| /* |
| * Copyright 2008-2009 Katholieke Universiteit Leuven |
| * Copyright 2012-2013 Ecole Normale Superieure |
| * Copyright 2014-2015 INRIA Rocquencourt |
| * Copyright 2016 Sven Verdoolaege |
| * |
| * 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 Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France |
| * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt, |
| * B.P. 105 - 78153 Le Chesnay, France |
| */ |
| |
| #include <isl_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> |
| #include <isl_vec_private.h> |
| |
| #include <bset_to_bmap.c> |
| #include <bset_from_bmap.c> |
| #include <set_to_map.c> |
| #include <set_from_map.c> |
| |
| 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; |
| } |
| } |
| |
| __isl_give isl_basic_map *isl_basic_map_normalize_constraints( |
| __isl_take 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; |
| } |
| |
| __isl_give isl_basic_set *isl_basic_set_normalize_constraints( |
| __isl_take isl_basic_set *bset) |
| { |
| isl_basic_map *bmap = bset_to_bmap(bset); |
| return bset_from_bmap(isl_basic_map_normalize_constraints(bmap)); |
| } |
| |
| /* Reduce the coefficient of the variable at position "pos" |
| * in integer division "div", such that it lies in the half-open |
| * interval (1/2,1/2], extracting any excess value from this integer division. |
| * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0 |
| * corresponds to the constant term. |
| * |
| * That is, the integer division is of the form |
| * |
| * floor((... + (c * d + r) * x_pos + ...)/d) |
| * |
| * with -d < 2 * r <= d. |
| * Replace it by |
| * |
| * floor((... + r * x_pos + ...)/d) + c * x_pos |
| * |
| * If 2 * ((c * d + r) % d) <= d, then c = floor((c * d + r)/d). |
| * Otherwise, c = floor((c * d + r)/d) + 1. |
| * |
| * This is the same normalization that is performed by isl_aff_floor. |
| */ |
| static __isl_give isl_basic_map *reduce_coefficient_in_div( |
| __isl_take isl_basic_map *bmap, int div, int pos) |
| { |
| isl_int shift; |
| int add_one; |
| |
| isl_int_init(shift); |
| isl_int_fdiv_r(shift, bmap->div[div][1 + pos], bmap->div[div][0]); |
| isl_int_mul_ui(shift, shift, 2); |
| add_one = isl_int_gt(shift, bmap->div[div][0]); |
| isl_int_fdiv_q(shift, bmap->div[div][1 + pos], bmap->div[div][0]); |
| if (add_one) |
| isl_int_add_ui(shift, shift, 1); |
| isl_int_neg(shift, shift); |
| bmap = isl_basic_map_shift_div(bmap, div, pos, shift); |
| isl_int_clear(shift); |
| |
| return bmap; |
| } |
| |
| /* Does the coefficient of the variable at position "pos" |
| * in integer division "div" need to be reduced? |
| * That is, does it lie outside the half-open interval (1/2,1/2]? |
| * The coefficient c/d lies outside this interval if abs(2 * c) >= d and |
| * 2 * c != d. |
| */ |
| static isl_bool needs_reduction(__isl_keep isl_basic_map *bmap, int div, |
| int pos) |
| { |
| isl_bool r; |
| |
| if (isl_int_is_zero(bmap->div[div][1 + pos])) |
| return isl_bool_false; |
| |
| isl_int_mul_ui(bmap->div[div][1 + pos], bmap->div[div][1 + pos], 2); |
| r = isl_int_abs_ge(bmap->div[div][1 + pos], bmap->div[div][0]) && |
| !isl_int_eq(bmap->div[div][1 + pos], bmap->div[div][0]); |
| isl_int_divexact_ui(bmap->div[div][1 + pos], |
| bmap->div[div][1 + pos], 2); |
| |
| return r; |
| } |
| |
| /* Reduce the coefficients (including the constant term) of |
| * integer division "div", if needed. |
| * In particular, make sure all coefficients lie in |
| * the half-open interval (1/2,1/2]. |
| */ |
| static __isl_give isl_basic_map *reduce_div_coefficients_of_div( |
| __isl_take isl_basic_map *bmap, int div) |
| { |
| int i; |
| unsigned total = 1 + isl_basic_map_total_dim(bmap); |
| |
| for (i = 0; i < total; ++i) { |
| isl_bool reduce; |
| |
| reduce = needs_reduction(bmap, div, i); |
| if (reduce < 0) |
| return isl_basic_map_free(bmap); |
| if (!reduce) |
| continue; |
| bmap = reduce_coefficient_in_div(bmap, div, i); |
| if (!bmap) |
| break; |
| } |
| |
| return bmap; |
| } |
| |
| /* Reduce the coefficients (including the constant term) of |
| * the known integer divisions, if needed |
| * In particular, make sure all coefficients lie in |
| * the half-open interval (1/2,1/2]. |
| */ |
| static __isl_give isl_basic_map *reduce_div_coefficients( |
| __isl_take isl_basic_map *bmap) |
| { |
| int i; |
| |
| if (!bmap) |
| return NULL; |
| if (bmap->n_div == 0) |
| return bmap; |
| |
| for (i = 0; i < bmap->n_div; ++i) { |
| if (isl_int_is_zero(bmap->div[i][0])) |
| continue; |
| bmap = reduce_div_coefficients_of_div(bmap, i); |
| if (!bmap) |
| break; |
| } |
| |
| return bmap; |
| } |
| |
| /* Remove any common factor in numerator and denominator of the div expression, |
| * not taking into account the constant term. |
| * That is, if the div is of the form |
| * |
| * floor((a + m f(x))/(m d)) |
| * |
| * then replace it by |
| * |
| * floor((floor(a/m) + f(x))/d) |
| * |
| * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d |
| * and can therefore not influence the result of the floor. |
| */ |
| static void normalize_div_expression(__isl_keep isl_basic_map *bmap, int div) |
| { |
| unsigned total = isl_basic_map_total_dim(bmap); |
| isl_ctx *ctx = bmap->ctx; |
| |
| if (isl_int_is_zero(bmap->div[div][0])) |
| return; |
| isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd); |
| isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, bmap->div[div][0]); |
| if (isl_int_is_one(ctx->normalize_gcd)) |
| return; |
| isl_int_fdiv_q(bmap->div[div][1], bmap->div[div][1], |
| ctx->normalize_gcd); |
| isl_int_divexact(bmap->div[div][0], bmap->div[div][0], |
| ctx->normalize_gcd); |
| isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2, |
| ctx->normalize_gcd, total); |
| } |
| |
| /* Remove any common factor in numerator and denominator of a div expression, |
| * not taking into account the constant term. |
| * That is, look for any div of the form |
| * |
| * floor((a + m f(x))/(m d)) |
| * |
| * and replace it by |
| * |
| * floor((floor(a/m) + f(x))/d) |
| * |
| * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d |
| * and can therefore not influence the result of the floor. |
| */ |
| static __isl_give isl_basic_map *normalize_div_expressions( |
| __isl_take isl_basic_map *bmap) |
| { |
| int i; |
| |
| if (!bmap) |
| return NULL; |
| if (bmap->n_div == 0) |
| return bmap; |
| |
| for (i = 0; i < bmap->n_div; ++i) |
| normalize_div_expression(bmap, i); |
| |
| return bmap; |
| } |
| |
| /* 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]); |
| normalize_div_expression(bmap, k); |
| } 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 __isl_give isl_basic_map *eliminate_div(__isl_take 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); |
| |
| bmap = isl_basic_map_drop_div(bmap, div); |
| |
| return bmap; |
| } |
| |
| /* Check if elimination of div "div" using equality "eq" would not |
| * result in a div depending on a later div. |
| */ |
| static isl_bool ok_to_eliminate_div(__isl_keep 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 isl_bool_true; |
| |
| for (k = 0; k <= last_div; ++k) { |
| if (isl_int_is_zero(bmap->div[k][0])) |
| continue; |
| if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos])) |
| return isl_bool_false; |
| } |
| |
| return isl_bool_true; |
| } |
| |
| /* Eliminate divs based on equalities |
| */ |
| static __isl_give isl_basic_map *eliminate_divs_eq( |
| __isl_take 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) { |
| isl_bool ok; |
| |
| if (!isl_int_is_one(bmap->eq[i][off + d]) && |
| !isl_int_is_negone(bmap->eq[i][off + d])) |
| continue; |
| ok = ok_to_eliminate_div(bmap, bmap->eq[i], d); |
| if (ok < 0) |
| return isl_basic_map_free(bmap); |
| if (!ok) |
| continue; |
| modified = 1; |
| *progress = 1; |
| bmap = eliminate_div(bmap, bmap->eq[i], d, 1); |
| if (isl_basic_map_drop_equality(bmap, i) < 0) |
| return isl_basic_map_free(bmap); |
| break; |
| } |
| } |
| if (modified) |
| return eliminate_divs_eq(bmap, progress); |
| return bmap; |
| } |
| |
| /* Eliminate divs based on inequalities |
| */ |
| static __isl_give isl_basic_map *eliminate_divs_ineq( |
| __isl_take 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; |
| } |
| |
| /* Does the equality constraint at position "eq" in "bmap" involve |
| * any local variables in the range [first, first + n) |
| * that are not marked as having an explicit representation? |
| */ |
| static isl_bool bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map *bmap, |
| int eq, unsigned first, unsigned n) |
| { |
| unsigned o_div; |
| int i; |
| |
| if (!bmap) |
| return isl_bool_error; |
| |
| o_div = isl_basic_map_offset(bmap, isl_dim_div); |
| for (i = 0; i < n; ++i) { |
| isl_bool unknown; |
| |
| if (isl_int_is_zero(bmap->eq[eq][o_div + first + i])) |
| continue; |
| unknown = isl_basic_map_div_is_marked_unknown(bmap, first + i); |
| if (unknown < 0) |
| return isl_bool_error; |
| if (unknown) |
| return isl_bool_true; |
| } |
| |
| return isl_bool_false; |
| } |
| |
| /* The last local variable involved in the equality constraint |
| * at position "eq" in "bmap" is the local variable at position "div". |
| * It can therefore be used to extract an explicit representation |
| * for that variable. |
| * Do so unless the local variable already has an explicit representation or |
| * the explicit representation would involve any other local variables |
| * that in turn do not have an explicit representation. |
| * An equality constraint involving local variables without an explicit |
| * representation can be used in isl_basic_map_drop_redundant_divs |
| * to separate out an independent local variable. Introducing |
| * an explicit representation here would block this transformation, |
| * while the partial explicit representation in itself is not very useful. |
| * Set *progress if anything is changed. |
| * |
| * The equality constraint is of the form |
| * |
| * f(x) + n e >= 0 |
| * |
| * with n a positive number. The explicit representation derived from |
| * this constraint is |
| * |
| * floor((-f(x))/n) |
| */ |
| static __isl_give isl_basic_map *set_div_from_eq(__isl_take isl_basic_map *bmap, |
| int div, int eq, int *progress) |
| { |
| unsigned total, o_div; |
| isl_bool involves; |
| |
| if (!bmap) |
| return NULL; |
| |
| if (!isl_int_is_zero(bmap->div[div][0])) |
| return bmap; |
| |
| involves = bmap_eq_involves_unknown_divs(bmap, eq, 0, div); |
| if (involves < 0) |
| return isl_basic_map_free(bmap); |
| if (involves) |
| return bmap; |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| o_div = isl_basic_map_offset(bmap, isl_dim_div); |
| isl_seq_neg(bmap->div[div] + 1, bmap->eq[eq], 1 + total); |
| isl_int_set_si(bmap->div[div][1 + o_div + div], 0); |
| isl_int_set(bmap->div[div][0], bmap->eq[eq][o_div + div]); |
| if (progress) |
| *progress = 1; |
| ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); |
| |
| return bmap; |
| } |
| |
| __isl_give isl_basic_map *isl_basic_map_gauss(__isl_take 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) |
| bmap = set_div_from_eq(bmap, last_var - total_var, |
| done, progress); |
| if (!bmap) |
| return NULL; |
| } |
| 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; |
| } |
| |
| __isl_give isl_basic_set *isl_basic_set_gauss( |
| __isl_take isl_basic_set *bset, int *progress) |
| { |
| return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(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; |
| } |
| |
| /* Hash table of inequalities in a basic map. |
| * "index" is an array of addresses of inequalities in the basic map, some |
| * of which are NULL. The inequalities are hashed on the coefficients |
| * except the constant term. |
| * "size" is the number of elements in the array and is always a power of two |
| * "bits" is the number of bits need to represent an index into the array. |
| * "total" is the total dimension of the basic map. |
| */ |
| struct isl_constraint_index { |
| unsigned int size; |
| int bits; |
| isl_int ***index; |
| unsigned total; |
| }; |
| |
| /* Fill in the "ci" data structure for holding the inequalities of "bmap". |
| */ |
| static isl_stat create_constraint_index(struct isl_constraint_index *ci, |
| __isl_keep isl_basic_map *bmap) |
| { |
| isl_ctx *ctx; |
| |
| ci->index = NULL; |
| if (!bmap) |
| return isl_stat_error; |
| ci->total = isl_basic_set_total_dim(bmap); |
| if (bmap->n_ineq == 0) |
| return isl_stat_ok; |
| ci->size = round_up(4 * (bmap->n_ineq + 1) / 3 - 1); |
| ci->bits = ffs(ci->size) - 1; |
| ctx = isl_basic_map_get_ctx(bmap); |
| ci->index = isl_calloc_array(ctx, isl_int **, ci->size); |
| if (!ci->index) |
| return isl_stat_error; |
| |
| return isl_stat_ok; |
| } |
| |
| /* Free the memory allocated by create_constraint_index. |
| */ |
| static void constraint_index_free(struct isl_constraint_index *ci) |
| { |
| free(ci->index); |
| } |
| |
| /* Return the position in ci->index that contains the address of |
| * an inequality that is equal to *ineq up to the constant term, |
| * provided this address is not identical to "ineq". |
| * If there is no such inequality, then return the position where |
| * such an inequality should be inserted. |
| */ |
| static int hash_index_ineq(struct isl_constraint_index *ci, isl_int **ineq) |
| { |
| int h; |
| uint32_t hash = isl_seq_get_hash_bits((*ineq) + 1, ci->total, ci->bits); |
| for (h = hash; ci->index[h]; h = (h+1) % ci->size) |
| if (ineq != ci->index[h] && |
| isl_seq_eq((*ineq) + 1, ci->index[h][0]+1, ci->total)) |
| break; |
| return h; |
| } |
| |
| /* Return the position in ci->index that contains the address of |
| * an inequality that is equal to the k'th inequality of "bmap" |
| * up to the constant term, provided it does not point to the very |
| * same inequality. |
| * If there is no such inequality, then return the position where |
| * such an inequality should be inserted. |
| */ |
| static int hash_index(struct isl_constraint_index *ci, |
