| /* |
| * Copyright 2008-2009 Katholieke Universiteit Leuven |
| * |
| * Use of this software is governed by the GNU LGPLv2.1 license |
| * |
| * Written by Sven Verdoolaege, K.U.Leuven, Departement |
| * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium |
| */ |
| |
| #include <strings.h> |
| #include <isl_ctx_private.h> |
| #include <isl_map_private.h> |
| #include "isl_equalities.h" |
| #include <isl/map.h> |
| #include <isl/seq.h> |
| #include "isl_tab.h" |
| #include <isl_space_private.h> |
| #include <isl_mat_private.h> |
| |
| static void swap_equality(struct isl_basic_map *bmap, int a, int b) |
| { |
| isl_int *t = bmap->eq[a]; |
| bmap->eq[a] = bmap->eq[b]; |
| bmap->eq[b] = t; |
| } |
| |
| static void swap_inequality(struct isl_basic_map *bmap, int a, int b) |
| { |
| if (a != b) { |
| isl_int *t = bmap->ineq[a]; |
| bmap->ineq[a] = bmap->ineq[b]; |
| bmap->ineq[b] = t; |
| } |
| } |
| |
| static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem) |
| { |
| isl_seq_cpy(c, c + n, rem); |
| isl_seq_clr(c + rem, n); |
| } |
| |
| /* Drop n dimensions starting at first. |
| * |
| * In principle, this frees up some extra variables as the number |
| * of columns remains constant, but we would have to extend |
| * the div array too as the number of rows in this array is assumed |
| * to be equal to extra. |
| */ |
| struct isl_basic_set *isl_basic_set_drop_dims( |
| struct isl_basic_set *bset, unsigned first, unsigned n) |
| { |
| int i; |
| |
| if (!bset) |
| goto error; |
| |
| isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error); |
| |
| if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set)) |
| return bset; |
| |
| bset = isl_basic_set_cow(bset); |
| if (!bset) |
| return NULL; |
| |
| for (i = 0; i < bset->n_eq; ++i) |
| constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n, |
| (bset->dim->n_out-first-n)+bset->extra); |
| |
| for (i = 0; i < bset->n_ineq; ++i) |
| constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n, |
| (bset->dim->n_out-first-n)+bset->extra); |
| |
| for (i = 0; i < bset->n_div; ++i) |
| constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n, |
| (bset->dim->n_out-first-n)+bset->extra); |
| |
| bset->dim = isl_space_drop_outputs(bset->dim, first, n); |
| if (!bset->dim) |
| goto error; |
| |
| ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED); |
| bset = isl_basic_set_simplify(bset); |
| return isl_basic_set_finalize(bset); |
| error: |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| struct isl_set *isl_set_drop_dims( |
| struct isl_set *set, unsigned first, unsigned n) |
| { |
| int i; |
| |
| if (!set) |
| goto error; |
| |
| isl_assert(set->ctx, first + n <= set->dim->n_out, goto error); |
| |
| if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set)) |
| return set; |
| set = isl_set_cow(set); |
| if (!set) |
| goto error; |
| set->dim = isl_space_drop_outputs(set->dim, first, n); |
| if (!set->dim) |
| goto error; |
| |
| for (i = 0; i < set->n; ++i) { |
| set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n); |
| if (!set->p[i]) |
| goto error; |
| } |
| |
| ISL_F_CLR(set, ISL_SET_NORMALIZED); |
| return set; |
| error: |
| isl_set_free(set); |
| return NULL; |
| } |
| |
| /* Move "n" divs starting at "first" to the end of the list of divs. |
| */ |
| static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap, |
| unsigned first, unsigned n) |
| { |
| isl_int **div; |
| int i; |
| |
| if (first + n == bmap->n_div) |
| return bmap; |
| |
| div = isl_alloc_array(bmap->ctx, isl_int *, n); |
| if (!div) |
| goto error; |
| for (i = 0; i < n; ++i) |
| div[i] = bmap->div[first + i]; |
| for (i = 0; i < bmap->n_div - first - n; ++i) |
| bmap->div[first + i] = bmap->div[first + n + i]; |
| for (i = 0; i < n; ++i) |
| bmap->div[bmap->n_div - n + i] = div[i]; |
| free(div); |
| return bmap; |
| error: |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| /* Drop "n" dimensions of type "type" starting at "first". |
| * |
| * In principle, this frees up some extra variables as the number |
| * of columns remains constant, but we would have to extend |
| * the div array too as the number of rows in this array is assumed |
| * to be equal to extra. |
| */ |
| struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap, |
| enum isl_dim_type type, unsigned first, unsigned n) |
| { |
| int i; |
| unsigned dim; |
| unsigned offset; |
| unsigned left; |
| |
| if (!bmap) |
| goto error; |
| |
| dim = isl_basic_map_dim(bmap, type); |
| isl_assert(bmap->ctx, first + n <= dim, goto error); |
| |
| if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type)) |
| return bmap; |
| |
| bmap = isl_basic_map_cow(bmap); |
| if (!bmap) |
| return NULL; |
| |
| offset = isl_basic_map_offset(bmap, type) + first; |
| left = isl_basic_map_total_dim(bmap) - (offset - 1) - n; |
| for (i = 0; i < bmap->n_eq; ++i) |
| constraint_drop_vars(bmap->eq[i]+offset, n, left); |
| |
| for (i = 0; i < bmap->n_ineq; ++i) |
| constraint_drop_vars(bmap->ineq[i]+offset, n, left); |
| |
| for (i = 0; i < bmap->n_div; ++i) |
| constraint_drop_vars(bmap->div[i]+1+offset, n, left); |
| |
| if (type == isl_dim_div) { |
| bmap = move_divs_last(bmap, first, n); |
| if (!bmap) |
| goto error; |
| isl_basic_map_free_div(bmap, n); |
| } else |
| bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n); |
| if (!bmap->dim) |
| goto error; |
| |
| ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); |
| bmap = isl_basic_map_simplify(bmap); |
| return isl_basic_map_finalize(bmap); |
| error: |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset, |
| enum isl_dim_type type, unsigned first, unsigned n) |
| { |
| return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset, |
| type, first, n); |
| } |
| |
| struct isl_basic_map *isl_basic_map_drop_inputs( |
| struct isl_basic_map *bmap, unsigned first, unsigned n) |
| { |
| return isl_basic_map_drop(bmap, isl_dim_in, first, n); |
| } |
| |
| struct isl_map *isl_map_drop(struct isl_map *map, |
| enum isl_dim_type type, unsigned first, unsigned n) |
| { |
| int i; |
| |
| if (!map) |
| goto error; |
| |
| isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error); |
| |
| if (n == 0 && !isl_space_get_tuple_name(map->dim, type)) |
| return map; |
| map = isl_map_cow(map); |
| if (!map) |
| goto error; |
| map->dim = isl_space_drop_dims(map->dim, type, first, n); |
| if (!map->dim) |
| goto error; |
| |
| for (i = 0; i < map->n; ++i) { |
| map->p[i] = isl_basic_map_drop(map->p[i], type, first, n); |
| if (!map->p[i]) |
| goto error; |
| } |
| ISL_F_CLR(map, ISL_MAP_NORMALIZED); |
| |
| return map; |
| error: |
| isl_map_free(map); |
| return NULL; |
| } |
| |
| struct isl_set *isl_set_drop(struct isl_set *set, |
| enum isl_dim_type type, unsigned first, unsigned n) |
| { |
| return (isl_set *)isl_map_drop((isl_map *)set, type, first, n); |
| } |
| |
| struct isl_map *isl_map_drop_inputs( |
| struct isl_map *map, unsigned first, unsigned n) |
| { |
| return isl_map_drop(map, isl_dim_in, first, n); |
| } |
| |
| /* |
| * We don't cow, as the div is assumed to be redundant. |
| */ |
| static struct isl_basic_map *isl_basic_map_drop_div( |
| struct isl_basic_map *bmap, unsigned div) |
| { |
| int i; |
| unsigned pos; |
| |
| if (!bmap) |
| goto error; |
| |
| pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div; |
| |
| isl_assert(bmap->ctx, div < bmap->n_div, goto error); |
| |
| for (i = 0; i < bmap->n_eq; ++i) |
| constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1); |
| |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| if (!isl_int_is_zero(bmap->ineq[i][pos])) { |
| isl_basic_map_drop_inequality(bmap, i); |
| --i; |
| continue; |
| } |
| constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1); |
| } |
| |
| for (i = 0; i < bmap->n_div; ++i) |
| constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1); |
| |
| if (div != bmap->n_div - 1) { |
| int j; |
| isl_int *t = bmap->div[div]; |
| |
| for (j = div; j < bmap->n_div - 1; ++j) |
| bmap->div[j] = bmap->div[j+1]; |
| |
| bmap->div[bmap->n_div - 1] = t; |
| } |
| ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); |
| isl_basic_map_free_div(bmap, 1); |
| |
| return bmap; |
| error: |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| struct isl_basic_map *isl_basic_map_normalize_constraints( |
| struct isl_basic_map *bmap) |
| { |
| int i; |
| isl_int gcd; |
| unsigned total = isl_basic_map_total_dim(bmap); |
| |
| if (!bmap) |
| return NULL; |
| |
| isl_int_init(gcd); |
| for (i = bmap->n_eq - 1; i >= 0; --i) { |
| isl_seq_gcd(bmap->eq[i]+1, total, &gcd); |
| if (isl_int_is_zero(gcd)) { |
| if (!isl_int_is_zero(bmap->eq[i][0])) { |
| bmap = isl_basic_map_set_to_empty(bmap); |
| break; |
| } |
| isl_basic_map_drop_equality(bmap, i); |
| continue; |
| } |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) |
| isl_int_gcd(gcd, gcd, bmap->eq[i][0]); |
| if (isl_int_is_one(gcd)) |
| continue; |
| if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) { |
| bmap = isl_basic_map_set_to_empty(bmap); |
| break; |
| } |
| isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total); |
| } |
| |
| for (i = bmap->n_ineq - 1; i >= 0; --i) { |
| isl_seq_gcd(bmap->ineq[i]+1, total, &gcd); |
