| /* |
| * Copyright 2008-2009 Katholieke Universiteit Leuven |
| * Copyright 2010 INRIA Saclay |
| * Copyright 2012-2013 Ecole Normale Superieure |
| * Copyright 2014 INRIA Rocquencourt |
| * Copyright 2016 INRIA Paris |
| * |
| * 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 |
| * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12, |
| * CS 42112, 75589 Paris Cedex 12, France |
| */ |
| |
| #include <isl_ctx_private.h> |
| #include "isl_map_private.h" |
| #include <isl_seq.h> |
| #include <isl/options.h> |
| #include "isl_tab.h" |
| #include <isl_mat_private.h> |
| #include <isl_local_space_private.h> |
| #include <isl_val_private.h> |
| #include <isl_vec_private.h> |
| #include <isl_aff_private.h> |
| #include <isl_equalities.h> |
| #include <isl_constraint_private.h> |
| |
| #include <set_to_map.c> |
| #include <set_from_map.c> |
| |
| #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 inequalities 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; |
| } |
| } |
| |
| 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; |
| } |
| |
| /* Return the first position of "status" in the list "con" of length "len". |
| * Return -1 if there is no such entry. |
| */ |
| static int find(int *con, unsigned len, int status) |
| { |
| int i; |
| |
| for (i = 0; i < len ; ++i) |
| if (con[i] == status) |
| return i; |
| return -1; |
| } |
| |
| 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; |
| }; |
| |
| /* Is there any (half of an) equality constraint in the description |
| * of the basic map represented by "info" that |
| * has position "status" with respect to the other basic map? |
| */ |
| static int any_eq(struct isl_coalesce_info *info, int status) |
| { |
| unsigned n_eq; |
| |
| n_eq = isl_basic_map_n_equality(info->bmap); |
| return any(info->eq, 2 * n_eq, status); |
| } |
| |
| /* Is there any inequality constraint in the description |
| * of the basic map represented by "info" that |
| * has position "status" with respect to the other basic map? |
| */ |
| static int any_ineq(struct isl_coalesce_info *info, int status) |
| { |
| unsigned n_ineq; |
| |
| n_ineq = isl_basic_map_n_inequality(info->bmap); |
| return any(info->ineq, n_ineq, status); |
| } |
| |
| /* Return the position of the first half on an equality constraint |
| * in the description of the basic map represented by "info" that |
| * has position "status" with respect to the other basic map. |
| * The returned value is twice the position of the equality constraint |
| * plus zero for the negative half and plus one for the positive half. |
| * Return -1 if there is no such entry. |
| */ |
| static int find_eq(struct isl_coalesce_info *info, int status) |
| { |
| unsigned n_eq; |
| |
| n_eq = isl_basic_map_n_equality(info->bmap); |
| return find(info->eq, 2 * n_eq, status); |
| } |
| |
| /* Return the position of the first inequality constraint in the description |
| * of the basic map represented by "info" that |
| * has position "status" with respect to the other basic map. |
| * Return -1 if there is no such entry. |
| */ |
| static int find_ineq(struct isl_coalesce_info *info, int status) |
| { |
| unsigned n_ineq; |
| |
| n_ineq = isl_basic_map_n_inequality(info->bmap); |
| return find(info->ineq, n_ineq, status); |
| } |
| |
| /* Return the number of (halves of) equality constraints in the description |
| * of the basic map represented by "info" that |
| * have position "status" with respect to the other basic map. |
| */ |
| static int count_eq(struct isl_coalesce_info *info, int status) |
| { |
| unsigned n_eq; |
| |
| n_eq = isl_basic_map_n_equality(info->bmap); |
| return count(info->eq, 2 * n_eq, status); |
| } |
| |
| /* Return the number of inequality constraints in the description |
| * of the basic map represented by "info" that |
| * have position "status" with respect to the other basic map. |
| */ |
| static int count_ineq(struct isl_coalesce_info *info, int status) |
| { |
| unsigned n_ineq; |
| |
| n_ineq = isl_basic_map_n_inequality(info->bmap); |
| return count(info->ineq, n_ineq, status); |
| } |
| |
| /* Are all non-redundant constraints of the basic map represented by "info" |
| * either valid or cut constraints with respect to the other basic map? |
| */ |
| static int all_valid_or_cut(struct isl_coalesce_info *info) |
| { |
| int i; |
| |
| for (i = 0; i < 2 * info->bmap->n_eq; ++i) { |
| if (info->eq[i] == STATUS_REDUNDANT) |
| continue; |
| if (info->eq[i] == STATUS_VALID) |
| continue; |
| if (info->eq[i] == STATUS_CUT) |
| continue; |
| return 0; |
| } |
| |
| for (i = 0; i < info->bmap->n_ineq; ++i) { |
| if (info->ineq[i] == STATUS_REDUNDANT) |
| continue; |
| if (info->ineq[i] == STATUS_VALID) |
| continue; |
| if (info->ineq[i] == STATUS_CUT) |
| continue; |
| return 0; |
| } |
| |
| return 1; |
| } |
| |
| /* 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 simplify the basic map |
| * 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; |
| int simplify = 0; |
| |
| 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; |
| 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); |
| |
| 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); |
| 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); |
| if (simplify || info[j].simplify) { |
| fused = isl_basic_map_simplify(fused); |
| info[i].simplify = 0; |
| } |
| fused = isl_basic_map_finalize(fused); |
| |
| 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; |
| } |
| |
| 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 isl_bool 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 isl_bool_error; |
| if (stat != STATUS_VALID) |
| return isl_bool_false; |
| stat = status_in(bmap->eq[k], tab); |
| if (stat < 0) |
| return isl_bool_error; |
| if (stat != STATUS_VALID) |
| return isl_bool_false; |
| } |
| |
| 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 isl_bool_error; |
| if (stat != STATUS_VALID) |
| return isl_bool_false; |
| } |
| return isl_bool_true; |
| } |
| |
| /* 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". |
| * To improve the chances of the subset relation being detected, |
| * any variable that only attains a single integer value |
| * in the tableau of "i" is first fixed to that value. |
| * If the result is a subset, 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); |
| isl_stat r; |
| isl_bool super; |
| |
| if (isl_tab_extend_cons(info[i].tab, 1 + info[j].bmap->n_ineq) < 0) |
| return isl_change_error; |
| |
| k = find_ineq(&info[i], STATUS_ADJ_INEQ); |
| if (k < 0) |
| 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; |
| } |
| if (isl_tab_detect_constants(info[i].tab) < 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_ineq(&info[i], STATUS_ADJ_INEQ); |
| count_j = count_ineq(&info[j], STATUS_ADJ_INEQ); |
| |
| if (count_i != 1 && count_j != 1) |
| return isl_change_none; |
| |
| cut_i = any_eq(&info[i], STATUS_CUT) || any_ineq(&info[i], STATUS_CUT); |
| cut_j = any_eq(&info[j], STATUS_CUT) || any_ineq(&info[j], 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; |
| } |
| |
| /* Given an affine transformation matrix "T", does row "row" represent |
| * anything other than a unit vector (possibly shifted by a constant) |
| * that is not involved in any of the other rows? |
| * |
| * That is, if a constraint involves the variable corresponding to |
| * the row, then could its preimage by "T" have any coefficients |
| * that are different from those in the original constraint? |
| */ |
| static int not_unique_unit_row(__isl_keep isl_mat *T, int row) |
| { |
| int i, j; |
| int len = T->n_col - 1; |
| |
| i = isl_seq_first_non_zero(T->row[row] + 1, len); |
| if (i < 0) |
| return 1; |
| if (!isl_int_is_one(T->row[row][1 + i]) && |
| !isl_int_is_negone(T->row[row][1 + i])) |
| return 1; |
| |
| j = isl_seq_first_non_zero(T->row[row] + 1 + i + 1, len - (i + 1)); |
| if (j >= 0) |
| return 1; |
| |
| for (j = 1; j < T->n_row; ++j) { |
| if (j == row) |
| continue; |
| if (!isl_int_is_zero(T->row[j][1 + i])) |
| return 1; |
| } |
| |
| return 0; |
| } |
| |
| /* Does inequality constraint "ineq" of "bmap" involve any of |
| * the variables marked in "affected"? |
| * "total" is the total number of variables, i.e., the number |
| * of entries in "affected". |
| */ |