| __isl_keep isl_basic_map *bmap, int k) |
| { |
| return hash_index_ineq(ci, &bmap->ineq[k]); |
| } |
| |
| static int set_hash_index(struct isl_constraint_index *ci, |
| __isl_keep isl_basic_set *bset, int k) |
| { |
| return hash_index(ci, bset, k); |
| } |
| |
| /* Fill in the "ci" data structure with the inequalities of "bset". |
| */ |
| static isl_stat setup_constraint_index(struct isl_constraint_index *ci, |
| __isl_keep isl_basic_set *bset) |
| { |
| int k, h; |
| |
| if (create_constraint_index(ci, bset) < 0) |
| return isl_stat_error; |
| |
| for (k = 0; k < bset->n_ineq; ++k) { |
| h = set_hash_index(ci, bset, k); |
| ci->index[h] = &bset->ineq[k]; |
| } |
| |
| return isl_stat_ok; |
| } |
| |
| /* Is the inequality ineq (obviously) redundant with respect |
| * to the constraints in "ci"? |
| * |
| * Look for an inequality in "ci" with the same coefficients and then |
| * check if the contant term of "ineq" is greater than or equal |
| * to the constant term of that inequality. If so, "ineq" is clearly |
| * redundant. |
| * |
| * Note that hash_index_ineq ignores a stored constraint if it has |
| * the same address as the passed inequality. It is ok to pass |
| * the address of a local variable here since it will never be |
| * the same as the address of a constraint in "ci". |
| */ |
| static isl_bool constraint_index_is_redundant(struct isl_constraint_index *ci, |
| isl_int *ineq) |
| { |
| int h; |
| |
| h = hash_index_ineq(ci, &ineq); |
| if (!ci->index[h]) |
| return isl_bool_false; |
| return isl_int_ge(ineq[0], (*ci->index[h])[0]); |
| } |
| |
| /* 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 __isl_give isl_basic_map *remove_duplicate_divs( |
| __isl_take 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; |
| |
| bmap = isl_basic_map_order_divs(bmap); |
| 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; |
| |
| size = round_up(4 * bmap->n_div / 3 - 1); |
| if (size == 0) |
| return bmap; |
| elim_for = isl_calloc_array(ctx, int, bmap->n_div); |
| bits = ffs(size) - 1; |
| index = isl_calloc_array(ctx, int, size); |
| if (!elim_for || !index) |
| goto out; |
| 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); |
| bmap = eliminate_div(bmap, eq.data, l, 1); |
| if (!bmap) |
| break; |
| 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 __isl_give isl_basic_map *normalize_divs(__isl_take 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 = NULL; |
| 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: |
| free(pos); |
| isl_mat_free(C); |
| isl_mat_free(C2); |
| isl_mat_free(T); |
| return bmap; |
| } |
| |
| static __isl_give isl_basic_map *set_div_from_lower_bound( |
| __isl_take 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 isl_bool ok_to_set_div_from_bound(__isl_keep 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 isl_bool_false; |
| } |
| |
| /* 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 isl_bool_false; |
| } |
| |
| return isl_bool_true; |
| } |
| |
| /* Would an expression for div "div" based on inequality "ineq" of "bmap" |
| * be a better expression than the current one? |
| * |
| * If we do not have any expression yet, then any expression would be better. |
| * Otherwise we check if the last variable involved in the inequality |
| * (disregarding the div that it would define) is in an earlier position |
| * than the last variable involved in the current div expression. |
| */ |
| static isl_bool better_div_constraint(__isl_keep isl_basic_map *bmap, |
| int div, int ineq) |
| { |
| unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all); |
| int last_div; |
| int last_ineq; |
| |
| if (isl_int_is_zero(bmap->div[div][0])) |
| return isl_bool_true; |
| |
| if (isl_seq_last_non_zero(bmap->ineq[ineq] + total + div + 1, |
| bmap->n_div - (div + 1)) >= 0) |
| return isl_bool_false; |
| |
| last_ineq = isl_seq_last_non_zero(bmap->ineq[ineq], total + div); |
| last_div = isl_seq_last_non_zero(bmap->div[div] + 1, |
| total + bmap->n_div); |
| |
| return last_ineq < last_div; |
| } |
| |
| /* 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 or |
| * a "better" expression for a div for which we already have an expression. |
| * "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 __isl_give isl_basic_map *check_for_div_constraints( |
| __isl_take 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) { |
| isl_bool set_div; |
| |
| if (isl_int_is_zero(bmap->ineq[k][total + i])) |
| continue; |
| if (isl_int_abs_ge(sum, bmap->ineq[k][total + i])) |
| continue; |
| set_div = better_div_constraint(bmap, i, k); |
| if (set_div >= 0 && set_div) |
| set_div = ok_to_set_div_from_bound(bmap, i, k); |
| if (set_div < 0) |
| return isl_basic_map_free(bmap); |
| if (!set_div) |
| 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; |
| } |
| |
| __isl_give isl_basic_map *isl_basic_map_remove_duplicate_constraints( |
| __isl_take isl_basic_map *bmap, int *progress, int detect_divs) |
| { |
| struct isl_constraint_index ci; |
| int k, l, h; |
| unsigned total = isl_basic_map_total_dim(bmap); |
| isl_int sum; |
| |
| if (!bmap || bmap->n_ineq <= 1) |
| return bmap; |
| |
| if (create_constraint_index(&ci, bmap) < 0) |
| return bmap; |
| |
| h = isl_seq_get_hash_bits(bmap->ineq[0] + 1, total, ci.bits); |
| ci.index[h] = &bmap->ineq[0]; |
| for (k = 1; k < bmap->n_ineq; ++k) { |
| h = hash_index(&ci, bmap, k); |
| if (!ci.index[h]) { |
| ci.index[h] = &bmap->ineq[k]; |
| continue; |
| } |
| if (progress) |
| *progress = 1; |
| l = ci.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(&ci, bmap, k); |
| isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total); |
| if (!ci.index[h]) |
| continue; |
| l = ci.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); |
| |
| constraint_index_free(&ci); |
| return bmap; |
| } |
| |
| /* Detect all pairs of inequalities that form an equality. |
| * |
| * isl_basic_map_remove_duplicate_constraints detects at most one such pair. |
| * Call it repeatedly while it is making progress. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_detect_inequality_pairs( |
| __isl_take isl_basic_map *bmap, int *progress) |
| { |
| int duplicate; |
| |
| do { |
| duplicate = 0; |
| bmap = isl_basic_map_remove_duplicate_constraints(bmap, |
| &duplicate, 0); |
| if (progress && duplicate) |
| *progress = 1; |
| } while (duplicate); |
| |
| return bmap; |
| } |
| |
| /* Eliminate knowns divs from constraints where they appear with |
| * a (positive or negative) unit coefficient. |
| * |
| * That is, replace |
| * |
| * floor(e/m) + f >= 0 |
| * |
| * by |
| * |
| * e + m f >= 0 |
| * |
| * and |
| * |
| * -floor(e/m) + f >= 0 |
| * |
| * by |
| * |
| * -e + m f + m - 1 >= 0 |
| * |
| * The first conversion is valid because floor(e/m) >= -f is equivalent |
| * to e/m >= -f because -f is an integral expression. |
| * The second conversion follows from the fact that |
| * |
| * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m) |
| * |
| * |
| * Note that one of the div constraints may have been eliminated |
| * due to being redundant with respect to the constraint that is |
| * being modified by this function. The modified constraint may |
| * no longer imply this div constraint, so we add it back to make |
| * sure we do not lose any information. |
| * |
| * We skip integral divs, i.e., those with denominator 1, as we would |
| * risk eliminating the div from the div constraints. We do not need |
| * to handle those divs here anyway since the div constraints will turn |
| * out to form an equality and this equality can then be used to eliminate |
| * the div from all constraints. |
| */ |
| static __isl_give isl_basic_map *eliminate_unit_divs( |
| __isl_take isl_basic_map *bmap, int *progress) |
| { |
| int i, j; |
| isl_ctx *ctx; |
| unsigned total; |
| |
| if (!bmap) |
| return NULL; |
| |
| ctx = isl_basic_map_get_ctx(bmap); |
| 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_one(bmap->div[i][0])) |
| continue; |
| for (j = 0; j < bmap->n_ineq; ++j) { |
| int s; |
| |
| if (!isl_int_is_one(bmap->ineq[j][total + i]) && |
| !isl_int_is_negone(bmap->ineq[j][total + i])) |
| continue; |
| |
| *progress = 1; |
| |
| s = isl_int_sgn(bmap->ineq[j][total + i]); |
| isl_int_set_si(bmap->ineq[j][total + i], 0); |
| if (s < 0) |
| isl_seq_combine(bmap->ineq[j], |
| ctx->negone, bmap->div[i] + 1, |
| bmap->div[i][0], bmap->ineq[j], |
| total + bmap->n_div); |
| else |
| isl_seq_combine(bmap->ineq[j], |
| ctx->one, bmap->div[i] + 1, |
| bmap->div[i][0], bmap->ineq[j], |
| total + bmap->n_div); |
| if (s < 0) { |
| isl_int_add(bmap->ineq[j][0], |
| bmap->ineq[j][0], bmap->div[i][0]); |
| isl_int_sub_ui(bmap->ineq[j][0], |
| bmap->ineq[j][0], 1); |
| } |
| |
| bmap = isl_basic_map_extend_constraints(bmap, 0, 1); |
| if (isl_basic_map_add_div_constraint(bmap, i, s) < 0) |
| return isl_basic_map_free(bmap); |
| } |
| } |
| |
| return bmap; |
| } |
| |
| __isl_give isl_basic_map *isl_basic_map_simplify(__isl_take isl_basic_map *bmap) |
| { |
| int progress = 1; |
| if (!bmap) |
| return NULL; |
| while (progress) { |
| isl_bool empty; |
| |
| progress = 0; |
| empty = isl_basic_map_plain_is_empty(bmap); |
| if (empty < 0) |
| return isl_basic_map_free(bmap); |
| if (empty) |
| break; |
| bmap = isl_basic_map_normalize_constraints(bmap); |
| bmap = reduce_div_coefficients(bmap); |
| bmap = normalize_div_expressions(bmap); |
| bmap = remove_duplicate_divs(bmap, &progress); |
| bmap = eliminate_unit_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 = isl_basic_map_remove_duplicate_constraints(bmap, |
| &progress, 1); |
| if (bmap && progress) |
| ISL_F_CLR(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS); |
| } |
| return bmap; |
| } |
| |
| struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset) |
| { |
| return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset))); |
| } |
| |
| |
| isl_bool isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap, |
| isl_int *constraint, unsigned div) |
| { |
| unsigned pos; |
| |
| if (!bmap) |
| return isl_bool_error; |
| |
| 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 isl_bool_false; |
| if (isl_seq_first_non_zero(constraint+pos+1, |
| bmap->n_div-div-1) != -1) |
| return isl_bool_false; |
| } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) { |
| if (!isl_seq_eq(constraint, bmap->div[div]+1, pos)) |
| return isl_bool_false; |
| if (isl_seq_first_non_zero(constraint+pos+1, |
| bmap->n_div-div-1) != -1) |
| return isl_bool_false; |
| } else |
| return isl_bool_false; |
| |
| return isl_bool_true; |
| } |
| |
| isl_bool isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset, |
| isl_int *constraint, unsigned div) |
| { |
| return isl_basic_map_is_div_constraint(bset, constraint, div); |
| } |
| |
| |
| /* 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 isl_bool div_is_redundant(__isl_keep 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 isl_bool_false; |
| |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| isl_bool red; |
| |
| if (isl_int_is_zero(bmap->ineq[i][pos])) |
| continue; |
| red = isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div); |
| if (red < 0 || !red) |
| return red; |
| } |
| |
| 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+pos])) |
| return isl_bool_false; |
| } |
| |
| return isl_bool_true; |
| } |
| |
| /* |
| * Remove divs that don't occur in any of the constraints or other divs. |
| * These can arise when dropping constraints from a basic map or |
| * when the divs of a basic map have been temporarily aligned |
| * with the divs of another basic map. |
| */ |
| static __isl_give isl_basic_map *remove_redundant_divs( |
| __isl_take isl_basic_map *bmap) |
| { |
| int i; |
| |
| if (!bmap) |
| return NULL; |
| |
| for (i = bmap->n_div-1; i >= 0; --i) { |
| isl_bool redundant; |
| |
| redundant = div_is_redundant(bmap, i); |
| if (redundant < 0) |
| return isl_basic_map_free(bmap); |
| if (!redundant) |
| continue; |
| bmap = isl_basic_map_drop_div(bmap, i); |
| } |
| return bmap; |
| } |
| |
| /* Mark "bmap" as final, without checking for obviously redundant |
| * integer divisions. This function should be used when "bmap" |
| * is known not to involve any such integer divisions. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_mark_final( |
| __isl_take isl_basic_map *bmap) |
| { |
| if (!bmap) |
| return NULL; |
| ISL_F_SET(bmap, ISL_BASIC_SET_FINAL); |
| return bmap; |
| } |
| |
| /* Mark "bmap" as final, after removing obviously redundant integer divisions. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_finalize(__isl_take isl_basic_map *bmap) |
| { |
| bmap = remove_redundant_divs(bmap); |
| bmap = isl_basic_map_mark_final(bmap); |
| return bmap; |
| } |
| |
| struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset) |
| { |
| return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset))); |
| } |
| |
| /* 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 __isl_give isl_basic_map *remove_dependent_vars( |
| __isl_take isl_basic_map *bmap, int pos) |
| { |
| int i; |
| |
| if (!bmap) |
| return NULL; |
| |
| 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; |
| bmap = isl_basic_map_mark_div_unknown(bmap, i); |
| if (!bmap) |
| return NULL; |
| } |
| return bmap; |
| } |
| |
| /* Eliminate the specified variables from the constraints using |
| * Fourier-Motzkin. The variables themselves are not removed. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_eliminate_vars( |
| __isl_take 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); |
| if (!bmap) |
| return NULL; |
| |
| 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 = isl_basic_map_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 bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset), |
| pos, n)); |
| } |
| |
| /* Eliminate the specified n dimensions starting at first from the |
| * constraints, without removing the dimensions from the space. |