| if (isl_int_is_zero(gcd)) { |
| if (isl_int_is_neg(bmap->ineq[i][0])) { |
| bmap = isl_basic_map_set_to_empty(bmap); |
| break; |
| } |
| isl_basic_map_drop_inequality(bmap, i); |
| continue; |
| } |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) |
| isl_int_gcd(gcd, gcd, bmap->ineq[i][0]); |
| if (isl_int_is_one(gcd)) |
| continue; |
| isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd); |
| isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total); |
| } |
| isl_int_clear(gcd); |
| |
| return bmap; |
| } |
| |
| struct isl_basic_set *isl_basic_set_normalize_constraints( |
| struct isl_basic_set *bset) |
| { |
| return (struct isl_basic_set *)isl_basic_map_normalize_constraints( |
| (struct isl_basic_map *)bset); |
| } |
| |
| /* Assumes divs have been ordered if keep_divs is set. |
| */ |
| static void eliminate_var_using_equality(struct isl_basic_map *bmap, |
| unsigned pos, isl_int *eq, int keep_divs, int *progress) |
| { |
| unsigned total; |
| unsigned space_total; |
| int k; |
| int last_div; |
| |
| total = isl_basic_map_total_dim(bmap); |
| space_total = isl_space_dim(bmap->dim, isl_dim_all); |
| last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div); |
| for (k = 0; k < bmap->n_eq; ++k) { |
| if (bmap->eq[k] == eq) |
| continue; |
| if (isl_int_is_zero(bmap->eq[k][1+pos])) |
| continue; |
| if (progress) |
| *progress = 1; |
| isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL); |
| isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total); |
| } |
| |
| for (k = 0; k < bmap->n_ineq; ++k) { |
| if (isl_int_is_zero(bmap->ineq[k][1+pos])) |
| continue; |
| if (progress) |
| *progress = 1; |
| isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL); |
| isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total); |
| ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); |
| } |
| |
| for (k = 0; k < bmap->n_div; ++k) { |
| if (isl_int_is_zero(bmap->div[k][0])) |
| continue; |
| if (isl_int_is_zero(bmap->div[k][1+1+pos])) |
| continue; |
| if (progress) |
| *progress = 1; |
| /* We need to be careful about circular definitions, |
| * so for now we just remove the definition of div k |
| * if the equality contains any divs. |
| * If keep_divs is set, then the divs have been ordered |
| * and we can keep the definition as long as the result |
| * is still ordered. |
| */ |
| if (last_div == -1 || (keep_divs && last_div < k)) |
| isl_seq_elim(bmap->div[k]+1, eq, |
| 1+pos, 1+total, &bmap->div[k][0]); |
| else |
| isl_seq_clr(bmap->div[k], 1 + total); |
| ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); |
| } |
| } |
| |
| /* Assumes divs have been ordered if keep_divs is set. |
| */ |
| static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, |
| unsigned div, int keep_divs) |
| { |
| unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div; |
| |
| eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL); |
| |
| isl_basic_map_drop_div(bmap, div); |
| } |
| |
| /* Check if elimination of div "div" using equality "eq" would not |
| * result in a div depending on a later div. |
| */ |
| static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq, |
| unsigned div) |
| { |
| int k; |
| int last_div; |
| unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all); |
| unsigned pos = space_total + div; |
| |
| last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div); |
| if (last_div < 0 || last_div <= div) |
| return 1; |
| |
| for (k = 0; k <= last_div; ++k) { |
| if (isl_int_is_zero(bmap->div[k][0])) |
| return 1; |
| if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos])) |
| return 0; |
| } |
| |
| return 1; |
| } |
| |
| /* Elimininate divs based on equalities |
| */ |
| static struct isl_basic_map *eliminate_divs_eq( |
| struct isl_basic_map *bmap, int *progress) |
| { |
| int d; |
| int i; |
| int modified = 0; |
| unsigned off; |
| |
| bmap = isl_basic_map_order_divs(bmap); |
| |
| if (!bmap) |
| return NULL; |
| |
| off = 1 + isl_space_dim(bmap->dim, isl_dim_all); |
| |
| for (d = bmap->n_div - 1; d >= 0 ; --d) { |
| for (i = 0; i < bmap->n_eq; ++i) { |
| if (!isl_int_is_one(bmap->eq[i][off + d]) && |
| !isl_int_is_negone(bmap->eq[i][off + d])) |
| continue; |
| if (!ok_to_eliminate_div(bmap, bmap->eq[i], d)) |
| continue; |
| modified = 1; |
| *progress = 1; |
| eliminate_div(bmap, bmap->eq[i], d, 1); |
| isl_basic_map_drop_equality(bmap, i); |
| break; |
| } |
| } |
| if (modified) |
| return eliminate_divs_eq(bmap, progress); |
| return bmap; |
| } |
| |
| /* Elimininate divs based on inequalities |
| */ |
| static struct isl_basic_map *eliminate_divs_ineq( |
| struct isl_basic_map *bmap, int *progress) |
| { |
| int d; |
| int i; |
| unsigned off; |
| struct isl_ctx *ctx; |
| |
| if (!bmap) |
| return NULL; |
| |
| ctx = bmap->ctx; |
| off = 1 + isl_space_dim(bmap->dim, isl_dim_all); |
| |
| for (d = bmap->n_div - 1; d >= 0 ; --d) { |
| for (i = 0; i < bmap->n_eq; ++i) |
| if (!isl_int_is_zero(bmap->eq[i][off + d])) |
| break; |
| if (i < bmap->n_eq) |
| continue; |
| for (i = 0; i < bmap->n_ineq; ++i) |
| if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one)) |
| break; |
| if (i < bmap->n_ineq) |
| continue; |
| *progress = 1; |
| bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1); |
| if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) |
| break; |
| bmap = isl_basic_map_drop_div(bmap, d); |
| if (!bmap) |
| break; |
| } |
| return bmap; |
| } |
| |
| struct isl_basic_map *isl_basic_map_gauss( |
| struct isl_basic_map *bmap, int *progress) |
| { |
| int k; |
| int done; |
| int last_var; |
| unsigned total_var; |
| unsigned total; |
| |
| bmap = isl_basic_map_order_divs(bmap); |
| |
| if (!bmap) |
| return NULL; |
| |
| total = isl_basic_map_total_dim(bmap); |
| total_var = total - bmap->n_div; |
| |
| last_var = total - 1; |
| for (done = 0; done < bmap->n_eq; ++done) { |
| for (; last_var >= 0; --last_var) { |
| for (k = done; k < bmap->n_eq; ++k) |
| if (!isl_int_is_zero(bmap->eq[k][1+last_var])) |
| break; |
| if (k < bmap->n_eq) |
| break; |
| } |
| if (last_var < 0) |
| break; |
| if (k != done) |
| swap_equality(bmap, k, done); |
| if (isl_int_is_neg(bmap->eq[done][1+last_var])) |
| isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total); |
| |
| eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1, |
| progress); |
| |
| if (last_var >= total_var && |
| isl_int_is_zero(bmap->div[last_var - total_var][0])) { |
| unsigned div = last_var - total_var; |
| isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total); |
| isl_int_set_si(bmap->div[div][1+1+last_var], 0); |
| isl_int_set(bmap->div[div][0], |
| bmap->eq[done][1+last_var]); |
| ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); |
| } |
| } |
| if (done == bmap->n_eq) |
| return bmap; |
| for (k = done; k < bmap->n_eq; ++k) { |
| if (isl_int_is_zero(bmap->eq[k][0])) |
| continue; |
| return isl_basic_map_set_to_empty(bmap); |
| } |
| isl_basic_map_free_equality(bmap, bmap->n_eq-done); |
| return bmap; |
| } |
| |
| struct isl_basic_set *isl_basic_set_gauss( |
| struct isl_basic_set *bset, int *progress) |
| { |
| return (struct isl_basic_set*)isl_basic_map_gauss( |
| (struct isl_basic_map *)bset, progress); |
| } |
| |
| |
| static unsigned int round_up(unsigned int v) |
| { |
| int old_v = v; |
| |
| while (v) { |
| old_v = v; |
| v ^= v & -v; |
| } |
| return old_v << 1; |
| } |
| |
| static int hash_index(isl_int ***index, unsigned int size, int bits, |
| struct isl_basic_map *bmap, int k) |
| { |
| int h; |
| unsigned total = isl_basic_map_total_dim(bmap); |
| uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits); |
| for (h = hash; index[h]; h = (h+1) % size) |
| if (&bmap->ineq[k] != index[h] && |
| isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total)) |
| break; |
| return h; |
| } |
| |
| static int set_hash_index(isl_int ***index, unsigned int size, int bits, |
| struct isl_basic_set *bset, int k) |
| { |
| return hash_index(index, size, bits, (struct isl_basic_map *)bset, k); |
| } |
| |
| /* If we can eliminate more than one div, then we need to make |
| * sure we do it from last div to first div, in order not to |
| * change the position of the other divs that still need to |
| * be removed. |
| */ |
| static struct isl_basic_map *remove_duplicate_divs( |
| struct isl_basic_map *bmap, int *progress) |
| { |
| unsigned int size; |
| int *index; |
| int *elim_for; |
| int k, l, h; |
| int bits; |
| struct isl_blk eq; |
| unsigned total_var; |
| unsigned total; |
| struct isl_ctx *ctx; |
| |
| if (!bmap || bmap->n_div <= 1) |
| return bmap; |
| |
| total_var = isl_space_dim(bmap->dim, isl_dim_all); |
| total = total_var + bmap->n_div; |
| |
| ctx = bmap->ctx; |
| for (k = bmap->n_div - 1; k >= 0; --k) |
| if (!isl_int_is_zero(bmap->div[k][0])) |
| break; |
| if (k <= 0) |
| return bmap; |
| |
| elim_for = isl_calloc_array(ctx, int, bmap->n_div); |
| size = round_up(4 * bmap->n_div / 3 - 1); |
| bits = ffs(size) - 1; |
| index = isl_calloc_array(ctx, int, size); |
| if (!index) |
| return bmap; |
| eq = isl_blk_alloc(ctx, 1+total); |
| if (isl_blk_is_error(eq)) |
| goto out; |
| |
| isl_seq_clr(eq.data, 1+total); |
| index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1; |