| static isl_bool is_affected(__isl_keep isl_basic_map *bmap, int ineq, |
| int *affected, int total) |
| { |
| int i; |
| |
| for (i = 0; i < total; ++i) { |
| if (!affected[i]) |
| continue; |
| if (!isl_int_is_zero(bmap->ineq[ineq][1 + i])) |
| return isl_bool_true; |
| } |
| |
| return isl_bool_false; |
| } |
| |
| /* Given the compressed version of inequality constraint "ineq" |
| * of info->bmap in "v", check if the constraint can be tightened, |
| * where the compression is based on an equality constraint valid |
| * for info->tab. |
| * If so, add the tightened version of the inequality constraint |
| * to info->tab. "v" may be modified by this function. |
| * |
| * That is, if the compressed constraint is of the form |
| * |
| * m f() + c >= 0 |
| * |
| * with 0 < c < m, then it is equivalent to |
| * |
| * f() >= 0 |
| * |
| * This means that c can also be subtracted from the original, |
| * uncompressed constraint without affecting the integer points |
| * in info->tab. Add this tightened constraint as an extra row |
| * to info->tab to make this information explicitly available. |
| */ |
| static __isl_give isl_vec *try_tightening(struct isl_coalesce_info *info, |
| int ineq, __isl_take isl_vec *v) |
| { |
| isl_ctx *ctx; |
| isl_stat r; |
| |
| if (!v) |
| return NULL; |
| |
| ctx = isl_vec_get_ctx(v); |
| isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd); |
| if (isl_int_is_zero(ctx->normalize_gcd) || |
| isl_int_is_one(ctx->normalize_gcd)) { |
| return v; |
| } |
| |
| v = isl_vec_cow(v); |
| if (!v) |
| return NULL; |
| |
| isl_int_fdiv_r(v->el[0], v->el[0], ctx->normalize_gcd); |
| if (isl_int_is_zero(v->el[0])) |
| return v; |
| |
| if (isl_tab_extend_cons(info->tab, 1) < 0) |
| return isl_vec_free(v); |
| |
| isl_int_sub(info->bmap->ineq[ineq][0], |
| info->bmap->ineq[ineq][0], v->el[0]); |
| r = isl_tab_add_ineq(info->tab, info->bmap->ineq[ineq]); |
| isl_int_add(info->bmap->ineq[ineq][0], |
| info->bmap->ineq[ineq][0], v->el[0]); |
| |
| if (r < 0) |
| return isl_vec_free(v); |
| |
| return v; |
| } |
| |
| /* Tighten the (non-redundant) constraints on the facet represented |
| * by info->tab. |
| * In particular, on input, info->tab represents the result |
| * of relaxing the "n" inequality constraints of info->bmap in "relaxed" |
| * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then |
| * replacing the one at index "l" by the corresponding equality, |
| * i.e., f_k + 1 = 0, with k = relaxed[l]. |
| * |
| * Compute a variable compression from the equality constraint f_k + 1 = 0 |
| * and use it to tighten the other constraints of info->bmap |
| * (that is, all constraints that have not been relaxed), |
| * updating info->tab (and leaving info->bmap untouched). |
| * The compression handles essentially two cases, one where a variable |
| * is assigned a fixed value and can therefore be eliminated, and one |
| * where one variable is a shifted multiple of some other variable and |
| * can therefore be replaced by that multiple. |
| * Gaussian elimination would also work for the first case, but for |
| * the second case, the effectiveness would depend on the order |
| * of the variables. |
| * After compression, some of the constraints may have coefficients |
| * with a common divisor. If this divisor does not divide the constant |
| * term, then the constraint can be tightened. |
| * The tightening is performed on the tableau info->tab by introducing |
| * extra (temporary) constraints. |
| * |
| * Only constraints that are possibly affected by the compression are |
| * considered. In particular, if the constraint only involves variables |
| * that are directly mapped to a distinct set of other variables, then |
| * no common divisor can be introduced and no tightening can occur. |
| * |
| * It is important to only consider the non-redundant constraints |
| * since the facet constraint has been relaxed prior to the call |
| * to this function, meaning that the constraints that were redundant |
| * prior to the relaxation may no longer be redundant. |
| * These constraints will be ignored in the fused result, so |
| * the fusion detection should not exploit them. |
| */ |
| static isl_stat tighten_on_relaxed_facet(struct isl_coalesce_info *info, |
| int n, int *relaxed, int l) |
| { |
| unsigned total; |
| isl_ctx *ctx; |
| isl_vec *v = NULL; |
| isl_mat *T; |
| int i; |
| int k; |
| int *affected; |
| |
| k = relaxed[l]; |
| ctx = isl_basic_map_get_ctx(info->bmap); |
| total = isl_basic_map_total_dim(info->bmap); |
| isl_int_add_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1); |
| T = isl_mat_sub_alloc6(ctx, info->bmap->ineq, k, 1, 0, 1 + total); |
| T = isl_mat_variable_compression(T, NULL); |
| isl_int_sub_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1); |
| if (!T) |
| return isl_stat_error; |
| if (T->n_col == 0) { |
| isl_mat_free(T); |
| return isl_stat_ok; |
| } |
| |
| affected = isl_alloc_array(ctx, int, total); |
| if (!affected) |
| goto error; |
| |
| for (i = 0; i < total; ++i) |
| affected[i] = not_unique_unit_row(T, 1 + i); |
| |
| for (i = 0; i < info->bmap->n_ineq; ++i) { |
| isl_bool handle; |
| if (any(relaxed, n, i)) |
| continue; |
| if (info->ineq[i] == STATUS_REDUNDANT) |
| continue; |
| handle = is_affected(info->bmap, i, affected, total); |
| if (handle < 0) |
| goto error; |
| if (!handle) |
| continue; |
| v = isl_vec_alloc(ctx, 1 + total); |
| if (!v) |
| goto error; |
| isl_seq_cpy(v->el, info->bmap->ineq[i], 1 + total); |
| v = isl_vec_mat_product(v, isl_mat_copy(T)); |
| v = try_tightening(info, i, v); |
| isl_vec_free(v); |
| if (!v) |
| goto error; |
| } |
| |
| isl_mat_free(T); |
| free(affected); |
| return isl_stat_ok; |
| error: |
| isl_mat_free(T); |
| free(affected); |
| return isl_stat_error; |
| } |
| |
| /* Replace the basic maps "i" and "j" by an extension of "i" |
| * along the "n" inequality constraints in "relax" by one. |
| * The tableau info[i].tab has already been extended. |
| * Extend info[i].bmap accordingly by relaxing all constraints in "relax" |
| * by one. |
| * 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 the extension in the position that is the smallest of i and j. |
| */ |
| static enum isl_change extend(int i, int j, int n, int *relax, |
| struct isl_coalesce_info *info) |
| { |
| int l; |
| unsigned total; |
| |
| 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; |
| } |
| for (l = 0; l < n; ++l) |
| isl_int_add_ui(info[i].bmap->ineq[relax[l]][0], |
| info[i].bmap->ineq[relax[l]][0], 1); |
| ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_FINAL); |
| drop(&info[j]); |
| if (j < i) |
| exchange(&info[i], &info[j]); |
| return isl_change_fuse; |
| } |
| |
| /* Basic map "i" has "n" inequality constraints (collected in "relax") |
| * that are such that they include basic map "j" if they are relaxed |
| * by one. All the other inequalities are valid for "j". |
| * Check if basic map "j" forms an extension of basic map "i". |
| * |
| * In particular, relax the constraints in "relax", compute the corresponding |
| * facets one by one and check whether each of these is included |
| * in the other basic map. |
| * Before testing for inclusion, the constraints on each facet |
| * are tightened to increase the chance of an inclusion being detected. |
| * (Adding the valid constraints of "j" to the tableau of "i", as is done |
| * in is_adj_ineq_extension, may further increase those chances, but this |
| * is not currently done.) |
| * If each facet is included, we know that relaxing the constraints extends |
| * the basic map with exactly the other basic map (we already know that this |
| * other basic map is included in the extension, because all other |
| * inequality constraints are valid of "j") and we can replace the |
| * two basic maps by this extension. |
| * |
| * If any of the relaxed constraints turn out to be redundant, then bail out. |
| * isl_tab_select_facet refuses to handle such constraints. It may be |
| * possible to handle them anyway by making a distinction between |
| * redundant constraints with a corresponding facet that still intersects |
| * the set (allowing isl_tab_select_facet to handle them) and |
| * those where the facet does not intersect the set (which can be ignored |
| * because the empty facet is trivially included in the other disjunct). |