| * If the set is rational, the dimensions are eliminated using Fourier-Motzkin. |
| * Otherwise, they are projected out and the original space is restored. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_eliminate( |
| __isl_take isl_basic_map *bmap, |
| enum isl_dim_type type, unsigned first, unsigned n) |
| { |
| isl_space *space; |
| |
| if (!bmap) |
| return NULL; |
| if (n == 0) |
| return bmap; |
| |
| if (first + n > isl_basic_map_dim(bmap, type) || first + n < first) |
| isl_die(bmap->ctx, isl_error_invalid, |
| "index out of bounds", goto error); |
| |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) { |
| first += isl_basic_map_offset(bmap, type) - 1; |
| bmap = isl_basic_map_eliminate_vars(bmap, first, n); |
| return isl_basic_map_finalize(bmap); |
| } |
| |
| space = isl_basic_map_get_space(bmap); |
| bmap = isl_basic_map_project_out(bmap, type, first, n); |
| bmap = isl_basic_map_insert_dims(bmap, type, first, n); |
| bmap = isl_basic_map_reset_space(bmap, space); |
| return bmap; |
| error: |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| __isl_give isl_basic_set *isl_basic_set_eliminate( |
| __isl_take isl_basic_set *bset, |
| enum isl_dim_type type, unsigned first, unsigned n) |
| { |
| return isl_basic_map_eliminate(bset, type, first, n); |
| } |
| |
| /* Remove all constraints from "bmap" that reference any unknown local |
| * variables (directly or indirectly). |
| * |
| * Dropping all constraints on a local variable will make it redundant, |
| * so it will get removed implicitly by |
| * isl_basic_map_drop_constraints_involving_dims. Some other local |
| * variables may also end up becoming redundant if they only appear |
| * in constraints together with the unknown local variable. |
| * Therefore, start over after calling |
| * isl_basic_map_drop_constraints_involving_dims. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_drop_constraint_involving_unknown_divs( |
| __isl_take isl_basic_map *bmap) |
| { |
| isl_bool known; |
| int i, n_div, o_div; |
| |
| known = isl_basic_map_divs_known(bmap); |
| if (known < 0) |
| return isl_basic_map_free(bmap); |
| if (known) |
| return bmap; |
| |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| o_div = isl_basic_map_offset(bmap, isl_dim_div) - 1; |
| |
| for (i = 0; i < n_div; ++i) { |
| known = isl_basic_map_div_is_known(bmap, i); |
| if (known < 0) |
| return isl_basic_map_free(bmap); |
| if (known) |
| continue; |
| bmap = remove_dependent_vars(bmap, o_div + i); |
| bmap = isl_basic_map_drop_constraints_involving_dims(bmap, |
| isl_dim_div, i, 1); |
| if (!bmap) |
| return NULL; |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| i = -1; |
| } |
| |
| return bmap; |
| } |
| |
| /* Remove all constraints from "map" that reference any unknown local |
| * variables (directly or indirectly). |
| * |
| * Since constraints may get dropped from the basic maps, |
| * they may no longer be disjoint from each other. |
| */ |
| __isl_give isl_map *isl_map_drop_constraint_involving_unknown_divs( |
| __isl_take isl_map *map) |
| { |
| int i; |
| isl_bool known; |
| |
| known = isl_map_divs_known(map); |
| if (known < 0) |
| return isl_map_free(map); |
| if (known) |
| return map; |
| |
| map = isl_map_cow(map); |
| if (!map) |
| return NULL; |
| |
| for (i = 0; i < map->n; ++i) { |
| map->p[i] = |
| isl_basic_map_drop_constraint_involving_unknown_divs( |
| map->p[i]); |
| if (!map->p[i]) |
| return isl_map_free(map); |
| } |
| |
| if (map->n > 1) |
| ISL_F_CLR(map, ISL_MAP_DISJOINT); |
| |
| return map; |
| } |
| |
| /* Don't assume equalities are in order, because align_divs |
| * may have changed the order of the divs. |
| */ |
| static void compute_elimination_index(__isl_keep 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(__isl_keep isl_basic_set *bset, |
| int *elim) |
| { |
| compute_elimination_index(bset_to_bmap(bset), elim); |
| } |
| |
| static int reduced_using_equalities(isl_int *dst, isl_int *src, |
| __isl_keep 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, |
| __isl_keep isl_basic_set *bset, int *elim) |
| { |
| return reduced_using_equalities(dst, src, |
| bset_to_bmap(bset), elim); |
| } |
| |
| static __isl_give isl_basic_set *isl_basic_set_reduce_using_equalities( |
| __isl_take isl_basic_set *bset, __isl_take 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; |
| } |
| |
| /* For each inequality in "ineq" that is a shifted (more relaxed) |
| * copy of an inequality in "context", mark the corresponding entry |
| * in "row" with -1. |
| * If an inequality only has a non-negative constant term, then |
| * mark it as well. |
| */ |
| static isl_stat mark_shifted_constraints(__isl_keep isl_mat *ineq, |
| __isl_keep isl_basic_set *context, int *row) |
| { |
| struct isl_constraint_index ci; |
| int n_ineq; |
| unsigned total; |
| int k; |
| |
| if (!ineq || !context) |
| return isl_stat_error; |
| if (context->n_ineq == 0) |
| return isl_stat_ok; |
| if (setup_constraint_index(&ci, context) < 0) |
| return isl_stat_error; |
| |
| n_ineq = isl_mat_rows(ineq); |
| total = isl_mat_cols(ineq) - 1; |
| for (k = 0; k < n_ineq; ++k) { |
| int l; |
| isl_bool redundant; |
| |
| l = isl_seq_first_non_zero(ineq->row[k] + 1, total); |
| if (l < 0 && isl_int_is_nonneg(ineq->row[k][0])) { |
| row[k] = -1; |
| continue; |
| } |
| redundant = constraint_index_is_redundant(&ci, ineq->row[k]); |
| if (redundant < 0) |
| goto error; |
| if (!redundant) |
| continue; |
| row[k] = -1; |
| } |
| constraint_index_free(&ci); |
| return isl_stat_ok; |
| error: |
| constraint_index_free(&ci); |
| return isl_stat_error; |
| } |
| |
| static __isl_give isl_basic_set *remove_shifted_constraints( |
| __isl_take isl_basic_set *bset, __isl_keep isl_basic_set *context) |
| { |
| struct isl_constraint_index ci; |
| int k; |
| |
| if (!bset || !context) |
| return bset; |
| |
| if (context->n_ineq == 0) |
| return bset; |
| if (setup_constraint_index(&ci, context) < 0) |
| return bset; |
| |
| for (k = 0; k < bset->n_ineq; ++k) { |
| isl_bool redundant; |
| |
| redundant = constraint_index_is_redundant(&ci, bset->ineq[k]); |
| if (redundant < 0) |
| goto error; |
| if (!redundant) |
| continue; |
| bset = isl_basic_set_cow(bset); |
| if (!bset) |
| goto error; |
| isl_basic_set_drop_inequality(bset, k); |
| --k; |
| } |
| constraint_index_free(&ci); |
| return bset; |
| error: |
| constraint_index_free(&ci); |
| return bset; |
| } |
| |
| /* Remove constraints from "bmap" that are identical to constraints |
| * in "context" or that are more relaxed (greater constant term). |
| * |
| * We perform the test for shifted copies on the pure constraints |
| * in remove_shifted_constraints. |
| */ |
| static __isl_give isl_basic_map *isl_basic_map_remove_shifted_constraints( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context) |
| { |
| isl_basic_set *bset, *bset_context; |
| |
| if (!bmap || !context) |
| goto error; |
| |
| if (bmap->n_ineq == 0 || context->n_ineq == 0) { |
| isl_basic_map_free(context); |
| return bmap; |
| } |
| |
| context = isl_basic_map_align_divs(context, bmap); |
| bmap = isl_basic_map_align_divs(bmap, context); |
| |
| bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap)); |
| bset_context = isl_basic_map_underlying_set(context); |
| bset = remove_shifted_constraints(bset, bset_context); |
| isl_basic_set_free(bset_context); |
| |
| bmap = isl_basic_map_overlying_set(bset, bmap); |
| |
| return bmap; |
| error: |
| isl_basic_map_free(bmap); |
| isl_basic_map_free(context); |
| return NULL; |
| } |
| |
| /* Does the (linear part of a) constraint "c" involve any of the "len" |
| * "relevant" dimensions? |
| */ |
| static int is_related(isl_int *c, int len, int *relevant) |
| { |
| int i; |
| |
| for (i = 0; i < len; ++i) { |
| if (!relevant[i]) |
| continue; |
| if (!isl_int_is_zero(c[i])) |
| return 1; |
| } |
| |
| return 0; |
| } |
| |
| /* Drop constraints from "bmap" that do not involve any of |
| * the dimensions marked "relevant". |
| */ |
| static __isl_give isl_basic_map *drop_unrelated_constraints( |
| __isl_take isl_basic_map *bmap, int *relevant) |
| { |
| int i, dim; |
| |
| dim = isl_basic_map_dim(bmap, isl_dim_all); |
| for (i = 0; i < dim; ++i) |
| if (!relevant[i]) |
| break; |
| if (i >= dim) |
| return bmap; |
| |
| for (i = bmap->n_eq - 1; i >= 0; --i) |
| if (!is_related(bmap->eq[i] + 1, dim, relevant)) { |
| bmap = isl_basic_map_cow(bmap); |
| if (isl_basic_map_drop_equality(bmap, i) < 0) |
| return isl_basic_map_free(bmap); |
| } |
| |
| for (i = bmap->n_ineq - 1; i >= 0; --i) |
| if (!is_related(bmap->ineq[i] + 1, dim, relevant)) { |
| bmap = isl_basic_map_cow(bmap); |
| if (isl_basic_map_drop_inequality(bmap, i) < 0) |
| return isl_basic_map_free(bmap); |
| } |
| |
| return bmap; |
| } |
| |
| /* Update the groups in "group" based on the (linear part of a) constraint "c". |
| * |
| * In particular, for any variable involved in the constraint, |
| * find the actual group id from before and replace the group |
| * of the corresponding variable by the minimal group of all |
| * the variables involved in the constraint considered so far |
| * (if this minimum is smaller) or replace the minimum by this group |
| * (if the minimum is larger). |
| * |
| * At the end, all the variables in "c" will (indirectly) point |
| * to the minimal of the groups that they referred to originally. |
| */ |
| static void update_groups(int dim, int *group, isl_int *c) |
| { |
| int j; |
| int min = dim; |
| |
| for (j = 0; j < dim; ++j) { |
| if (isl_int_is_zero(c[j])) |
| continue; |
| while (group[j] >= 0 && group[group[j]] != group[j]) |
| group[j] = group[group[j]]; |
| if (group[j] == min) |
| continue; |
| if (group[j] < min) { |
| if (min >= 0 && min < dim) |
| group[min] = group[j]; |
| min = group[j]; |
| } else |
| group[group[j]] = min; |
| } |
| } |
| |
| /* Allocate an array of groups of variables, one for each variable |
| * in "context", initialized to zero. |
| */ |
| static int *alloc_groups(__isl_keep isl_basic_set *context) |
| { |
| isl_ctx *ctx; |
| int dim; |
| |
| dim = isl_basic_set_dim(context, isl_dim_set); |
| ctx = isl_basic_set_get_ctx(context); |
| return isl_calloc_array(ctx, int, dim); |
| } |
| |
| /* Drop constraints from "bmap" that only involve variables that are |
| * not related to any of the variables marked with a "-1" in "group". |
| * |
| * We construct groups of variables that collect variables that |
| * (indirectly) appear in some common constraint of "bmap". |
| * Each group is identified by the first variable in the group, |
| * except for the special group of variables that was already identified |
| * in the input as -1 (or are related to those variables). |
| * If group[i] is equal to i (or -1), then the group of i is i (or -1), |
| * otherwise the group of i is the group of group[i]. |
| * |
| * We first initialize groups for the remaining variables. |
| * Then we iterate over the constraints of "bmap" and update the |
| * group of the variables in the constraint by the smallest group. |
| * Finally, we resolve indirect references to groups by running over |
| * the variables. |
| * |
| * After computing the groups, we drop constraints that do not involve |
| * any variables in the -1 group. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_drop_unrelated_constraints( |
| __isl_take isl_basic_map *bmap, __isl_take int *group) |
| { |
| int dim; |
| int i; |
| int last; |
| |
| if (!bmap) |
| return NULL; |
| |
| dim = isl_basic_map_dim(bmap, isl_dim_all); |
| |
| last = -1; |
| for (i = 0; i < dim; ++i) |
| if (group[i] >= 0) |
| last = group[i] = i; |
| if (last < 0) { |
| free(group); |
| return bmap; |
| } |
| |
| for (i = 0; i < bmap->n_eq; ++i) |
| update_groups(dim, group, bmap->eq[i] + 1); |
| for (i = 0; i < bmap->n_ineq; ++i) |
| update_groups(dim, group, bmap->ineq[i] + 1); |
| |
| for (i = 0; i < dim; ++i) |
| if (group[i] >= 0) |
| group[i] = group[group[i]]; |
| |
| for (i = 0; i < dim; ++i) |
| group[i] = group[i] == -1; |
| |
| bmap = drop_unrelated_constraints(bmap, group); |
| |
| free(group); |
| return bmap; |
| } |
| |
| /* Drop constraints from "context" that are irrelevant for computing |
| * the gist of "bset". |
| * |
| * In particular, drop constraints in variables that are not related |
| * to any of the variables involved in the constraints of "bset" |
| * in the sense that there is no sequence of constraints that connects them. |
| * |
| * We first mark all variables that appear in "bset" as belonging |
| * to a "-1" group and then continue with group_and_drop_irrelevant_constraints. |
| */ |
| static __isl_give isl_basic_set *drop_irrelevant_constraints( |
| __isl_take isl_basic_set *context, __isl_keep isl_basic_set *bset) |
| { |
| int *group; |
| int dim; |
| int i, j; |
| |
| if (!context || !bset) |
| return isl_basic_set_free(context); |
| |
| group = alloc_groups(context); |
| |
| if (!group) |
| return isl_basic_set_free(context); |
| |
| dim = isl_basic_set_dim(bset, isl_dim_set); |
| for (i = 0; i < dim; ++i) { |
| for (j = 0; j < bset->n_eq; ++j) |
| if (!isl_int_is_zero(bset->eq[j][1 + i])) |
| break; |
| if (j < bset->n_eq) { |
| group[i] = -1; |
| continue; |
| } |
| for (j = 0; j < bset->n_ineq; ++j) |
| if (!isl_int_is_zero(bset->ineq[j][1 + i])) |
| break; |
| if (j < bset->n_ineq) |
| group[i] = -1; |
| } |
| |
| return isl_basic_map_drop_unrelated_constraints(context, group); |
| } |
| |
| /* Drop constraints from "context" that are irrelevant for computing |
| * the gist of the inequalities "ineq". |
| * Inequalities in "ineq" for which the corresponding element of row |
| * is set to -1 have already been marked for removal and should be ignored. |
| * |
| * In particular, drop constraints in variables that are not related |
| * to any of the variables involved in "ineq" |
| * in the sense that there is no sequence of constraints that connects them. |