| for (--k; k >= 0; --k) { |
| uint32_t hash; |
| |
| if (isl_int_is_zero(bmap->div[k][0])) |
| continue; |
| |
| hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits); |
| for (h = hash; index[h]; h = (h+1) % size) |
| if (isl_seq_eq(bmap->div[k], |
| bmap->div[index[h]-1], 2+total)) |
| break; |
| if (index[h]) { |
| *progress = 1; |
| l = index[h] - 1; |
| elim_for[l] = k + 1; |
| } |
| index[h] = k+1; |
| } |
| for (l = bmap->n_div - 1; l >= 0; --l) { |
| if (!elim_for[l]) |
| continue; |
| k = elim_for[l] - 1; |
| isl_int_set_si(eq.data[1+total_var+k], -1); |
| isl_int_set_si(eq.data[1+total_var+l], 1); |
| eliminate_div(bmap, eq.data, l, 0); |
| isl_int_set_si(eq.data[1+total_var+k], 0); |
| isl_int_set_si(eq.data[1+total_var+l], 0); |
| } |
| |
| isl_blk_free(ctx, eq); |
| out: |
| free(index); |
| free(elim_for); |
| return bmap; |
| } |
| |
| static int n_pure_div_eq(struct isl_basic_map *bmap) |
| { |
| int i, j; |
| unsigned total; |
| |
| total = isl_space_dim(bmap->dim, isl_dim_all); |
| for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) { |
| while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j])) |
| --j; |
| if (j < 0) |
| break; |
| if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1) |
| return 0; |
| } |
| return i; |
| } |
| |
| /* Normalize divs that appear in equalities. |
| * |
| * In particular, we assume that bmap contains some equalities |
| * of the form |
| * |
| * a x = m * e_i |
| * |
| * and we want to replace the set of e_i by a minimal set and |
| * such that the new e_i have a canonical representation in terms |
| * of the vector x. |
| * If any of the equalities involves more than one divs, then |
| * we currently simply bail out. |
| * |
| * Let us first additionally assume that all equalities involve |
| * a div. The equalities then express modulo constraints on the |
| * remaining variables and we can use "parameter compression" |
| * to find a minimal set of constraints. The result is a transformation |
| * |
| * x = T(x') = x_0 + G x' |
| * |
| * with G a lower-triangular matrix with all elements below the diagonal |
| * non-negative and smaller than the diagonal element on the same row. |
| * We first normalize x_0 by making the same property hold in the affine |
| * T matrix. |
| * The rows i of G with a 1 on the diagonal do not impose any modulo |
| * constraint and simply express x_i = x'_i. |
| * For each of the remaining rows i, we introduce a div and a corresponding |
| * equality. In particular |
| * |
| * g_ii e_j = x_i - g_i(x') |
| * |
| * where each x'_k is replaced either by x_k (if g_kk = 1) or the |
| * corresponding div (if g_kk != 1). |
| * |
| * If there are any equalities not involving any div, then we |
| * first apply a variable compression on the variables x: |
| * |
| * x = C x'' x'' = C_2 x |
| * |
| * and perform the above parameter compression on A C instead of on A. |
| * The resulting compression is then of the form |
| * |
| * x'' = T(x') = x_0 + G x' |
| * |
| * and in constructing the new divs and the corresponding equalities, |
| * we have to replace each x'', i.e., the x'_k with (g_kk = 1), |
| * by the corresponding row from C_2. |
| */ |
| static struct isl_basic_map *normalize_divs( |
| struct isl_basic_map *bmap, int *progress) |
| { |
| int i, j, k; |
| int total; |
| int div_eq; |
| struct isl_mat *B; |
| struct isl_vec *d; |
| struct isl_mat *T = NULL; |
| struct isl_mat *C = NULL; |
| struct isl_mat *C2 = NULL; |
| isl_int v; |
| int *pos; |
| int dropped, needed; |
| |
| if (!bmap) |
| return NULL; |
| |
| if (bmap->n_div == 0) |
| return bmap; |
| |
| if (bmap->n_eq == 0) |
| return bmap; |
| |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS)) |
| return bmap; |
| |
| total = isl_space_dim(bmap->dim, isl_dim_all); |
| div_eq = n_pure_div_eq(bmap); |
| if (div_eq == 0) |
| return bmap; |
| |
| if (div_eq < bmap->n_eq) { |
| B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq, |
| bmap->n_eq - div_eq, 0, 1 + total); |
| C = isl_mat_variable_compression(B, &C2); |
| if (!C || !C2) |
| goto error; |
| if (C->n_col == 0) { |
| bmap = isl_basic_map_set_to_empty(bmap); |
| isl_mat_free(C); |
| isl_mat_free(C2); |
| goto done; |
| } |
| } |
| |
| d = isl_vec_alloc(bmap->ctx, div_eq); |
| if (!d) |
| goto error; |
| for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) { |
| while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j])) |
| --j; |
| isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]); |
| } |
| B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total); |
| |
| if (C) { |
| B = isl_mat_product(B, C); |
| C = NULL; |
| } |
| |
| T = isl_mat_parameter_compression(B, d); |
| if (!T) |
| goto error; |
| if (T->n_col == 0) { |
| bmap = isl_basic_map_set_to_empty(bmap); |
| isl_mat_free(C2); |
| isl_mat_free(T); |
| goto done; |
| } |
| isl_int_init(v); |
| for (i = 0; i < T->n_row - 1; ++i) { |
| isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]); |
| if (isl_int_is_zero(v)) |
| continue; |
| isl_mat_col_submul(T, 0, v, 1 + i); |
| } |
| isl_int_clear(v); |
| pos = isl_alloc_array(bmap->ctx, int, T->n_row); |
| if (!pos) |
| goto error; |
| /* We have to be careful because dropping equalities may reorder them */ |
| dropped = 0; |
| for (j = bmap->n_div - 1; j >= 0; --j) { |
| for (i = 0; i < bmap->n_eq; ++i) |
| if (!isl_int_is_zero(bmap->eq[i][1 + total + j])) |
| break; |
| if (i < bmap->n_eq) { |
| bmap = isl_basic_map_drop_div(bmap, j); |
| isl_basic_map_drop_equality(bmap, i); |
| ++dropped; |
| } |
| } |
| pos[0] = 0; |
| needed = 0; |
| for (i = 1; i < T->n_row; ++i) { |
| if (isl_int_is_one(T->row[i][i])) |
| pos[i] = i; |
| else |
| needed++; |
| } |
| if (needed > dropped) { |
| bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), |
| needed, needed, 0); |
| if (!bmap) |
| goto error; |
| } |
| for (i = 1; i < T->n_row; ++i) { |
| if (isl_int_is_one(T->row[i][i])) |
| continue; |
| k = isl_basic_map_alloc_div(bmap); |
| pos[i] = 1 + total + k; |
| isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div); |
| isl_int_set(bmap->div[k][0], T->row[i][i]); |
| if (C2) |
| isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total); |
| else |
| isl_int_set_si(bmap->div[k][1 + i], 1); |
| for (j = 0; j < i; ++j) { |
| if (isl_int_is_zero(T->row[i][j])) |
| continue; |
| if (pos[j] < T->n_row && C2) |
| isl_seq_submul(bmap->div[k] + 1, T->row[i][j], |
| C2->row[pos[j]], 1 + total); |
| else |
| isl_int_neg(bmap->div[k][1 + pos[j]], |
| T->row[i][j]); |
| } |
| j = isl_basic_map_alloc_equality(bmap); |
| isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div); |
| isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]); |
| } |
| free(pos); |
| isl_mat_free(C2); |
| isl_mat_free(T); |
| |
| if (progress) |
| *progress = 1; |
| done: |
| ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS); |
| |
| return bmap; |
| error: |
| isl_mat_free(C); |
| isl_mat_free(C2); |
| isl_mat_free(T); |
| return bmap; |
| } |
| |
| static struct isl_basic_map *set_div_from_lower_bound( |
| struct isl_basic_map *bmap, int div, int ineq) |
| { |
| unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all); |
| |
| isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div); |
| isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]); |
| isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]); |
| isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1); |
| isl_int_set_si(bmap->div[div][1 + total + div], 0); |
| |
| return bmap; |
| } |
| |
| /* Check whether it is ok to define a div based on an inequality. |
| * To avoid the introduction of circular definitions of divs, we |
| * do not allow such a definition if the resulting expression would refer to |
| * any other undefined divs or if any known div is defined in |
| * terms of the unknown div. |
| */ |
| static int ok_to_set_div_from_bound(struct isl_basic_map *bmap, |
| int div, int ineq) |
| { |
| int j; |
| unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all); |
| |
| /* Not defined in terms of unknown divs */ |
| for (j = 0; j < bmap->n_div; ++j) { |
| if (div == j) |
| continue; |
| if (isl_int_is_zero(bmap->ineq[ineq][total + j])) |
| continue; |
| if (isl_int_is_zero(bmap->div[j][0])) |
| return 0; |
| } |
| |
| /* No other div defined in terms of this one => avoid loops */ |
| for (j = 0; j < bmap->n_div; ++j) { |
| if (div == j) |
| continue; |
| if (isl_int_is_zero(bmap->div[j][0])) |
| continue; |
| if (!isl_int_is_zero(bmap->div[j][1 + total + div])) |
| return 0; |
| } |
| |
| return 1; |
| } |
| |
| /* Given two constraints "k" and "l" that are opposite to each other, |
| * except for the constant term, check if we can use them |
| * to obtain an expression for one of the hitherto unknown divs. |
| * "sum" is the sum of the constant terms of the constraints. |
| * If this sum is strictly smaller than the coefficient of one |
| * of the divs, then this pair can be used define the div. |
| * To avoid the introduction of circular definitions of divs, we |
| * do not use the pair if the resulting expression would refer to |
| * any other undefined divs or if any known div is defined in |
| * terms of the unknown div. |
| */ |