| * However, relaxed constraints that turn out to be redundant should |
| * be fairly rare and no such instance has been reported where |
| * coalescing would be successful. |
| * ____ _____ |
| * / || / | |
| * / || / | |
| * \ || => \ | |
| * \ || \ | |
| * \___|| \____| |
| * |
| * |
| * \ |\ |
| * |\\ | \ |
| * | \\ | \ |
| * | | => | / |
| * | / | / |
| * |/ |/ |
| */ |
| static enum isl_change is_relaxed_extension(int i, int j, int n, int *relax, |
| struct isl_coalesce_info *info) |
| { |
| int l; |
| isl_bool super; |
| struct isl_tab_undo *snap, *snap2; |
| unsigned n_eq = info[i].bmap->n_eq; |
| |
| for (l = 0; l < n; ++l) |
| if (isl_tab_is_equality(info[i].tab, n_eq + relax[l])) |
| return isl_change_none; |
| |
| snap = isl_tab_snap(info[i].tab); |
| for (l = 0; l < n; ++l) |
| if (isl_tab_relax(info[i].tab, n_eq + relax[l]) < 0) |
| return isl_change_error; |
| for (l = 0; l < n; ++l) { |
| if (!isl_tab_is_redundant(info[i].tab, n_eq + relax[l])) |
| continue; |
| if (isl_tab_rollback(info[i].tab, snap) < 0) |
| return isl_change_error; |
| return isl_change_none; |
| } |
| snap2 = isl_tab_snap(info[i].tab); |
| for (l = 0; l < n; ++l) { |
| if (isl_tab_rollback(info[i].tab, snap2) < 0) |
| return isl_change_error; |
| if (isl_tab_select_facet(info[i].tab, n_eq + relax[l]) < 0) |
| return isl_change_error; |
| if (tighten_on_relaxed_facet(&info[i], n, relax, l) < 0) |
| return isl_change_error; |
| super = contains(&info[j], info[i].tab); |
| if (super < 0) |
| return isl_change_error; |
| if (super) |
| continue; |
| if (isl_tab_rollback(info[i].tab, snap) < 0) |
| return isl_change_error; |
| return isl_change_none; |
| } |
| |
| if (isl_tab_rollback(info[i].tab, snap2) < 0) |
| return isl_change_error; |
| return extend(i, j, n, relax, info); |
| } |
| |
| /* 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 isl_stat 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); |
| |
| return isl_stat_ok; |
| } |
| |
| /* 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 isl_stat 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 isl_stat_error; |
| ctx = isl_mat_get_ctx(mat); |
| wraps->bound = isl_options_get_coalesce_bounded_wrapping(ctx); |
| if (!wraps->bound) |
| return isl_stat_ok; |
| isl_int_init(wraps->max); |
| isl_int_set_si(wraps->max, 0); |
| if (wraps_update_max(wraps, &info[i]) < 0) |
| return isl_stat_error; |
| if (wraps_update_max(wraps, &info[j]) < 0) |
| return isl_stat_error; |
| |
| return isl_stat_ok; |
| } |
| |
| /* 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 isl_stat 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 isl_stat_error; |
| 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 isl_stat_error; |
| if (!added) |
| goto unbounded; |
| ++w; |
| } |
| } |
| |
| wraps->mat->n_row = w; |
| return isl_stat_ok; |
| unbounded: |
| wraps->mat->n_row = 0; |
| return isl_stat_ok; |
| } |
| |
| /* 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 isl_stat 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 isl_stat_error; |
| if (isl_tab_detect_redundant(info->tab) < 0) |
| return isl_stat_error; |
| |
| isl_seq_neg(bound, info->bmap->ineq[k], 1 + total); |
| |
| n = wraps->mat->n_row; |
| if (add_wraps(wraps, info, bound, set) < 0) |
| return isl_stat_error; |
| |
| if (isl_tab_rollback(info->tab, snap) < 0) |
| return isl_stat_error; |
| if (check_wraps(wraps->mat, n, info->tab) < 0) |
| return isl_stat_error; |
| |
| return isl_stat_ok; |
| } |
| |
| /* 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); |
| if (wraps_init(&wraps, mat, info, i, j) < 0) |
| goto error; |
| bound = isl_vec_alloc(ctx, 1 + total); |
| if (!set_i || !set_j || !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_normalize(ctx, bound->el, 1 + total); |
| |
| 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 cut constraint t(x) >= 0 of basic map i, stored in row "w" |
| * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and |
| * add wrapping constraints to wrap.mat for all constraints |
| * of basic map j that bound the part of basic map j that sticks out |
| * of the cut constraint. |
| * "set_i" is the underlying set of basic map i. |
| * If any wrapping fails, then wraps->mat.n_row is reset to zero. |
| * |
| * 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. |
| */ |
| static isl_stat wrap_in_facet(struct isl_wraps *wraps, int w, |
| struct isl_coalesce_info *info_j, __isl_keep isl_set *set_i, |
| struct isl_tab_undo *snap) |
| { |
| 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) |
| return isl_stat_error; |
| if (isl_tab_detect_redundant(info_j->tab) < 0) |
| return isl_stat_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) |
| return isl_stat_error; |
| |
| if (isl_tab_rollback(info_j->tab, snap) < 0) |
| return isl_stat_error; |
| |
| return isl_stat_ok; |
| } |
| |
| /* 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. |
| * "set_i" is the underlying set of basic map i. |
| * "wraps" has been initialized to be of the right size. |
| * |
| * 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. |
| * |
| * 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 try_wrap_in_facets(int i, int j, |
| struct isl_coalesce_info *info, struct isl_wraps *wraps, |
| __isl_keep isl_set *set_i) |
| { |
| int k, l, w; |
| unsigned total; |
| struct isl_tab_undo *snap; |
| |
| total = isl_basic_map_total_dim(info[i].bmap); |
| |
| snap = isl_tab_snap(info[j].tab); |
| |
| wraps->mat->n_row = 0; |
| |
| for (k = 0; k < info[i].bmap->n_eq; ++k) { |
| for (l = 0; l < 2; ++l) { |
| if (info[i].eq[2 * k + l] != STATUS_CUT) |
| continue; |
| w = wraps->mat->n_row++; |
| if (l == 0) |
| isl_seq_neg(wraps->mat->row[w], |
| info[i].bmap->eq[k], 1 + total); |
| else |
| isl_seq_cpy(wraps->mat->row[w], |
| info[i].bmap->eq[k], 1 + total); |
| if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0) |
| return isl_change_error; |
| |
| if (!wraps->mat->n_row) |
| return isl_change_none; |
| } |
| } |
| |
| for (k = 0; k < info[i].bmap->n_ineq; ++k) { |
| if (info[i].ineq[k] != STATUS_CUT) |
| continue; |
| w = wraps->mat->n_row++; |
| isl_seq_cpy(wraps->mat->row[w], |
| info[i].bmap->ineq[k], 1 + total); |
| if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0) |
| return isl_change_error; |
| |
| if (!wraps->mat->n_row) |
| return isl_change_none; |
| } |
| |
| return fuse(i, j, info, wraps->mat, 0, 1); |
| } |
| |
| /* 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. |
| * |
| * The core computation is performed by try_wrap_in_facets. |
| * This function simply extracts an underlying set representation |
| * of basic map i and initializes the data structure for keeping |
| * track of wrapping constraints. |
| */ |
| static enum isl_change wrap_in_facets(int i, int j, 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; |
| |
| if (isl_tab_extend_cons(info[j].tab, 1) < 0) |
| return isl_change_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); |
| if (wraps_init(&wraps, mat, info, i, j) < 0) |
| goto error; |
| if (!set_i) |
| goto error; |
| |
| change = try_wrap_in_facets(i, j, info, &wraps, set_i); |
| |
| wraps_free(&wraps); |
| isl_set_free(set_i); |
| |
| return change; |
| error: |
| wraps_free(&wraps); |
| isl_set_free(set_i); |
| return isl_change_error; |
| } |
| |
| /* Return the effect of inequality "ineq" on the tableau "tab", |
| * after relaxing the constant term of "ineq" by one. |
| */ |
| static enum isl_ineq_type type_of_relaxed(struct isl_tab *tab, isl_int *ineq) |
| { |
| enum isl_ineq_type type; |
| |
| isl_int_add_ui(ineq[0], ineq[0], 1); |
| type = isl_tab_ineq_type(tab, ineq); |
| isl_int_sub_ui(ineq[0], ineq[0], 1); |
| |
| return type; |
| } |
| |
| /* Given two basic sets i and j, |
| * check if relaxing all the cut constraints 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) |
| { |
| int k, l; |
| int n; |
| unsigned total; |
| |
| 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_eq(&info[i], STATUS_CUT) + count_ineq(&info[i], STATUS_CUT); |
| if (n == 0) |
| return isl_change_none; |
| |
| total = isl_basic_map_total_dim(info[i].bmap); |
| for (k = 0; k < info[i].bmap->n_eq; ++k) { |
| for (l = 0; l < 2; ++l) { |
| enum isl_ineq_type type; |
| |
| if (info[i].eq[2 * k + l] != STATUS_CUT) |