| * |
| * We first mark all variables that appear in "bset" as belonging |
| * to a "-1" group and then continue with group_and_drop_irrelevant_constraints. |
| */ |
| static __isl_give isl_basic_set *drop_irrelevant_constraints_marked( |
| __isl_take isl_basic_set *context, __isl_keep isl_mat *ineq, int *row) |
| { |
| int *group; |
| int dim; |
| int i, j, n; |
| |
| if (!context || !ineq) |
| return isl_basic_set_free(context); |
| |
| group = alloc_groups(context); |
| |
| if (!group) |
| return isl_basic_set_free(context); |
| |
| dim = isl_basic_set_dim(context, isl_dim_set); |
| n = isl_mat_rows(ineq); |
| for (i = 0; i < dim; ++i) { |
| for (j = 0; j < n; ++j) { |
| if (row[j] < 0) |
| continue; |
| if (!isl_int_is_zero(ineq->row[j][1 + i])) |
| break; |
| } |
| if (j < n) |
| group[i] = -1; |
| } |
| |
| return isl_basic_map_drop_unrelated_constraints(context, group); |
| } |
| |
| /* Do all "n" entries of "row" contain a negative value? |
| */ |
| static int all_neg(int *row, int n) |
| { |
| int i; |
| |
| for (i = 0; i < n; ++i) |
| if (row[i] >= 0) |
| return 0; |
| |
| return 1; |
| } |
| |
| /* Update the inequalities in "bset" based on the information in "row" |
| * and "tab". |
| * |
| * In particular, the array "row" contains either -1, meaning that |
| * the corresponding inequality of "bset" is redundant, or the index |
| * of an inequality in "tab". |
| * |
| * If the row entry is -1, then drop the inequality. |
| * Otherwise, if the constraint is marked redundant in the tableau, |
| * then drop the inequality. Similarly, if it is marked as an equality |
| * in the tableau, then turn the inequality into an equality and |
| * perform Gaussian elimination. |
| */ |
| static __isl_give isl_basic_set *update_ineq(__isl_take isl_basic_set *bset, |
| __isl_keep int *row, struct isl_tab *tab) |
| { |
| int i; |
| unsigned n_ineq; |
| unsigned n_eq; |
| int found_equality = 0; |
| |
| if (!bset) |
| return NULL; |
| if (tab && tab->empty) |
| return isl_basic_set_set_to_empty(bset); |
| |
| n_ineq = bset->n_ineq; |
| for (i = n_ineq - 1; i >= 0; --i) { |
| if (row[i] < 0) { |
| if (isl_basic_set_drop_inequality(bset, i) < 0) |
| return isl_basic_set_free(bset); |
| continue; |
| } |
| if (!tab) |
| continue; |
| n_eq = tab->n_eq; |
| if (isl_tab_is_equality(tab, n_eq + row[i])) { |
| isl_basic_map_inequality_to_equality(bset, i); |
| found_equality = 1; |
| } else if (isl_tab_is_redundant(tab, n_eq + row[i])) { |
| if (isl_basic_set_drop_inequality(bset, i) < 0) |
| return isl_basic_set_free(bset); |
| } |
| } |
| |
| if (found_equality) |
| bset = isl_basic_set_gauss(bset, NULL); |
| bset = isl_basic_set_finalize(bset); |
| return bset; |
| } |
| |
| /* Update the inequalities in "bset" based on the information in "row" |
| * and "tab" and free all arguments (other than "bset"). |
| */ |
| static __isl_give isl_basic_set *update_ineq_free( |
| __isl_take isl_basic_set *bset, __isl_take isl_mat *ineq, |
| __isl_take isl_basic_set *context, __isl_take int *row, |
| struct isl_tab *tab) |
| { |
| isl_mat_free(ineq); |
| isl_basic_set_free(context); |
| |
| bset = update_ineq(bset, row, tab); |
| |
| free(row); |
| isl_tab_free(tab); |
| return bset; |
| } |
| |
| /* Remove all information from bset that is redundant in the context |
| * of context. |
| * "ineq" contains the (possibly transformed) inequalities of "bset", |
| * in the same order. |
| * The (explicit) equalities of "bset" are assumed to have been taken |
| * into account by the transformation such that only the inequalities |
| * are relevant. |
| * "context" is assumed not to be empty. |
| * |
| * "row" keeps track of the constraint index of a "bset" inequality in "tab". |
| * A value of -1 means that the inequality is obviously redundant and may |
| * not even appear in "tab". |
| * |
| * We first mark the inequalities of "bset" |
| * that are obviously redundant with respect to some inequality in "context". |
| * Then we remove those constraints from "context" that have become |
| * irrelevant for computing the gist of "bset". |
| * Note that this removal of constraints cannot be replaced by |
| * a factorization because factors in "bset" may still be connected |
| * to each other through constraints 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_mat *ineq, __isl_take isl_basic_set *context) |
| { |
| int i, r; |
| int *row = NULL; |
| isl_ctx *ctx; |
| isl_basic_set *combined = NULL; |
| struct isl_tab *tab = NULL; |
| unsigned n_eq, context_ineq; |
| |
| if (!bset || !ineq || !context) |
| goto error; |
| |
| if (bset->n_ineq == 0 || isl_basic_set_plain_is_universe(context)) { |
| isl_basic_set_free(context); |
| isl_mat_free(ineq); |
| return bset; |
| } |
| |
| ctx = isl_basic_set_get_ctx(context); |
| row = isl_calloc_array(ctx, int, bset->n_ineq); |
| if (!row) |
| goto error; |
| |
| if (mark_shifted_constraints(ineq, context, row) < 0) |
| goto error; |
| if (all_neg(row, bset->n_ineq)) |
| return update_ineq_free(bset, ineq, context, row, NULL); |
| |
| context = drop_irrelevant_constraints_marked(context, ineq, row); |
| if (!context) |
| goto error; |
| if (isl_basic_set_plain_is_universe(context)) |
| return update_ineq_free(bset, ineq, context, row, NULL); |
| |
| n_eq = context->n_eq; |
| 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, 0); |
| for (i = 0; i < context_ineq; ++i) |
| if (isl_tab_freeze_constraint(tab, n_eq + i) < 0) |
| goto error; |
| if (isl_tab_extend_cons(tab, bset->n_ineq) < 0) |
| goto error; |
| r = context_ineq; |
| for (i = 0; i < bset->n_ineq; ++i) { |
| if (row[i] < 0) |
| continue; |
| combined = isl_basic_set_add_ineq(combined, ineq->row[i]); |
| if (isl_tab_add_ineq(tab, ineq->row[i]) < 0) |
| goto error; |
| row[i] = r++; |
| } |
| if (isl_tab_detect_implicit_equalities(tab) < 0) |
| goto error; |
| if (isl_tab_detect_redundant(tab) < 0) |
| goto error; |
| for (i = bset->n_ineq - 1; i >= 0; --i) { |
| isl_basic_set *test; |
| int is_empty; |
| |
| if (row[i] < 0) |
| continue; |
| r = row[i]; |
| if (tab->con[n_eq + r].is_redundant) |
| continue; |
| test = isl_basic_set_dup(combined); |
| if (isl_inequality_negate(test, r) < 0) |
| test = isl_basic_set_free(test); |
| test = isl_basic_set_update_from_tab(test, tab); |
| is_empty = isl_basic_set_is_empty(test); |
| isl_basic_set_free(test); |
| if (is_empty < 0) |
| goto error; |
| if (is_empty) |
| tab->con[n_eq + r].is_redundant = 1; |
| } |
| bset = update_ineq_free(bset, ineq, context, row, tab); |
| if (bset) { |
| ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT); |
| ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT); |
| } |
| |
| isl_basic_set_free(combined); |
| return bset; |
| error: |
| free(row); |
| isl_mat_free(ineq); |
| isl_tab_free(tab); |
| isl_basic_set_free(combined); |
| isl_basic_set_free(context); |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| /* Extract the inequalities of "bset" as an isl_mat. |
| */ |
| static __isl_give isl_mat *extract_ineq(__isl_keep isl_basic_set *bset) |
| { |
| unsigned total; |
| isl_ctx *ctx; |
| isl_mat *ineq; |
| |
| if (!bset) |
| return NULL; |
| |
| ctx = isl_basic_set_get_ctx(bset); |
| total = isl_basic_set_total_dim(bset); |
| ineq = isl_mat_sub_alloc6(ctx, bset->ineq, 0, bset->n_ineq, |
| 0, 1 + total); |
| |
| return ineq; |
| } |
| |
| /* Remove all information from "bset" that is redundant in the context |
| * of "context", for the case where both "bset" and "context" are |
| * full-dimensional. |
| */ |
| static __isl_give isl_basic_set *uset_gist_uncompressed( |
| __isl_take isl_basic_set *bset, __isl_take isl_basic_set *context) |
| { |
| isl_mat *ineq; |
| |
| ineq = extract_ineq(bset); |
| return uset_gist_full(bset, ineq, context); |
| } |
| |
| /* Remove all information from "bset" that is redundant in the context |
| * of "context", for the case where the combined equalities of |
| * "bset" and "context" allow for a compression that can be obtained |
| * by preapplication of "T". |
| * |
| * "bset" itself is not transformed by "T". Instead, the inequalities |
| * are extracted from "bset" and those are transformed by "T". |
| * uset_gist_full then determines which of the transformed inequalities |
| * are redundant with respect to the transformed "context" and removes |
| * the corresponding inequalities from "bset". |
| * |
| * After preapplying "T" to the inequalities, any common factor is |
| * removed from the coefficients. If this results in a tightening |
| * of the constant term, then the same tightening is applied to |
| * the corresponding untransformed inequality in "bset". |
| * That is, if after plugging in T, a constraint f(x) >= 0 is of the form |
| * |
| * g f'(x) + r >= 0 |
| * |
| * with 0 <= r < g, then it is equivalent to |
| * |
| * f'(x) >= 0 |
| * |
| * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine |
| * subspace compressed by T since the latter would be transformed to |
| * |
| * g f'(x) >= 0 |
| */ |
| static __isl_give isl_basic_set *uset_gist_compressed( |
| __isl_take isl_basic_set *bset, __isl_take isl_basic_set *context, |
| __isl_take isl_mat *T) |
| { |
| isl_ctx *ctx; |
| isl_mat *ineq; |
| int i, n_row, n_col; |
| isl_int rem; |
| |
| ineq = extract_ineq(bset); |
| ineq = isl_mat_product(ineq, isl_mat_copy(T)); |
| context = isl_basic_set_preimage(context, T); |
| |
| if (!ineq || !context) |
| goto error; |
| if (isl_basic_set_plain_is_empty(context)) { |
| isl_mat_free(ineq); |
| isl_basic_set_free(context); |
| return isl_basic_set_set_to_empty(bset); |
| } |
| |
| ctx = isl_mat_get_ctx(ineq); |
| n_row = isl_mat_rows(ineq); |
| n_col = isl_mat_cols(ineq); |
| isl_int_init(rem); |
| for (i = 0; i < n_row; ++i) { |
| isl_seq_gcd(ineq->row[i] + 1, n_col - 1, &ctx->normalize_gcd); |
| if (isl_int_is_zero(ctx->normalize_gcd)) |
| continue; |
| if (isl_int_is_one(ctx->normalize_gcd)) |
| continue; |
| isl_seq_scale_down(ineq->row[i] + 1, ineq->row[i] + 1, |
| ctx->normalize_gcd, n_col - 1); |
| isl_int_fdiv_r(rem, ineq->row[i][0], ctx->normalize_gcd); |
| isl_int_fdiv_q(ineq->row[i][0], |
| ineq->row[i][0], ctx->normalize_gcd); |
| if (isl_int_is_zero(rem)) |
| continue; |
| bset = isl_basic_set_cow(bset); |
| if (!bset) |
| break; |
| isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], rem); |
| } |
| isl_int_clear(rem); |
| |
| return uset_gist_full(bset, ineq, context); |
| error: |
| isl_mat_free(ineq); |
| isl_basic_set_free(context); |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| /* Project "bset" onto the variables that are involved in "template". |
| */ |
| static __isl_give isl_basic_set *project_onto_involved( |
| __isl_take isl_basic_set *bset, __isl_keep isl_basic_set *template) |
| { |
| int i, n; |
| |
| if (!bset || !template) |
| return isl_basic_set_free(bset); |
| |
| n = isl_basic_set_dim(template, isl_dim_set); |
| |
| for (i = 0; i < n; ++i) { |
| isl_bool involved; |
| |
| involved = isl_basic_set_involves_dims(template, |
| isl_dim_set, i, 1); |
| if (involved < 0) |
| return isl_basic_set_free(bset); |
| if (involved) |
| continue; |
| bset = isl_basic_set_eliminate_vars(bset, i, 1); |
| } |
| |
| return bset; |
| } |
| |
| /* 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. |
| * |
| * First of all, we drop those constraints from "context" |
| * that are irrelevant for computing the gist of "bset". |
| * Alternatively, we could factorize the intersection of "context" and "bset". |
| * |
| * We first compute the intersection of the integer affine hulls |
| * of "bset" and "context", |
| * compute the gist inside this intersection and then reduce |
| * the constraints with respect to the equalities of the context |
| * that only involve variables already involved in the input. |
| * |
| * 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; |
| isl_basic_set *aff; |
| isl_basic_set *aff_context; |
| unsigned total; |
| |
| if (!bset || !context) |
| goto error; |
| |
| context = drop_irrelevant_constraints(context, bset); |
| |
| bset = isl_basic_set_detect_equalities(bset); |
| aff = isl_basic_set_copy(bset); |
| aff = isl_basic_set_plain_affine_hull(aff); |
| context = isl_basic_set_detect_equalities(context); |
| aff_context = isl_basic_set_copy(context); |
| aff_context = isl_basic_set_plain_affine_hull(aff_context); |
| aff = isl_basic_set_intersect(aff, aff_context); |
| if (!aff) |
| goto error; |
| if (isl_basic_set_plain_is_empty(aff)) { |
| isl_basic_set_free(bset); |
| isl_basic_set_free(context); |
| return aff; |
| } |
| bset = isl_basic_set_sort_constraints(bset); |
| if (aff->n_eq == 0) { |
| isl_basic_set_free(aff); |
| return uset_gist_uncompressed(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, NULL); |
| isl_basic_set_free(aff); |
| if (T && T->n_col == 0) { |
| isl_mat_free(T); |
| isl_basic_set_free(context); |
| return isl_basic_set_set_to_empty(bset); |
| } |
| |
| aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context)); |
| aff_context = project_onto_involved(aff_context, bset); |
| |
| bset = uset_gist_compressed(bset, context, T); |
| 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; |
| } |
| |
| /* Return the number of equality constraints in "bmap" that involve |
| * local variables. This function assumes that Gaussian elimination |
| * has been applied to the equality constraints. |
| */ |
| static int n_div_eq(__isl_keep isl_basic_map *bmap) |
| { |
| int i; |
| int total, n_div; |
| |
| if (!bmap) |
| return -1; |
| |
| if (bmap->n_eq == 0) |
| return 0; |
| |
| 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 < bmap->n_eq; ++i) |
| if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, |
| n_div) == -1) |
| return i; |
| |
| return bmap->n_eq; |
| } |
| |
| /* Construct a basic map in "space" defined by the equality constraints in "eq". |
| * The constraints are assumed not to involve any local variables. |
| */ |