| static struct isl_basic_map *check_for_div_constraints( |
| struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress) |
| { |
| int i; |
| unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all); |
| |
| for (i = 0; i < bmap->n_div; ++i) { |
| if (!isl_int_is_zero(bmap->div[i][0])) |
| continue; |
| if (isl_int_is_zero(bmap->ineq[k][total + i])) |
| continue; |
| if (isl_int_abs_ge(sum, bmap->ineq[k][total + i])) |
| continue; |
| if (!ok_to_set_div_from_bound(bmap, i, k)) |
| break; |
| if (isl_int_is_pos(bmap->ineq[k][total + i])) |
| bmap = set_div_from_lower_bound(bmap, i, k); |
| else |
| bmap = set_div_from_lower_bound(bmap, i, l); |
| if (progress) |
| *progress = 1; |
| break; |
| } |
| return bmap; |
| } |
| |
| static struct isl_basic_map *remove_duplicate_constraints( |
| struct isl_basic_map *bmap, int *progress, int detect_divs) |
| { |
| unsigned int size; |
| isl_int ***index; |
| int k, l, h; |
| int bits; |
| unsigned total = isl_basic_map_total_dim(bmap); |
| isl_int sum; |
| isl_ctx *ctx; |
| |
| if (!bmap || bmap->n_ineq <= 1) |
| return bmap; |
| |
| size = round_up(4 * (bmap->n_ineq+1) / 3 - 1); |
| bits = ffs(size) - 1; |
| ctx = isl_basic_map_get_ctx(bmap); |
| index = isl_calloc_array(ctx, isl_int **, size); |
| if (!index) |
| return bmap; |
| |
| index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0]; |
| for (k = 1; k < bmap->n_ineq; ++k) { |
| h = hash_index(index, size, bits, bmap, k); |
| if (!index[h]) { |
| index[h] = &bmap->ineq[k]; |
| continue; |
| } |
| if (progress) |
| *progress = 1; |
| l = index[h] - &bmap->ineq[0]; |
| if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0])) |
| swap_inequality(bmap, k, l); |
| isl_basic_map_drop_inequality(bmap, k); |
| --k; |
| } |
| isl_int_init(sum); |
| for (k = 0; k < bmap->n_ineq-1; ++k) { |
| isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total); |
| h = hash_index(index, size, bits, bmap, k); |
| isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total); |
| if (!index[h]) |
| continue; |
| l = index[h] - &bmap->ineq[0]; |
| isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]); |
| if (isl_int_is_pos(sum)) { |
| if (detect_divs) |
| bmap = check_for_div_constraints(bmap, k, l, |
| sum, progress); |
| continue; |
| } |
| if (isl_int_is_zero(sum)) { |
| /* We need to break out of the loop after these |
| * changes since the contents of the hash |
| * will no longer be valid. |
| * Plus, we probably we want to regauss first. |
| */ |
| if (progress) |
| *progress = 1; |
| isl_basic_map_drop_inequality(bmap, l); |
| isl_basic_map_inequality_to_equality(bmap, k); |
| } else |
| bmap = isl_basic_map_set_to_empty(bmap); |
| break; |
| } |
| isl_int_clear(sum); |
| |
| free(index); |
| return bmap; |
| } |
| |
| |
| struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap) |
| { |
| int progress = 1; |
| if (!bmap) |
| return NULL; |
| while (progress) { |
| progress = 0; |
| bmap = isl_basic_map_normalize_constraints(bmap); |
| bmap = remove_duplicate_divs(bmap, &progress); |
| bmap = eliminate_divs_eq(bmap, &progress); |
| bmap = eliminate_divs_ineq(bmap, &progress); |
| bmap = isl_basic_map_gauss(bmap, &progress); |
| /* requires equalities in normal form */ |
| bmap = normalize_divs(bmap, &progress); |
| bmap = remove_duplicate_constraints(bmap, &progress, 1); |
| } |
| return bmap; |
| } |
| |
| struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset) |
| { |
| return (struct isl_basic_set *) |
| isl_basic_map_simplify((struct isl_basic_map *)bset); |
| } |
| |
| |
| int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap, |
| isl_int *constraint, unsigned div) |
| { |
| unsigned pos; |
| |
| if (!bmap) |
| return -1; |
| |
| pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div; |
| |
| if (isl_int_eq(constraint[pos], bmap->div[div][0])) { |
| int neg; |
| isl_int_sub(bmap->div[div][1], |
| bmap->div[div][1], bmap->div[div][0]); |
| isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1); |
| neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos); |
| isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1); |
| isl_int_add(bmap->div[div][1], |
| bmap->div[div][1], bmap->div[div][0]); |
| if (!neg) |
| return 0; |
| if (isl_seq_first_non_zero(constraint+pos+1, |
| bmap->n_div-div-1) != -1) |
| return 0; |
| } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) { |
| if (!isl_seq_eq(constraint, bmap->div[div]+1, pos)) |
| return 0; |
| if (isl_seq_first_non_zero(constraint+pos+1, |
| bmap->n_div-div-1) != -1) |
| return 0; |
| } else |
| return 0; |
| |
| return 1; |
| } |
| |
| |
| /* If the only constraints a div d=floor(f/m) |
| * appears in are its two defining constraints |
| * |
| * f - m d >=0 |
| * -(f - (m - 1)) + m d >= 0 |
| * |
| * then it can safely be removed. |
| */ |
| static int div_is_redundant(struct isl_basic_map *bmap, int div) |
| { |
| int i; |
| unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div; |
| |
| for (i = 0; i < bmap->n_eq; ++i) |
| if (!isl_int_is_zero(bmap->eq[i][pos])) |
| return 0; |
| |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| if (isl_int_is_zero(bmap->ineq[i][pos])) |
| continue; |
| if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div)) |
| return 0; |
| } |
| |
| for (i = 0; i < bmap->n_div; ++i) |
| if (!isl_int_is_zero(bmap->div[i][1+pos])) |
| return 0; |
| |
| return 1; |
| } |
| |
| /* |
| * Remove divs that don't occur in any of the constraints or other divs. |
| * These can arise when dropping some of the variables in a quast |
| * returned by piplib. |
| */ |
| static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap) |
| { |
| int i; |
| |
| if (!bmap) |
| return NULL; |
| |
| for (i = bmap->n_div-1; i >= 0; --i) { |
| if (!div_is_redundant(bmap, i)) |
| continue; |
| bmap = isl_basic_map_drop_div(bmap, i); |
| } |
| return bmap; |
| } |
| |
| struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap) |
| { |
| bmap = remove_redundant_divs(bmap); |
| if (!bmap) |
| return NULL; |
| ISL_F_SET(bmap, ISL_BASIC_SET_FINAL); |
| return bmap; |
| } |
| |
| struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset) |
| { |
| return (struct isl_basic_set *) |
| isl_basic_map_finalize((struct isl_basic_map *)bset); |
| } |
| |
| struct isl_set *isl_set_finalize(struct isl_set *set) |
| { |
| int i; |
| |
| if (!set) |
| return NULL; |
| for (i = 0; i < set->n; ++i) { |
| set->p[i] = isl_basic_set_finalize(set->p[i]); |
| if (!set->p[i]) |
| goto error; |
| } |
| return set; |
| error: |
| isl_set_free(set); |
| return NULL; |
| } |
| |
| struct isl_map *isl_map_finalize(struct isl_map *map) |
| { |
| int i; |
| |
| if (!map) |
| return NULL; |
| for (i = 0; i < map->n; ++i) { |
| map->p[i] = isl_basic_map_finalize(map->p[i]); |
| if (!map->p[i]) |
| goto error; |
| } |
| ISL_F_CLR(map, ISL_MAP_NORMALIZED); |
| return map; |
| error: |
| isl_map_free(map); |
| return NULL; |
| } |
| |
| |
| /* Remove definition of any div that is defined in terms of the given variable. |
| * The div itself is not removed. Functions such as |
| * eliminate_divs_ineq depend on the other divs remaining in place. |
| */ |
| static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap, |
| int pos) |
| { |
| int i; |
| |
| for (i = 0; i < bmap->n_div; ++i) { |
| if (isl_int_is_zero(bmap->div[i][0])) |
| continue; |
| if (isl_int_is_zero(bmap->div[i][1+1+pos])) |
| continue; |
| isl_int_set_si(bmap->div[i][0], 0); |
| } |
| return bmap; |
| } |
| |
| /* Eliminate the specified variables from the constraints using |
| * Fourier-Motzkin. The variables themselves are not removed. |
| */ |
| struct isl_basic_map *isl_basic_map_eliminate_vars( |
| struct isl_basic_map *bmap, unsigned pos, unsigned n) |
| { |
| int d; |
| int i, j, k; |
| unsigned total; |
| int need_gauss = 0; |
| |
| if (n == 0) |
| return bmap; |
| if (!bmap) |
| return NULL; |
| total = isl_basic_map_total_dim(bmap); |
| |
| bmap = isl_basic_map_cow(bmap); |
| for (d = pos + n - 1; d >= 0 && d >= pos; --d) |
| bmap = remove_dependent_vars(bmap, d); |
| |
| for (d = pos + n - 1; |
| d >= 0 && d >= total - bmap->n_div && d >= pos; --d) |
| isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total); |
| for (d = pos + n - 1; d >= 0 && d >= pos; --d) { |
| int n_lower, n_upper; |
| if (!bmap) |
| return NULL; |
| for (i = 0; i < bmap->n_eq; ++i) { |
| if (isl_int_is_zero(bmap->eq[i][1+d])) |
| continue; |
| eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL); |
| isl_basic_map_drop_equality(bmap, i); |
| need_gauss = 1; |
| break; |
| } |
| if (i < bmap->n_eq) |
| continue; |
| n_lower = 0; |
| n_upper = 0; |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| if (isl_int_is_pos(bmap->ineq[i][1+d])) |
| n_lower++; |
| else if (isl_int_is_neg(bmap->ineq[i][1+d])) |
| n_upper++; |
| } |
| bmap = isl_basic_map_extend_constraints(bmap, |
| 0, n_lower * n_upper); |
| if (!bmap) |
| goto error; |
| for (i = bmap->n_ineq - 1; i >= 0; --i) { |
| int last; |
| if (isl_int_is_zero(bmap->ineq[i][1+d])) |
| continue; |
| last = -1; |
| for (j = 0; j < i; ++j) { |
| if (isl_int_is_zero(bmap->ineq[j][1+d])) |
| continue; |
| last = j; |
| if (isl_int_sgn(bmap->ineq[i][1+d]) == |
| isl_int_sgn(bmap->ineq[j][1+d])) |