| continue; |
| |
| if (l == 0) |
| isl_seq_neg(info[i].bmap->eq[k], |
| info[i].bmap->eq[k], 1 + total); |
| type = type_of_relaxed(info[j].tab, |
| info[i].bmap->eq[k]); |
| if (l == 0) |
| isl_seq_neg(info[i].bmap->eq[k], |
| info[i].bmap->eq[k], 1 + total); |
| if (type == isl_ineq_error) |
| return isl_change_error; |
| if (type != isl_ineq_redundant) |
| return isl_change_none; |
| } |
| } |
| |
| for (k = 0; k < info[i].bmap->n_ineq; ++k) { |
| enum isl_ineq_type type; |
| |
| if (info[i].ineq[k] != STATUS_CUT) |
| continue; |
| |
| type = type_of_relaxed(info[j].tab, info[i].bmap->ineq[k]); |
| if (type == isl_ineq_error) |
| return isl_change_error; |
| if (type != isl_ineq_redundant) |
| return isl_change_none; |
| } |
| |
| return wrap_in_facets(i, j, n, info); |
| } |
| |
| /* Check if either i or j has only cut constraints 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; |
| |
| change = can_wrap_in_set(i, j, info); |
| if (change != isl_change_none) |
| return change; |
| |
| change = can_wrap_in_set(j, i, info); |
| return change; |
| } |
| |
| /* Check if all inequality constraints of "i" that cut "j" cease |
| * to be cut constraints if they are relaxed by one. |
| * If so, collect the cut constraints in "list". |
| * The caller is responsible for allocating "list". |
| */ |
| static isl_bool all_cut_by_one(int i, int j, struct isl_coalesce_info *info, |
| int *list) |
| { |
| int l, n; |
| |
| n = 0; |
| for (l = 0; l < info[i].bmap->n_ineq; ++l) { |
| enum isl_ineq_type type; |
| |
| if (info[i].ineq[l] != STATUS_CUT) |
| continue; |
| type = type_of_relaxed(info[j].tab, info[i].bmap->ineq[l]); |
| if (type == isl_ineq_error) |
| return isl_bool_error; |
| if (type != isl_ineq_redundant) |
| return isl_bool_false; |
| list[n++] = l; |
| } |
| |
| return isl_bool_true; |
| } |
| |
| /* Given two basic maps such that "j" has at least one equality constraint |
| * that is adjacent to an inequality constraint of "i" and such that "i" has |
| * exactly one inequality constraint that is adjacent to an equality |
| * constraint of "j", check whether "i" can be extended to include "j" or |
| * whether "j" can be wrapped into "i". |
| * All remaining constraints of "i" and "j" are assumed to be valid |
| * or cut constraints of the other basic map. |
| * However, none of the equality constraints of "i" are cut constraints. |
| * |
| * If "i" has any "cut" inequality constraints, then check if relaxing |
| * each of them by one is sufficient for them to become valid. |
| * If so, check if the inequality constraint adjacent to an equality |
| * constraint of "j" along with all these cut constraints |
| * can be relaxed by one to contain exactly "j". |
| * Otherwise, or if this fails, check if "j" can be wrapped into "i". |
| */ |
| static enum isl_change check_single_adj_eq(int i, int j, |
| struct isl_coalesce_info *info) |
| { |
| enum isl_change change = isl_change_none; |
| int k; |
| int n_cut; |
| int *relax; |
| isl_ctx *ctx; |
| isl_bool try_relax; |
| |
| n_cut = count_ineq(&info[i], STATUS_CUT); |
| |
| k = find_ineq(&info[i], STATUS_ADJ_EQ); |
| |
| if (n_cut > 0) { |
| ctx = isl_basic_map_get_ctx(info[i].bmap); |
| relax = isl_calloc_array(ctx, int, 1 + n_cut); |
| if (!relax) |
| return isl_change_error; |
| relax[0] = k; |
| try_relax = all_cut_by_one(i, j, info, relax + 1); |
| if (try_relax < 0) |
| change = isl_change_error; |
| } else { |
| try_relax = isl_bool_true; |
| relax = &k; |
| } |
| if (try_relax && change == isl_change_none) |
| change = is_relaxed_extension(i, j, 1 + n_cut, relax, info); |
| if (n_cut > 0) |
| free(relax); |
| if (change != isl_change_none) |
| return change; |
| |
| change = can_wrap_in_facet(i, j, k, info, n_cut > 0); |
| |
| return change; |
| } |
| |
| /* At least one of the basic maps has an equality that is adjacent |
| * to an 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. |
| * If the other basic map does not have such an inequality, then |
| * check if all its constraints are either valid or cut constraints |
| * and, if so, try wrapping in the first map into the second. |
| * Otherwise, try to extend one basic map with the other or |
| * wrap one basic map in the other. |
| */ |
| static enum isl_change check_adj_eq(int i, int j, |
| struct isl_coalesce_info *info) |
| { |
| if (any_eq(&info[i], STATUS_ADJ_INEQ) && |
| any_eq(&info[j], STATUS_ADJ_INEQ)) |
| /* ADJ EQ TOO MANY */ |
| return isl_change_none; |
| |
| if (any_eq(&info[i], STATUS_ADJ_INEQ)) |
| return check_adj_eq(j, i, info); |
| |
| /* j has an equality adjacent to an inequality in i */ |
| |
| if (count_ineq(&info[i], STATUS_ADJ_EQ) != 1) { |
| if (all_valid_or_cut(&info[i])) |
| return can_wrap_in_set(i, j, info); |
| return isl_change_none; |
| } |
| if (any_eq(&info[i], STATUS_CUT)) |
| return isl_change_none; |
| if (any_ineq(&info[j], STATUS_ADJ_EQ) || |
| any_ineq(&info[i], STATUS_ADJ_INEQ) || |
| any_ineq(&info[j], STATUS_ADJ_INEQ)) |
| /* ADJ EQ TOO MANY */ |
| return isl_change_none; |
| |
| return check_single_adj_eq(i, j, info); |
| } |
| |
| /* Disjunct "j" lies on a hyperplane that is adjacent to disjunct "i". |
| * In particular, disjunct "i" has an inequality constraint that is adjacent |
| * to a (combination of) equality constraint(s) of disjunct "j", |
| * but disjunct "j" has no explicit equality constraint adjacent |
| * to an inequality constraint of disjunct "i". |
| * |
| * Disjunct "i" is already known not to have any equality constraints |
| * that are adjacent to an equality or inequality constraint. |
| * Check that, other than the inequality constraint mentioned above, |
| * all other constraints of disjunct "i" are valid for disjunct "j". |
| * If so, try and wrap in disjunct "j". |
| */ |
| static enum isl_change check_ineq_adj_eq(int i, int j, |
| struct isl_coalesce_info *info) |
| { |
| int k; |
| |
| if (any_eq(&info[i], STATUS_CUT)) |
| return isl_change_none; |
| if (any_ineq(&info[i], STATUS_CUT)) |
| return isl_change_none; |
| if (any_ineq(&info[i], STATUS_ADJ_INEQ)) |
| return isl_change_none; |
| if (count_ineq(&info[i], STATUS_ADJ_EQ) != 1) |
| return isl_change_none; |
| |
| k = find_ineq(&info[i], STATUS_ADJ_EQ); |
| |
| return can_wrap_in_facet(i, j, k, info, 0); |
| } |
| |
| /* 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_eq(&info[i], STATUS_ADJ_EQ) != 1) |
| detect_equalities = 1; |
| |
| k = find_eq(&info[i], STATUS_ADJ_EQ); |
| |
| 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); |
| if (wraps_init(&wraps, mat, info, i, j) < 0) |
| goto error; |
| bound = isl_vec_alloc(ctx, 1 + total); |
| if (!set_i || !set_j || !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; |
| } |
| |
| /* Initialize the "eq" and "ineq" fields of "info". |
| */ |
| static void init_status(struct isl_coalesce_info *info) |
| { |
| info->eq = info->ineq = NULL; |
| } |
| |
| /* Set info->eq to the positions of the equalities of info->bmap |
| * with respect to the basic map represented by "tab". |
| * If info->eq has already been computed, then do not compute it again. |
| */ |
| static void set_eq_status_in(struct isl_coalesce_info *info, |
| struct isl_tab *tab) |
| { |
| if (info->eq) |
| return; |
| info->eq = eq_status_in(info->bmap, tab); |
| } |
| |
| /* Set info->ineq to the positions of the inequalities of info->bmap |
| * with respect to the basic map represented by "tab". |
| * If info->ineq has already been computed, then do not compute it again. |
| */ |
| static void set_ineq_status_in(struct isl_coalesce_info *info, |
| struct isl_tab *tab) |
| { |
| if (info->ineq) |
| return; |
| info->ineq = ineq_status_in(info->bmap, info->tab, tab); |
| } |
| |
| /* Free the memory allocated by the "eq" and "ineq" fields of "info". |
| * This function assumes that init_status has been called on "info" first, |
| * after which the "eq" and "ineq" fields may or may not have been |
| * assigned a newly allocated array. |
| */ |
| static void clear_status(struct isl_coalesce_info *info) |
| { |
| free(info->eq); |
| free(info->ineq); |
| } |
| |
| /* Are all inequality constraints of the basic map represented by "info" |
| * valid for the other basic map, except for a single constraint |
| * that is adjacent to an inequality constraint of the other basic map? |