| static __isl_give isl_basic_map *basic_map_from_equalities( |
| __isl_take isl_space *space, __isl_take isl_mat *eq) |
| { |
| int i, k; |
| isl_basic_map *bmap = NULL; |
| |
| if (!space || !eq) |
| goto error; |
| |
| if (1 + isl_space_dim(space, isl_dim_all) != eq->n_col) |
| isl_die(isl_space_get_ctx(space), isl_error_internal, |
| "unexpected number of columns", goto error); |
| |
| bmap = isl_basic_map_alloc_space(isl_space_copy(space), |
| 0, eq->n_row, 0); |
| for (i = 0; i < eq->n_row; ++i) { |
| k = isl_basic_map_alloc_equality(bmap); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(bmap->eq[k], eq->row[i], eq->n_col); |
| } |
| |
| isl_space_free(space); |
| isl_mat_free(eq); |
| return bmap; |
| error: |
| isl_space_free(space); |
| isl_mat_free(eq); |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| /* Construct and return a variable compression based on the equality |
| * constraints in "bmap1" and "bmap2" that do not involve the local variables. |
| * "n1" is the number of (initial) equality constraints in "bmap1" |
| * that do involve local variables. |
| * "n2" is the number of (initial) equality constraints in "bmap2" |
| * that do involve local variables. |
| * "total" is the total number of other variables. |
| * This function assumes that Gaussian elimination |
| * has been applied to the equality constraints in both "bmap1" and "bmap2" |
| * such that the equality constraints not involving local variables |
| * are those that start at "n1" or "n2". |
| * |
| * If either of "bmap1" and "bmap2" does not have such equality constraints, |
| * then simply compute the compression based on the equality constraints |
| * in the other basic map. |
| * Otherwise, combine the equality constraints from both into a new |
| * basic map such that Gaussian elimination can be applied to this combination |
| * and then construct a variable compression from the resulting |
| * equality constraints. |
| */ |
| static __isl_give isl_mat *combined_variable_compression( |
| __isl_keep isl_basic_map *bmap1, int n1, |
| __isl_keep isl_basic_map *bmap2, int n2, int total) |
| { |
| isl_ctx *ctx; |
| isl_mat *E1, *E2, *V; |
| isl_basic_map *bmap; |
| |
| ctx = isl_basic_map_get_ctx(bmap1); |
| if (bmap1->n_eq == n1) { |
| E2 = isl_mat_sub_alloc6(ctx, bmap2->eq, |
| n2, bmap2->n_eq - n2, 0, 1 + total); |
| return isl_mat_variable_compression(E2, NULL); |
| } |
| if (bmap2->n_eq == n2) { |
| E1 = isl_mat_sub_alloc6(ctx, bmap1->eq, |
| n1, bmap1->n_eq - n1, 0, 1 + total); |
| return isl_mat_variable_compression(E1, NULL); |
| } |
| E1 = isl_mat_sub_alloc6(ctx, bmap1->eq, |
| n1, bmap1->n_eq - n1, 0, 1 + total); |
| E2 = isl_mat_sub_alloc6(ctx, bmap2->eq, |
| n2, bmap2->n_eq - n2, 0, 1 + total); |
| E1 = isl_mat_concat(E1, E2); |
| bmap = basic_map_from_equalities(isl_basic_map_get_space(bmap1), E1); |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| if (!bmap) |
| return NULL; |
| E1 = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total); |
| V = isl_mat_variable_compression(E1, NULL); |
| isl_basic_map_free(bmap); |
| |
| return V; |
| } |
| |
| /* Extract the stride constraints from "bmap", compressed |
| * with respect to both the stride constraints in "context" and |
| * the remaining equality constraints in both "bmap" and "context". |
| * "bmap_n_eq" is the number of (initial) stride constraints in "bmap". |
| * "context_n_eq" is the number of (initial) stride constraints in "context". |
| * |
| * Let x be all variables in "bmap" (and "context") other than the local |
| * variables. First compute a variable compression |
| * |
| * x = V x' |
| * |
| * based on the non-stride equality constraints in "bmap" and "context". |
| * Consider the stride constraints of "context", |
| * |
| * A(x) + B(y) = 0 |
| * |
| * with y the local variables and plug in the variable compression, |
| * resulting in |
| * |
| * A(V x') + B(y) = 0 |
| * |
| * Use these constraints to compute a parameter compression on x' |
| * |
| * x' = T x'' |
| * |
| * Now consider the stride constraints of "bmap" |
| * |
| * C(x) + D(y) = 0 |
| * |
| * and plug in x = V*T x''. |
| * That is, return A = [C*V*T D]. |
| */ |
| static __isl_give isl_mat *extract_compressed_stride_constraints( |
| __isl_keep isl_basic_map *bmap, int bmap_n_eq, |
| __isl_keep isl_basic_map *context, int context_n_eq) |
| { |
| int total, n_div; |
| isl_ctx *ctx; |
| isl_mat *A, *B, *T, *V; |
| |
| total = isl_basic_map_dim(context, isl_dim_all); |
| n_div = isl_basic_map_dim(context, isl_dim_div); |
| total -= n_div; |
| |
| ctx = isl_basic_map_get_ctx(bmap); |
| |
| V = combined_variable_compression(bmap, bmap_n_eq, |
| context, context_n_eq, total); |
| |
| A = isl_mat_sub_alloc6(ctx, context->eq, 0, context_n_eq, 0, 1 + total); |
| B = isl_mat_sub_alloc6(ctx, context->eq, |
| 0, context_n_eq, 1 + total, n_div); |
| A = isl_mat_product(A, isl_mat_copy(V)); |
| T = isl_mat_parameter_compression_ext(A, B); |
| T = isl_mat_product(V, T); |
| |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| T = isl_mat_diagonal(T, isl_mat_identity(ctx, n_div)); |
| |
| A = isl_mat_sub_alloc6(ctx, bmap->eq, |
| 0, bmap_n_eq, 0, 1 + total + n_div); |
| A = isl_mat_product(A, T); |
| |
| return A; |
| } |
| |
| /* Remove the prime factors from *g that have an exponent that |
| * is strictly smaller than the exponent in "c". |
| * All exponents in *g are known to be smaller than or equal |
| * to those in "c". |
| * |
| * That is, if *g is equal to |
| * |
| * p_1^{e_1} p_2^{e_2} ... p_n^{e_n} |
| * |
| * and "c" is equal to |
| * |
| * p_1^{f_1} p_2^{f_2} ... p_n^{f_n} |
| * |
| * then update *g to |
| * |
| * p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ... |
| * p_n^{e_n * (e_n = f_n)} |
| * |
| * If e_i = f_i, then c / *g does not have any p_i factors and therefore |
| * neither does the gcd of *g and c / *g. |
| * If e_i < f_i, then the gcd of *g and c / *g has a positive |
| * power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors. |
| * Dividing *g by this gcd therefore strictly reduces the exponent |
| * of the prime factors that need to be removed, while leaving the |
| * other prime factors untouched. |
| * Repeating this process until gcd(*g, c / *g) = 1 therefore |
| * removes all undesired factors, without removing any others. |
| */ |
| static void remove_incomplete_powers(isl_int *g, isl_int c) |
| { |
| isl_int t; |
| |
| isl_int_init(t); |
| for (;;) { |
| isl_int_divexact(t, c, *g); |
| isl_int_gcd(t, t, *g); |
| if (isl_int_is_one(t)) |
| break; |
| isl_int_divexact(*g, *g, t); |
| } |
| isl_int_clear(t); |
| } |
| |
| /* Reduce the "n" stride constraints in "bmap" based on a copy "A" |
| * of the same stride constraints in a compressed space that exploits |
| * all equalities in the context and the other equalities in "bmap". |
| * |
| * If the stride constraints of "bmap" are of the form |
| * |
| * C(x) + D(y) = 0 |
| * |
| * then A is of the form |
| * |
| * B(x') + D(y) = 0 |
| * |
| * If any of these constraints involves only a single local variable y, |
| * then the constraint appears as |
| * |
| * f(x) + m y_i = 0 |
| * |
| * in "bmap" and as |
| * |
| * h(x') + m y_i = 0 |
| * |
| * in "A". |
| * |
| * Let g be the gcd of m and the coefficients of h. |
| * Then, in particular, g is a divisor of the coefficients of h and |
| * |
| * f(x) = h(x') |
| * |
| * is known to be a multiple of g. |
| * If some prime factor in m appears with the same exponent in g, |
| * then it can be removed from m because f(x) is already known |
| * to be a multiple of g and therefore in particular of this power |
| * of the prime factors. |
| * Prime factors that appear with a smaller exponent in g cannot |
| * be removed from m. |
| * Let g' be the divisor of g containing all prime factors that |
| * appear with the same exponent in m and g, then |
| * |
| * f(x) + m y_i = 0 |
| * |
| * can be replaced by |
| * |
| * f(x) + m/g' y_i' = 0 |
| * |
| * Note that (if g' != 1) this changes the explicit representation |
| * of y_i to that of y_i', so the integer division at position i |
| * is marked unknown and later recomputed by a call to |
| * isl_basic_map_gauss. |
| */ |
| static __isl_give isl_basic_map *reduce_stride_constraints( |
| __isl_take isl_basic_map *bmap, int n, __isl_keep isl_mat *A) |
| { |
| int i; |
| int total, n_div; |
| int any = 0; |
| isl_int gcd; |
| |
| if (!bmap || !A) |
| return isl_basic_map_free(bmap); |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| total -= n_div; |
| |
| isl_int_init(gcd); |
| for (i = 0; i < n; ++i) { |
| int div; |
| |
| div = isl_seq_first_non_zero(bmap->eq[i] + 1 + total, n_div); |
| if (div < 0) |
| isl_die(isl_basic_map_get_ctx(bmap), isl_error_internal, |
| "equality constraints modified unexpectedly", |
| goto error); |
| if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total + div + 1, |
| n_div - div - 1) != -1) |
| continue; |
| if (isl_mat_row_gcd(A, i, &gcd) < 0) |
| goto error; |
| if (isl_int_is_one(gcd)) |
| continue; |
| remove_incomplete_powers(&gcd, bmap->eq[i][1 + total + div]); |
| if (isl_int_is_one(gcd)) |
| continue; |
| isl_int_divexact(bmap->eq[i][1 + total + div], |
| bmap->eq[i][1 + total + div], gcd); |
| bmap = isl_basic_map_mark_div_unknown(bmap, div); |
| if (!bmap) |
| goto error; |
| any = 1; |
| } |
| isl_int_clear(gcd); |
| |
| if (any) |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| |
| return bmap; |
| error: |
| isl_int_clear(gcd); |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| /* Simplify the stride constraints in "bmap" based on |
| * the remaining equality constraints in "bmap" and all equality |
| * constraints in "context". |
| * Only do this if both "bmap" and "context" have stride constraints. |
| * |
| * First extract a copy of the stride constraints in "bmap" in a compressed |
| * space exploiting all the other equality constraints and then |
| * use this compressed copy to simplify the original stride constraints. |
| */ |
| static __isl_give isl_basic_map *gist_strides(__isl_take isl_basic_map *bmap, |
| __isl_keep isl_basic_map *context) |
| { |
| int bmap_n_eq, context_n_eq; |
| isl_mat *A; |
| |
| if (!bmap || !context) |
| return isl_basic_map_free(bmap); |
| |
| bmap_n_eq = n_div_eq(bmap); |
| context_n_eq = n_div_eq(context); |
| |
| if (bmap_n_eq < 0 || context_n_eq < 0) |
| return isl_basic_map_free(bmap); |
| if (bmap_n_eq == 0 || context_n_eq == 0) |
| return bmap; |
| |
| A = extract_compressed_stride_constraints(bmap, bmap_n_eq, |
| context, context_n_eq); |
| bmap = reduce_stride_constraints(bmap, bmap_n_eq, A); |
| |
| isl_mat_free(A); |
| |
| return bmap; |
| } |
| |
| /* Return a basic map that has the same intersection with "context" as "bmap" |
| * and that is as "simple" as possible. |
| * |
| * The core computation is performed on the pure constraints. |
| * When we add back the meaning of the integer divisions, we need |
| * to (re)introduce the div constraints. If we happen to have |
| * discovered that some of these integer divisions are equal to |
| * some affine combination of other variables, then these div |
| * constraints may end up getting simplified in terms of the equalities, |
| * resulting in extra inequalities on the other variables that |
| * may have been removed already or that may not even have been |
| * part of the input. We try and remove those constraints of |
| * this form that are most obviously redundant with respect to |
| * the context. We also remove those div constraints that are |
| * redundant with respect to the other constraints in the result. |
| * |
| * The stride constraints among the equality constraints in "bmap" are |
| * also simplified with respecting to the other equality constraints |
| * in "bmap" and with respect to all equality constraints in "context". |
| */ |
| __isl_give isl_basic_map *isl_basic_map_gist(__isl_take isl_basic_map *bmap, |
| __isl_take isl_basic_map *context) |
| { |
| isl_basic_set *bset, *eq; |
| isl_basic_map *eq_bmap; |
| unsigned total, n_div, extra, n_eq, n_ineq; |
| |
| if (!bmap || !context) |
| goto error; |
| |
| if (isl_basic_map_plain_is_universe(bmap)) { |
| isl_basic_map_free(context); |
| return bmap; |
| } |
| if (isl_basic_map_plain_is_empty(context)) { |
| isl_space *space = isl_basic_map_get_space(bmap); |
| isl_basic_map_free(bmap); |
| isl_basic_map_free(context); |
| return isl_basic_map_universe(space); |
| } |
| 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) |
| goto error; |
| |
| context = isl_basic_map_align_divs(context, bmap); |
| n_div = isl_basic_map_dim(context, isl_dim_div); |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| extra = n_div - isl_basic_map_dim(bmap, isl_dim_div); |
| |
| bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap)); |
| bset = isl_basic_set_add_dims(bset, isl_dim_set, extra); |
| bset = uset_gist(bset, |
| isl_basic_map_underlying_set(isl_basic_map_copy(context))); |
| bset = isl_basic_set_project_out(bset, isl_dim_set, total, extra); |
| |
| if (!bset || bset->n_eq == 0 || n_div == 0 || |
| isl_basic_set_plain_is_empty(bset)) { |
| isl_basic_map_free(context); |
| return isl_basic_map_overlying_set(bset, bmap); |
| } |
| |
| n_eq = bset->n_eq; |
| n_ineq = bset->n_ineq; |
| eq = isl_basic_set_copy(bset); |
| eq = isl_basic_set_cow(eq); |
| if (isl_basic_set_free_inequality(eq, n_ineq) < 0) |
| eq = isl_basic_set_free(eq); |
| if (isl_basic_set_free_equality(bset, n_eq) < 0) |
| bset = isl_basic_set_free(bset); |
| |
| eq_bmap = isl_basic_map_overlying_set(eq, isl_basic_map_copy(bmap)); |
| eq_bmap = gist_strides(eq_bmap, context); |
| eq_bmap = isl_basic_map_remove_shifted_constraints(eq_bmap, context); |
| bmap = isl_basic_map_overlying_set(bset, bmap); |
| bmap = isl_basic_map_intersect(bmap, eq_bmap); |
| bmap = isl_basic_map_remove_redundancies(bmap); |
| |
| return 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_space *space = isl_map_get_space(map); |