| continue; |
| k = isl_basic_map_alloc_inequality(bmap); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(bmap->ineq[k], bmap->ineq[i], |
| 1+total); |
| isl_seq_elim(bmap->ineq[k], bmap->ineq[j], |
| 1+d, 1+total, NULL); |
| } |
| isl_basic_map_drop_inequality(bmap, i); |
| i = last + 1; |
| } |
| if (n_lower > 0 && n_upper > 0) { |
| bmap = isl_basic_map_normalize_constraints(bmap); |
| bmap = remove_duplicate_constraints(bmap, NULL, 0); |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| bmap = isl_basic_map_remove_redundancies(bmap); |
| need_gauss = 0; |
| if (!bmap) |
| goto error; |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) |
| break; |
| } |
| } |
| ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); |
| if (need_gauss) |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| return bmap; |
| error: |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| struct isl_basic_set *isl_basic_set_eliminate_vars( |
| struct isl_basic_set *bset, unsigned pos, unsigned n) |
| { |
| return (struct isl_basic_set *)isl_basic_map_eliminate_vars( |
| (struct isl_basic_map *)bset, pos, n); |
| } |
| |
| /* Eliminate the specified n dimensions starting at first from the |
| * constraints using Fourier-Motzkin. The dimensions themselves |
| * are not removed. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_eliminate( |
| __isl_take isl_basic_map *bmap, |
| enum isl_dim_type type, unsigned first, unsigned n) |
| { |
| if (!bmap) |
| return NULL; |
| if (n == 0) |
| return bmap; |
| |
| if (first + n > isl_basic_map_dim(bmap, type)) |
| isl_die(bmap->ctx, isl_error_invalid, |
| "index out of bounds", goto error); |
| |
| first += isl_basic_map_offset(bmap, type) - 1; |
| bmap = isl_basic_map_eliminate_vars(bmap, first, n); |
| return isl_basic_map_finalize(bmap); |
| error: |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| /* Don't assume equalities are in order, because align_divs |
| * may have changed the order of the divs. |
| */ |
| static void compute_elimination_index(struct isl_basic_map *bmap, int *elim) |
| { |
| int d, i; |
| unsigned total; |
| |
| total = isl_space_dim(bmap->dim, isl_dim_all); |
| for (d = 0; d < total; ++d) |
| elim[d] = -1; |
| for (i = 0; i < bmap->n_eq; ++i) { |
| for (d = total - 1; d >= 0; --d) { |
| if (isl_int_is_zero(bmap->eq[i][1+d])) |
| continue; |
| elim[d] = i; |
| break; |
| } |
| } |
| } |
| |
| static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim) |
| { |
| compute_elimination_index((struct isl_basic_map *)bset, elim); |
| } |
| |
| static int reduced_using_equalities(isl_int *dst, isl_int *src, |
| struct isl_basic_map *bmap, int *elim) |
| { |
| int d; |
| int copied = 0; |
| unsigned total; |
| |
| total = isl_space_dim(bmap->dim, isl_dim_all); |
| for (d = total - 1; d >= 0; --d) { |
| if (isl_int_is_zero(src[1+d])) |
| continue; |
| if (elim[d] == -1) |
| continue; |
| if (!copied) { |
| isl_seq_cpy(dst, src, 1 + total); |
| copied = 1; |
| } |
| isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL); |
| } |
| return copied; |
| } |
| |
| static int set_reduced_using_equalities(isl_int *dst, isl_int *src, |
| struct isl_basic_set *bset, int *elim) |
| { |
| return reduced_using_equalities(dst, src, |
| (struct isl_basic_map *)bset, elim); |
| } |
| |
| static struct isl_basic_set *isl_basic_set_reduce_using_equalities( |
| struct isl_basic_set *bset, struct isl_basic_set *context) |
| { |
| int i; |
| int *elim; |
| |
| if (!bset || !context) |
| goto error; |
| |
| if (context->n_eq == 0) { |
| isl_basic_set_free(context); |
| return bset; |
| } |
| |
| bset = isl_basic_set_cow(bset); |
| if (!bset) |
| goto error; |
| |
| elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset)); |
| if (!elim) |
| goto error; |
| set_compute_elimination_index(context, elim); |
| for (i = 0; i < bset->n_eq; ++i) |
| set_reduced_using_equalities(bset->eq[i], bset->eq[i], |
| context, elim); |
| for (i = 0; i < bset->n_ineq; ++i) |
| set_reduced_using_equalities(bset->ineq[i], bset->ineq[i], |
| context, elim); |
| isl_basic_set_free(context); |
| free(elim); |
| bset = isl_basic_set_simplify(bset); |
| bset = isl_basic_set_finalize(bset); |
| return bset; |
| error: |
| isl_basic_set_free(bset); |
| isl_basic_set_free(context); |
| return NULL; |
| } |
| |
| static struct isl_basic_set *remove_shifted_constraints( |
| struct isl_basic_set *bset, struct isl_basic_set *context) |
| { |
| unsigned int size; |
| isl_int ***index; |
| int bits; |
| int k, h, l; |
| isl_ctx *ctx; |
| |
| if (!bset) |
| return NULL; |
| |
| size = round_up(4 * (context->n_ineq+1) / 3 - 1); |
| bits = ffs(size) - 1; |
| ctx = isl_basic_set_get_ctx(bset); |
| index = isl_calloc_array(ctx, isl_int **, size); |
| if (!index) |
| return bset; |
| |
| for (k = 0; k < context->n_ineq; ++k) { |
| h = set_hash_index(index, size, bits, context, k); |
| index[h] = &context->ineq[k]; |
| } |
| for (k = 0; k < bset->n_ineq; ++k) { |
| h = set_hash_index(index, size, bits, bset, k); |
| if (!index[h]) |
| continue; |
| l = index[h] - &context->ineq[0]; |
| if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0])) |
| continue; |
| bset = isl_basic_set_cow(bset); |
| if (!bset) |
| goto error; |
| isl_basic_set_drop_inequality(bset, k); |
| --k; |
| } |
| free(index); |
| return bset; |
| error: |
| free(index); |
| return bset; |
| } |
| |
| /* Remove all information from bset that is redundant in the context |
| * of context. Both bset and context are assumed to be full-dimensional. |
| * |
| * We first * remove the inequalities from "bset" |
| * that are obviously redundant with respect to some inequality in "context". |
| * |
| * If there are any inequalities left, we construct a tableau for |
| * the context and then add the inequalities of "bset". |
| * Before adding these inequalities, we freeze all constraints such that |
| * they won't be considered redundant in terms of the constraints of "bset". |
| * Then we detect all redundant constraints (among the |
| * constraints that weren't frozen), first by checking for redundancy in the |
| * the tableau and then by checking if replacing a constraint by its negation |
| * would lead to an empty set. This last step is fairly expensive |
| * and could be optimized by more reuse of the tableau. |
| * Finally, we update bset according to the results. |
| */ |
| static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset, |
| __isl_take isl_basic_set *context) |
| { |
| int i, k; |
| isl_basic_set *combined = NULL; |
| struct isl_tab *tab = NULL; |
| unsigned context_ineq; |
| unsigned total; |
| |
| if (!bset || !context) |
| goto error; |
| |
| if (isl_basic_set_is_universe(bset)) { |
| isl_basic_set_free(context); |
| return bset; |
| } |
| |
| if (isl_basic_set_is_universe(context)) { |
| isl_basic_set_free(context); |
| return bset; |
| } |
| |
| bset = remove_shifted_constraints(bset, context); |
| if (!bset) |
| goto error; |
| if (bset->n_ineq == 0) |
| goto done; |
| |
| context_ineq = context->n_ineq; |
| combined = isl_basic_set_cow(isl_basic_set_copy(context)); |
| combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq); |
| tab = isl_tab_from_basic_set(combined); |
| for (i = 0; i < context_ineq; ++i) |
| if (isl_tab_freeze_constraint(tab, i) < 0) |
| goto error; |
| tab = isl_tab_extend(tab, bset->n_ineq); |
| for (i = 0; i < bset->n_ineq; ++i) |
| if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0) |
| goto error; |
| bset = isl_basic_set_add_constraints(combined, bset, 0); |
| combined = NULL; |
| if (!bset) |
| goto error; |
| if (isl_tab_detect_redundant(tab) < 0) |
| goto error; |
| total = isl_basic_set_total_dim(bset); |
| for (i = context_ineq; i < bset->n_ineq; ++i) { |
| int is_empty; |
| if (tab->con[i].is_redundant) |
| continue; |
| tab->con[i].is_redundant = 1; |
| combined = isl_basic_set_dup(bset); |
| combined = isl_basic_set_update_from_tab(combined, tab); |
| combined = isl_basic_set_extend_constraints(combined, 0, 1); |
| k = isl_basic_set_alloc_inequality(combined); |
| if (k < 0) |
| goto error; |
| isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total); |
| isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1); |
| is_empty = isl_basic_set_is_empty(combined); |
| if (is_empty < 0) |
| goto error; |
| isl_basic_set_free(combined); |
| combined = NULL; |
| if (!is_empty) |
| tab->con[i].is_redundant = 0; |
| } |
| for (i = 0; i < context_ineq; ++i) |
| tab->con[i].is_redundant = 1; |
| bset = isl_basic_set_update_from_tab(bset, tab); |
| if (bset) { |
| ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT); |
| ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT); |
| } |
| |
| isl_tab_free(tab); |
| done: |
| bset = isl_basic_set_simplify(bset); |
| bset = isl_basic_set_finalize(bset); |
| isl_basic_set_free(context); |
| return bset; |
| error: |
| isl_tab_free(tab); |
| isl_basic_set_free(combined); |
| isl_basic_set_free(context); |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| /* Remove all information from bset that is redundant in the context |
| * of context. In particular, equalities that are linear combinations |
| * of those in context are removed. Then the inequalities that are |
