/* * Copyright 2008-2009 Katholieke Universiteit Leuven * Copyright 2010 INRIA Saclay * Copyright 2012-2013 Ecole Normale Superieure * Copyright 2014 INRIA Rocquencourt * * Use of this software is governed by the MIT license * * Written by Sven Verdoolaege, K.U.Leuven, Departement * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite, * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt, * B.P. 105 - 78153 Le Chesnay, France */ #include "isl_map_private.h" #include #include #include "isl_tab.h" #include #include #include #include #define STATUS_ERROR -1 #define STATUS_REDUNDANT 1 #define STATUS_VALID 2 #define STATUS_SEPARATE 3 #define STATUS_CUT 4 #define STATUS_ADJ_EQ 5 #define STATUS_ADJ_INEQ 6 static int status_in(isl_int *ineq, struct isl_tab *tab) { enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq); switch (type) { default: case isl_ineq_error: return STATUS_ERROR; case isl_ineq_redundant: return STATUS_VALID; case isl_ineq_separate: return STATUS_SEPARATE; case isl_ineq_cut: return STATUS_CUT; case isl_ineq_adj_eq: return STATUS_ADJ_EQ; case isl_ineq_adj_ineq: return STATUS_ADJ_INEQ; } } /* Compute the position of the equalities of basic map "bmap_i" * with respect to the basic map represented by "tab_j". * The resulting array has twice as many entries as the number * of equalities corresponding to the two inequalties to which * each equality corresponds. */ static int *eq_status_in(__isl_keep isl_basic_map *bmap_i, struct isl_tab *tab_j) { int k, l; int *eq = isl_calloc_array(bmap_i->ctx, int, 2 * bmap_i->n_eq); unsigned dim; if (!eq) return NULL; dim = isl_basic_map_total_dim(bmap_i); for (k = 0; k < bmap_i->n_eq; ++k) { for (l = 0; l < 2; ++l) { isl_seq_neg(bmap_i->eq[k], bmap_i->eq[k], 1+dim); eq[2 * k + l] = status_in(bmap_i->eq[k], tab_j); if (eq[2 * k + l] == STATUS_ERROR) goto error; } if (eq[2 * k] == STATUS_SEPARATE || eq[2 * k + 1] == STATUS_SEPARATE) break; } return eq; error: free(eq); return NULL; } /* Compute the position of the inequalities of basic map "bmap_i" * (also represented by "tab_i", if not NULL) with respect to the basic map * represented by "tab_j". */ static int *ineq_status_in(__isl_keep isl_basic_map *bmap_i, struct isl_tab *tab_i, struct isl_tab *tab_j) { int k; unsigned n_eq = bmap_i->n_eq; int *ineq = isl_calloc_array(bmap_i->ctx, int, bmap_i->n_ineq); if (!ineq) return NULL; for (k = 0; k < bmap_i->n_ineq; ++k) { if (tab_i && isl_tab_is_redundant(tab_i, n_eq + k)) { ineq[k] = STATUS_REDUNDANT; continue; } ineq[k] = status_in(bmap_i->ineq[k], tab_j); if (ineq[k] == STATUS_ERROR) goto error; if (ineq[k] == STATUS_SEPARATE) break; } return ineq; error: free(ineq); return NULL; } static int any(int *con, unsigned len, int status) { int i; for (i = 0; i < len ; ++i) if (con[i] == status) return 1; return 0; } static int count(int *con, unsigned len, int status) { int i; int c = 0; for (i = 0; i < len ; ++i) if (con[i] == status) c++; return c; } static int all(int *con, unsigned len, int status) { int i; for (i = 0; i < len ; ++i) { if (con[i] == STATUS_REDUNDANT) continue; if (con[i] != status) return 0; } return 1; } /* Internal information associated to a basic map in a map * that is to be coalesced by isl_map_coalesce. * * "bmap" is the basic map itself (or NULL if "removed" is set) * "tab" is the corresponding tableau (or NULL if "removed" is set) * "hull_hash" identifies the affine space in which "bmap" lives. * "removed" is set if this basic map has been removed from the map * "simplify" is set if this basic map may have some unknown integer * divisions that were not present in the input basic maps. The basic * map should then be simplified such that we may be able to find * a definition among the constraints. * * "eq" and "ineq" are only set if we are currently trying to coalesce * this basic map with another basic map, in which case they represent * the position of the inequalities of this basic map with respect to * the other basic map. The number of elements in the "eq" array * is twice the number of equalities in the "bmap", corresponding * to the two inequalities that make up each equality. */ struct isl_coalesce_info { isl_basic_map *bmap; struct isl_tab *tab; uint32_t hull_hash; int removed; int simplify; int *eq; int *ineq; }; /* Compute the hash of the (apparent) affine hull of info->bmap (with * the existentially quantified variables removed) and store it * in info->hash. */ static int coalesce_info_set_hull_hash(struct isl_coalesce_info *info) { isl_basic_map *hull; unsigned n_div; hull = isl_basic_map_copy(info->bmap); hull = isl_basic_map_plain_affine_hull(hull); n_div = isl_basic_map_dim(hull, isl_dim_div); hull = isl_basic_map_drop_constraints_involving_dims(hull, isl_dim_div, 0, n_div); info->hull_hash = isl_basic_map_get_hash(hull); isl_basic_map_free(hull); return hull ? 0 : -1; } /* Free all the allocated memory in an array * of "n" isl_coalesce_info elements. */ static void clear_coalesce_info(int n, struct isl_coalesce_info *info) { int i; if (!info) return; for (i = 0; i < n; ++i) { isl_basic_map_free(info[i].bmap); isl_tab_free(info[i].tab); } free(info); } /* Drop the basic map represented by "info". * That is, clear the memory associated to the entry and * mark it as having been removed. */ static void drop(struct isl_coalesce_info *info) { info->bmap = isl_basic_map_free(info->bmap); isl_tab_free(info->tab); info->tab = NULL; info->removed = 1; } /* Exchange the information in "info1" with that in "info2". */ static void exchange(struct isl_coalesce_info *info1, struct isl_coalesce_info *info2) { struct isl_coalesce_info info; info = *info1; *info1 = *info2; *info2 = info; } /* This type represents the kind of change that has been performed * while trying to coalesce two basic maps. * * isl_change_none: nothing was changed * isl_change_drop_first: the first basic map was removed * isl_change_drop_second: the second basic map was removed * isl_change_fuse: the two basic maps were replaced by a new basic map. */ enum isl_change { isl_change_error = -1, isl_change_none = 0, isl_change_drop_first, isl_change_drop_second, isl_change_fuse, }; /* Update "change" based on an interchange of the first and the second * basic map. That is, interchange isl_change_drop_first and * isl_change_drop_second. */ static enum isl_change invert_change(enum isl_change change) { switch (change) { case isl_change_error: return isl_change_error; case isl_change_none: return isl_change_none; case isl_change_drop_first: return isl_change_drop_second; case isl_change_drop_second: return isl_change_drop_first; case isl_change_fuse: return isl_change_fuse; } return isl_change_error; } /* Add the valid constraints of the basic map represented by "info" * to "bmap". "len" is the size of the constraints. * If only one of the pair of inequalities that make up an equality * is valid, then add that inequality. */ static __isl_give isl_basic_map *add_valid_constraints( __isl_take isl_basic_map *bmap, struct isl_coalesce_info *info, unsigned len) { int k, l; if (!bmap) return NULL; for (k = 0; k < info->bmap->n_eq; ++k) { if (info->eq[2 * k] == STATUS_VALID && info->eq[2 * k + 1] == STATUS_VALID) { l = isl_basic_map_alloc_equality(bmap); if (l < 0) return isl_basic_map_free(bmap); isl_seq_cpy(bmap->eq[l], info->bmap->eq[k], len); } else if (info->eq[2 * k] == STATUS_VALID) { l = isl_basic_map_alloc_inequality(bmap); if (l < 0) return isl_basic_map_free(bmap); isl_seq_neg(bmap->ineq[l], info->bmap->eq[k], len); } else if (info->eq[2 * k + 1] == STATUS_VALID) { l = isl_basic_map_alloc_inequality(bmap); if (l < 0) return isl_basic_map_free(bmap); isl_seq_cpy(bmap->ineq[l], info->bmap->eq[k], len); } } for (k = 0; k < info->bmap->n_ineq; ++k) { if (info->ineq[k] != STATUS_VALID) continue; l = isl_basic_map_alloc_inequality(bmap); if (l < 0) return isl_basic_map_free(bmap); isl_seq_cpy(bmap->ineq[l], info->bmap->ineq[k], len); } return bmap; } /* Is "bmap" defined by a number of (non-redundant) constraints that * is greater than the number of constraints of basic maps i and j combined? * Equalities are counted as two inequalities. */ static int number_of_constraints_increases(int i, int j, struct isl_coalesce_info *info, __isl_keep isl_basic_map *bmap, struct isl_tab *tab) { int k, n_old, n_new; n_old = 2 * info[i].bmap->n_eq + info[i].bmap->n_ineq; n_old += 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq; n_new = 2 * bmap->n_eq; for (k = 0; k < bmap->n_ineq; ++k) if (!isl_tab_is_redundant(tab, bmap->n_eq + k)) ++n_new; return n_new > n_old; } /* Replace the pair of basic maps i and j by the basic map bounded * by the valid constraints in both basic maps and the constraints * in extra (if not NULL). * Place the fused basic map in the position that is the smallest of i and j. * * If "detect_equalities" is set, then look for equalities encoded * as pairs of inequalities. * If "check_number" is set, then the original basic maps are only * replaced if the total number of constraints does not increase. * While the number of integer divisions in the two basic maps * is assumed to be the same, the actual definitions may be different. * We only copy the definition from one of the basic map if it is * the same as that of the other basic map. Otherwise, we mark * the integer division as unknown and schedule for the basic map * to be simplified in an attempt to recover the integer division definition. */ static enum isl_change fuse(int i, int j, struct isl_coalesce_info *info, __isl_keep isl_mat *extra, int detect_equalities, int check_number) { int k, l; struct