linear constraints on C correspond to the valid affine
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* constraints on P.
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* This is essentially Farkas' lemma.
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*
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* Since
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* [ 1 0 ]
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* [ w y ] = [t_0 t] [ b A ]
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*
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* we have
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*
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* C' = { w, y | exists t_0, t >= 0 : y = t A and w = t_0 + t b }
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* or
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*
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* C' = { w, y | exists t >= 0 : y = t A and w - t b >= 0 }
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*
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* In practice, we introduce an extra variable (w), shifting all
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* other variables to the right, and an extra inequality
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* (w - t b >= 0) corresponding to the positivity constraint on
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* the homogeneous coordinate.
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*
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* When going back from coefficients to solutions, we immediately
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* plug in 1 for z, which corresponds to shifting all variables
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* to the left, with the leftmost ending up in the constant position.
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*/
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/* Add the given prefix to all named isl_dim_set dimensions in "dim".
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*/
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static __isl_give isl_space *isl_space_prefix(__isl_take isl_space *dim,
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const char *prefix)
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{
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int i;
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isl_ctx *ctx;
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unsigned nvar;
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size_t prefix_len = strlen(prefix);
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if (!dim)
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return NULL;
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ctx = isl_space_get_ctx(dim);
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nvar = isl_space_dim(dim, isl_dim_set);
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for (i = 0; i < nvar; ++i) {
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const char *name;
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char *prefix_name;
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name = isl_space_get_dim_name(dim, isl_dim_set, i);
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if (!name)
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continue;
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prefix_name = isl_alloc_array(ctx, char,
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prefix_len + strlen(name) + 1);
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if (!prefix_name)
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goto error;
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memcpy(prefix_name, prefix, prefix_len);
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strcpy(prefix_name + prefix_len, name);
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dim = isl_space_set_dim_name(dim, isl_dim_set, i, prefix_name);
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free(prefix_name);
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}
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return dim;
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error:
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isl_space_free(dim);
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return NULL;
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}
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/* Given a dimension specification of the solutions space, construct
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* a dimension specification for the space of coefficients.
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*
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* In particular transform
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*
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* [params] -> { S }
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*
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* to
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*
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* { coefficients[[cst, params] -> S] }
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*
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* and prefix each dimension name with "c_".
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*/
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static __isl_give isl_space *isl_space_coefficients(__isl_take isl_space *dim)
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{
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isl_space *dim_param;
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unsigned nvar;
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unsigned nparam;
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nvar = isl_space_dim(dim, isl_dim_set);
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nparam = isl_space_dim(dim, isl_dim_param);
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dim_param = isl_space_copy(dim);
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dim_param = isl_space_drop_dims(dim_param, isl_dim_set, 0, nvar);
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dim_param = isl_space_move_dims(dim_param, isl_dim_set, 0,
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isl_dim_param, 0, nparam);
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dim_param = isl_space_prefix(dim_param, "c_");
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dim_param = isl_space_insert_dims(dim_param, isl_dim_set, 0, 1);
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dim_param = isl_space_set_dim_name(dim_param, isl_dim_set, 0, "c_cst");
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dim = isl_space_drop_dims(dim, isl_dim_param, 0, nparam);
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dim = isl_space_prefix(dim, "c_");
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dim = isl_space_join(isl_space_from_domain(dim_param),
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isl_space_from_range(dim));
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dim = isl_space_wrap(dim);
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dim = isl_space_set_tuple_name(dim, isl_dim_set, "coefficients");
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return dim;
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}
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/* Drop the given prefix from all named dimensions of type "type" in "dim".
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*/
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static __isl_give isl_space *isl_space_unprefix(__isl_take isl_space *dim,
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enum isl_dim_type type, const char *prefix)
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{
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int i;
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unsigned n;
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size_t prefix_len = strlen(prefix);
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n = isl_space_dim(dim, type);
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for (i = 0; i < n; ++i) {
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const char *name;
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name = isl_space_get_dim_name(dim, type, i);
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if (!name)
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continue;
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if (strncmp(name, prefix, prefix_len))
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continue;
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dim = isl_space_set_dim_name(dim, type, i, name + prefix_len);
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}
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return dim;
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}
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/* Given a dimension specification of the space of coefficients, construct
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* a dimension specification for the space of solutions.