| * redundant in the context of the equalities and inequalities of |
| * context are removed. |
| * |
| * We first compute the integer affine hull of the intersection, |
| * compute the gist inside this affine hull and then add back |
| * those equalities that are not implied by the context. |
| * |
| * If two constraints are mutually redundant, then uset_gist_full |
| * will remove the second of those constraints. We therefore first |
| * sort the constraints so that constraints not involving existentially |
| * quantified variables are given precedence over those that do. |
| * We have to perform this sorting before the variable compression, |
| * because that may effect the order of the variables. |
| */ |
| static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset, |
| __isl_take isl_basic_set *context) |
| { |
| isl_mat *eq; |
| isl_mat *T, *T2; |
| isl_basic_set *aff; |
| isl_basic_set *aff_context; |
| unsigned total; |
| |
| if (!bset || !context) |
| goto error; |
| |
| bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context)); |
| if (isl_basic_set_plain_is_empty(bset)) { |
| isl_basic_set_free(context); |
| return bset; |
| } |
| bset = isl_basic_set_sort_constraints(bset); |
| aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset)); |
| if (!aff) |
| goto error; |
| if (isl_basic_set_plain_is_empty(aff)) { |
| isl_basic_set_free(aff); |
| isl_basic_set_free(context); |
| return bset; |
| } |
| if (aff->n_eq == 0) { |
| isl_basic_set_free(aff); |
| return uset_gist_full(bset, context); |
| } |
| total = isl_basic_set_total_dim(bset); |
| eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total); |
| eq = isl_mat_cow(eq); |
| T = isl_mat_variable_compression(eq, &T2); |
| if (T && T->n_col == 0) { |
| isl_mat_free(T); |
| isl_mat_free(T2); |
| isl_basic_set_free(context); |
| isl_basic_set_free(aff); |
| return isl_basic_set_set_to_empty(bset); |
| } |
| |
| aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context)); |
| |
| bset = isl_basic_set_preimage(bset, isl_mat_copy(T)); |
| context = isl_basic_set_preimage(context, T); |
| |
| bset = uset_gist_full(bset, context); |
| bset = isl_basic_set_preimage(bset, T2); |
| bset = isl_basic_set_intersect(bset, aff); |
| bset = isl_basic_set_reduce_using_equalities(bset, aff_context); |
| |
| if (bset) { |
| ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT); |
| ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT); |
| } |
| |
| return bset; |
| error: |
| isl_basic_set_free(bset); |
| isl_basic_set_free(context); |
| return NULL; |
| } |
| |
| /* Normalize the divs in "bmap" in the context of the equalities in "context". |
| * We simply add the equalities in context to bmap and then do a regular |
| * div normalizations. Better results can be obtained by normalizing |
| * only the divs in bmap than do not also appear in context. |
| * We need to be careful to reduce the divs using the equalities |
| * so that later calls to isl_basic_map_overlying_set wouldn't introduce |
| * spurious constraints. |
| */ |
| static struct isl_basic_map *normalize_divs_in_context( |
| struct isl_basic_map *bmap, struct isl_basic_map *context) |
| { |
| int i; |
| unsigned total_context; |
| int div_eq; |
| |
| div_eq = n_pure_div_eq(bmap); |
| if (div_eq == 0) |
| return bmap; |
| |
| if (context->n_div > 0) |
| bmap = isl_basic_map_align_divs(bmap, context); |
| |
| total_context = isl_basic_map_total_dim(context); |
| bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0); |
| for (i = 0; i < context->n_eq; ++i) { |
| int k; |
| k = isl_basic_map_alloc_equality(bmap); |
| isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context); |
| isl_seq_clr(bmap->eq[k] + 1 + total_context, |
| isl_basic_map_total_dim(bmap) - total_context); |
| } |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| bmap = normalize_divs(bmap, NULL); |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| return bmap; |
| } |
| |
| struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap, |
| struct isl_basic_map *context) |
| { |
| struct isl_basic_set *bset; |
| |
| if (!bmap || !context) |
| goto error; |
| |
| if (isl_basic_map_is_universe(bmap)) { |
| isl_basic_map_free(context); |
| return bmap; |
| } |
| if (isl_basic_map_plain_is_empty(context)) { |
| isl_basic_map_free(bmap); |
| return context; |
| } |
| if (isl_basic_map_plain_is_empty(bmap)) { |
| isl_basic_map_free(context); |
| return bmap; |
| } |
| |
| bmap = isl_basic_map_remove_redundancies(bmap); |
| context = isl_basic_map_remove_redundancies(context); |
| |
| if (context->n_eq) |
| bmap = normalize_divs_in_context(bmap, context); |
| |
| context = isl_basic_map_align_divs(context, bmap); |
| bmap = isl_basic_map_align_divs(bmap, context); |
| |
| bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)), |
| isl_basic_map_underlying_set(context)); |
| |
| return isl_basic_map_overlying_set(bset, bmap); |
| error: |
| isl_basic_map_free(bmap); |
| isl_basic_map_free(context); |
| return NULL; |
| } |
| |
| /* |
| * Assumes context has no implicit divs. |
| */ |
| __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map, |
| __isl_take isl_basic_map *context) |
| { |
| int i; |
| |
| if (!map || !context) |
| goto error;; |
| |
| if (isl_basic_map_plain_is_empty(context)) { |
| isl_map_free(map); |
| return isl_map_from_basic_map(context); |
| } |
| |
| context = isl_basic_map_remove_redundancies(context); |
| map = isl_map_cow(map); |
| if (!map || !context) |
| goto error;; |
| isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error); |
| map = isl_map_compute_divs(map); |
| for (i = 0; i < map->n; ++i) |
| context = isl_basic_map_align_divs(context, map->p[i]); |
| for (i = map->n - 1; i >= 0; --i) { |
| map->p[i] = isl_basic_map_gist(map->p[i], |
| isl_basic_map_copy(context)); |
| if (!map->p[i]) |
| goto error; |
| if (isl_basic_map_plain_is_empty(map->p[i])) { |
| isl_basic_map_free(map->p[i]); |
| if (i != map->n - 1) |
| map->p[i] = map->p[map->n - 1]; |
| map->n--; |
| } |
| } |
| isl_basic_map_free(context); |
| ISL_F_CLR(map, ISL_MAP_NORMALIZED); |
| return map; |
| error: |
| isl_map_free(map); |
| isl_basic_map_free(context); |
| return NULL; |
| } |
| |
| static __isl_give isl_map *map_gist(__isl_take isl_map *map, |
| __isl_take isl_map *context) |
| { |
| context = isl_map_compute_divs(context); |
| return isl_map_gist_basic_map(map, isl_map_simple_hull(context)); |
| } |
| |
| __isl_give isl_map *isl_map_gist(__isl_take isl_map *map, |
| __isl_take isl_map *context) |
| { |
| return isl_map_align_params_map_map_and(map, context, &map_gist); |
| } |
| |
| struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset, |
| struct isl_basic_set *context) |
| { |
| return (struct isl_basic_set *)isl_basic_map_gist( |
| (struct isl_basic_map *)bset, (struct isl_basic_map *)context); |
| } |
| |
| __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set, |
| __isl_take isl_basic_set *context) |
| { |
| return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set, |
| (struct isl_basic_map *)context); |
| } |
| |
| __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set, |
| __isl_take isl_basic_set *context) |
| { |
| isl_space *space = isl_set_get_space(set); |
| isl_basic_set *dom_context = isl_basic_set_universe(space); |
| dom_context = isl_basic_set_intersect_params(dom_context, context); |
| return isl_set_gist_basic_set(set, dom_context); |
| } |
| |
| __isl_give isl_set *isl_set_gist(__isl_take isl_set *set, |
| __isl_take isl_set *context) |
| { |
| return (struct isl_set *)isl_map_gist((struct isl_map *)set, |
| (struct isl_map *)context); |
| } |
| |
| __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map, |
| __isl_take isl_set *context) |
| { |
| isl_map *map_context = isl_map_universe(isl_map_get_space(map)); |
| map_context = isl_map_intersect_domain(map_context, context); |
| return isl_map_gist(map, map_context); |
| } |
| |
| __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map, |
| __isl_take isl_set *context) |
| { |
| isl_map *map_context = isl_map_universe(isl_map_get_space(map)); |
| map_context = isl_map_intersect_range(map_context, context); |
| return isl_map_gist(map, map_context); |
| } |
| |
| __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map, |
| __isl_take isl_set *context) |
| { |
| isl_map *map_context = isl_map_universe(isl_map_get_space(map)); |
| map_context = isl_map_intersect_params(map_context, context); |
| return isl_map_gist(map, map_context); |
| } |
| |
| __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set, |
| __isl_take isl_set *context) |
| { |
| return isl_map_gist_params(set, context); |
| } |
| |
| /* Quick check to see if two basic maps are disjoint. |
| * In particular, we reduce the equalities and inequalities of |
| * one basic map in the context of the equalities of the other |
| * basic map and check if we get a contradiction. |
| */ |
| int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1, |
| __isl_keep isl_basic_map *bmap2) |
| { |
| struct isl_vec *v = NULL; |
| int *elim = NULL; |
| unsigned total; |
| int i; |
| |
| if (!bmap1 || !bmap2) |
| return -1; |
| isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), |