isl_basic_map *fused = NULL; struct isl_tab *fused_tab = NULL; unsigned total = isl_basic_map_total_dim(info[i].bmap); unsigned extra_rows = extra ? extra->n_row : 0; unsigned n_eq, n_ineq; if (j < i) return fuse(j, i, info, extra, detect_equalities, check_number); n_eq = info[i].bmap->n_eq + info[j].bmap->n_eq; n_ineq = info[i].bmap->n_ineq + info[j].bmap->n_ineq; fused = isl_basic_map_alloc_space(isl_space_copy(info[i].bmap->dim), info[i].bmap->n_div, n_eq, n_eq + n_ineq + extra_rows); fused = add_valid_constraints(fused, &info[i], 1 + total); fused = add_valid_constraints(fused, &info[j], 1 + total); if (!fused) goto error; for (k = 0; k < info[i].bmap->n_div; ++k) { int l = isl_basic_map_alloc_div(fused); if (l < 0) goto error; if (isl_seq_eq(info[i].bmap->div[k], info[j].bmap->div[k], 1 + 1 + total)) { isl_seq_cpy(fused->div[l], info[i].bmap->div[k], 1 + 1 + total); } else { isl_int_set_si(fused->div[l][0], 0); info[i].simplify = 1; } } for (k = 0; k < extra_rows; ++k) { l = isl_basic_map_alloc_inequality(fused); if (l < 0) goto error; isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total); } if (detect_equalities) fused = isl_basic_map_detect_inequality_pairs(fused, NULL); fused = isl_basic_map_gauss(fused, NULL); ISL_F_SET(fused, ISL_BASIC_MAP_FINAL); if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) && ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL)) ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL); fused_tab = isl_tab_from_basic_map(fused, 0); if (isl_tab_detect_redundant(fused_tab) < 0) goto error; if (check_number && number_of_constraints_increases(i, j, info, fused, fused_tab)) { isl_tab_free(fused_tab); isl_basic_map_free(fused); return isl_change_none; } info[i].simplify |= info[j].simplify; isl_basic_map_free(info[i].bmap); info[i].bmap = fused; isl_tab_free(info[i].tab); info[i].tab = fused_tab; drop(&info[j]); return isl_change_fuse; error: isl_tab_free(fused_tab); isl_basic_map_free(fused); return isl_change_error; } /* Given a pair of basic maps i and j such that all constraints are either * "valid" or "cut", check if the facets corresponding to the "cut" * constraints of i lie entirely within basic map j. * If so, replace the pair by the basic map consisting of the valid * constraints in both basic maps. * Checking whether the facet lies entirely within basic map j * is performed by checking whether the constraints of basic map j * are valid for the facet. These tests are performed on a rational * tableau to avoid the theoretical possibility that a constraint * that was considered to be a cut constraint for the entire basic map i * happens to be considered to be a valid constraint for the facet, * even though it cuts off the same rational points. * * To see that we are not introducing any extra points, call the * two basic maps A and B and the resulting map U and let x * be an element of U \setminus ( A \cup B ). * A line connecting x with an element of A \cup B meets a facet F * of either A or B. Assume it is a facet of B and let c_1 be * the corresponding facet constraint. We have c_1(x) < 0 and * so c_1 is a cut constraint. This implies that there is some * (possibly rational) point x' satisfying the constraints of A * and the opposite of c_1 as otherwise c_1 would have been marked * valid for A. The line connecting x and x' meets a facet of A * in a (possibly rational) point that also violates c_1, but this * is impossible since all cut constraints of B are valid for all * cut facets of A. * In case F is a facet of A rather than B, then we can apply the * above reasoning to find a facet of B separating x from A \cup B first. */ static enum isl_change check_facets(int i, int j, struct isl_coalesce_info *info) { int k, l; struct isl_tab_undo *snap, *snap2; unsigned n_eq = info[i].bmap->n_eq; snap = isl_tab_snap(info[i].tab); if (isl_tab_mark_rational(info[i].tab) < 0) return isl_change_error; snap2 = isl_tab_snap(info[i].tab); for (k = 0; k < info[i].bmap->n_ineq; ++k) { if (info[i].ineq[k] != STATUS_CUT) continue; if (isl_tab_select_facet(info[i].tab, n_eq + k) < 0) return isl_change_error; for (l = 0; l < info[j].bmap->n_ineq; ++l) { int stat; if (info[j].ineq[l] != STATUS_CUT) continue; stat = status_in(info[j].bmap->ineq[l], info[i].tab); if (stat < 0) return isl_change_error; if (stat != STATUS_VALID) break; } if (isl_tab_rollback(info[i].tab, snap2) < 0) return isl_change_error; if (l < info[j].bmap->n_ineq) break; } if (k < info[i].bmap->n_ineq) { if (isl_tab_rollback(info[i].tab, snap) < 0) return isl_change_error; return isl_change_none; } return fuse(i, j, info, NULL, 0, 0); } /* Check if info->bmap contains the basic map represented * by the tableau "tab". * For each equality, we check both the constraint itself * (as an inequality) and its negation. Make sure the * equality is returned to its original state before returning. */ static int contains(struct isl_coalesce_info *info, struct isl_tab *tab) { int k; unsigned dim; isl_basic_map *bmap = info->bmap; dim = isl_basic_map_total_dim(bmap); for (k = 0; k < bmap->n_eq; ++k) { int stat; isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim); stat = status_in(bmap->eq[k], tab); isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim); if (stat < 0) return -1; if (stat != STATUS_VALID) return 0; stat = status_in(bmap->eq[k], tab); if (stat < 0) return -1; if (stat != STATUS_VALID) return 0; } for (k = 0; k < bmap->n_ineq; ++k) { int stat; if (info->ineq[k] == STATUS_REDUNDANT) continue; stat = status_in(bmap->ineq[k], tab); if (stat < 0) return -1; if (stat != STATUS_VALID) return 0; } return 1; } /* Basic map "i" has an inequality (say "k") that is adjacent * to some inequality of basic map "j". All the other inequalities * are valid for "j". * Check if basic map "j" forms an extension of basic map "i". * * Note that this function is only called if some of the equalities or * inequalities of basic map "j" do cut basic map "i". The function is * correct even if there are no such cut constraints, but in that case * the additional checks performed by this function are overkill. * * In particular, we replace constraint k, say f >= 0, by constraint * f <= -1, add the inequalities of "j" that are valid for "i" * and check if the result is a subset of basic map "j". * If so, then we know that this result is exactly equal to basic map "j" * since all its constraints are valid for basic map "j". * By combining the valid constraints of "i" (all equalities and all * inequalities except "k") and the valid constraints of "j" we therefore * obtain a basic map that is equal to their union. * In this case, there is no need to perform a rollback of the tableau * since it is going to be destroyed in fuse(). * * * |\__ |\__ * | \__ | \__ * | \_ => | \__ * |_______| _ |_________\ * * * |\ |\ * | \ | \ * | \ | \ * | | | \ * | ||\ => | \ * | || \ | \ * | || | | | * |__||_/ |_____/ */ static enum isl_change is_adj_ineq_extension(int i, int j, struct isl_coalesce_info *info) { int k; struct isl_tab_undo *snap; unsigned n_eq = info[i].bmap->n_eq; unsigned total = isl_basic_map_total_dim(info[i].bmap); int r; int super; if (isl_tab_extend_cons(info[i].tab, 1 + info[j].bmap->n_ineq) < 0) return isl_change_error; for (k = 0; k < info[i].bmap->n_ineq; ++k) if (info[i].ineq[k] == STATUS_ADJ_INEQ) break; if (k >= info[i].bmap->n_ineq) isl_die(isl_basic_map_get_ctx(info[i].bmap), isl_error_internal, "info[i].ineq should have exactly one STATUS_ADJ_INEQ", return isl_change_error); snap = isl_tab_snap(info[i].tab); if (isl_tab_unrestrict(info[i].tab, n_eq + k) < 0) return isl_change_error; isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total); isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1); r = isl_tab_add_ineq(info[i].tab, info[i].bmap->ineq[k]); isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total); isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1); if (r < 0) return isl_change_error; for (k = 0; k < info[j].bmap->n_ineq; ++k) { if (info[j].ineq[k] != STATUS_VALID) continue; if (isl_tab_add_ineq(info[i].tab, info[j].bmap->ineq[k]) < 0) return isl_change_error; } super = contains(&info[j], info[i].tab); if (super < 0) return isl_change_error; if (super) return fuse(i, j, info, NULL, 0, 0); if (isl_tab_rollback(info[i].tab, snap) < 0) return isl_change_error; return isl_change_none; } /* Both basic maps have at least one inequality with and adjacent * (but opposite) inequality in the other basic map. * Check that there are no cut constraints and that there is only * a single pair of adjacent inequalities. * If so, we can replace the pair by a single basic map described * by all but the pair of adjacent inequalities. * Any additional points introduced lie strictly between the two * adjacent hyperplanes and can therefore be integral. * * ____ _____ * / ||\ / \ * / || \ / \ * \ || \ => \ \ * \ || / \ / * \___||_/ \_____/ * * The test for a single pair of adjancent inequalities is important * for avoiding the combination of two basic maps like the following * * /| * / | * /__| * _____ * | | * | | * |___| * * If there are some cut constraints on one side, then we may * still be able to fuse the two basic maps, but we need to perform * some additional checks in is_adj_ineq_extension. */ static enum isl_change check_adj_ineq(int i, int j, struct isl_coalesce_info *info) { int count_i, count_j; int cut_i, cut_j; count_i = count(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_INEQ); count_j = count(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_INEQ); if (count_i != 1 && count_j != 1) return