| */ |
| static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info *info) |
| { |
| int i; |
| int k = -1; |
| |
| for (i = 0; i < info->bmap->n_ineq; ++i) { |
| if (info->ineq[i] == STATUS_REDUNDANT) |
| continue; |
| if (info->ineq[i] == STATUS_VALID) |
| continue; |
| if (info->ineq[i] != STATUS_ADJ_INEQ) |
| return 0; |
| if (k != -1) |
| return 0; |
| k = i; |
| } |
| |
| return k != -1; |
| } |
| |
| /* Basic map "i" has one or more equality constraints that separate it |
| * from basic map "j". Check if it happens to be an extension |
| * of basic map "j". |
| * In particular, check that all constraints of "j" are valid for "i", |
| * except for one inequality constraint that is adjacent |
| * to an inequality constraints of "i". |
| * If so, check for "i" being an extension of "j" by calling |
| * is_adj_ineq_extension. |
| * |
| * Clean up the memory allocated for keeping track of the status |
| * of the constraints before returning. |
| */ |
| static enum isl_change separating_equality(int i, int j, |
| struct isl_coalesce_info *info) |
| { |
| enum isl_change change = isl_change_none; |
| |
| if (all(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_VALID) && |
| all_ineq_valid_or_single_adj_ineq(&info[j])) |
| change = is_adj_ineq_extension(j, i, info); |
| |
| clear_status(&info[i]); |
| clear_status(&info[j]); |
| 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. |
| * The "eq" and "ineq" fields of info[i] and info[j] are assumed |
| * to have been initialized by the caller, either to NULL or |
| * to valid information. |
| * |
| * 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 inequality adjacent to 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_reuse(int i, int j, |
| struct isl_coalesce_info *info) |
| { |
| enum isl_change change = isl_change_none; |
| |
| set_ineq_status_in(&info[i], info[j].tab); |
| if (info[i].bmap->n_ineq && !info[i].ineq) |
| goto error; |
| if (any_ineq(&info[i], STATUS_ERROR)) |
| goto error; |
| if (any_ineq(&info[i], STATUS_SEPARATE)) |
| goto done; |
| |
| set_ineq_status_in(&info[j], info[i].tab); |
| if (info[j].bmap->n_ineq && !info[j].ineq) |
| goto error; |
| if (any_ineq(&info[j], STATUS_ERROR)) |
| goto error; |
| if (any_ineq(&info[j], STATUS_SEPARATE)) |
| goto done; |
| |
| set_eq_status_in(&info[i], info[j].tab); |
| if (info[i].bmap->n_eq && !info[i].eq) |
| goto error; |
| if (any_eq(&info[i], STATUS_ERROR)) |
| goto error; |
| |
| set_eq_status_in(&info[j], info[i].tab); |
| if (info[j].bmap->n_eq && !info[j].eq) |
| goto error; |
| if (any_eq(&info[j], STATUS_ERROR)) |
| goto error; |
| |
| if (any_eq(&info[i], STATUS_SEPARATE)) |
| return separating_equality(i, j, info); |
| if (any_eq(&info[j], STATUS_SEPARATE)) |
| return separating_equality(j, i, info); |
| |
| 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_eq(&info[i], STATUS_ADJ_EQ)) { |
| change = check_eq_adj_eq(i, j, info); |
| } else if (any_eq(&info[j], STATUS_ADJ_EQ)) { |
| change = check_eq_adj_eq(j, i, info); |
| } else if (any_eq(&info[i], STATUS_ADJ_INEQ) || |
| any_eq(&info[j], STATUS_ADJ_INEQ)) { |
| change = check_adj_eq(i, j, info); |
| } else if (any_ineq(&info[i], STATUS_ADJ_EQ)) { |
| change = check_ineq_adj_eq(i, j, info); |
| } else if (any_ineq(&info[j], STATUS_ADJ_EQ)) { |
| change = check_ineq_adj_eq(j, i, info); |
| } else if (any_ineq(&info[i], STATUS_ADJ_INEQ) || |
| any_ineq(&info[j], STATUS_ADJ_INEQ)) { |
| change = check_adj_ineq(i, j, info); |
| } else { |
| if (!any_eq(&info[i], STATUS_CUT) && |
| !any_eq(&info[j], STATUS_CUT)) |
| change = check_facets(i, j, info); |
| if (change == isl_change_none) |
| change = check_wrap(i, j, info); |
| } |
| |
| done: |
| clear_status(&info[i]); |
| clear_status(&info[j]); |
| return change; |
| error: |
| clear_status(&info[i]); |
| clear_status(&info[j]); |
| return isl_change_error; |
| } |
| |
| /* 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. |
| */ |
| static enum isl_change coalesce_local_pair(int i, int j, |
| struct isl_coalesce_info *info) |
| { |
| init_status(&info[i]); |
| init_status(&info[j]); |
| return coalesce_local_pair_reuse(i, j, info); |
| } |
| |
| /* 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 isl_stat 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 isl_stat_error; |
| |
| 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 isl_stat_error; |
| |
| return isl_stat_ok; |
| } |
| |
| /* If the integer division at position "div" is defined by an equality, |
| * i.e., a stride constraint, then change the integer division expression |
| * to have a constant term equal to zero. |
| * |
| * Let the equality constraint be |
| * |
| * c + f + m a = 0 |
| * |
| * The integer division expression is then typically of the form |
| * |
| * a = floor((-f - c')/m) |
| * |
| * The integer division is first shifted by t = floor(c/m), |
| * turning the equality constraint into |
| * |
| * c - m floor(c/m) + f + m a' = 0 |
| * |
| * i.e., |
| * |
| * (c mod m) + f + m a' = 0 |
| * |
| * That is, |
| * |
| * a' = (-f - (c mod m))/m = floor((-f)/m) |
| * |
| * because a' is an integer and 0 <= (c mod m) < m. |
| * The constant term of a' can therefore be zeroed out, |
| * but only if the integer division expression is of the expected form. |
| */ |
| static isl_stat normalize_stride_div(struct isl_coalesce_info *info, int div) |
| { |
| isl_bool defined, valid; |
| isl_stat r; |
| isl_constraint *c; |
| isl_int shift, stride; |
| |
| defined = isl_basic_map_has_defining_equality(info->bmap, isl_dim_div, |
| div, &c); |
| if (defined < 0) |
| return isl_stat_error; |
| if (!defined) |
| return isl_stat_ok; |
| if (!c) |
| return isl_stat_error; |
| valid = isl_constraint_is_div_equality(c, div); |
| isl_int_init(shift); |
| isl_int_init(stride); |
| isl_constraint_get_constant(c, &shift); |
| isl_constraint_get_coefficient(c, isl_dim_div, div, &stride); |
| isl_int_fdiv_q(shift, shift, stride); |
| r = shift_div(info, div, shift); |
| isl_int_clear(stride); |
| isl_int_clear(shift); |
| isl_constraint_free(c); |
| if (r < 0 || valid < 0) |
| return isl_stat_error; |
| if (!valid) |
| return isl_stat_ok; |
| info->bmap = isl_basic_map_set_div_expr_constant_num_si_inplace( |
| info->bmap, div, 0); |
| if (!info->bmap) |
| return isl_stat_error; |
| return isl_stat_ok; |
| } |
| |
| /* The basic maps represented by "info1" and "info2" are known |
| * to have the same number of integer divisions. |
| * Check if pairs of integer divisions are equal to each other |
| * despite the fact that they differ by a rational constant. |
| * |
| * In particular, look for any pair of integer divisions that |
| * only differ in their constant terms. |
| * If either of these integer divisions is defined |
| * by stride constraints, then modify it to have a zero constant term. |
| * If both are defined by stride constraints then in the end they will have |
| * the same (zero) constant term. |
| */ |
| static isl_stat harmonize_stride_divs(struct isl_coalesce_info *info1, |
| struct isl_coalesce_info *info2) |
| { |
| int i, n; |
| |
| n = isl_basic_map_dim(info1->bmap, isl_dim_div); |
| for (i = 0; i < n; ++i) { |
| isl_bool known, harmonize; |
| |
| known = isl_basic_map_div_is_known(info1->bmap, i); |
| if (known >= 0 && known) |
| known = isl_basic_map_div_is_known(info2->bmap, i); |
| if (known < 0) |
| return isl_stat_error; |
| if (!known) |
| continue; |
| harmonize = isl_basic_map_equal_div_expr_except_constant( |
| info1->bmap, i, info2->bmap, i); |
| if (harmonize < 0) |
| return isl_stat_error; |
| if (!harmonize) |
| continue; |
| if (normalize_stride_div(info1, i) < 0) |
| return isl_stat_error; |
| if (normalize_stride_div(info2, i) < 0) |
| return isl_stat_error; |
| } |
| |
| return isl_stat_ok; |
| } |
| |
| /* If "shift" is an integer constant, then shift the integer division |
| * at position "div" of the basic map represented by "info" by "shift". |
| * If "shift" is not an integer constant, then do nothing. |
| * If "shift" is equal to zero, then no shift needs to be performed either. |
| * |
| * 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 isl_stat shift_if_cst_int(struct isl_coalesce_info *info, int div, |
| __isl_keep isl_aff *shift) |
| { |
| isl_bool cst; |
| isl_stat r; |