| return -1); |
| if (bmap1->n_div || bmap2->n_div) |
| return 0; |
| if (!bmap1->n_eq && !bmap2->n_eq) |
| return 0; |
| |
| total = isl_space_dim(bmap1->dim, isl_dim_all); |
| if (total == 0) |
| return 0; |
| v = isl_vec_alloc(bmap1->ctx, 1 + total); |
| if (!v) |
| goto error; |
| elim = isl_alloc_array(bmap1->ctx, int, total); |
| if (!elim) |
| goto error; |
| compute_elimination_index(bmap1, elim); |
| for (i = 0; i < bmap2->n_eq; ++i) { |
| int reduced; |
| reduced = reduced_using_equalities(v->block.data, bmap2->eq[i], |
| bmap1, elim); |
| if (reduced && !isl_int_is_zero(v->block.data[0]) && |
| isl_seq_first_non_zero(v->block.data + 1, total) == -1) |
| goto disjoint; |
| } |
| for (i = 0; i < bmap2->n_ineq; ++i) { |
| int reduced; |
| reduced = reduced_using_equalities(v->block.data, |
| bmap2->ineq[i], bmap1, elim); |
| if (reduced && isl_int_is_neg(v->block.data[0]) && |
| isl_seq_first_non_zero(v->block.data + 1, total) == -1) |
| goto disjoint; |
| } |
| compute_elimination_index(bmap2, elim); |
| for (i = 0; i < bmap1->n_ineq; ++i) { |
| int reduced; |
| reduced = reduced_using_equalities(v->block.data, |
| bmap1->ineq[i], bmap2, elim); |
| if (reduced && isl_int_is_neg(v->block.data[0]) && |
| isl_seq_first_non_zero(v->block.data + 1, total) == -1) |
| goto disjoint; |
| } |
| isl_vec_free(v); |
| free(elim); |
| return 0; |
| disjoint: |
| isl_vec_free(v); |
| free(elim); |
| return 1; |
| error: |
| isl_vec_free(v); |
| free(elim); |
| return -1; |
| } |
| |
| int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1, |
| __isl_keep isl_basic_set *bset2) |
| { |
| return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1, |
| (struct isl_basic_map *)bset2); |
| } |
| |
| int isl_map_plain_is_disjoint(__isl_keep isl_map *map1, |
| __isl_keep isl_map *map2) |
| { |
| int i, j; |
| |
| if (!map1 || !map2) |
| return -1; |
| |
| if (isl_map_plain_is_equal(map1, map2)) |
| return 0; |
| |
| for (i = 0; i < map1->n; ++i) { |
| for (j = 0; j < map2->n; ++j) { |
| int d = isl_basic_map_plain_is_disjoint(map1->p[i], |
| map2->p[j]); |
| if (d != 1) |
| return d; |
| } |
| } |
| return 1; |
| } |
| |
| int isl_set_plain_is_disjoint(__isl_keep isl_set *set1, |
| __isl_keep isl_set *set2) |
| { |
| return isl_map_plain_is_disjoint((struct isl_map *)set1, |
| (struct isl_map *)set2); |
| } |
| |
| int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2) |
| { |
| return isl_set_plain_is_disjoint(set1, set2); |
| } |
| |
| /* Check if we can combine a given div with lower bound l and upper |
| * bound u with some other div and if so return that other div. |
| * Otherwise return -1. |
| * |
| * We first check that |
| * - the bounds are opposites of each other (except for the constant |
| * term) |
| * - the bounds do not reference any other div |
| * - no div is defined in terms of this div |
| * |
| * Let m be the size of the range allowed on the div by the bounds. |
| * That is, the bounds are of the form |
| * |
| * e <= a <= e + m - 1 |
| * |
| * with e some expression in the other variables. |
| * We look for another div b such that no third div is defined in terms |
| * of this second div b and such that in any constraint that contains |
| * a (except for the given lower and upper bound), also contains b |
| * with a coefficient that is m times that of b. |
| * That is, all constraints (execpt for the lower and upper bound) |
| * are of the form |
| * |
| * e + f (a + m b) >= 0 |
| * |
| * If so, we return b so that "a + m b" can be replaced by |
| * a single div "c = a + m b". |
| */ |
| static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs, |
| unsigned div, unsigned l, unsigned u) |
| { |
| int i, j; |
| unsigned dim; |
| int coalesce = -1; |
| |
| if (bmap->n_div <= 1) |
| return -1; |
| dim = isl_space_dim(bmap->dim, isl_dim_all); |
| if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1) |
| return -1; |
| if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1, |
| bmap->n_div - div - 1) != -1) |
| return -1; |
| if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1, |
| dim + bmap->n_div)) |
| return -1; |
| |
| for (i = 0; i < bmap->n_div; ++i) { |
| if (isl_int_is_zero(bmap->div[i][0])) |
| continue; |
| if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div])) |
| return -1; |
| } |
| |
| isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]); |
| if (isl_int_is_neg(bmap->ineq[l][0])) { |
| isl_int_sub(bmap->ineq[l][0], |
| bmap->ineq[l][0], bmap->ineq[u][0]); |
| bmap = isl_basic_map_copy(bmap); |
| bmap = isl_basic_map_set_to_empty(bmap); |
| isl_basic_map_free(bmap); |
| return -1; |
| } |
| isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1); |
| for (i = 0; i < bmap->n_div; ++i) { |
| if (i == div) |
| continue; |
| if (!pairs[i]) |
| continue; |
| for (j = 0; j < bmap->n_div; ++j) { |
| if (isl_int_is_zero(bmap->div[j][0])) |
| continue; |
| if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i])) |
| break; |
| } |
| if (j < bmap->n_div) |
| continue; |
| for (j = 0; j < bmap->n_ineq; ++j) { |
| int valid; |
| if (j == l || j == u) |
| continue; |
| if (isl_int_is_zero(bmap->ineq[j][1 + dim + div])) |
| continue; |
| if (isl_int_is_zero(bmap->ineq[j][1 + dim + i])) |
| break; |
| isl_int_mul(bmap->ineq[j][1 + dim + div], |
| bmap->ineq[j][1 + dim + div], |
| bmap->ineq[l][0]); |
| valid = isl_int_eq(bmap->ineq[j][1 + dim + div], |
| bmap->ineq[j][1 + dim + i]); |
| isl_int_divexact(bmap->ineq[j][1 + dim + div], |
| bmap->ineq[j][1 + dim + div], |
| bmap->ineq[l][0]); |
| if (!valid) |
| break; |
| } |
| if (j < bmap->n_ineq) |
| continue; |
| coalesce = i; |
| break; |
| } |
| isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1); |
| isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]); |
| return coalesce; |
| } |
| |
| /* Given a lower and an upper bound on div i, construct an inequality |
| * that when nonnegative ensures that this pair of bounds always allows |
| * for an integer value of the given div. |
| * The lower bound is inequality l, while the upper bound is inequality u. |
| * The constructed inequality is stored in ineq. |
| * g, fl, fu are temporary scalars. |
| * |
| * Let the upper bound be |
| * |
| * -n_u a + e_u >= 0 |
| * |
| * and the lower bound |
| * |
| * n_l a + e_l >= 0 |
| * |
| * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l). |
| * We have |
| * |
| * - f_u e_l <= f_u f_l g a <= f_l e_u |
| * |
| * Since all variables are integer valued, this is equivalent to |
| * |
| * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1) |
| * |
| * If this interval is at least f_u f_l g, then it contains at least |
| * one integer value for a. |
| * That is, the test constraint is |
| * |
| * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g |
| */ |
| static void construct_test_ineq(struct isl_basic_map *bmap, int i, |
| int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu) |
| { |
| unsigned dim; |
| dim = isl_space_dim(bmap->dim, isl_dim_all); |
| |
| isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]); |
| isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g); |
| isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g); |
| isl_int_neg(fu, fu); |
| isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l], |
| 1 + dim + bmap->n_div); |
| isl_int_add(ineq[0], ineq[0], fl); |
| isl_int_add(ineq[0], ineq[0], fu); |
| isl_int_sub_ui(ineq[0], ineq[0], 1); |
| isl_int_mul(g, g, fl); |
| isl_int_mul(g, g, fu); |
| isl_int_sub(ineq[0], ineq[0], g); |
| } |
| |
| /* Remove more kinds of divs that are not strictly needed. |
| * In particular, if all pairs of lower and upper bounds on a div |
| * are such that they allow at least one integer value of the div, |
| * the we can eliminate the div using Fourier-Motzkin without |
| * introducing any spurious solutions. |
| */ |
| static struct isl_basic_map *drop_more_redundant_divs( |
| struct isl_basic_map *bmap, int *pairs, int n) |
| { |
| struct isl_tab *tab = NULL; |
| struct isl_vec *vec = NULL; |
| unsigned dim; |
| int remove = -1; |
| isl_int g, fl, fu; |
| |
| isl_int_init(g); |
| isl_int_init(fl); |
| isl_int_init(fu); |
| |
| if (!bmap) |
| goto error; |
| |
| dim = isl_space_dim(bmap->dim, isl_dim_all); |
| vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div); |
| if (!vec) |
| goto error; |
| |
| tab = isl_tab_from_basic_map(bmap); |
| |
| while (n > 0) { |
| int i, l, u; |
| int best = -1; |
| enum isl_lp_result res; |
| |
| for (i = 0; i < bmap->n_div; ++i) { |
| if (!pairs[i]) |
| continue; |
| if (best >= 0 && pairs[best] <= pairs[i]) |
| continue; |
| best = i; |
| } |
| |
| i = best; |
| for (l = 0; l < bmap->n_ineq; ++l) { |
| if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i])) |
| continue; |
| for (u = 0; u < bmap->n_ineq; ++u) { |
| if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i])) |
| continue; |
| construct_test_ineq(bmap, i, l, u, |
| vec->el, g, fl, fu); |
| res = isl_tab_min(tab, vec->el, |
| bmap->ctx->one, &g, NULL, 0); |
| if (res == isl_lp_error) |
| goto error; |
| if (res == isl_lp_empty) { |
| bmap = isl_basic_map_set_to_empty(bmap); |
| break; |
| } |
| if (res != isl_lp_ok || isl_int_is_neg(g)) |
| break; |
| } |
| if (u < bmap->n_ineq) |
| break; |