isl_change_none; cut_i = any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_CUT) || any(info[i].ineq, info[i].bmap->n_ineq, STATUS_CUT); cut_j = any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_CUT) || any(info[j].ineq, info[j].bmap->n_ineq, STATUS_CUT); if (!cut_i && !cut_j && count_i == 1 && count_j == 1) return fuse(i, j, info, NULL, 0, 0); if (count_i == 1 && !cut_i) return is_adj_ineq_extension(i, j, info); if (count_j == 1 && !cut_j) return is_adj_ineq_extension(j, i, info); return isl_change_none; } /* Basic map "i" has an inequality "k" that is adjacent to some equality * of basic map "j". All the other inequalities are valid for "j". * Check if basic map "j" forms an extension of basic map "i". * * In particular, we relax constraint "k", compute the corresponding * facet and check whether it is included in the other basic map. * If so, we know that relaxing the constraint extends the basic * map with exactly the other basic map (we already know that this * other basic map is included in the extension, because there * were no "cut" inequalities in "i") and we can replace the * two basic maps by this extension. * Each integer division that does not have exactly the same * definition in "i" and "j" is marked unknown and the basic map * is scheduled to be simplified in an attempt to recover * the integer division definition. * Place this extension in the position that is the smallest of i and j. * ____ _____ * / || / | * / || / | * \ || => \ | * \ || \ | * \___|| \____| */ static enum isl_change is_adj_eq_extension(int i, int j, int k, struct isl_coalesce_info *info) { int change = isl_change_none; int super; struct isl_tab_undo *snap, *snap2; unsigned n_eq = info[i].bmap->n_eq; if (isl_tab_is_equality(info[i].tab, n_eq + k)) return isl_change_none; snap = isl_tab_snap(info[i].tab); if (isl_tab_relax(info[i].tab, n_eq + k) < 0) return isl_change_error; snap2 = isl_tab_snap(info[i].tab); if (isl_tab_select_facet(info[i].tab, n_eq + k) < 0) return isl_change_error; super = contains(&info[j], info[i].tab); if (super < 0) return isl_change_error; if (super) { int l; unsigned total; if (isl_tab_rollback(info[i].tab, snap2) < 0) return isl_change_error; info[i].bmap = isl_basic_map_cow(info[i].bmap); if (!info[i].bmap) return isl_change_error; total = isl_basic_map_total_dim(info[i].bmap); for (l = 0; l < info[i].bmap->n_div; ++l) if (!isl_seq_eq(info[i].bmap->div[l], info[j].bmap->div[l], 1 + 1 + total)) { isl_int_set_si(info[i].bmap->div[l][0], 0); info[i].simplify = 1; } isl_int_add_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1); ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_FINAL); drop(&info[j]); if (j < i) exchange(&info[i], &info[j]); change = isl_change_fuse; } else if (isl_tab_rollback(info[i].tab, snap) < 0) return isl_change_error; return change; } /* Data structure that keeps track of the wrapping constraints * and of information to bound the coefficients of those constraints. * * bound is set if we want to apply a bound on the coefficients * mat contains the wrapping constraints * max is the bound on the coefficients (if bound is set) */ struct isl_wraps { int bound; isl_mat *mat; isl_int max; }; /* Update wraps->max to be greater than or equal to the coefficients * in the equalities and inequalities of info->bmap that can be removed * if we end up applying wrapping. */ static void wraps_update_max(struct isl_wraps *wraps, struct isl_coalesce_info *info) { int k; isl_int max_k; unsigned total = isl_basic_map_total_dim(info->bmap); isl_int_init(max_k); for (k = 0; k < info->bmap->n_eq; ++k) { if (info->eq[2 * k] == STATUS_VALID && info->eq[2 * k + 1] == STATUS_VALID) continue; isl_seq_abs_max(info->bmap->eq[k] + 1, total, &max_k); if (isl_int_abs_gt(max_k, wraps->max)) isl_int_set(wraps->max, max_k); } for (k = 0; k < info->bmap->n_ineq; ++k) { if (info->ineq[k] == STATUS_VALID || info->ineq[k] == STATUS_REDUNDANT) continue; isl_seq_abs_max(info->bmap->ineq[k] + 1, total, &max_k); if (isl_int_abs_gt(max_k, wraps->max)) isl_int_set(wraps->max, max_k); } isl_int_clear(max_k); } /* Initialize the isl_wraps data structure. * If we want to bound the coefficients of the wrapping constraints, * we set wraps->max to the largest coefficient * in the equalities and inequalities that can be removed if we end up * applying wrapping. */ static void wraps_init(struct isl_wraps *wraps, __isl_take isl_mat *mat, struct isl_coalesce_info *info, int i, int j) { isl_ctx *ctx; wraps->bound = 0; wraps->mat = mat; if (!mat) return; ctx = isl_mat_get_ctx(mat); wraps->bound = isl_options_get_coalesce_bounded_wrapping(ctx); if (!wraps->bound) return; isl_int_init(wraps->max); isl_int_set_si(wraps->max, 0); wraps_update_max(wraps, &info[i]); wraps_update_max(wraps, &info[j]); } /* Free the contents of the isl_wraps data structure. */ static void wraps_free(struct isl_wraps *wraps) { isl_mat_free(wraps->mat); if (wraps->bound) isl_int_clear(wraps->max); } /* Is the wrapping constraint in row "row" allowed? * * If wraps->bound is set, we check that none of the coefficients * is greater than wraps->max. */ static int allow_wrap(struct isl_wraps *wraps, int row) { int i; if (!wraps->bound) return 1; for (i = 1; i < wraps->mat->n_col; ++i) if (isl_int_abs_gt(wraps->mat->row[row][i], wraps->max)) return 0; return 1; } /* Wrap "ineq" (or its opposite if "negate" is set) around "bound" * to include "set" and add the result in position "w" of "wraps". * "len" is the total number of coefficients in "bound" and "ineq". * Return 1 on success, 0 on failure and -1 on error. * Wrapping can fail if the result of wrapping is equal to "bound" * or if we want to bound the sizes of the coefficients and * the wrapped constraint does not satisfy this bound. */ static int add_wrap(struct isl_wraps *wraps, int w, isl_int *bound, isl_int *ineq, unsigned len, __isl_keep isl_set *set, int negate) { isl_seq_cpy(wraps->mat->row[w], bound, len); if (negate) { isl_seq_neg(wraps->mat->row[w + 1], ineq, len); ineq = wraps->mat->row[w + 1]; } if (!isl_set_wrap_facet(set, wraps->mat->row[w], ineq)) return -1; if (isl_seq_eq(wraps->mat->row[w], bound, len)) return 0; if (!allow_wrap(wraps, w)) return 0; return 1; } /* For each constraint in info->bmap that is not redundant (as determined * by info->tab) and that is not a valid constraint for the other basic map, * wrap the constraint around "bound" such that it includes the whole * set "set" and append the resulting constraint to "wraps". * Note that the constraints that are valid for the other basic map * will be added to the combined basic map by default, so there is * no need to wrap them. * The caller wrap_in_facets even relies on this function not wrapping * any constraints that are already valid. * "wraps" is assumed to have been pre-allocated to the appropriate size. * wraps->n_row is the number of actual wrapped constraints that have * been added. * If any of the wrapping problems results in a constraint that is * identical to "bound", then this means that "set" is unbounded in such * way that no wrapping is possible. If this happens then wraps->n_row * is reset to zero. * Similarly, if we want to bound the coefficients of the wrapping * constraints and a newly added wrapping constraint does not * satisfy the bound, then wraps->n_row is also reset to zero. */ static int add_wraps(struct isl_wraps *wraps, struct isl_coalesce_info *info, isl_int *bound, __isl_keep isl_set *set) { int l, m; int w; int added; isl_basic_map *bmap = info->bmap; unsigned len = 1 + isl_basic_map_total_dim(bmap); w = wraps->mat->n_row; for (l = 0; l < bmap->n_ineq; ++l) { if (info->ineq[l] == STATUS_VALID || info->ineq[l] == STATUS_REDUNDANT) continue; if (isl_seq_is_neg(bound, bmap->ineq[l], len)) continue; if (isl_seq_eq(bound, bmap->ineq[l], len)) continue; if (isl_tab_is_redundant(info->tab, bmap->n_eq + l)) continue; added = add_wrap(wraps, w, bound, bmap->ineq[l], len, set, 0); if (added < 0) return -1; if (!added) goto unbounded; ++w; } for (l = 0; l < bmap->n_eq; ++l) { if (isl_seq_is_neg(bound, bmap->eq[l], len)) continue; if (isl_seq_eq(bound, bmap->eq[l], len)) continue; for (m = 0; m < 2; ++m) { if (info->eq[2 * l + m] == STATUS_VALID) continue; added = add_wrap(wraps, w, bound, bmap->eq[l], len, set, !m); if (added < 0) return -1; if (!added) goto unbounded; ++w; } } wraps->mat->n_row = w; return 0; unbounded: wraps->mat->n_row = 0; return 0; } /* Check if the constraints in "wraps" from "first" until the last * are all valid for the basic set represented by "tab". * If not, wraps->n_row is set to zero. */ static int check_wraps(__isl_keep isl_mat *wraps, int first, struct isl_tab *tab) { int i; for (i = first; i < wraps->n_row; ++i) { enum isl_ineq_type type; type = isl_tab_ineq_type(tab, wraps->row[i]); if (type == isl_ineq_error) return -1; if (type == isl_ineq_redundant) continue; wraps->n_row = 0; return 0; } return 0; } /* Return a set that corresponds to the non-redundant constraints * (as recorded in tab) of bmap. * * It's important to remove the redundant constraints as some * of the other constraints may have been modified after the * constraints were marked redundant. * In particular, a constraint may have been relaxed. * Redundant constraints are ignored when a constraint is relaxed * and should therefore continue to be ignored ever after. * Otherwise, the relaxation might be thwarted by some of * these constraints. * * Update the underlying set to ensure that the dimension doesn't change. * Otherwise the integer divisions could get dropped if the tab * turns out to be