| isl_int d; |
| isl_val *c; |
| |
| cst = isl_aff_is_cst(shift); |
| if (cst < 0 || !cst) |
| return cst < 0 ? isl_stat_error : isl_stat_ok; |
| |
| c = isl_aff_get_constant_val(shift); |
| cst = isl_val_is_int(c); |
| if (cst >= 0 && cst) |
| cst = isl_bool_not(isl_val_is_zero(c)); |
| if (cst < 0 || !cst) { |
| isl_val_free(c); |
| return cst < 0 ? isl_stat_error : isl_stat_ok; |
| } |
| |
| isl_int_init(d); |
| r = isl_val_get_num_isl_int(c, &d); |
| if (r >= 0) |
| r = shift_div(info, div, d); |
| isl_int_clear(d); |
| |
| isl_val_free(c); |
| |
| return r; |
| } |
| |
| /* 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", taking into account the equality constraints "eq1" of "info1" |
| * and "eq2" of "info2". If so, align them with those of "info2". |
| * "info1" and "info2" are assumed to have the same number |
| * of integer divisions. |
| * |
| * An integer division is considered to be a shift of another integer |
| * division if, after simplification with respect to the equality |
| * constraints of the other basic map, one is equal to the other |
| * plus a constant. |
| * |
| * In particular, for each pair of integer divisions, if both are known, |
| * have the same denominator and are not already equal to each other, |
| * simplify each with respect to the equality constraints |
| * of the other basic map. If the difference is an integer constant, |
| * then move this difference outside. |
| * That is, if, after simplification, 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_1(x) + c_1 + n * d)/d) - n, |
| * |
| * where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d) |
| * after simplification with respect to the equality constraints. |
| */ |
| static isl_stat harmonize_divs_with_hulls(struct isl_coalesce_info *info1, |
| struct isl_coalesce_info *info2, __isl_keep isl_basic_set *eq1, |
| __isl_keep isl_basic_set *eq2) |
| { |
| int i; |
| int total; |
| isl_local_space *ls1, *ls2; |
| |
| total = isl_basic_map_total_dim(info1->bmap); |
| ls1 = isl_local_space_wrap(isl_basic_map_get_local_space(info1->bmap)); |
| ls2 = isl_local_space_wrap(isl_basic_map_get_local_space(info2->bmap)); |
| for (i = 0; i < info1->bmap->n_div; ++i) { |
| isl_stat r; |
| isl_aff *div1, *div2; |
| |
| if (!isl_local_space_div_is_known(ls1, i) || |
| !isl_local_space_div_is_known(ls2, i)) |
| continue; |
| if (isl_int_ne(info1->bmap->div[i][0], info2->bmap->div[i][0])) |
| continue; |
| if (isl_seq_eq(info1->bmap->div[i] + 1, |
| info2->bmap->div[i] + 1, 1 + total)) |
| continue; |
| div1 = isl_local_space_get_div(ls1, i); |
| div2 = isl_local_space_get_div(ls2, i); |
| div1 = isl_aff_substitute_equalities(div1, |
| isl_basic_set_copy(eq2)); |
| div2 = isl_aff_substitute_equalities(div2, |
| isl_basic_set_copy(eq1)); |
| div2 = isl_aff_sub(div2, div1); |
| r = shift_if_cst_int(info1, i, div2); |
| isl_aff_free(div2); |
| if (r < 0) |
| break; |
| } |
| isl_local_space_free(ls1); |
| isl_local_space_free(ls2); |
| |
| if (i < info1->bmap->n_div) |
| return isl_stat_error; |
| return isl_stat_ok; |
| } |
| |
| /* 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, after simplification with respect to the equality |
| * constraints of the other basic map, one is equal to the other |
| * plus a constant. |
| * |
| * First check if pairs of integer divisions are equal to each other |
| * despite the fact that they differ by a rational constant. |
| * If so, try and arrange for them to have the same constant term. |
| * |
| * Then, extract the equality constraints and continue with |
| * harmonize_divs_with_hulls. |
| * |
| * If the equality constraints of both basic maps are the same, |
| * then there is no need to perform any shifting since |
| * the coefficients of the integer divisions should have been |
| * reduced in the same way. |
| */ |
| static isl_stat harmonize_divs(struct isl_coalesce_info *info1, |
| struct isl_coalesce_info *info2) |
| { |
| isl_bool equal; |
| isl_basic_map *bmap1, *bmap2; |
| isl_basic_set *eq1, *eq2; |
| isl_stat r; |
| |
| if (!info1->bmap || !info2->bmap) |
| return isl_stat_error; |
| |
| if (info1->bmap->n_div != info2->bmap->n_div) |
| return isl_stat_ok; |
| if (info1->bmap->n_div == 0) |
| return isl_stat_ok; |
| |
| if (harmonize_stride_divs(info1, info2) < 0) |
| return isl_stat_error; |
| |
| bmap1 = isl_basic_map_copy(info1->bmap); |
| bmap2 = isl_basic_map_copy(info2->bmap); |
| eq1 = isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1)); |
| eq2 = isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2)); |
| equal = isl_basic_set_plain_is_equal(eq1, eq2); |
| if (equal < 0) |
| r = isl_stat_error; |
| else if (equal) |
| r = isl_stat_ok; |
| else |
| r = harmonize_divs_with_hulls(info1, info2, eq1, eq2); |
| isl_basic_set_free(eq1); |
| isl_basic_set_free(eq2); |
| |
| return r; |
| } |
| |
| /* 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 isl_bool same_divs(__isl_keep isl_basic_map *bmap1, |
| __isl_keep isl_basic_map *bmap2) |
| { |
| int i; |
| isl_bool known; |
| int total; |
| |
| if (!bmap1 || !bmap2) |
| return isl_bool_error; |
| if (bmap1->n_div != bmap2->n_div) |
| return isl_bool_false; |
| |
| if (bmap1->n_div == 0) |
| return isl_bool_true; |
| |
| 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 isl_bool_false; |
| |
| return isl_bool_true; |
| } |
| |
| /* Assuming that "tab" contains the equality constraints and |
| * the initial inequality constraints of "bmap", copy the remaining |
| * inequality constraints of "bmap" to "Tab". |
| */ |
| static isl_stat copy_ineq(struct isl_tab *tab, __isl_keep isl_basic_map *bmap) |
| { |
| int i, n_ineq; |
| |
| if (!bmap) |
| return isl_stat_error; |
| |
| n_ineq = tab->n_con - tab->n_eq; |
| for (i = n_ineq; i < bmap->n_ineq; ++i) |
| if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0) |
| return isl_stat_error; |
| |
| return isl_stat_ok; |
| } |
| |
| /* Description of an integer division that is added |
| * during an expansion. |
| * "pos" is the position of the corresponding variable. |
| * "cst" indicates whether this integer division has a fixed value. |
| * "val" contains the fixed value, if the value is fixed. |
| */ |
| struct isl_expanded { |
| int pos; |
| isl_bool cst; |
| isl_int val; |
| }; |
| |
| /* For each of the "n" integer division variables "expanded", |
| * if the variable has a fixed value, then add two inequality |
| * constraints expressing the fixed value. |
| * Otherwise, add the corresponding div constraints. |
| * The caller is responsible for removing the div constraints |
| * that it added for all these "n" integer divisions. |
| * |
| * The div constraints and the pair of inequality constraints |
| * forcing the fixed value cannot both be added for a given variable |
| * as the combination may render some of the original constraints redundant. |
| * These would then be ignored during the coalescing detection, |
| * while they could remain in the fused result. |
| * |
| * The two added inequality constraints are |
| * |
| * -a + v >= 0 |
| * a - v >= 0 |
| * |
| * with "a" the variable and "v" its fixed value. |
| * The facet corresponding to one of these two constraints is selected |
| * in the tableau to ensure that the pair of inequality constraints |
| * is treated as an equality constraint. |
| * |
| * The information in info->ineq is thrown away because it was |
| * computed in terms of div constraints, while some of those |
| * have now been replaced by these pairs of inequality constraints. |
| */ |
| static isl_stat fix_constant_divs(struct isl_coalesce_info *info, |
| int n, struct isl_expanded *expanded) |
| { |
| unsigned o_div; |
| int i; |
| isl_vec *ineq; |
| |
| o_div = isl_basic_map_offset(info->bmap, isl_dim_div) - 1; |
| ineq = isl_vec_alloc(isl_tab_get_ctx(info->tab), 1 + info->tab->n_var); |
| if (!ineq) |
| return isl_stat_error; |
| isl_seq_clr(ineq->el + 1, info->tab->n_var); |
| |
| for (i = 0; i < n; ++i) { |
| if (!expanded[i].cst) { |
| info->bmap = isl_basic_map_extend_constraints( |
| info->bmap, 0, 2); |
| if (isl_basic_map_add_div_constraints(info->bmap, |
| expanded[i].pos - o_div) < 0) |
| break; |
| } else { |
| isl_int_set_si(ineq->el[1 + expanded[i].pos], -1); |
| isl_int_set(ineq->el[0], expanded[i].val); |
| info->bmap = isl_basic_map_add_ineq(info->bmap, |