| } |
| if (l == bmap->n_ineq) { |
| remove = i; |
| break; |
| } |
| pairs[i] = 0; |
| --n; |
| } |
| |
| isl_tab_free(tab); |
| isl_vec_free(vec); |
| |
| isl_int_clear(g); |
| isl_int_clear(fl); |
| isl_int_clear(fu); |
| |
| free(pairs); |
| |
| if (remove < 0) |
| return bmap; |
| |
| bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1); |
| return isl_basic_map_drop_redundant_divs(bmap); |
| error: |
| free(pairs); |
| isl_basic_map_free(bmap); |
| isl_tab_free(tab); |
| isl_vec_free(vec); |
| isl_int_clear(g); |
| isl_int_clear(fl); |
| isl_int_clear(fu); |
| return NULL; |
| } |
| |
| /* Given a pair of divs div1 and div2 such that, expect for the lower bound l |
| * and the upper bound u, div1 always occurs together with div2 in the form |
| * (div1 + m div2), where m is the constant range on the variable div1 |
| * allowed by l and u, replace the pair div1 and div2 by a single |
| * div that is equal to div1 + m div2. |
| * |
| * The new div will appear in the location that contains div2. |
| * We need to modify all constraints that contain |
| * div2 = (div - div1) / m |
| * (If a constraint does not contain div2, it will also not contain div1.) |
| * If the constraint also contains div1, then we know they appear |
| * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div, |
| * i.e., the coefficient of div is f. |
| * |
| * Otherwise, we first need to introduce div1 into the constraint. |
| * Let the l be |
| * |
| * div1 + f >=0 |
| * |
| * and u |
| * |
| * -div1 + f' >= 0 |
| * |
| * A lower bound on div2 |
| * |
| * n div2 + t >= 0 |
| * |
| * can be replaced by |
| * |
| * (n * (m div 2 + div1) + m t + n f)/g >= 0 |
| * |
| * with g = gcd(m,n). |
| * An upper bound |
| * |
| * -n div2 + t >= 0 |
| * |
| * can be replaced by |
| * |
| * (-n * (m div2 + div1) + m t + n f')/g >= 0 |
| * |
| * These constraint are those that we would obtain from eliminating |
| * div1 using Fourier-Motzkin. |
| * |
| * After all constraints have been modified, we drop the lower and upper |
| * bound and then drop div1. |
| */ |
| static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap, |
| unsigned div1, unsigned div2, unsigned l, unsigned u) |
| { |
| isl_int a; |
| isl_int b; |
| isl_int m; |
| unsigned dim, total; |
| int i; |
| |
| dim = isl_space_dim(bmap->dim, isl_dim_all); |
| total = 1 + dim + bmap->n_div; |
| |
| isl_int_init(a); |
| isl_int_init(b); |
| isl_int_init(m); |
| isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]); |
| isl_int_add_ui(m, m, 1); |
| |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| if (i == l || i == u) |
| continue; |
| if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2])) |
| continue; |
| if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) { |
| isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]); |
| isl_int_divexact(a, m, b); |
| isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b); |
| if (isl_int_is_pos(b)) { |
| isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i], |
| b, bmap->ineq[l], total); |
| } else { |
| isl_int_neg(b, b); |
| isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i], |
| b, bmap->ineq[u], total); |
| } |
| } |
| isl_int_set(bmap->ineq[i][1 + dim + div2], |
| bmap->ineq[i][1 + dim + div1]); |
| isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0); |
| } |
| |
| isl_int_clear(a); |
| isl_int_clear(b); |
| isl_int_clear(m); |
| if (l > u) { |
| isl_basic_map_drop_inequality(bmap, l); |
| isl_basic_map_drop_inequality(bmap, u); |
| } else { |
| isl_basic_map_drop_inequality(bmap, u); |
| isl_basic_map_drop_inequality(bmap, l); |
| } |
| bmap = isl_basic_map_drop_div(bmap, div1); |
| return bmap; |
| } |
| |
| /* First check if we can coalesce any pair of divs and |
| * then continue with dropping more redundant divs. |
| * |
| * We loop over all pairs of lower and upper bounds on a div |
| * with coefficient 1 and -1, respectively, check if there |
| * is any other div "c" with which we can coalesce the div |
| * and if so, perform the coalescing. |
| */ |
| static struct isl_basic_map *coalesce_or_drop_more_redundant_divs( |
| struct isl_basic_map *bmap, int *pairs, int n) |
| { |
| int i, l, u; |
| unsigned dim; |
| |
| dim = isl_space_dim(bmap->dim, isl_dim_all); |
| |
| for (i = 0; i < bmap->n_div; ++i) { |
| if (!pairs[i]) |
| continue; |
| for (l = 0; l < bmap->n_ineq; ++l) { |
| if (!isl_int_is_one(bmap->ineq[l][1 + dim + i])) |
| continue; |
| for (u = 0; u < bmap->n_ineq; ++u) { |
| int c; |
| |
| if (!isl_int_is_negone(bmap->ineq[u][1+dim+i])) |
| continue; |
| c = div_find_coalesce(bmap, pairs, i, l, u); |
| if (c < 0) |
| continue; |
| free(pairs); |
| bmap = coalesce_divs(bmap, i, c, l, u); |
| return isl_basic_map_drop_redundant_divs(bmap); |
| } |
| } |
| } |
| |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) |
| return bmap; |
| |
| return drop_more_redundant_divs(bmap, pairs, n); |
| } |
| |
| /* Remove divs that are not strictly needed. |
| * In particular, if a div only occurs positively (or negatively) |
| * in constraints, then it can simply be dropped. |
| * Also, if a div occurs only occurs in two constraints and if moreover |
| * those two constraints are opposite to each other, except for the constant |
| * term and if the sum of the constant terms is such that for any value |
| * of the other values, there is always at least one integer value of the |
| * div, i.e., if one plus this sum is greater than or equal to |
| * the (absolute value) of the coefficent of the div in the constraints, |
| * then we can also simply drop the div. |
| * |
| * If any divs are left after these simple checks then we move on |
| * to more complicated cases in drop_more_redundant_divs. |
| */ |
| struct isl_basic_map *isl_basic_map_drop_redundant_divs( |
| struct isl_basic_map *bmap) |
| { |
| int i, j; |
| unsigned off; |
| int *pairs = NULL; |
| int n = 0; |
| |
| if (!bmap) |
| goto error; |
| |
| off = isl_space_dim(bmap->dim, isl_dim_all); |
| pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div); |
| if (!pairs) |
| goto error; |
| |
| for (i = 0; i < bmap->n_div; ++i) { |
| int pos, neg; |
| int last_pos, last_neg; |
| int redundant; |
| int defined; |
| |
| defined = !isl_int_is_zero(bmap->div[i][0]); |
| for (j = 0; j < bmap->n_eq; ++j) |
| if (!isl_int_is_zero(bmap->eq[j][1 + off + i])) |
| break; |
| if (j < bmap->n_eq) |
| continue; |
| ++n; |
| pos = neg = 0; |
| for (j = 0; j < bmap->n_ineq; ++j) { |
| if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) { |
| last_pos = j; |
| ++pos; |
| } |
| if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) { |
| last_neg = j; |
| ++neg; |
| } |
| } |
| pairs[i] = pos * neg; |
| if (pairs[i] == 0) { |
| for (j = bmap->n_ineq - 1; j >= 0; --j) |
| if (!isl_int_is_zero(bmap->ineq[j][1+off+i])) |
| isl_basic_map_drop_inequality(bmap, j); |
| bmap = isl_basic_map_drop_div(bmap, i); |
| free(pairs); |
| return isl_basic_map_drop_redundant_divs(bmap); |
| } |
| if (pairs[i] != 1) |
| continue; |
| if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1, |
| bmap->ineq[last_neg] + 1, |
| off + bmap->n_div)) |
| continue; |
| |
| isl_int_add(bmap->ineq[last_pos][0], |
| bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]); |
| isl_int_add_ui(bmap->ineq[last_pos][0], |
| bmap->ineq[last_pos][0], 1); |
| redundant = isl_int_ge(bmap->ineq[last_pos][0], |
| bmap->ineq[last_pos][1+off+i]); |
| isl_int_sub_ui(bmap->ineq[last_pos][0], |
| bmap->ineq[last_pos][0], 1); |
| isl_int_sub(bmap->ineq[last_pos][0], |
| bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]); |
| if (!redundant) { |
| if (defined || |
| !ok_to_set_div_from_bound(bmap, i, last_pos)) { |
| pairs[i] = 0; |
| --n; |
| continue; |
| } |
| bmap = set_div_from_lower_bound(bmap, i, last_pos); |
| bmap = isl_basic_map_simplify(bmap); |
| free(pairs); |
| return isl_basic_map_drop_redundant_divs(bmap); |
| } |
| if (last_pos > last_neg) { |
| isl_basic_map_drop_inequality(bmap, last_pos); |
| isl_basic_map_drop_inequality(bmap, last_neg); |
| } else { |
| isl_basic_map_drop_inequality(bmap, last_neg); |
| isl_basic_map_drop_inequality(bmap, last_pos); |
| } |
| bmap = isl_basic_map_drop_div(bmap, i); |
| free(pairs); |
| return isl_basic_map_drop_redundant_divs(bmap); |
| } |
| |
| if (n > 0) |
| return coalesce_or_drop_more_redundant_divs(bmap, pairs, n); |
| |
| free(pairs); |
| return bmap; |
| error: |
| free(pairs); |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| struct isl_basic_set *isl_basic_set_drop_redundant_divs( |
| struct isl_basic_set *bset) |
| { |
| return (struct isl_basic_set *) |
| isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset); |
| } |
| |
| struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map) |
| { |
| int i; |
| |
| if (!map) |
| return NULL; |
| for (i = 0; i < map->n; ++i) { |
| map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]); |
| if (!map->p[i]) |
| goto error; |
| } |
| ISL_F_CLR(map, ISL_MAP_NORMALIZED); |
| return map; |
| error: |
| isl_map_free(map); |
| return NULL; |
| } |
| |
| struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set) |
| { |
| return (struct isl_set *) |
| isl_map_drop_redundant_divs((struct isl_map *)set); |
| } |