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*
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* In particular transform
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*
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* { coefficients[[cst, params] -> S] }
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*
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* to
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*
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* [params] -> { S }
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*
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* and drop the "c_" prefix from the dimension names.
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*/
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static __isl_give isl_space *isl_space_solutions(__isl_take isl_space *dim)
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{
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unsigned nparam;
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dim = isl_space_unwrap(dim);
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dim = isl_space_drop_dims(dim, isl_dim_in, 0, 1);
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dim = isl_space_unprefix(dim, isl_dim_in, "c_");
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dim = isl_space_unprefix(dim, isl_dim_out, "c_");
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nparam = isl_space_dim(dim, isl_dim_in);
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dim = isl_space_move_dims(dim, isl_dim_param, 0, isl_dim_in, 0, nparam);
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dim = isl_space_range(dim);
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return dim;
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}
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/* Return the rational universe basic set in the given space.
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*/
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static __isl_give isl_basic_set *rational_universe(__isl_take isl_space *space)
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{
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isl_basic_set *bset;
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bset = isl_basic_set_universe(space);
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bset = isl_basic_set_set_rational(bset);
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return bset;
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}
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/* Compute the dual of "bset" by applying Farkas' lemma.
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* As explained above, we add an extra dimension to represent
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* the coefficient of the constant term when going from solutions
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* to coefficients (shift == 1) and we drop the extra dimension when going
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* in the opposite direction (shift == -1). "dim" is the space in which
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* the dual should be created.
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*
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* If "bset" is (obviously) empty, then the way this emptiness
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* is represented by the constraints does not allow for the application
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* of the standard farkas algorithm. We therefore handle this case
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* specifically and return the universe basic set.
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*/
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static __isl_give isl_basic_set *farkas(__isl_take isl_space *space,
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__isl_take isl_basic_set *bset, int shift)
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{
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int i, j, k;
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isl_basic_set *dual = NULL;
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unsigned total;
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if (isl_basic_set_plain_is_empty(bset)) {
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isl_basic_set_free(bset);
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return rational_universe(space);
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}
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total = isl_basic_set_total_dim(bset);
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dual = isl_basic_set_alloc_space(space, bset->n_eq + bset->n_ineq,
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total, bset->n_ineq + (shift > 0));
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dual = isl_basic_set_set_rational(dual);
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for (i = 0; i < bset->n_eq + bset->n_ineq; ++i) {
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k = isl_basic_set_alloc_div(dual);
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if (k < 0)
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goto error;
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isl_int_set_si(dual->div[k][0], 0);
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}
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for (i = 0; i < total; ++i) {
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k = isl_basic_set_alloc_equality(dual);
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if (k < 0)
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goto error;
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isl_seq_clr(dual->eq[k], 1 + shift + total);
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isl_int_set_si(dual->eq[k][1 + shift + i], -1);
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for (j = 0; j < bset->n_eq; ++j)
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isl_int_set(dual->eq[k][1 + shift + total + j],
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bset->eq[j][1 + i]);
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for (j = 0; j < bset->n_ineq; ++j)
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isl_int_set(dual->eq[k][1 + shift + total + bset->n_eq + j],
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bset->ineq[j][1 + i]);
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}
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for (i = 0; i < bset->n_ineq; ++i) {
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k = isl_basic_set_alloc_inequality(dual);
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if (k < 0)
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goto error;
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isl_seq_clr(dual->ineq[k],
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1 + shift + total + bset->n_eq + bset->n_ineq);
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isl_int_set_si(dual->ineq[k][1 + shift + total + bset->n_eq + i], 1);
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}
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if (shift > 0) {
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k = isl_basic_set_alloc_inequality(dual);
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if (k < 0)
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goto error;
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isl_seq_clr(dual->ineq[k], 2 + total);
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isl_int_set_si(dual->ineq[k][1], 1);
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for (j = 0; j < bset->n_eq; ++j)
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isl_int_neg(dual->ineq[k][2 + total + j],
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bset->eq[j][0]);
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for (j = 0; j < bset->n_ineq; ++j)
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isl_int_neg(dual->ineq[k][2 + total + bset->n_eq + j],
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bset->ineq[j][0]);
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}
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dual = isl_basic_set_remove_divs(dual);
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isl_basic_set_simplify(dual);
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isl_basic_set_finalize(dual);
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isl_basic_set_free(bset);
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return dual;
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error:
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isl_basic_set_free(bset);
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isl_basic_set_free(dual);
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return NULL;
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}
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/* Construct a basic set containing the tuples of coefficients of all
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* valid affine constraints on the given basic set.