| ineq->el); |
| isl_int_set_si(ineq->el[1 + expanded[i].pos], 1); |
| isl_int_neg(ineq->el[0], expanded[i].val); |
| info->bmap = isl_basic_map_add_ineq(info->bmap, |
| ineq->el); |
| isl_int_set_si(ineq->el[1 + expanded[i].pos], 0); |
| } |
| if (copy_ineq(info->tab, info->bmap) < 0) |
| break; |
| if (expanded[i].cst && |
| isl_tab_select_facet(info->tab, info->tab->n_con - 1) < 0) |
| break; |
| } |
| |
| isl_vec_free(ineq); |
| |
| clear_status(info); |
| init_status(info); |
| |
| return i < n ? isl_stat_error : isl_stat_ok; |
| } |
| |
| /* Insert the "n" integer division variables "expanded" |
| * into info->tab and info->bmap and |
| * update info->ineq with respect to the redundant constraints |
| * in the resulting tableau. |
| * "bmap" contains the result of this insertion in info->bmap, |
| * while info->bmap is the original version |
| * of "bmap", i.e., the one that corresponds to the current |
| * state of info->tab. The number of constraints in info->bmap |
| * is assumed to be the same as the number of constraints |
| * in info->tab. This is required to be able to detect |
| * the extra constraints in "bmap". |
| * |
| * In particular, introduce extra variables corresponding |
| * to the extra integer divisions and add the div constraints |
| * that were added to "bmap" after info->tab was created |
| * from info->bmap. |
| * Furthermore, check if these extra integer divisions happen |
| * to attain a fixed integer value in info->tab. |
| * If so, replace the corresponding div constraints by pairs |
| * of inequality constraints that fix these |
| * integer divisions to their single integer values. |
| * Replace info->bmap by "bmap" to match the changes to info->tab. |
| * info->ineq was computed without a tableau and therefore |
| * does not take into account the redundant constraints |
| * in the tableau. Mark them here. |
| * There is no need to check the newly added div constraints |
| * since they cannot be redundant. |
| * The redundancy check is not performed when constants have been discovered |
| * since info->ineq is completely thrown away in this case. |
| */ |
| static isl_stat tab_insert_divs(struct isl_coalesce_info *info, |
| int n, struct isl_expanded *expanded, __isl_take isl_basic_map *bmap) |
| { |
| int i, n_ineq; |
| unsigned n_eq; |
| struct isl_tab_undo *snap; |
| int any; |
| |
| if (!bmap) |
| return isl_stat_error; |
| if (info->bmap->n_eq + info->bmap->n_ineq != info->tab->n_con) |
| isl_die(isl_basic_map_get_ctx(bmap), isl_error_internal, |
| "original tableau does not correspond " |
| "to original basic map", goto error); |
| |
| if (isl_tab_extend_vars(info->tab, n) < 0) |
| goto error; |
| if (isl_tab_extend_cons(info->tab, 2 * n) < 0) |
| goto error; |
| |
| for (i = 0; i < n; ++i) { |
| if (isl_tab_insert_var(info->tab, expanded[i].pos) < 0) |
| goto error; |
| } |
| |
| snap = isl_tab_snap(info->tab); |
| |
| n_ineq = info->tab->n_con - info->tab->n_eq; |
| if (copy_ineq(info->tab, bmap) < 0) |
| goto error; |
| |
| isl_basic_map_free(info->bmap); |
| info->bmap = bmap; |
| |
| any = 0; |
| for (i = 0; i < n; ++i) { |
| expanded[i].cst = isl_tab_is_constant(info->tab, |
| expanded[i].pos, &expanded[i].val); |
| if (expanded[i].cst < 0) |
| return isl_stat_error; |
| if (expanded[i].cst) |
| any = 1; |
| } |
| |
| if (any) { |
| if (isl_tab_rollback(info->tab, snap) < 0) |
| return isl_stat_error; |
| info->bmap = isl_basic_map_cow(info->bmap); |
| if (isl_basic_map_free_inequality(info->bmap, 2 * n) < 0) |
| return isl_stat_error; |
| |
| return fix_constant_divs(info, n, expanded); |
| } |
| |
| n_eq = info->bmap->n_eq; |
| for (i = 0; i < n_ineq; ++i) { |
| if (isl_tab_is_redundant(info->tab, n_eq + i)) |
| info->ineq[i] = STATUS_REDUNDANT; |
| } |
| |
| return isl_stat_ok; |
| error: |
| isl_basic_map_free(bmap); |
| return isl_stat_error; |
| } |
| |
| /* Expand info->tab and info->bmap in the same way "bmap" was expanded |
| * in isl_basic_map_expand_divs using the expansion "exp" and |
| * update info->ineq with respect to the redundant constraints |
| * in the resulting tableau. info->bmap is the original version |
| * of "bmap", i.e., the one that corresponds to the current |
| * state of info->tab. The number of constraints in info->bmap |
| * is assumed to be the same as the number of constraints |
| * in info->tab. This is required to be able to detect |
| * the extra constraints in "bmap". |
| * |
| * Extract the positions where extra local variables are introduced |
| * from "exp" and call tab_insert_divs. |
| */ |
| static isl_stat expand_tab(struct isl_coalesce_info *info, int *exp, |
| __isl_take isl_basic_map *bmap) |
| { |
| isl_ctx *ctx; |
| struct isl_expanded *expanded; |
| int i, j, k, n; |
| int extra_var; |
| unsigned total, pos, n_div; |
| isl_stat r; |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| pos = total - n_div; |
| extra_var = total - info->tab->n_var; |
| n = n_div - extra_var; |
| |
| ctx = isl_basic_map_get_ctx(bmap); |
| expanded = isl_calloc_array(ctx, struct isl_expanded, extra_var); |
| if (extra_var && !expanded) |
| goto error; |
| |
| i = 0; |
| k = 0; |
| for (j = 0; j < n_div; ++j) { |
| if (i < n && exp[i] == j) { |
| ++i; |
| continue; |
| } |
| expanded[k++].pos = pos + j; |
| } |
| |
| for (k = 0; k < extra_var; ++k) |
| isl_int_init(expanded[k].val); |
| |
| r = tab_insert_divs(info, extra_var, expanded, bmap); |
| |
| for (k = 0; k < extra_var; ++k) |
| isl_int_clear(expanded[k].val); |
| free(expanded); |
| |
| return r; |
| error: |
| isl_basic_map_free(bmap); |
| return isl_stat_error; |
| } |
| |
| /* Check if the union of the basic maps represented by info[i] and info[j] |
| * can be represented by a single basic map, |
| * after expanding the divs of info[i] to match those of info[j]. |
| * 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 caller has already checked for info[j] being a subset of info[i]. |
| * If some of the divs of info[j] are unknown, then the expanded info[i] |
| * will not have the corresponding div constraints. The other patterns |
| * therefore cannot apply. Skip the computation in this case. |
| * |
| * The expansion is performed using the divs "div" and expansion "exp" |
| * computed by the caller. |
| * info[i].bmap has already been expanded and the result is passed in |
| * as "bmap". |
| * The "eq" and "ineq" fields of info[i] reflect the status of |
| * the constraints of the expanded "bmap" with respect to info[j].tab. |
| * However, inequality constraints that are redundant in info[i].tab |
| * have not yet been marked as such because no tableau was available. |
| * |
| * Replace info[i].bmap by "bmap" and expand info[i].tab as well, |
| * updating info[i].ineq with respect to the redundant constraints. |
| * Then try and coalesce the expanded info[i] with info[j], |
| * reusing the information in info[i].eq and info[i].ineq. |
| * If this does not result in any coalescing or if it results in info[j] |
| * getting dropped (which should not happen in practice, since the case |
| * of info[j] being a subset of info[i] has already been checked by |
| * the caller), then revert info[i] to its original state. |
| */ |
| static enum isl_change coalesce_expand_tab_divs(__isl_take isl_basic_map *bmap, |
| int i, int j, struct isl_coalesce_info *info, __isl_keep isl_mat *div, |
| int *exp) |
| { |
| isl_bool known; |
| isl_basic_map *bmap_i; |
| struct isl_tab_undo *snap; |
| enum isl_change change = isl_change_none; |
| |
| known = isl_basic_map_divs_known(info[j].bmap); |
| if (known < 0 || !known) { |
| clear_status(&info[i]); |
| isl_basic_map_free(bmap); |
| return known < 0 ? isl_change_error : isl_change_none; |
| } |
| |
| bmap_i = isl_basic_map_copy(info[i].bmap); |
| snap = isl_tab_snap(info[i].tab); |
| if (expand_tab(&info[i], exp, bmap) < 0) |
| change = isl_change_error; |
| |
| init_status(&info[j]); |
| if (change == isl_change_none) |
| change = coalesce_local_pair_reuse(i, j, info); |
| else |
| clear_status(&info[i]); |
| if (change != isl_change_none && change != isl_change_drop_second) { |
| isl_basic_map_free(bmap_i); |
| } else { |
| isl_basic_map_free(info[i].bmap); |
| info[i].bmap = bmap_i; |
| |
| if (isl_tab_rollback(info[i].tab, snap) < 0) |
| change = isl_change_error; |