empty. */ static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap, struct isl_tab *tab) { isl_basic_set *bset; bmap = isl_basic_map_copy(bmap); bset = isl_basic_map_underlying_set(bmap); bset = isl_basic_set_cow(bset); bset = isl_basic_set_update_from_tab(bset, tab); return isl_set_from_basic_set(bset); } /* Wrap the constraints of info->bmap that bound the facet defined * by inequality "k" around (the opposite of) this inequality to * include "set". "bound" may be used to store the negated inequality. * Since the wrapped constraints are not guaranteed to contain the whole * of info->bmap, we check them in check_wraps. * If any of the wrapped constraints turn out to be invalid, then * check_wraps will reset wrap->n_row to zero. */ static int add_wraps_around_facet(struct isl_wraps *wraps, struct isl_coalesce_info *info, int k, isl_int *bound, __isl_keep isl_set *set) { struct isl_tab_undo *snap; int n; unsigned total = isl_basic_map_total_dim(info->bmap); snap = isl_tab_snap(info->tab); if (isl_tab_select_facet(info->tab, info->bmap->n_eq + k) < 0) return -1; if (isl_tab_detect_redundant(info->tab) < 0) return -1; isl_seq_neg(bound, info->bmap->ineq[k], 1 + total); n = wraps->mat->n_row; if (add_wraps(wraps, info, bound, set) < 0) return -1; if (isl_tab_rollback(info->tab, snap) < 0) return -1; if (check_wraps(wraps->mat, n, info->tab) < 0) return -1; return 0; } /* Given a basic set i with a constraint k that is adjacent to * basic set j, check if we can wrap * both the facet corresponding to k (if "wrap_facet" is set) and basic map j * (always) around their ridges to include the other set. * If so, replace the pair of basic sets by their union. * * All constraints of i (except k) are assumed to be valid or * cut constraints for j. * Wrapping the cut constraints to include basic map j may result * in constraints that are no longer valid of basic map i * we have to check that the resulting wrapping constraints are valid for i. * If "wrap_facet" is not set, then all constraints of i (except k) * are assumed to be valid for j. * ____ _____ * / | / \ * / || / | * \ || => \ | * \ || \ | * \___|| \____| * */ static enum isl_change can_wrap_in_facet(int i, int j, int k, struct isl_coalesce_info *info, int wrap_facet) { enum isl_change change = isl_change_none; struct isl_wraps wraps; isl_ctx *ctx; isl_mat *mat; struct isl_set *set_i = NULL; struct isl_set *set_j = NULL; struct isl_vec *bound = NULL; unsigned total = isl_basic_map_total_dim(info[i].bmap); set_i = set_from_updated_bmap(info[i].bmap, info[i].tab); set_j = set_from_updated_bmap(info[j].bmap, info[j].tab); ctx = isl_basic_map_get_ctx(info[i].bmap); mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) + info[i].bmap->n_ineq + info[j].bmap->n_ineq, 1 + total); wraps_init(&wraps, mat, info, i, j); bound = isl_vec_alloc(ctx, 1 + total); if (!set_i || !set_j || !wraps.mat || !bound) goto error; isl_seq_cpy(bound->el, info[i].bmap->ineq[k], 1 + total); isl_int_add_ui(bound->el[0], bound->el[0], 1); isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total); wraps.mat->n_row = 1; if (add_wraps(&wraps, &info[j], bound->el, set_i) < 0) goto error; if (!wraps.mat->n_row) goto unbounded; if (wrap_facet) { if (add_wraps_around_facet(&wraps, &info[i], k, bound->el, set_j) < 0) goto error; if (!wraps.mat->n_row) goto unbounded; } change = fuse(i, j, info, wraps.mat, 0, 0); unbounded: wraps_free(&wraps); isl_set_free(set_i); isl_set_free(set_j); isl_vec_free(bound); return change; error: wraps_free(&wraps); isl_vec_free(bound); isl_set_free(set_i); isl_set_free(set_j); return isl_change_error; } /* Given a pair of basic maps i and j such that j sticks out * of i at n cut constraints, each time by at most one, * try to compute wrapping constraints and replace the two * basic maps by a single basic map. * The other constraints of i are assumed to be valid for j. * * For each cut constraint t(x) >= 0 of i, we add the relaxed version * t(x) + 1 >= 0, along with wrapping constraints for all constraints * of basic map j that bound the part of basic map j that sticks out * of the cut constraint. * In particular, we first intersect basic map j with t(x) + 1 = 0. * If the result is empty, then t(x) >= 0 was actually a valid constraint * (with respect to the integer points), so we add t(x) >= 0 instead. * Otherwise, we wrap the constraints of basic map j that are not * redundant in this intersection and that are not already valid * for basic map i over basic map i. * Note that it is sufficient to wrap the constraints to include * basic map i, because we will only wrap the constraints that do * not include basic map i already. The wrapped constraint will * therefore be more relaxed compared to the original constraint. * Since the original constraint is valid for basic map j, so is * the wrapped constraint. * * If any wrapping fails, i.e., if we cannot wrap to touch * the union, then we give up. * Otherwise, the pair of basic maps is replaced by their union. */ static enum isl_change wrap_in_facets(int i, int j, int *cuts, int n, struct isl_coalesce_info *info) { enum isl_change change = isl_change_none; struct isl_wraps wraps; isl_ctx *ctx; isl_mat *mat; isl_set *set_i = NULL; unsigned total = isl_basic_map_total_dim(info[i].bmap); int max_wrap; int k, w; struct isl_tab_undo *snap; if (isl_tab_extend_cons(info[j].tab, 1) < 0) goto error; max_wrap = 1 + 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq; max_wrap *= n; set_i = set_from_updated_bmap(info[i].bmap, info[i].tab); ctx = isl_basic_map_get_ctx(info[i].bmap); mat = isl_mat_alloc(ctx, max_wrap, 1 + total); wraps_init(&wraps, mat, info, i, j); if (!set_i || !wraps.mat) goto error; snap = isl_tab_snap(info[j].tab); wraps.mat->n_row = 0; for (k = 0; k < n; ++k) { w = wraps.mat->n_row++; isl_seq_cpy(wraps.mat->row[w], info[i].bmap->ineq[cuts[k]], 1 + total); isl_int_add_ui(wraps.mat->row[w][0], wraps.mat->row[w][0], 1); if (isl_tab_add_eq(info[j].tab, wraps.mat->row[w]) < 0) goto error; if (isl_tab_detect_redundant(info[j].tab) < 0) goto error; if (info[j].tab->empty) isl_int_sub_ui(wraps.mat->row[w][0], wraps.mat->row[w][0], 1); else if (add_wraps(&wraps, &info[j], wraps.mat->row[w], set_i) < 0) goto error; if (isl_tab_rollback(info[j].tab, snap) < 0) goto error; if (!wraps.mat->n_row) break; } if (k == n) change = fuse(i, j, info, wraps.mat, 0, 1); wraps_free(&wraps); isl_set_free(set_i); return change; error: wraps_free(&wraps); isl_set_free(set_i); return isl_change_error; } /* Given two basic sets i and j such that i has no cut equalities, * check if relaxing all the cut inequalities of i by one turns * them into valid constraint for j and check if we can wrap in * the bits that are sticking out. * If so, replace the pair by their union. * * We first check if all relaxed cut inequalities of i are valid for j * and then try to wrap in the intersections of the relaxed cut inequalities * with j. * * During this wrapping, we consider the points of j that lie at a distance * of exactly 1 from i. In particular, we ignore the points that lie in * between this lower-dimensional space and the basic map i. * We can therefore only apply this to integer maps. * ____ _____ * / ___|_ / \ * / | | / | * \ | | => \ | * \|____| \ | * \___| \____/ * * _____ ______ * | ____|_ | \ * | | | | | * | | | => | | * |_| | | | * |_____| \______| * * _______ * | | * | |\ | * | | \ | * | | \ | * | | \| * | | \ * | |_____\ * | | * |_______| * * Wrapping can fail if the result of wrapping one of the facets * around its edges does not produce any new facet constraint. * In particular, this happens when we try to wrap in unbounded sets. * * _______________________________________________________________________ * | * | ___ * | | | * |_| |_________________________________________________________________ * |___| * * The following is not an acceptable result of coalescing the above two * sets as it includes extra integer points. * _______________________________________________________________________ * | * | * | * | * \______________________________________________________________________ */ static enum isl_change can_wrap_in_set(int i, int j, struct isl_coalesce_info *info) { enum isl_change change = isl_change_none; int k, m; int n; int *cuts = NULL; isl_ctx *ctx; if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) || ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL)) return isl_change_none; n = count(info[i].ineq, info[i].bmap->n_ineq, STATUS_CUT); if (n == 0) return isl_change_none; ctx = isl_basic_map_get_ctx(info[i].bmap); cuts = isl_alloc_array(ctx, int, n); if (!cuts) return isl_change_error; for (k = 0, m = 0; m < n; ++k) { enum isl_ineq_type type; if (info[i].ineq[k] != STATUS_CUT) continue; isl_int_add_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1); type = isl_tab_ineq_type(info[j].tab, info[i].bmap->ineq[k]); isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1); if (type == isl_ineq_error) goto error; if (type != isl_ineq_redundant) break; cuts[m] = k; ++m; } if (m == n) change = wrap_in_facets(i, j, cuts, n, info); free(cuts); return change; error: free(cuts); return isl_change_error; } /* Check if either i or j has only cut inequalities that can * be used to wrap in (a facet of) the other basic set. * if so, replace the pair by their union. */ static enum isl_change check_wrap(int i, int j, struct isl_coalesce_info *info) { enum isl_change change = isl_change_none; if (!any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_CUT)) change = can_wrap_in_set(i, j, info); if (change != isl_change_none) return