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*/
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__isl_give isl_basic_set *isl_basic_set_coefficients(
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__isl_take isl_basic_set *bset)
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{
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isl_space *dim;
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if (!bset)
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return NULL;
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if (bset->n_div)
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isl_die(bset->ctx, isl_error_invalid,
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"input set not allowed to have local variables",
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goto error);
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dim = isl_basic_set_get_space(bset);
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dim = isl_space_coefficients(dim);
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return farkas(dim, bset, 1);
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error:
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isl_basic_set_free(bset);
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return NULL;
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}
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/* Construct a basic set containing the elements that satisfy all
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* affine constraints whose coefficient tuples are
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* contained in the given basic set.
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*/
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__isl_give isl_basic_set *isl_basic_set_solutions(
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__isl_take isl_basic_set *bset)
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{
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isl_space *dim;
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if (!bset)
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return NULL;
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if (bset->n_div)
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isl_die(bset->ctx, isl_error_invalid,
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"input set not allowed to have local variables",
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goto error);
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dim = isl_basic_set_get_space(bset);
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dim = isl_space_solutions(dim);
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return farkas(dim, bset, -1);
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error:
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isl_basic_set_free(bset);
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return NULL;
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}
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/* Construct a basic set containing the tuples of coefficients of all
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* valid affine constraints on the given set.
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*/
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__isl_give isl_basic_set *isl_set_coefficients(__isl_take isl_set *set)
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{
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int i;
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isl_basic_set *coeff;
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if (!set)
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return NULL;
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if (set->n == 0) {
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isl_space *space = isl_set_get_space(set);
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space = isl_space_coefficients(space);
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isl_set_free(set);
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return rational_universe(space);
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}
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coeff = isl_basic_set_coefficients(isl_basic_set_copy(set->p[0]));
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for (i = 1; i < set->n; ++i) {
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isl_basic_set *bset, *coeff_i;
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bset = isl_basic_set_copy(set->p[i]);
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coeff_i = isl_basic_set_coefficients(bset);
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coeff = isl_basic_set_intersect(coeff, coeff_i);
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}
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isl_set_free(set);
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return coeff;
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}
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/* Construct a basic set containing the elements that satisfy all
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* affine constraints whose coefficient tuples are
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* contained in the given set.
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*/
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__isl_give isl_basic_set *isl_set_solutions(__isl_take isl_set *set)
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{
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int i;
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isl_basic_set *sol;
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if (!set)
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return NULL;
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if (set->n == 0) {
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isl_space *space = isl_set_get_space(set);
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space = isl_space_solutions(space);
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isl_set_free(set);
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return rational_universe(space);
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}
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sol = isl_basic_set_solutions(isl_basic_set_copy(set->p[0]));
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for (i = 1; i < set->n; ++i) {
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isl_basic_set *bset, *sol_i;
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bset = isl_basic_set_copy(set->p[i]);
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sol_i = isl_basic_set_solutions(bset);
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sol = isl_basic_set_intersect(sol, sol_i);
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}
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isl_set_free(set);
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return sol;
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}
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