| } |
| |
| return change; |
| } |
| |
| /* Check if the union of "bmap" and the basic map represented by info[j] |
| * can be represented by a single basic map, |
| * after expanding the divs of "bmap" to match those of info[j]. |
| * 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. |
| * |
| * In particular, check if the expanded "bmap" contains the basic map |
| * represented by the tableau info[j].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 |
| * info[j].tab. |
| * |
| * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap. |
| * In this case, the positions of the constraints of info[i].bmap |
| * with respect to the basic map represented by info[j] are stored |
| * in info[i]. |
| * |
| * If the expanded "bmap" does not contain the basic map |
| * represented by the tableau info[j].tab and if "i" is not -1, |
| * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab |
| * as well and check if that results in coalescing. |
| */ |
| static enum isl_change coalesce_with_expanded_divs( |
| __isl_keep isl_basic_map *bmap, int i, int j, |
| struct isl_coalesce_info *info, __isl_keep isl_mat *div, int *exp) |
| { |
| enum isl_change change = isl_change_none; |
| struct isl_coalesce_info info_local, *info_i; |
| |
| info_i = i >= 0 ? &info[i] : &info_local; |
| init_status(info_i); |
| bmap = isl_basic_map_copy(bmap); |
| bmap = isl_basic_map_expand_divs(bmap, isl_mat_copy(div), exp); |
| bmap = isl_basic_map_mark_final(bmap); |
| |
| if (!bmap) |
| goto error; |
| |
| info_local.bmap = bmap; |
| info_i->eq = eq_status_in(bmap, info[j].tab); |
| if (bmap->n_eq && !info_i->eq) |
| goto error; |
| if (any_eq(info_i, STATUS_ERROR)) |
| goto error; |
| if (any_eq(info_i, STATUS_SEPARATE)) |
| goto done; |
| |
| info_i->ineq = ineq_status_in(bmap, NULL, info[j].tab); |
| if (bmap->n_ineq && !info_i->ineq) |
| goto error; |
| if (any_ineq(info_i, STATUS_ERROR)) |
| goto error; |
| if (any_ineq(info_i, STATUS_SEPARATE)) |
| goto done; |
| |
| if (all(info_i->eq, 2 * bmap->n_eq, STATUS_VALID) && |
| all(info_i->ineq, bmap->n_ineq, STATUS_VALID)) { |
| drop(&info[j]); |
| change = isl_change_drop_second; |
| } |
| |
| if (change == isl_change_none && i != -1) |
| return coalesce_expand_tab_divs(bmap, i, j, info, div, exp); |
| |
| done: |
| isl_basic_map_free(bmap); |
| clear_status(info_i); |
| return change; |
| error: |
| isl_basic_map_free(bmap); |
| clear_status(info_i); |
| return isl_change_error; |
| } |
| |
| /* Check if the union of "bmap_i" and the basic map represented by info[j] |
| * can be represented by a single basic map, |
| * after aligning the divs of "bmap_i" to match those of info[j]. |
| * 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. |
| * |
| * In particular, check if "bmap_i" contains 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 info[j].bmap. If so, we pass control over to |
| * coalesce_with_expanded_divs. |
| * |
| * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap. |
| */ |
| static enum isl_change coalesce_after_aligning_divs( |
| __isl_keep isl_basic_map *bmap_i, int i, int j, |
| struct isl_coalesce_info *info) |
| { |
| isl_bool known; |
| isl_mat *div_i, *div_j, *div; |
| int *exp1 = NULL; |
| int *exp2 = NULL; |
| isl_ctx *ctx; |
| enum isl_change change; |
| |
| known = isl_basic_map_divs_known(bmap_i); |
| if (known < 0) |
| return isl_change_error; |
| if (!known) |
| return isl_change_none; |
| |
| 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) |
| change = coalesce_with_expanded_divs(bmap_i, |
| i, j, info, div, exp1); |
| else |
| change = isl_change_none; |
| |
| isl_mat_free(div); |
| |
| isl_mat_free(div_i); |
| isl_mat_free(div_j); |
| |
| free(exp2); |
| free(exp1); |
| |
| return change; |
| error: |
| isl_mat_free(div_i); |
| isl_mat_free(div_j); |
| free(exp1); |
| free(exp2); |
| return isl_change_error; |
| } |
| |
| /* 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" and return isl_change_drop_second. |
| * |
| * 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 enum isl_change coalesce_subset_with_equalities(int i, int j, |
| struct isl_coalesce_info *info) |
| { |
| isl_basic_map *hull_i, *hull_j, *bmap_i; |
| int equal, empty; |
| enum isl_change change; |
| |
| if (info[j].bmap->n_eq == 0) |
| return isl_change_none; |
| if (info[i].bmap->n_div == 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 || equal || empty < 0 || empty) { |
| isl_basic_map_free(hull_j); |
| if (equal < 0 || empty < 0) |
| return isl_change_error; |
| return isl_change_none; |
| } |
| |
| bmap_i = isl_basic_map_copy(info[i].bmap); |
| bmap_i = isl_basic_map_intersect(bmap_i, hull_j); |
| if (!bmap_i) |
| return isl_change_error; |
| |
| if (bmap_i->n_div > info[j].bmap->n_div) { |
| isl_basic_map_free(bmap_i); |
| return isl_change_none; |
| } |
| |
| change = coalesce_after_aligning_divs(bmap_i, -1, j, info); |
| |
| isl_basic_map_free(bmap_i); |
| |
| return change; |
| } |
| |
| /* Check if the union of and the basic maps represented by info[i] and info[j] |
| * can be represented by a single basic map, by aligning or equating |
| * their integer divisions. |
| * 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. |
| * |
| * 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 coalesce_divs(int i, int j, |
| struct isl_coalesce_info *info) |
| { |
| enum isl_change change = isl_change_none; |
| |
| if (info[i].bmap->n_div < info[j].bmap->n_div) |
| change = coalesce_after_aligning_divs(info[i].bmap, i, j, info); |
| if (change != isl_change_none) |
| return change; |
| |
| if (info[j].bmap->n_div < info[i].bmap->n_div) |
| change = coalesce_after_aligning_divs(info[j].bmap, j, i, info); |
| if (change != isl_change_none) |
| return invert_change(change); |
| |
| change = coalesce_subset_with_equalities(i, j, info); |
| if (change != isl_change_none) |
| return change; |
| |
| change = coalesce_subset_with_equalities(j, i, info); |
| if (change != isl_change_none) |
| return invert_change(change); |
| |
| return isl_change_none; |
| } |
| |
| /* Does "bmap" involve any divs that themselves refer to divs? |
| */ |
| static isl_bool 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 isl_bool_true; |
| |
| return isl_bool_false; |
| } |
| |
| /* 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_basic_map_equal_div_expr_part(bmap_i, i, bmap_j, j, |
| 0, 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". |
| * |
| * The newly added existentially quantified variables are not given |
| * an explicit representation because the corresponding div constraints |
| * do not appear in info->bmap. These constraints are not added |
| * to info->bmap because for internal consistency, they would need to |
| * be added to info->tab as well, where they could combine with the equality |
| * that is added later to result in constraints that do not hold |
| * in the original input. |
| */ |
| static isl_stat add_sub_vars(struct isl_coalesce_info *info, |
| __isl_keep isl_aff_list *list, int dim, int extra_var) |
| { |
| int i, j, n, d; |
| 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 isl_stat_error; |
| 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 isl_stat_error; |
| if (is_nan) |
| continue; |
| |
| if (isl_tab_insert_var(info->tab, dim + i) < 0) |
| return isl_stat_error; |
| d = isl_basic_map_alloc_div(info->bmap); |
| if (d < 0) |
| return isl_stat_error; |
| info->bmap = isl_basic_map_mark_div_unknown(info->bmap, d); |
| if (!info->bmap) |
| return isl_stat_error; |
| for (j = d; j > i; --j) |
| isl_basic_map_swap_div(info->bmap, j - 1, j); |
| } |
| |
| return isl_stat_ok; |
| } |
| |
| /* 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". |
| * |
| * This function assumes that a sufficient number of rows and |
| * elements in the constraint array are available in the tableau. |
| */ |
| 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) |
| { |
| isl_bool 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) |
| { |
| isl_bool 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 = coalesce_divs(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. |
| */ |
| __isl_give isl_map *isl_map_coalesce(__isl_take 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 set_from_map(isl_map_coalesce(set_to_map(set))); |
| } |