| isl_map_free(map); |
| isl_basic_map_free(context); |
| return isl_map_universe(space); |
| } |
| |
| 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); |
| if (!map) |
| goto error; |
| 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; |
| } |
| |
| /* Drop all inequalities from "bmap" that also appear in "context". |
| * "context" is assumed to have only known local variables and |
| * the initial local variables of "bmap" are assumed to be the same |
| * as those of "context". |
| * The constraints of both "bmap" and "context" are assumed |
| * to have been sorted using isl_basic_map_sort_constraints. |
| * |
| * Run through the inequality constraints of "bmap" and "context" |
| * in sorted order. |
| * If a constraint of "bmap" involves variables not in "context", |
| * then it cannot appear in "context". |
| * If a matching constraint is found, it is removed from "bmap". |
| */ |
| static __isl_give isl_basic_map *drop_inequalities( |
| __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context) |
| { |
| int i1, i2; |
| unsigned total, extra; |
| |
| if (!bmap || !context) |
| return isl_basic_map_free(bmap); |
| |
| total = isl_basic_map_total_dim(context); |
| extra = isl_basic_map_total_dim(bmap) - total; |
| |
| i1 = bmap->n_ineq - 1; |
| i2 = context->n_ineq - 1; |
| while (bmap && i1 >= 0 && i2 >= 0) { |
| int cmp; |
| |
| if (isl_seq_first_non_zero(bmap->ineq[i1] + 1 + total, |
| extra) != -1) { |
| --i1; |
| continue; |
| } |
| cmp = isl_basic_map_constraint_cmp(context, bmap->ineq[i1], |
| context->ineq[i2]); |
| if (cmp < 0) { |
| --i2; |
| continue; |
| } |
| if (cmp > 0) { |
| --i1; |
| continue; |
| } |
| if (isl_int_eq(bmap->ineq[i1][0], context->ineq[i2][0])) { |
| bmap = isl_basic_map_cow(bmap); |
| if (isl_basic_map_drop_inequality(bmap, i1) < 0) |
| bmap = isl_basic_map_free(bmap); |
| } |
| --i1; |
| --i2; |
| } |
| |
| return bmap; |
| } |
| |
| /* Drop all equalities from "bmap" that also appear in "context". |
| * "context" is assumed to have only known local variables and |
| * the initial local variables of "bmap" are assumed to be the same |
| * as those of "context". |
| * |
| * Run through the equality constraints of "bmap" and "context" |
| * in sorted order. |
| * If a constraint of "bmap" involves variables not in "context", |
| * then it cannot appear in "context". |
| * If a matching constraint is found, it is removed from "bmap". |
| */ |
| static __isl_give isl_basic_map *drop_equalities( |
| __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context) |
| { |
| int i1, i2; |
| unsigned total, extra; |
| |
| if (!bmap || !context) |
| return isl_basic_map_free(bmap); |
| |
| total = isl_basic_map_total_dim(context); |
| extra = isl_basic_map_total_dim(bmap) - total; |
| |
| i1 = bmap->n_eq - 1; |
| i2 = context->n_eq - 1; |
| |
| while (bmap && i1 >= 0 && i2 >= 0) { |
| int last1, last2; |
| |
| if (isl_seq_first_non_zero(bmap->eq[i1] + 1 + total, |
| extra) != -1) |
| break; |
| last1 = isl_seq_last_non_zero(bmap->eq[i1] + 1, total); |
| last2 = isl_seq_last_non_zero(context->eq[i2] + 1, total); |
| if (last1 > last2) { |
| --i2; |
| continue; |
| } |
| if (last1 < last2) { |
| --i1; |
| continue; |
| } |
| if (isl_seq_eq(bmap->eq[i1], context->eq[i2], 1 + total)) { |
| bmap = isl_basic_map_cow(bmap); |
| if (isl_basic_map_drop_equality(bmap, i1) < 0) |
| bmap = isl_basic_map_free(bmap); |
| } |
| --i1; |
| --i2; |
| } |
| |
| return bmap; |
| } |
| |
| /* Remove the constraints in "context" from "bmap". |
| * "context" is assumed to have explicit representations |
| * for all local variables. |
| * |
| * First align the divs of "bmap" to those of "context" and |
| * sort the constraints. Then drop all constraints from "bmap" |
| * that appear in "context". |
| */ |
| __isl_give isl_basic_map *isl_basic_map_plain_gist( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context) |
| { |
| isl_bool done, known; |
| |
| done = isl_basic_map_plain_is_universe(context); |
| if (done == isl_bool_false) |
| done = isl_basic_map_plain_is_universe(bmap); |
| if (done == isl_bool_false) |
| done = isl_basic_map_plain_is_empty(context); |
| if (done == isl_bool_false) |
| done = isl_basic_map_plain_is_empty(bmap); |
| if (done < 0) |
| goto error; |
| if (done) { |
| isl_basic_map_free(context); |
| return bmap; |
| } |
| known = isl_basic_map_divs_known(context); |
| if (known < 0) |
| goto error; |
| if (!known) |
| isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid, |
| "context has unknown divs", goto error); |
| |
| bmap = isl_basic_map_align_divs(bmap, context); |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| bmap = isl_basic_map_sort_constraints(bmap); |
| context = isl_basic_map_sort_constraints(context); |
| |
| bmap = drop_inequalities(bmap, context); |
| bmap = drop_equalities(bmap, context); |
| |
| isl_basic_map_free(context); |
| bmap = isl_basic_map_finalize(bmap); |
| return bmap; |
| error: |
| isl_basic_map_free(bmap); |
| isl_basic_map_free(context); |
| return NULL; |
| } |
| |
| /* Replace "map" by the disjunct at position "pos" and free "context". |
| */ |
| static __isl_give isl_map *replace_by_disjunct(__isl_take isl_map *map, |
| int pos, __isl_take isl_basic_map *context) |
| { |
| isl_basic_map *bmap; |
| |
| bmap = isl_basic_map_copy(map->p[pos]); |
| isl_map_free(map); |
| isl_basic_map_free(context); |
| return isl_map_from_basic_map(bmap); |
| } |
| |
| /* Remove the constraints in "context" from "map". |
| * If any of the disjuncts in the result turns out to be the universe, |
| * then return this universe. |
| * "context" is assumed to have explicit representations |
| * for all local variables. |
| */ |
| __isl_give isl_map *isl_map_plain_gist_basic_map(__isl_take isl_map *map, |
| __isl_take isl_basic_map *context) |
| { |
| int i; |
| isl_bool univ, known; |
| |
| univ = isl_basic_map_plain_is_universe(context); |
| if (univ < 0) |
| goto error; |
| if (univ) { |
| isl_basic_map_free(context); |
| return map; |
| } |
| known = isl_basic_map_divs_known(context); |
| if (known < 0) |
| goto error; |
| if (!known) |
| isl_die(isl_map_get_ctx(map), isl_error_invalid, |
| "context has unknown divs", goto error); |
| |
| map = isl_map_cow(map); |
| if (!map) |
| goto error; |
| for (i = 0; i < map->n; ++i) { |
| map->p[i] = isl_basic_map_plain_gist(map->p[i], |
| isl_basic_map_copy(context)); |
| univ = isl_basic_map_plain_is_universe(map->p[i]); |
| if (univ < 0) |
| goto error; |
| if (univ && map->n > 1) |
| return replace_by_disjunct(map, i, context); |
| } |
| |
| isl_basic_map_free(context); |
| ISL_F_CLR(map, ISL_MAP_NORMALIZED); |
| if (map->n > 1) |
| ISL_F_CLR(map, ISL_MAP_DISJOINT); |
| return map; |
| error: |
| isl_map_free(map); |
| isl_basic_map_free(context); |
| return NULL; |
| } |
| |
| /* Remove the constraints in "context" from "set". |
| * If any of the disjuncts in the result turns out to be the universe, |
| * then return this universe. |
| * "context" is assumed to have explicit representations |
| * for all local variables. |
| */ |
| __isl_give isl_set *isl_set_plain_gist_basic_set(__isl_take isl_set *set, |
| __isl_take isl_basic_set *context) |
| { |
| return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set), |
| bset_to_bmap(context))); |
| } |
| |
| /* Remove the constraints in "context" from "map". |
| * If any of the disjuncts in the result turns out to be the universe, |
| * then return this universe. |
| * "context" is assumed to consist of a single disjunct and |
| * to have explicit representations for all local variables. |
| */ |
| __isl_give isl_map *isl_map_plain_gist(__isl_take isl_map *map, |
| __isl_take isl_map *context) |
| { |
| isl_basic_map *hull; |
| |
| hull = isl_map_unshifted_simple_hull(context); |
| return isl_map_plain_gist_basic_map(map, hull); |
| } |
| |
| /* Replace "map" by a universe map in the same space and free "drop". |
| */ |
| static __isl_give isl_map *replace_by_universe(__isl_take isl_map *map, |
| __isl_take isl_map *drop) |
| { |
| isl_map *res; |
| |
| res = isl_map_universe(isl_map_get_space(map)); |
| isl_map_free(map); |
| isl_map_free(drop); |
| return res; |
| } |
| |
| /* Return a map that has the same intersection with "context" as "map" |
| * and that is as "simple" as possible. |
| * |
| * If "map" is already the universe, then we cannot make it any simpler. |
| * Similarly, if "context" is the universe, then we cannot exploit it |
| * to simplify "map" |
| * If "map" and "context" are identical to each other, then we can |
| * return the corresponding universe. |
| * |
| * If either "map" or "context" consists of multiple disjuncts, |
| * then check if "context" happens to be a subset of "map", |
| * in which case all constraints can be removed. |
| * In case of multiple disjuncts, the standard procedure |
| * may not be able to detect that all constraints can be removed. |
| * |
| * If none of these cases apply, we have to work a bit harder. |
| * During this computation, we make use of a single disjunct context, |
| * so if the original context consists of more than one disjunct |
| * then we need to approximate the context by a single disjunct set. |
| * Simply taking the simple hull may drop constraints that are |
| * only implicitly available in each disjunct. We therefore also |
| * look for constraints among those defining "map" that are valid |
| * for the context. These can then be used to simplify away |
| * the corresponding constraints in "map". |
| */ |
| static __isl_give isl_map *map_gist(__isl_take isl_map *map, |
| __isl_take isl_map *context) |
| { |
| int equal; |
| int is_universe; |
| int single_disjunct_map, single_disjunct_context; |
| isl_bool subset; |
| isl_basic_map *hull; |
| |
| is_universe = isl_map_plain_is_universe(map); |
| if (is_universe >= 0 && !is_universe) |
| is_universe = isl_map_plain_is_universe(context); |
| if (is_universe < 0) |
| goto error; |
| if (is_universe) { |
| isl_map_free(context); |
| return map; |
| } |
| |
| equal = isl_map_plain_is_equal(map, context); |
| if (equal < 0) |
| goto error; |
| if (equal) |
| return replace_by_universe(map, context); |
| |
| single_disjunct_map = isl_map_n_basic_map(map) == 1; |
| single_disjunct_context = isl_map_n_basic_map(context) == 1; |
| if (!single_disjunct_map || !single_disjunct_context) { |
| subset = isl_map_is_subset(context, map); |
| if (subset < 0) |
| goto error; |
| if (subset) |
| return replace_by_universe(map, context); |
| } |
| |
| context = isl_map_compute_divs(context); |
| if (!context) |
| goto error; |
| if (single_disjunct_context) { |
| hull = isl_map_simple_hull(context); |
| } else { |
| isl_ctx *ctx; |
| isl_map_list *list; |
| |
| ctx = isl_map_get_ctx(map); |
| list = isl_map_list_alloc(ctx, 2); |
| list = isl_map_list_add(list, isl_map_copy(context)); |
| list = isl_map_list_add(list, isl_map_copy(map)); |
| hull = isl_map_unshifted_simple_hull_from_map_list(context, |
| list); |
| } |
| return isl_map_gist_basic_map(map, hull); |
| error: |
| isl_map_free(map); |
| isl_map_free(context); |
| return NULL; |
| } |
| |
| __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 bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset), |
| bset_to_bmap(context))); |
| } |
| |
| __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set, |
| __isl_take isl_basic_set *context) |
| { |
| return set_from_map(isl_map_gist_basic_map(set_to_map(set), |
| bset_to_bmap(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 set_from_map(isl_map_gist(set_to_map(set), set_to_map(context))); |
| } |
| |
| /* Compute the gist of "bmap" with respect to the constraints "context" |
| * on the domain. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_gist_domain( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *context) |
| { |
| isl_space *space = isl_basic_map_get_space(bmap); |
| isl_basic_map *bmap_context = isl_basic_map_universe(space); |
| |
| bmap_context = isl_basic_map_intersect_domain(bmap_context, context); |
| return isl_basic_map_gist(bmap, bmap_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. |
| */ |
| isl_bool 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 isl_bool_error; |
| isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), |
| return isl_bool_error); |
| if (bmap1->n_div || bmap2->n_div) |
| return isl_bool_false; |
| if (!bmap1->n_eq && !bmap2->n_eq) |
| return isl_bool_false; |
| |
| total = isl_space_dim(bmap1->dim, isl_dim_all); |
| if (total == 0) |
| return isl_bool_false; |
| 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 isl_bool_false; |
| disjoint: |
| isl_vec_free(v); |
| free(elim); |
| return isl_bool_true; |
| error: |
| isl_vec_free(v); |
| free(elim); |
| return isl_bool_error; |
| } |
| |
| 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(bset_to_bmap(bset1), |
| bset_to_bmap(bset2)); |
| } |
| |
| /* Does "test" hold for all pairs of basic maps in "map1" and "map2"? |
| */ |
| static isl_bool all_pairs(__isl_keep isl_map *map1, __isl_keep isl_map *map2, |
| isl_bool (*test)(__isl_keep isl_basic_map *bmap1, |
| __isl_keep isl_basic_map *bmap2)) |
| { |
| int i, j; |
| |
| if (!map1 || !map2) |
| return isl_bool_error; |
| |
| for (i = 0; i < map1->n; ++i) { |
| for (j = 0; j < map2->n; ++j) { |
| isl_bool d = test(map1->p[i], map2->p[j]); |
| if (d != isl_bool_true) |
| return d; |
| } |
| } |
| |
| return isl_bool_true; |
| } |
| |
| /* Are "map1" and "map2" obviously disjoint, based on information |
| * that can be derived without looking at the individual basic maps? |
| * |
| * In particular, if one of them is empty or if they live in different spaces |
| * (ignoring parameters), then they are clearly disjoint. |
| */ |
| static isl_bool isl_map_plain_is_disjoint_global(__isl_keep isl_map *map1, |
| __isl_keep isl_map *map2) |
| { |
| isl_bool disjoint; |
| isl_bool match; |
| |
| if (!map1 || !map2) |