change; if (!any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_CUT)) change = can_wrap_in_set(j, i, info); return change; } /* At least one of the basic maps has an equality that is adjacent * to inequality. Make sure that only one of the basic maps has * such an equality and that the other basic map has exactly one * inequality adjacent to an equality. * We call the basic map that has the inequality "i" and the basic * map that has the equality "j". * If "i" has any "cut" (in)equality, then relaxing the inequality * by one would not result in a basic map that contains the other * basic map. However, it may still be possible to wrap in the other * basic map. */ static enum isl_change check_adj_eq(int i, int j, struct isl_coalesce_info *info) { enum isl_change change = isl_change_none; int k; int any_cut; if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_INEQ) && any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_ADJ_INEQ)) /* ADJ EQ TOO MANY */ return isl_change_none; if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_INEQ)) return check_adj_eq(j, i, info); /* j has an equality adjacent to an inequality in i */ if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_CUT)) return isl_change_none; any_cut = any(info[i].ineq, info[i].bmap->n_ineq, STATUS_CUT); if (count(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_EQ) != 1 || any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_EQ) || any(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_INEQ) || any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_INEQ)) /* ADJ EQ TOO MANY */ return isl_change_none; for (k = 0; k < info[i].bmap->n_ineq; ++k) if (info[i].ineq[k] == STATUS_ADJ_EQ) break; if (!any_cut) { change = is_adj_eq_extension(i, j, k, info); if (change != isl_change_none) return change; } change = can_wrap_in_facet(i, j, k, info, any_cut); return change; } /* The two basic maps lie on adjacent hyperplanes. In particular, * basic map "i" has an equality that lies parallel to basic map "j". * Check if we can wrap the facets around the parallel hyperplanes * to include the other set. * * We perform basically the same operations as can_wrap_in_facet, * except that we don't need to select a facet of one of the sets. * _ * \\ \\ * \\ => \\ * \ \| * * If there is more than one equality of "i" adjacent to an equality of "j", * then the result will satisfy one or more equalities that are a linear * combination of these equalities. These will be encoded as pairs * of inequalities in the wrapping constraints and need to be made * explicit. */ static enum isl_change check_eq_adj_eq(int i, int j, struct isl_coalesce_info *info) { int k; enum isl_change change = isl_change_none; int detect_equalities = 0; struct isl_wraps wraps; isl_ctx *ctx; isl_mat *mat; struct isl_set *set_i = NULL; struct isl_set *set_j = NULL; struct isl_vec *bound = NULL; unsigned total = isl_basic_map_total_dim(info[i].bmap); if (count(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_EQ) != 1) detect_equalities = 1; for (k = 0; k < 2 * info[i].bmap->n_eq ; ++k) if (info[i].eq[k] == STATUS_ADJ_EQ) break; set_i = set_from_updated_bmap(info[i].bmap, info[i].tab); set_j = set_from_updated_bmap(info[j].bmap, info[j].tab); ctx = isl_basic_map_get_ctx(info[i].bmap); mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) + info[i].bmap->n_ineq + info[j].bmap->n_ineq, 1 + total); wraps_init(&wraps, mat, info, i, j); bound = isl_vec_alloc(ctx, 1 + total); if (!set_i || !set_j || !wraps.mat || !bound) goto error; if (k % 2 == 0) isl_seq_neg(bound->el, info[i].bmap->eq[k / 2], 1 + total); else isl_seq_cpy(bound->el, info[i].bmap->eq[k / 2], 1 + total); isl_int_add_ui(bound->el[0], bound->el[0], 1); isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total); wraps.mat->n_row = 1; if (add_wraps(&wraps, &info[j], bound->el, set_i) < 0) goto error; if (!wraps.mat->n_row) goto unbounded; isl_int_sub_ui(bound->el[0], bound->el[0], 1); isl_seq_neg(bound->el, bound->el, 1 + total); isl_seq_cpy(wraps.mat->row[wraps.mat->n_row], bound->el, 1 + total); wraps.mat->n_row++; if (add_wraps(&wraps, &info[i], bound->el, set_j) < 0) goto error; if (!wraps.mat->n_row) goto unbounded; change = fuse(i, j, info, wraps.mat, detect_equalities, 0); if (0) { error: change = isl_change_error; } unbounded: wraps_free(&wraps); isl_set_free(set_i); isl_set_free(set_j); isl_vec_free(bound); return change; } /* Check if the union of the given pair of basic maps * can be represented by a single basic map. * If so, replace the pair by the single basic map and return * isl_change_drop_first, isl_change_drop_second or isl_change_fuse. * Otherwise, return isl_change_none. * The two basic maps are assumed to live in the same local space. * * We first check the effect of each constraint of one basic map * on the other basic map. * The constraint may be * redundant the constraint is redundant in its own * basic map and should be ignore and removed * in the end * valid all (integer) points of the other basic map * satisfy the constraint * separate no (integer) point of the other basic map * satisfies the constraint * cut some but not all points of the other basic map * satisfy the constraint * adj_eq the given constraint is adjacent (on the outside) * to an equality of the other basic map * adj_ineq the given constraint is adjacent (on the outside) * to an inequality of the other basic map * * We consider seven cases in which we can replace the pair by a single * basic map. We ignore all "redundant" constraints. * * 1. all constraints of one basic map are valid * => the other basic map is a subset and can be removed * * 2. all constraints of both basic maps are either "valid" or "cut" * and the facets corresponding to the "cut" constraints * of one of the basic maps lies entirely inside the other basic map * => the pair can be replaced by a basic map consisting * of the valid constraints in both basic maps * * 3. there is a single pair of adjacent inequalities * (all other constraints are "valid") * => the pair can be replaced by a basic map consisting * of the valid constraints in both basic maps * * 4. one basic map has a single adjacent inequality, while the other * constraints are "valid". The other basic map has some * "cut" constraints, but replacing the adjacent inequality by * its opposite and adding the valid constraints of the other * basic map results in a subset of the other basic map * => the pair can be replaced by a basic map consisting * of the valid constraints in both basic maps * * 5. there is a single adjacent pair of an inequality and an equality, * the other constraints of the basic map containing the inequality are * "valid". Moreover, if the inequality the basic map is relaxed * and then turned into an equality, then resulting facet lies * entirely inside the other basic map * => the pair can be replaced by the basic map containing * the inequality, with the inequality relaxed. * * 6. there is a single adjacent pair of an inequality and an equality, * the other constraints of the basic map containing the inequality are * "valid". Moreover, the facets corresponding to both * the inequality and the equality can be wrapped around their * ridges to include the other basic map * => the pair can be replaced by a basic map consisting * of the valid constraints in both basic maps together * with all wrapping constraints * * 7. one of the basic maps extends beyond the other by at most one. * Moreover, the facets corresponding to the cut constraints and * the pieces of the other basic map at offset one from these cut * constraints can be wrapped around their ridges to include * the union of the two basic maps * => the pair can be replaced by a basic map consisting * of the valid constraints in both basic maps together * with all wrapping constraints * * 8. the two basic maps live in adjacent hyperplanes. In principle * such sets can always be combined through wrapping, but we impose * that there is only one such pair, to avoid overeager coalescing. * * Throughout the computation, we maintain a collection of tableaus * corresponding to the basic maps. When the basic maps are dropped * or combined, the tableaus are modified accordingly. */ static enum isl_change coalesce_local_pair(int i, int j, struct isl_coalesce_info *info) { enum isl_change change = isl_change_none; info[i].eq = info[i].ineq = NULL; info[j].eq = info[j].ineq = NULL; info[i].eq = eq_status_in(info[i].bmap, info[j].tab); if (info[i].bmap->n_eq && !info[i].eq) goto error; if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ERROR)) goto error; if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_SEPARATE)) goto done; info[j].eq = eq_status_in(info[j].bmap, info[i].tab); if (info[j].bmap->n_eq && !info[j].eq) goto error; if (any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_ERROR)) goto error; if (any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_SEPARATE)) goto done; info[i].ineq = ineq_status_in(info[i].bmap, info[i].tab, info[j].tab); if (info[i].bmap->n_ineq && !info[i].ineq) goto error; if (any(info[i].ineq, info[i].bmap->n_ineq, STATUS_ERROR)) goto error; if (any(info[i].ineq, info[i].bmap->n_ineq, STATUS_SEPARATE)) goto done; info[j].ineq = ineq_status_in(info[j].bmap, info[j].tab, info[i].tab); if (info[j].bmap->n_ineq && !info[j].ineq) goto error; if (any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ERROR)) goto error; if (any(info[j].ineq, info[j].bmap->n_ineq, STATUS_SEPARATE)) goto done; if (all(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_VALID) && all(info[i].ineq, info[i].bmap->n_ineq, STATUS_VALID)) { drop(&info[j]); change = isl_change_drop_second; } else if (all(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_VALID) && all(info[j].ineq, info[j].bmap->n_ineq, STATUS_VALID)) { drop(&info[i]); change = isl_change_drop_first; } else if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_EQ)) { change = check_eq_adj_eq(i, j, info); } else if (any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_ADJ_EQ)) { change = check_eq_adj_eq(j, i, info); } else if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_INEQ) || any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_ADJ_INEQ)) { change = check_adj_eq(i, j, info); } else if (any(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_EQ) || any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_EQ)) { /* Can't happen */ /* BAD ADJ INEQ */ } else if (any(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_INEQ) || any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_INEQ)) { change = check_adj_ineq(i, j, info); } else { if (!any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_CUT) && !any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_CUT)) change = check_facets(i, j, info); if (change == isl_change_none) change = check_wrap(i, j, info); } done: free(info[i].eq); free(info[j].eq); free(info[i].ineq); free(info[j].ineq); return change; error: free(info[i].eq); free(info[j].eq); free(info[i].ineq); free(info[j].ineq); return isl_change_error; } /* Shift the integer division at position "div" of the basic map * represented by "info" by "shift". * * That is, if the integer division has the form * * floor(f(x)/d) * * then replace it by * * floor((f(x) + shift * d)/d) - shift */ static int shift_div(struct isl_coalesce_info *info, int div, isl_int shift) { unsigned total; info->bmap = isl_basic_map_shift_div(info->bmap, div, 0, shift); if (!info->bmap) return -1; total = isl_basic_map_dim(info->bmap, isl_dim_all); total -= isl_basic_map_dim(info->bmap, isl_dim_div); if (isl_tab_shift_var(info->tab, total + div, shift) < 0) return -1; return 0; } /* Check if some of the divs in the basic map represented by "info1" * are shifts of the corresponding divs in the basic map represented * by "info2". If so, align them with those of "info2". * Only do this if "info1" and "info2" have the same number * of integer divisions. * * An integer division is considered to be a shift of another integer * division if one is equal to the other plus a constant. * * In particular, for each pair of integer divisions, if both are known, * have identical coefficients (apart from the constant term) and * if the difference between the constant terms (taking into account * the denominator) is an integer, then move the difference outside. * That is, if one integer division is of the form * * floor((f(x) + c_1)/d) * * while the other is of the form * * floor((f(x) + c_2)/d) * * and n = (c_2 - c_1)/d is an integer, then replace the first * integer division by * * floor((f(x) + c_1 + n * d)/d) - n = floor((f(x) + c_2)/d) - n */ static int harmonize_divs(struct isl_coalesce_info *info1, struct isl_coalesce_info *info2) { int i; int total; if (!info1->bmap || !info2->bmap) return -1; if (info1->bmap->n_div != info2->bmap->n_div) return 0; if (info1->bmap->n_div == 0) return 0; total = isl_basic_map_total_dim(info1->bmap); for (i = 0; i < info1->bmap->n_div; ++i) { isl_int d; int r = 0; if (isl_int_is_zero(info1->bmap->div[i][0]) || isl_int_is_zero(info2->bmap->div[i][0])) continue; if (isl_int_ne(info1->bmap->div[i][0], info2->bmap->div[i][0])) continue; if (isl_int_eq(info1->bmap->div[i][1], info2->bmap->div[i][1])) continue; if (!isl_seq_eq(info1->bmap->div[i] + 2, info2->bmap->div[i] + 2, total)) continue; isl_int_init(d); isl_int_sub(d, info2->bmap->div[i][1], info1->bmap->div[i][1]); if (isl_int_is_divisible_by(d, info1->bmap->div[i][0])) { isl_int_divexact(d, d, info1->bmap->div[i][0]); r = shift_div(info1, i, d); } isl_int_clear(d); if (r < 0) return -1; } return 0; } /* Do the two basic maps live in the same local space, i.e., * do they have the same (known) divs? * If either basic map has any unknown divs, then we can only assume * that they do not live in the same local space. */ static int same_divs(__isl_keep isl_basic_map *bmap1, __isl_keep isl_basic_map *bmap2) { int i; int known; int total; if (!bmap1 || !bmap2) return -1; if (bmap1->n_div != bmap2->n_div) return 0; if (bmap1->n_div == 0) return 1; known = isl_basic_map_divs_known(bmap1); if (known < 0 || !known) return known; known = isl_basic_map_divs_known(bmap2); if (known < 0 || !known) return known; total = isl_basic_map_total_dim(bmap1); for (i = 0; i < bmap1->n_div; ++i) if (!isl_seq_eq(bmap1->div[i], bmap2->div[i], 2 + total)) return 0; return 1; } /* Does "bmap" contain the basic map represented by the tableau "tab" * after expanding the divs of "bmap" to match those of "tab"? * The expansion is performed using the divs "div" and expansion "exp" * computed by the caller. * Then we check if all constraints of the expanded "bmap" are valid for "tab". */ static int contains_with_expanded_divs(__isl_keep isl_basic_map *bmap, struct isl_tab *tab, __isl_keep isl_mat *div, int *exp) { int superset = 0; int *eq_i = NULL; int *ineq_i = NULL; bmap = isl_basic_map_copy(bmap); bmap = isl_basic_set_expand_divs(bmap, isl_mat_copy(div), exp); if (!bmap) goto error; eq_i = eq_status_in(bmap, tab); if (bmap->n_eq && !eq_i) goto error; if (any(eq_i, 2 * bmap->n_eq, STATUS_ERROR)) goto error; if (any(eq_i, 2 * bmap->n_eq, STATUS_SEPARATE)) goto done; ineq_i = ineq_status_in(bmap, NULL, tab); if (bmap->n_ineq && !ineq_i) goto error; if (any(ineq_i, bmap->n_ineq, STATUS_ERROR)) goto error; if (any(ineq_i, bmap->n_ineq, STATUS_SEPARATE)) goto done; if (all(eq_i, 2 * bmap->n_eq, STATUS_VALID) && all(ineq_i, bmap->n_ineq, STATUS_VALID)) superset = 1; done: isl_basic_map_free(bmap); free(eq_i); free(ineq_i); return superset; error: isl_basic_map_free(bmap); free(eq_i); free(ineq_i); return -1; } /* Does "bmap_i" contain the basic map represented by "info_j" * after aligning the divs of "bmap_i" to those of "info_j". * Note that this can only succeed if the number of divs of "bmap_i" * is smaller than (or equal to) the number of divs of "info_j". * * We first check if the divs of "bmap_i" are all known and form a subset * of those of "bmap_j". If so, we pass control over to * contains_with_expanded_divs. */ static int contains_after_aligning_divs(__isl_keep isl_basic_map *bmap_i, struct isl_coalesce_info *info_j) { int known; isl_mat *div_i, *div_j, *div; int *exp1 = NULL; int *exp2 = NULL; isl_ctx *ctx; int subset; known = isl_basic_map_divs_known(bmap_i); if (known < 0 || !known) return known; ctx = isl_basic_map_get_ctx(bmap_i); div_i = isl_basic_map_get_divs(bmap_i); div_j = isl_basic_map_get_divs(info_j->bmap); if (!div_i || !div_j) goto error; exp1 = isl_alloc_array(ctx, int, div_i->n_row); exp2 = isl_alloc_array(ctx, int, div_j->n_row); if ((div_i->n_row && !exp1) || (div_j->n_row && !exp2)) goto error; div = isl_merge_divs(div_i, div_j, exp1, exp2); if (!div) goto error; if (div->n_row == div_j->n_row) subset = contains_with_expanded_divs(bmap_i, info_j->tab, div, exp1); else subset = 0; isl_mat_free(div); isl_mat_free(div_i); isl_mat_free(div_j); free(exp2); free(exp1); return subset; error: isl_mat_free(div_i); isl_mat_free(div_j); free(exp1); free(exp2); return -1; } /* Check if the basic map "j" is a subset of basic map "i", * if "i" has fewer divs that "j". * If so, remove basic map "j". * * If the two basic maps have the same number of divs, then * they must necessarily be different. Otherwise, we would have * called coalesce_local_pair. We therefore don't try anything * in this case. */ static int coalesced_subset(int i, int j, struct isl_coalesce_info *info) { int superset; if (info[i].bmap->n_div >= info[j].bmap->n_div) return 0; superset = contains_after_aligning_divs(info[i].bmap, &info[j]); if (superset < 0) return -1; if (superset) drop(&info[j]); return superset; } /* Check if basic map "j" is a subset of basic map "i" after * exploiting the extra equalities of "j" to simplify the divs of "i". * If so, remove basic map "j". * * If "j" does not have any equalities or if they are the same * as those of "i", then we cannot exploit them to simplify the divs. * Similarly, if there are no divs in "i", then they cannot be simplified. * If, on the other hand, the affine hulls of "i" and "j" do not intersect, * then "j" cannot be a subset of "i". * * Otherwise, we intersect "i" with the affine hull of "j" and then * check if "j" is a subset of the result after aligning the divs. * If so, then "j" is definitely a subset of "i" and can be removed. * Note that if after intersection with the affine hull of "j". * "i" still has more divs than "j", then there is no way we can * align the divs of "i" to those of "j". */ static int coalesced_subset_with_equalities(int i, int j, struct isl_coalesce_info *info) { isl_basic_map *hull_i, *hull_j, *bmap_i; int equal, empty, subset; if (info[j].bmap->n_eq == 0) return 0; if (info[i].bmap->n_div == 0) return 0; hull_i = isl_basic_map_copy(info[i].bmap); hull_i = isl_basic_map_plain_affine_hull(hull_i); hull_j = isl_basic_map_copy(info[j].bmap); hull_j = isl_basic_map_plain_affine_hull(hull_j); hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i)); equal = isl_basic_map_plain_is_equal(hull_i, hull_j); empty = isl_basic_map_plain_is_empty(hull_j); isl_basic_map_free(hull_i); if (equal < 0 || equal || empty < 0 || empty) { isl_basic_map_free(hull_j); return equal < 0 || empty < 0 ? -1 : 0; } bmap_i = isl_basic_map_copy(info[i].bmap); bmap_i = isl_basic_map_intersect(bmap_i, hull_j); if (!bmap_i) return -1; if (bmap_i->n_div > info[j].bmap->n_div) { isl_basic_map_free(bmap_i); return 0; } subset = contains_after_aligning_divs(bmap_i, &info[j]); isl_basic_map_free(bmap_i); if (subset < 0) return -1; if (subset) drop(&info[j]); return subset; } /* Check if one of the basic maps is a subset of the other and, if so, * drop the subset. * Note that we only perform any test if the number of divs is different * in the two basic maps. In case the number of divs is the same, * we have already established that the divs are different * in the two basic maps. * In particular, if the number of divs of basic map i is smaller than * the number of divs of basic map j, then we check if j is a subset of i * and vice versa. */ static enum isl_change check_coalesce_subset(int i, int j, struct isl_coalesce_info *info) { int changed; changed = coalesced_subset(i, j, info); if (changed < 0 || changed) return changed < 0 ? isl_change_error : isl_change_drop_second; changed = coalesced_subset(j, i, info); if (changed < 0 || changed) return changed < 0 ? isl_change_error : isl_change_drop_first; changed = coalesced_subset_with_equalities(i, j, info); if (changed < 0 || changed) return changed < 0 ? isl_change_error : isl_change_drop_second; changed = coalesced_subset_with_equalities(j, i, info); if (changed < 0 || changed) return changed < 0 ? isl_change_error : isl_change_drop_first; return isl_change_none; } /* Does "bmap" involve any divs that themselves refer to divs? */ static int has_nested_div(__isl_keep isl_basic_map *bmap) { int i; unsigned total; unsigned n_div; total = isl_basic_map_dim(bmap, isl_dim_all); n_div = isl_basic_map_dim(bmap, isl_dim_div); total -= n_div; for (i = 0; i < n_div; ++i) if (isl_seq_first_non_zero(bmap->div[i] + 2 + total, n_div) != -1) return 1; return 0; } /* Return a list of affine expressions, one for each integer division * in "bmap_i". For each integer division that also appears in "bmap_j", * the affine expression is set to NaN. The number of NaNs in the list * is equal to the number of integer divisions in "bmap_j". * For the other integer divisions of "bmap_i", the corresponding * element in the list is a purely affine expression equal to the integer * division in "hull". * If no such list can be constructed, then the number of elements * in the returned list is smaller than the number of integer divisions * in "bmap_i". */ static __isl_give isl_aff_list *set_up_substitutions( __isl_keep isl_basic_map *bmap_i, __isl_keep isl_basic_map *bmap_j, __isl_take isl_basic_map *hull) { unsigned n_div_i, n_div_j, total; isl_ctx *ctx; isl_local_space *ls; isl_basic_set *wrap_hull; isl_aff *aff_nan; isl_aff_list *list; int i, j; if (!hull) return NULL; ctx = isl_basic_map_get_ctx(hull); n_div_i = isl_basic_map_dim(bmap_i, isl_dim_div); n_div_j = isl_basic_map_dim(bmap_j, isl_dim_div); total = isl_basic_map_total_dim(bmap_i) - n_div_i; ls = isl_basic_map_get_local_space(bmap_i); ls = isl_local_space_wrap(ls); wrap_hull = isl_basic_map_wrap(hull); aff_nan = isl_aff_nan_on_domain(isl_local_space_copy(ls)); list = isl_aff_list_alloc(ctx, n_div_i); j = 0; for (i = 0; i < n_div_i; ++i) { isl_aff *aff; if (j < n_div_j && isl_seq_eq(bmap_i->div[i], bmap_j->div[j], 2 + total)) { ++j; list = isl_aff_list_add(list, isl_aff_copy(aff_nan)); continue; } if (n_div_i - i <= n_div_j - j) break; aff = isl_local_space_get_div(ls, i); aff = isl_aff_substitute_equalities(aff, isl_basic_set_copy(wrap_hull)); aff = isl_aff_floor(aff); if (!aff) goto error; if (isl_aff_dim(aff, isl_dim_div) != 0) { isl_aff_free(aff); break; } list = isl_aff_list_add(list, aff); } isl_aff_free(aff_nan); isl_local_space_free(ls); isl_basic_set_free(wrap_hull); return list; error: isl_aff_free(aff_nan); isl_local_space_free(ls); isl_basic_set_free(wrap_hull); isl_aff_list_free(list); return NULL; } /* Add variables to info->bmap and info->tab corresponding to the elements * in "list" that are not set to NaN. * "extra_var" is the number of these elements. * "dim" is the offset in the variables of "tab" where we should * start considering the elements in "list". * When this function returns, the total number of variables in "tab" * is equal to "dim" plus the number of elements in "list". */ static int add_sub_vars(struct isl_coalesce_info *info, __isl_keep isl_aff_list *list, int dim, int extra_var) { int i, j, n; isl_space *space; space = isl_basic_map_get_space(info->bmap); info->bmap = isl_basic_map_cow(info->bmap); info->bmap = isl_basic_map_extend_space(info->bmap, space, extra_var, 0, 0); if (!info->bmap) return -1; n = isl_aff_list_n_aff(list); for (i = 0; i < n; ++i) { int is_nan; isl_aff *aff; aff = isl_aff_list_get_aff(list, i); is_nan = isl_aff_is_nan(aff); isl_aff_free(aff); if (is_nan < 0) return -1; if (is_nan) continue; if (isl_tab_insert_var(info->tab, dim + i) < 0) return -1; if (isl_basic_map_alloc_div(info->bmap) < 0) return -1; for (j = n - 1; j > i; --j) isl_basic_map_swap_div(info->bmap, j - 1, j); } return 0; } /* For each element in "list" that is not set to NaN, fix the corresponding * variable in "tab" to the purely affine expression defined by the element. * "dim" is the offset in the variables of "tab" where we should * start considering the elements in "list". */ static int add_sub_equalities(struct isl_tab *tab, __isl_keep isl_aff_list *list, int dim) { int i, n; isl_ctx *ctx; isl_vec *sub; isl_aff *aff; n = isl_aff_list_n_aff(list); ctx = isl_tab_get_ctx(tab); sub = isl_vec_alloc(ctx, 1 + dim + n); if (!sub) return -1; isl_seq_clr(sub->el + 1 + dim, n); for (i = 0; i < n; ++i) { aff = isl_aff_list_get_aff(list, i); if (!aff) goto error; if (isl_aff_is_nan(aff)) { isl_aff_free(aff); continue; } isl_seq_cpy(sub->el, aff->v->el + 1, 1 + dim); isl_int_neg(sub->el[1 + dim + i], aff->v->el[0]); if (isl_tab_add_eq(tab, sub->el) < 0) goto error; isl_int_set_si(sub->el[1 + dim + i], 0); isl_aff_free(aff); } isl_vec_free(sub); return 0; error: isl_aff_free(aff); isl_vec_free(sub); return -1; } /* Add variables to info->tab and info->bmap corresponding to the elements * in "list" that are not set to NaN. The value of the added variable * in info->tab is fixed to the purely affine expression defined by the element. * "dim" is the offset in the variables of info->tab where we should * start considering the elements in "list". * When this function returns, the total number of variables in info->tab * is equal to "dim" plus the number of elements in "list". */ static int add_subs(struct isl_coalesce_info *info, __isl_keep isl_aff_list *list, int dim) { int extra_var; int n; if (!list) return -1; n = isl_aff_list_n_aff(list); extra_var = n - (info->tab->n_var - dim); if (isl_tab_extend_vars(info->tab, extra_var) < 0) return -1; if (isl_tab_extend_cons(info->tab, 2 * extra_var) < 0) return -1; if (add_sub_vars(info, list, dim, extra_var) < 0) return -1; return add_sub_equalities(info->tab, list, dim); } /* Coalesce basic map "j" into basic map "i" after adding the extra integer * divisions in "i" but not in "j" to basic map "j", with values * specified by "list". The total number of elements in "list" * is equal to the number of integer divisions in "i", while the number * of NaN elements in the list is equal to the number of integer divisions * in "j". * * If no coalescing can be performed, then we need to revert basic map "j" * to its original state. We do the same if basic map "i" gets dropped * during the coalescing, even though this should not happen in practice * since we have already checked for "j" being a subset of "i" * before we reach this stage. */ static enum isl_change coalesce_with_subs(int i, int j, struct isl_coalesce_info *info, __isl_keep isl_aff_list *list) { isl_basic_map *bmap_j; struct isl_tab_undo *snap; unsigned dim; enum isl_change change; bmap_j = isl_basic_map_copy(info[j].bmap); snap = isl_tab_snap(info[j].tab); dim = isl_basic_map_dim(bmap_j, isl_dim_all); dim -= isl_basic_map_dim(bmap_j, isl_dim_div); if (add_subs(&info[j], list, dim) < 0) goto error; change = coalesce_local_pair(i, j, info); if (change != isl_change_none && change != isl_change_drop_first) { isl_basic_map_free(bmap_j); } else { isl_basic_map_free(info[j].bmap); info[j].bmap = bmap_j; if (isl_tab_rollback(info[j].tab, snap) < 0) return isl_change_error; } return change; error: isl_basic_map_free(bmap_j); return isl_change_error; } /* Check if we can coalesce basic map "j" into basic map "i" after copying * those extra integer divisions in "i" that can be simplified away * using the extra equalities in "j". * All divs are assumed to be known and not contain any nested divs. * * We first check if there are any extra equalities in "j" that we * can exploit. Then we check if every integer division in "i" * either already appears in "j" or can be simplified using the * extra equalities to a purely affine expression. * If these tests succeed, then we try to coalesce the two basic maps * by introducing extra dimensions in "j" corresponding to * the extra integer divsisions "i" fixed to the corresponding * purely affine expression. */ static enum isl_change check_coalesce_into_eq(int i, int j, struct isl_coalesce_info *info) { unsigned n_div_i, n_div_j; isl_basic_map *hull_i, *hull_j; int equal, empty; isl_aff_list *list; enum isl_change change; n_div_i = isl_basic_map_dim(info[i].bmap, isl_dim_div); n_div_j = isl_basic_map_dim(info[j].bmap, isl_dim_div); if (n_div_i <= n_div_j) return isl_change_none; if (info[j].bmap->n_eq == 0) return isl_change_none; hull_i = isl_basic_map_copy(info[i].bmap); hull_i = isl_basic_map_plain_affine_hull(hull_i); hull_j = isl_basic_map_copy(info[j].bmap); hull_j = isl_basic_map_plain_affine_hull(hull_j); hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i)); equal = isl_basic_map_plain_is_equal(hull_i, hull_j); empty = isl_basic_map_plain_is_empty(hull_j); isl_basic_map_free(hull_i); if (equal < 0 || empty < 0) goto error; if (equal || empty) { isl_basic_map_free(hull_j); return isl_change_none; } list = set_up_substitutions(info[i].bmap, info[j].bmap, hull_j); if (!list) return isl_change_error; if (isl_aff_list_n_aff(list) < n_div_i) change = isl_change_none; else change = coalesce_with_subs(i, j, info, list); isl_aff_list_free(list); return change; error: isl_basic_map_free(hull_j); return isl_change_error; } /* Check if we can coalesce basic maps "i" and "j" after copying * those extra integer divisions in one of the basic maps that can * be simplified away using the extra equalities in the other basic map. * We require all divs to be known in both basic maps. * Furthermore, to simplify the comparison of div expressions, * we do not allow any nested integer divisions. */ static enum isl_change check_coalesce_eq(int i, int j, struct isl_coalesce_info *info) { int known, nested; enum isl_change change; known = isl_basic_map_divs_known(info[i].bmap); if (known < 0 || !known) return known < 0 ? isl_change_error : isl_change_none; known = isl_basic_map_divs_known(info[j].bmap); if (known < 0 || !known) return known < 0 ? isl_change_error : isl_change_none; nested = has_nested_div(info[i].bmap); if (nested < 0 || nested) return nested < 0 ? isl_change_error : isl_change_none; nested = has_nested_div(info[j].bmap); if (nested < 0 || nested) return nested < 0 ? isl_change_error : isl_change_none; change = check_coalesce_into_eq(i, j, info); if (change != isl_change_none) return change; change = check_coalesce_into_eq(j, i, info); if (change != isl_change_none) return invert_change(change); return isl_change_none; } /* Check if the union of the given pair of basic maps * can be represented by a single basic map. * If so, replace the pair by the single basic map and return * isl_change_drop_first, isl_change_drop_second or isl_change_fuse. * Otherwise, return isl_change_none. * * We first check if the two basic maps live in the same local space, * after aligning the divs that differ by only an integer constant. * If so, we do the complete check. Otherwise, we check if they have * the same number of integer divisions and can be coalesced, if one is * an obvious subset of the other or if the extra integer divisions * of one basic map can be simplified away using the extra equalities * of the other basic map. */ static enum isl_change coalesce_pair(int i, int j, struct isl_coalesce_info *info) { int same; enum isl_change change; if (harmonize_divs(&info[i], &info[j]) < 0) return isl_change_error; same = same_divs(info[i].bmap, info[j].bmap); if (same < 0) return isl_change_error; if (same) return coalesce_local_pair(i, j, info); if (info[i].bmap->n_div == info[j].bmap->n_div) { change = coalesce_local_pair(i, j, info); if (change != isl_change_none) return change; } change = check_coalesce_subset(i, j, info); if (change != isl_change_none) return change; return check_coalesce_eq(i, j, info); } /* Return the maximum of "a" and "b". */ static int isl_max(int a, int b) { return a > b ? a : b; } /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info" * with those in the range [start2, end2[, skipping basic maps * that have been removed (either before or within this function). * * For each basic map i in the first range, we check if it can be coalesced * with respect to any previously considered basic map j in the second range. * If i gets dropped (because it was a subset of some j), then * we can move on to the next basic map. * If j gets dropped, we need to continue checking against the other * previously considered basic maps. * If the two basic maps got fused, then we recheck the fused basic map * against the previously considered basic maps, starting at i + 1 * (even if start2 is greater than i + 1). */ static int coalesce_range(isl_ctx *ctx, struct isl_coalesce_info *info, int start1, int end1, int start2, int end2) { int i, j; for (i = end1 - 1; i >= start1; --i) { if (info[i].removed) continue; for (j = isl_max(i + 1, start2); j < end2; ++j) { enum isl_change changed; if (info[j].removed) continue; if (info[i].removed) isl_die(ctx, isl_error_internal, "basic map unexpectedly removed", return -1); changed = coalesce_pair(i, j, info); switch (changed) { case isl_change_error: return -1; case isl_change_none: case isl_change_drop_second: continue; case isl_change_drop_first: j = end2; break; case isl_change_fuse: j = i; break; } } } return 0; } /* Pairwise coalesce the basic maps described by the "n" elements of "info". * * We consider groups of basic maps that live in the same apparent * affine hull and we first coalesce within such a group before we * coalesce the elements in the group with elements of previously * considered groups. If a fuse happens during the second phase, * then we also reconsider the elements within the group. */ static int coalesce(isl_ctx *ctx, int n, struct isl_coalesce_info *info) { int start, end; for (end = n; end > 0; end = start) { start = end - 1; while (start >= 1 && info[start - 1].hull_hash == info[start].hull_hash) start--; if (coalesce_range(ctx, info, start, end, start, end) < 0) return -1; if (coalesce_range(ctx, info, start, end, end, n) < 0) return -1; } return 0; } /* Update the basic maps in "map" based on the information in "info". * In particular, remove the basic maps that have been marked removed and * update the others based on the information in the corresponding tableau. * Since we detected implicit equalities without calling * isl_basic_map_gauss, we need to do it now. * Also call isl_basic_map_simplify if we may have lost the definition * of one or more integer divisions. */ static __isl_give isl_map *update_basic_maps(__isl_take isl_map *map, int n, struct isl_coalesce_info *info) { int i; if (!map) return NULL; for (i = n - 1; i >= 0; --i) { if (info[i].removed) { isl_basic_map_free(map->p[i]); if (i != map->n - 1) map->p[i] = map->p[map->n - 1]; map->n--; continue; } info[i].bmap = isl_basic_map_update_from_tab(info[i].bmap, info[i].tab); info[i].bmap = isl_basic_map_gauss(info[i].bmap, NULL); if (info[i].simplify) info[i].bmap = isl_basic_map_simplify(info[i].bmap); info[i].bmap = isl_basic_map_finalize(info[i].bmap); if (!info[i].bmap) return isl_map_free(map); ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT); ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT); isl_basic_map_free(map->p[i]); map->p[i] = info[i].bmap; info[i].bmap = NULL; } return map; } /* For each pair of basic maps in the map, check if the union of the two * can be represented by a single basic map. * If so, replace the pair by the single basic map and start over. * * We factor out any (hidden) common factor from the constraint * coefficients to improve the detection of adjacent constraints. * * Since we are constructing the tableaus of the basic maps anyway, * we exploit them to detect implicit equalities and redundant constraints. * This also helps the coalescing as it can ignore the redundant constraints. * In order to avoid confusion, we make all implicit equalities explicit * in the basic maps. We don't call isl_basic_map_gauss, though, * as that may affect the number of constraints. * This means that we have to call isl_basic_map_gauss at the end * of the computation (in update_basic_maps) to ensure that * the basic maps are not left in an unexpected state. * For each basic map, we also compute the hash of the apparent affine hull * for use in coalesce. */ struct isl_map *isl_map_coalesce(struct isl_map *map) { int i; unsigned n; isl_ctx *ctx; struct isl_coalesce_info *info = NULL; map = isl_map_remove_empty_parts(map); if (!map) return NULL; if (map->n <= 1) return map; ctx = isl_map_get_ctx(map); map = isl_map_sort_divs(map); map = isl_map_cow(map); if (!map) return NULL; n = map->n; info = isl_calloc_array(map->ctx, struct isl_coalesce_info, n); if (!info) goto error; for (i = 0; i < map->n; ++i) { map->p[i] = isl_basic_map_reduce_coefficients(map->p[i]); if (!map->p[i]) goto error; info[i].bmap = isl_basic_map_copy(map->p[i]); info[i].tab = isl_tab_from_basic_map(info[i].bmap, 0); if (!info[i].tab) goto error; if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT)) if (isl_tab_detect_implicit_equalities(info[i].tab) < 0) goto error; info[i].bmap = isl_tab_make_equalities_explicit(info[i].tab, info[i].bmap); if (!info[i].bmap) goto error; if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT)) if (isl_tab_detect_redundant(info[i].tab) < 0) goto error; if (coalesce_info_set_hull_hash(&info[i]) < 0) goto error; } for (i = map->n - 1; i >= 0; --i) if (info[i].tab->empty) drop(&info[i]); if (coalesce(ctx, n, info) < 0) goto error; map = update_basic_maps(map, n, info); clear_coalesce_info(n, info); return map; error: clear_coalesce_info(n, info); isl_map_free(map); return NULL; } /* For each pair of basic sets in the set, check if the union of the two * can be represented by a single basic set. * If so, replace the pair by the single basic set and start over. */ struct isl_set *isl_set_coalesce(struct isl_set *set) { return (struct isl_set *)isl_map_coalesce((struct isl_map *)set); }