| return isl_bool_error; |
| |
| disjoint = isl_map_plain_is_empty(map1); |
| if (disjoint < 0 || disjoint) |
| return disjoint; |
| |
| disjoint = isl_map_plain_is_empty(map2); |
| if (disjoint < 0 || disjoint) |
| return disjoint; |
| |
| match = isl_space_tuple_is_equal(map1->dim, isl_dim_in, |
| map2->dim, isl_dim_in); |
| if (match < 0 || !match) |
| return match < 0 ? isl_bool_error : isl_bool_true; |
| |
| match = isl_space_tuple_is_equal(map1->dim, isl_dim_out, |
| map2->dim, isl_dim_out); |
| if (match < 0 || !match) |
| return match < 0 ? isl_bool_error : isl_bool_true; |
| |
| return isl_bool_false; |
| } |
| |
| /* Are "map1" and "map2" obviously disjoint? |
| * |
| * If one of them is empty or if they live in different spaces (ignoring |
| * parameters), then they are clearly disjoint. |
| * This is checked by isl_map_plain_is_disjoint_global. |
| * |
| * If they have different parameters, then we skip any further tests. |
| * |
| * If they are obviously equal, but not obviously empty, then we will |
| * not be able to detect if they are disjoint. |
| * |
| * Otherwise we check if each basic map in "map1" is obviously disjoint |
| * from each basic map in "map2". |
| */ |
| isl_bool isl_map_plain_is_disjoint(__isl_keep isl_map *map1, |
| __isl_keep isl_map *map2) |
| { |
| isl_bool disjoint; |
| isl_bool intersect; |
| isl_bool match; |
| |
| disjoint = isl_map_plain_is_disjoint_global(map1, map2); |
| if (disjoint < 0 || disjoint) |
| return disjoint; |
| |
| match = isl_map_has_equal_params(map1, map2); |
| if (match < 0 || !match) |
| return match < 0 ? isl_bool_error : isl_bool_false; |
| |
| intersect = isl_map_plain_is_equal(map1, map2); |
| if (intersect < 0 || intersect) |
| return intersect < 0 ? isl_bool_error : isl_bool_false; |
| |
| return all_pairs(map1, map2, &isl_basic_map_plain_is_disjoint); |
| } |
| |
| /* Are "map1" and "map2" disjoint? |
| * The parameters are assumed to have been aligned. |
| * |
| * In particular, check whether all pairs of basic maps are disjoint. |
| */ |
| static isl_bool isl_map_is_disjoint_aligned(__isl_keep isl_map *map1, |
| __isl_keep isl_map *map2) |
| { |
| return all_pairs(map1, map2, &isl_basic_map_is_disjoint); |
| } |
| |
| /* Are "map1" and "map2" disjoint? |
| * |
| * They are disjoint if they are "obviously disjoint" or if one of them |
| * is empty. Otherwise, they are not disjoint if one of them is universal. |
| * If the two inputs are (obviously) equal and not empty, then they are |
| * not disjoint. |
| * If none of these cases apply, then check if all pairs of basic maps |
| * are disjoint after aligning the parameters. |
| */ |
| isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2) |
| { |
| isl_bool disjoint; |
| isl_bool intersect; |
| |
| disjoint = isl_map_plain_is_disjoint_global(map1, map2); |
| if (disjoint < 0 || disjoint) |
| return disjoint; |
| |
| disjoint = isl_map_is_empty(map1); |
| if (disjoint < 0 || disjoint) |
| return disjoint; |
| |
| disjoint = isl_map_is_empty(map2); |
| if (disjoint < 0 || disjoint) |
| return disjoint; |
| |
| intersect = isl_map_plain_is_universe(map1); |
| if (intersect < 0 || intersect) |
| return intersect < 0 ? isl_bool_error : isl_bool_false; |
| |
| intersect = isl_map_plain_is_universe(map2); |
| if (intersect < 0 || intersect) |
| return intersect < 0 ? isl_bool_error : isl_bool_false; |
| |
| intersect = isl_map_plain_is_equal(map1, map2); |
| if (intersect < 0 || intersect) |
| return isl_bool_not(intersect); |
| |
| return isl_map_align_params_map_map_and_test(map1, map2, |
| &isl_map_is_disjoint_aligned); |
| } |
| |
| /* Are "bmap1" and "bmap2" disjoint? |
| * |
| * They are disjoint if they are "obviously disjoint" or if one of them |
| * is empty. Otherwise, they are not disjoint if one of them is universal. |
| * If none of these cases apply, we compute the intersection and see if |
| * the result is empty. |
| */ |
| isl_bool isl_basic_map_is_disjoint(__isl_keep isl_basic_map *bmap1, |
| __isl_keep isl_basic_map *bmap2) |
| { |
| isl_bool disjoint; |
| isl_bool intersect; |
| isl_basic_map *test; |
| |
| disjoint = isl_basic_map_plain_is_disjoint(bmap1, bmap2); |
| if (disjoint < 0 || disjoint) |
| return disjoint; |
| |
| disjoint = isl_basic_map_is_empty(bmap1); |
| if (disjoint < 0 || disjoint) |
| return disjoint; |
| |
| disjoint = isl_basic_map_is_empty(bmap2); |
| if (disjoint < 0 || disjoint) |
| return disjoint; |
| |
| intersect = isl_basic_map_plain_is_universe(bmap1); |
| if (intersect < 0 || intersect) |
| return intersect < 0 ? isl_bool_error : isl_bool_false; |
| |
| intersect = isl_basic_map_plain_is_universe(bmap2); |
| if (intersect < 0 || intersect) |
| return intersect < 0 ? isl_bool_error : isl_bool_false; |
| |
| test = isl_basic_map_intersect(isl_basic_map_copy(bmap1), |
| isl_basic_map_copy(bmap2)); |
| disjoint = isl_basic_map_is_empty(test); |
| isl_basic_map_free(test); |
| |
| return disjoint; |
| } |
| |
| /* Are "bset1" and "bset2" disjoint? |
| */ |
| isl_bool isl_basic_set_is_disjoint(__isl_keep isl_basic_set *bset1, |
| __isl_keep isl_basic_set *bset2) |
| { |
| return isl_basic_map_is_disjoint(bset1, bset2); |
| } |
| |
| isl_bool isl_set_plain_is_disjoint(__isl_keep isl_set *set1, |
| __isl_keep isl_set *set2) |
| { |
| return isl_map_plain_is_disjoint(set_to_map(set1), set_to_map(set2)); |
| } |
| |
| /* Are "set1" and "set2" disjoint? |
| */ |
| isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2) |
| { |
| return isl_map_is_disjoint(set1, set2); |
| } |
| |
| /* Is "v" equal to 0, 1 or -1? |
| */ |
| static int is_zero_or_one(isl_int v) |
| { |
| return isl_int_is_zero(v) || isl_int_is_one(v) || isl_int_is_negone(v); |
| } |
| |
| /* 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 (except for the lower and upper bound) |
| * are of the form |
| * |
| * e + f (a + m b) >= 0 |
| * |
| * Furthermore, in the constraints that only contain b, the coefficient |
| * of b should be equal to 1 or -1. |
| * 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])) { |
| if (is_zero_or_one(bmap->ineq[j][1 + dim + i])) |
| continue; |
| break; |
| } |
| 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; |
| } |
| |
| /* Internal data structure used during the construction and/or evaluation of |
| * an inequality that ensures that a pair of bounds always allows |
| * for an integer value. |
| * |
| * "tab" is the tableau in which the inequality is evaluated. It may |
| * be NULL until it is actually needed. |
| * "v" contains the inequality coefficients. |
| * "g", "fl" and "fu" are temporary scalars used during the construction and |
| * evaluation. |
| */ |
| struct test_ineq_data { |
| struct isl_tab *tab; |
| isl_vec *v; |
| isl_int g; |
| isl_int fl; |
| isl_int fu; |
| }; |
| |
| /* Free all the memory allocated by the fields of "data". |
| */ |
| static void test_ineq_data_clear(struct test_ineq_data *data) |
| { |
| isl_tab_free(data->tab); |
| isl_vec_free(data->v); |
| isl_int_clear(data->g); |
| isl_int_clear(data->fl); |
| isl_int_clear(data->fu); |
| } |
| |
| /* Is the inequality stored in data->v satisfied by "bmap"? |
| * That is, does it only attain non-negative values? |
| * data->tab is a tableau corresponding to "bmap". |
| */ |
| static isl_bool test_ineq_is_satisfied(__isl_keep isl_basic_map *bmap, |
| struct test_ineq_data *data) |
| { |
| isl_ctx *ctx; |
| enum isl_lp_result res; |
| |
| ctx = isl_basic_map_get_ctx(bmap); |
| if (!data->tab) |
| data->tab = isl_tab_from_basic_map(bmap, 0); |
| res = isl_tab_min(data->tab, data->v->el, ctx->one, &data->g, NULL, 0); |
| if (res == isl_lp_error) |
| return isl_bool_error; |
| return res == isl_lp_ok && isl_int_is_nonneg(data->g); |
| } |
| |
| /* Given a lower and an upper bound on div i, do they always allow |
| * for an integer value of the given div? |
| * Determine this property by constructing an inequality |
| * such that the property is guaranteed when the inequality is nonnegative. |
| * The lower bound is inequality l, while the upper bound is inequality u. |
| * The constructed inequality is stored in data->v. |
| * |
| * 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 |
| * |
| * or |
| * |
| * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0 |
| * |
| * If the coefficients of f_l e_u + f_u e_l have a common divisor g', |
| * then the constraint can be scaled down by a factor g', |
| * with the constant term replaced by |
| * floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g'). |
| * Note that the result of applying Fourier-Motzkin to this pair |
| * of constraints is |
| * |
| * f_l e_u + f_u e_l >= 0 |
| * |
| * If the constant term of the scaled down version of this constraint, |
| * i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant |
| * term of the scaled down test constraint, then the test constraint |
| * is known to hold and no explicit evaluation is required. |
| * This is essentially the Omega test. |
| * |
| * If the test constraint consists of only a constant term, then |
| * it is sufficient to look at the sign of this constant term. |
| */ |
| static isl_bool int_between_bounds(__isl_keep isl_basic_map *bmap, int i, |
| int l, int u, struct test_ineq_data *data) |
| { |
| unsigned offset, n_div; |
| offset = isl_basic_map_offset(bmap, isl_dim_div); |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| |
| isl_int_gcd(data->g, |
| bmap->ineq[l][offset + i], bmap->ineq[u][offset + i]); |
| isl_int_divexact(data->fl, bmap->ineq[l][offset + i], data->g); |
| isl_int_divexact(data->fu, bmap->ineq[u][offset + i], data->g); |
| isl_int_neg(data->fu, data->fu); |
| isl_seq_combine(data->v->el, data->fl, bmap->ineq[u], |
| data->fu, bmap->ineq[l], offset + n_div); |
| isl_int_mul(data->g, data->g, data->fl); |
| isl_int_mul(data->g, data->g, data->fu); |
| isl_int_sub(data->g, data->g, data->fl); |
| isl_int_sub(data->g, data->g, data->fu); |
| isl_int_add_ui(data->g, data->g, 1); |
| isl_int_sub(data->fl, data->v->el[0], data->g); |
| |
| isl_seq_gcd(data->v->el + 1, offset - 1 + n_div, &data->g); |
| if (isl_int_is_zero(data->g)) |
| return isl_int_is_nonneg(data->fl); |
| if (isl_int_is_one(data->g)) { |
| isl_int_set(data->v->el[0], data->fl); |
| return test_ineq_is_satisfied(bmap, data); |
| } |
| isl_int_fdiv_q(data->fl, data->fl, data->g); |
| isl_int_fdiv_q(data->v->el[0], data->v->el[0], data->g); |
| if (isl_int_eq(data->fl, data->v->el[0])) |
| return isl_bool_true; |
| isl_int_set(data->v->el[0], data->fl); |
| isl_seq_scale_down(data->v->el + 1, data->v->el + 1, data->g, |
| offset - 1 + n_div); |
| |
| return test_ineq_is_satisfied(bmap, data); |
| } |
| |
| /* 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, |
| * then we can eliminate the div using Fourier-Motzkin without |
| * introducing any spurious solutions. |
| * |
| * If at least one of the two constraints has a unit coefficient for the div, |
| * then the presence of such a value is guaranteed so there is no need to check. |
| * In particular, the value attained by the bound with unit coefficient |
| * can serve as this intermediate value. |
| */ |
| static __isl_give isl_basic_map *drop_more_redundant_divs( |
| __isl_take isl_basic_map *bmap, __isl_take int *pairs, int n) |
| { |
| isl_ctx *ctx; |
| struct test_ineq_data data = { NULL, NULL }; |
| unsigned off, n_div; |
| int remove = -1; |
| |
| isl_int_init(data.g); |
| isl_int_init(data.fl); |
| isl_int_init(data.fu); |
| |
| if (!bmap) |
| goto error; |
| |
| ctx = isl_basic_map_get_ctx(bmap); |
| off = isl_basic_map_offset(bmap, isl_dim_div); |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| data.v = isl_vec_alloc(ctx, off + n_div); |
| if (!data.v) |
| goto error; |
| |
| while (n > 0) { |
| int i, l, u; |
| int best = -1; |
| isl_bool has_int; |
| |
| for (i = 0; i < 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][off + i])) |
| continue; |
| if (isl_int_is_one(bmap->ineq[l][off + i])) |
| continue; |
| for (u = 0; u < bmap->n_ineq; ++u) { |
| if (!isl_int_is_neg(bmap->ineq[u][off + i])) |
| continue; |
| if (isl_int_is_negone(bmap->ineq[u][off + i])) |
| continue; |
| has_int = int_between_bounds(bmap, i, l, u, |
| &data); |
| if (has_int < 0) |
| goto error; |
| if (data.tab && data.tab->empty) |
| break; |
| if (!has_int) |
| break; |
| } |
| if (u < bmap->n_ineq) |
| break; |
| } |
| if (data.tab && data.tab->empty) { |
| bmap = isl_basic_map_set_to_empty(bmap); |
| break; |
| } |
| if (l == bmap->n_ineq) { |
| remove = i; |
| break; |
| } |
| pairs[i] = 0; |
| --n; |
| } |
| |
| test_ineq_data_clear(&data); |
| |
| 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); |
| test_ineq_data_clear(&data); |
| return NULL; |
| } |
| |
| /* Given a pair of divs div1 and div2 such that, except 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 |
| * The coefficient of div2 is known to be equal to 1 or -1. |
| * (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 l be |
| * |
| * div1 + f >=0 |
| * |
| * and u |
| * |
| * -div1 + f' >= 0 |
| * |
| * A lower bound on div2 |
| * |
| * div2 + t >= 0 |
| * |
| * can be replaced by |
| * |
| * m div2 + div1 + m t + f >= 0 |
| * |
| * An upper bound |
| * |
| * -div2 + t >= 0 |
| * |
| * can be replaced by |
| * |
| * -(m div2 + div1) + m t + f' >= 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. |
| * Since the new div is only placed in the same location that used |
| * to store div2, but otherwise has a different meaning, any possible |
| * explicit representation of the original div2 is removed. |
| */ |
| static __isl_give isl_basic_map *coalesce_divs(__isl_take isl_basic_map *bmap, |
| unsigned div1, unsigned div2, unsigned l, unsigned u) |
| { |
| isl_ctx *ctx; |
| isl_int m; |
| unsigned dim, total; |
| int i; |
| |
| ctx = isl_basic_map_get_ctx(bmap); |
| |
| dim = isl_space_dim(bmap->dim, isl_dim_all); |
| total = 1 + dim + bmap->n_div; |
| |
| 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])) { |
| if (isl_int_is_pos(bmap->ineq[i][1 + dim + div2])) |
| isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i], |
| ctx->one, bmap->ineq[l], total); |
| else |
| isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i], |
| ctx->one, 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(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_mark_div_unknown(bmap, div2); |
| 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 __isl_give isl_basic_map *coalesce_or_drop_more_redundant_divs( |
| __isl_take 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)) { |
| free(pairs); |
| return bmap; |
| } |
| |
| return drop_more_redundant_divs(bmap, pairs, n); |
| } |
| |
| /* Are the "n" coefficients starting at "first" of inequality constraints |
| * "i" and "j" of "bmap" equal to each other? |
| */ |
| static int is_parallel_part(__isl_keep isl_basic_map *bmap, int i, int j, |
| int first, int n) |
| { |
| return isl_seq_eq(bmap->ineq[i] + first, bmap->ineq[j] + first, n); |
| } |
| |
| /* Are the "n" coefficients starting at "first" of inequality constraints |
| * "i" and "j" of "bmap" opposite to each other? |
| */ |
| static int is_opposite_part(__isl_keep isl_basic_map *bmap, int i, int j, |
| int first, int n) |
| { |
| return isl_seq_is_neg(bmap->ineq[i] + first, bmap->ineq[j] + first, n); |
| } |
| |
| /* Are inequality constraints "i" and "j" of "bmap" opposite to each other, |
| * apart from the constant term? |
| */ |
| static isl_bool is_opposite(__isl_keep isl_basic_map *bmap, int i, int j) |
| { |
| unsigned total; |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| return is_opposite_part(bmap, i, j, 1, total); |
| } |
| |
| /* Are inequality constraints "i" and "j" of "bmap" equal to each other, |
| * apart from the constant term and the coefficient at position "pos"? |
| */ |
| static int is_parallel_except(__isl_keep isl_basic_map *bmap, int i, int j, |
| int pos) |
| { |
| unsigned total; |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| return is_parallel_part(bmap, i, j, 1, pos - 1) && |
| is_parallel_part(bmap, i, j, pos + 1, total - pos); |
| } |
| |
| /* Are inequality constraints "i" and "j" of "bmap" opposite to each other, |
| * apart from the constant term and the coefficient at position "pos"? |
| */ |
| static int is_opposite_except(__isl_keep isl_basic_map *bmap, int i, int j, |
| int pos) |
| { |
| unsigned total; |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| return is_opposite_part(bmap, i, j, 1, pos - 1) && |
| is_opposite_part(bmap, i, j, pos + 1, total - pos); |
| } |
| |
| /* Restart isl_basic_map_drop_redundant_divs after "bmap" has |
| * been modified, simplying it if "simplify" is set. |
| * Free the temporary data structure "pairs" that was associated |
| * to the old version of "bmap". |
| */ |
| static __isl_give isl_basic_map *drop_redundant_divs_again( |
| __isl_take isl_basic_map *bmap, __isl_take int *pairs, int simplify) |
| { |
| if (simplify) |
| bmap = isl_basic_map_simplify(bmap); |
| free(pairs); |
| return isl_basic_map_drop_redundant_divs(bmap); |
| } |
| |
| /* Is "div" the single unknown existentially quantified variable |
| * in inequality constraint "ineq" of "bmap"? |
| * "div" is known to have a non-zero coefficient in "ineq". |
| */ |
| static isl_bool single_unknown(__isl_keep isl_basic_map *bmap, int ineq, |
| int div) |
| { |
| int i; |
| unsigned n_div, o_div; |
| isl_bool known; |
| |
| known = isl_basic_map_div_is_known(bmap, div); |
| if (known < 0 || known) |
| return isl_bool_not(known); |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| if (n_div == 1) |
| return isl_bool_true; |
| o_div = isl_basic_map_offset(bmap, isl_dim_div); |
| for (i = 0; i < n_div; ++i) { |
| isl_bool known; |
| |
| if (i == div) |
| continue; |
| if (isl_int_is_zero(bmap->ineq[ineq][o_div + i])) |
| continue; |
| known = isl_basic_map_div_is_known(bmap, i); |
| if (known < 0 || !known) |
| return known; |
| } |
| |
| return isl_bool_true; |
| } |
| |
| /* Does integer division "div" have coefficient 1 in inequality constraint |
| * "ineq" of "map"? |
| */ |
| static isl_bool has_coef_one(__isl_keep isl_basic_map *bmap, int div, int ineq) |
| { |
| unsigned o_div; |
| |
| o_div = isl_basic_map_offset(bmap, isl_dim_div); |
| if (isl_int_is_one(bmap->ineq[ineq][o_div + div])) |
| return isl_bool_true; |
| |
| return isl_bool_false; |
| } |
| |
| /* Turn inequality constraint "ineq" of "bmap" into an equality and |
| * then try and drop redundant divs again, |
| * freeing the temporary data structure "pairs" that was associated |
| * to the old version of "bmap". |
| */ |
| static __isl_give isl_basic_map *set_eq_and_try_again( |
| __isl_take isl_basic_map *bmap, int ineq, __isl_take int *pairs) |
| { |
| bmap = isl_basic_map_cow(bmap); |
| isl_basic_map_inequality_to_equality(bmap, ineq); |
| return drop_redundant_divs_again(bmap, pairs, 1); |
| } |
| |
| /* Drop the integer division at position "div", along with the two |
| * inequality constraints "ineq1" and "ineq2" in which it appears |
| * from "bmap" and then try and drop redundant divs again, |
| * freeing the temporary data structure "pairs" that was associated |
| * to the old version of "bmap". |
| */ |
| static __isl_give isl_basic_map *drop_div_and_try_again( |
| __isl_take isl_basic_map *bmap, int div, int ineq1, int ineq2, |
| __isl_take int *pairs) |
| { |
| if (ineq1 > ineq2) { |
| isl_basic_map_drop_inequality(bmap, ineq1); |
| isl_basic_map_drop_inequality(bmap, ineq2); |
| } else { |
| isl_basic_map_drop_inequality(bmap, ineq2); |
| isl_basic_map_drop_inequality(bmap, ineq1); |
| } |
| bmap = isl_basic_map_drop_div(bmap, div); |
| return drop_redundant_divs_again(bmap, pairs, 0); |
| } |
| |
| /* Given two inequality constraints |
| * |
| * f(x) + n d + c >= 0, (ineq) |
| * |
| * with d the variable at position "pos", and |
| * |
| * f(x) + c0 >= 0, (lower) |
| * |
| * compute the maximal value of the lower bound ceil((-f(x) - c)/n) |
| * determined by the first constraint. |
| * That is, store |
| * |
| * ceil((c0 - c)/n) |
| * |
| * in *l. |
| */ |
| static void lower_bound_from_parallel(__isl_keep isl_basic_map *bmap, |
| int ineq, int lower, int pos, isl_int *l) |
| { |
| isl_int_neg(*l, bmap->ineq[ineq][0]); |
| isl_int_add(*l, *l, bmap->ineq[lower][0]); |
| isl_int_cdiv_q(*l, *l, bmap->ineq[ineq][pos]); |
| } |
| |
| /* Given two inequality constraints |
| * |
| * f(x) + n d + c >= 0, (ineq) |
| * |
| * with d the variable at position "pos", and |
| * |
| * -f(x) - c0 >= 0, (upper) |
| * |
| * compute the minimal value of the lower bound ceil((-f(x) - c)/n) |
| * determined by the first constraint. |
| * That is, store |
| * |
| * ceil((-c1 - c)/n) |
| * |
| * in *u. |
| */ |
| static void lower_bound_from_opposite(__isl_keep isl_basic_map *bmap, |
| int ineq, int upper, int pos, isl_int *u) |
| { |
| isl_int_neg(*u, bmap->ineq[ineq][0]); |
| isl_int_sub(*u, *u, bmap->ineq[upper][0]); |
| isl_int_cdiv_q(*u, *u, bmap->ineq[ineq][pos]); |
| } |
| |
| /* Given a lower bound constraint "ineq" on "div" in "bmap", |
| * does the corresponding lower bound have a fixed value in "bmap"? |
| * |
| * In particular, "ineq" is of the form |
| * |
| * f(x) + n d + c >= 0 |
| * |
| * with n > 0, c the constant term and |
| * d the existentially quantified variable "div". |
| * That is, the lower bound is |
| * |
| * ceil((-f(x) - c)/n) |
| * |
| * Look for a pair of constraints |
| * |
| * f(x) + c0 >= 0 |
| * -f(x) + c1 >= 0 |
| * |
| * i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value. |
| * That is, check that |
| * |
| * ceil((-c1 - c)/n) = ceil((c0 - c)/n) |
| * |
| * If so, return the index of inequality f(x) + c0 >= 0. |
| * Otherwise, return -1. |
| */ |
| static int lower_bound_is_cst(__isl_keep isl_basic_map *bmap, int div, int ineq) |
| { |
| int i; |
| int lower = -1, upper = -1; |
| unsigned o_div; |
| isl_int l, u; |
| int equal; |
| |
| o_div = isl_basic_map_offset(bmap, isl_dim_div); |
| for (i = 0; i < bmap->n_ineq && (lower < 0 || upper < 0); ++i) { |
| if (i == ineq) |
| continue; |
| if (!isl_int_is_zero(bmap->ineq[i][o_div + div])) |
| continue; |
| if (lower < 0 && |
| is_parallel_except(bmap, ineq, i, o_div + div)) { |
| lower = i; |
| continue; |
| } |
| if (upper < 0 && |
| is_opposite_except(bmap, ineq, i, o_div + div)) { |
| upper = i; |
| } |
| } |
| |
| if (lower < 0 || upper < 0) |
| return -1; |
| |
| isl_int_init(l); |
| isl_int_init(u); |
| |
| lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &l); |
| lower_bound_from_opposite(bmap, ineq, upper, o_div + div, &u); |
| |
| equal = isl_int_eq(l, u); |
| |
| isl_int_clear(l); |
| isl_int_clear(u); |
| |
| return equal ? lower : -1; |
| } |
| |
| /* Given a lower bound constraint "ineq" on the existentially quantified |
| * variable "div", such that the corresponding lower bound has |
| * a fixed value in "bmap", assign this fixed value to the variable and |
| * then try and drop redundant divs again, |
| * freeing the temporary data structure "pairs" that was associated |
| * to the old version of "bmap". |
| * "lower" determines the constant value for the lower bound. |
| * |
| * In particular, "ineq" is of the form |
| * |
| * f(x) + n d + c >= 0, |
| * |
| * while "lower" is of the form |
| * |
| * f(x) + c0 >= 0 |
| * |
| * The lower bound is ceil((-f(x) - c)/n) and its constant value |
| * is ceil((c0 - c)/n). |
| */ |
| static __isl_give isl_basic_map *fix_cst_lower(__isl_take isl_basic_map *bmap, |
| int div, int ineq, int lower, int *pairs) |
| { |
| isl_int c; |
| unsigned o_div; |
| |
| isl_int_init(c); |
| |
| o_div = isl_basic_map_offset(bmap, isl_dim_div); |
| lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &c); |
| bmap = isl_basic_map_fix(bmap, isl_dim_div, div, c); |
| free(pairs); |
| |
| isl_int_clear(c); |
| |
| return isl_basic_map_drop_redundant_divs(bmap); |
| } |
| |
| /* Remove divs that are not strictly needed based on the inequality |
| * constraints. |
| * In particular, if a div only occurs positively (or negatively) |
| * in constraints, then it can simply be dropped. |
| * Also, if a div occurs in only 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 coefficient of the div in the constraints, |
| * then we can also simply drop the div. |
| * |
| * If an existentially quantified variable does not have an explicit |
| * representation, appears in only a single lower bound that does not |
| * involve any other such existentially quantified variables and appears |
| * in this lower bound with coefficient 1, |
| * then fix the variable to the value of the lower bound. That is, |
| * turn the inequality into an equality. |
| * If for any value of the other variables, there is any value |
| * for the existentially quantified variable satisfying the constraints, |
| * then this lower bound also satisfies the constraints. |
| * It is therefore safe to pick this lower bound. |
| * |
| * The same reasoning holds even if the coefficient is not one. |
| * However, fixing the variable to the value of the lower bound may |
| * in general introduce an extra integer division, in which case |
| * it may be better to pick another value. |
| * If this integer division has a known constant value, then plugging |
| * in this constant value removes the existentially quantified variable |
| * completely. In particular, if the lower bound is of the form |
| * ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and |
| * -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n), |
| * then the existentially quantified variable can be assigned this |
| * shared value. |
| * |
| * We skip divs that appear in equalities or in the definition of other divs. |
| * Divs that appear in the definition of other divs usually occur in at least |
| * 4 constraints, but the constraints may have been simplified. |
| * |
| * If any divs are left after these simple checks then we move on |
| * to more complicated cases in drop_more_redundant_divs. |
| */ |
| static __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs_ineq( |
| __isl_take isl_basic_map *bmap) |
| { |
| int i, j; |
| unsigned off; |
| int *pairs = NULL; |
| int n = 0; |
| |
| if (!bmap) |
| goto error; |
| if (bmap->n_div == 0) |
| return bmap; |
| |
| 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; |
| isl_bool opp, set_div; |
| |
| defined = !isl_int_is_zero(bmap->div[i][0]); |
| for (j = i; j < bmap->n_div; ++j) |
| if (!isl_int_is_zero(bmap->div[j][1 + 1 + off + i])) |
| break; |
| if (j < bmap->n_div) |
| continue; |
| 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); |
| return drop_redundant_divs_again(bmap, pairs, 0); |
| } |
| if (pairs[i] != 1) |
| opp = isl_bool_false; |
| else |
| opp = is_opposite(bmap, last_pos, last_neg); |
| if (opp < 0) |
| goto error; |
| if (!opp) { |
| int lower; |
| isl_bool single, one; |
| |
| if (pos != 1) |
| continue; |
| single = single_unknown(bmap, last_pos, i); |
| if (single < 0) |
| goto error; |
| if (!single) |
| continue; |
| one = has_coef_one(bmap, i, last_pos); |
| if (one < 0) |
| goto error; |
| if (one) |
| return set_eq_and_try_again(bmap, last_pos, |
| pairs); |
| lower = lower_bound_is_cst(bmap, i, last_pos); |
| if (lower >= 0) |
| return fix_cst_lower(bmap, i, last_pos, lower, |
| pairs); |
| 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) |
| return drop_div_and_try_again(bmap, i, |
| last_pos, last_neg, pairs); |
| if (defined) |
| set_div = isl_bool_false; |
| else |
| set_div = ok_to_set_div_from_bound(bmap, i, last_pos); |
| if (set_div < 0) |
| return isl_basic_map_free(bmap); |
| if (set_div) { |
| bmap = set_div_from_lower_bound(bmap, i, last_pos); |
| return drop_redundant_divs_again(bmap, pairs, 1); |
| } |
| pairs[i] = 0; |
| --n; |
| } |
| |
| 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; |
| } |
| |
| /* Consider the coefficients at "c" as a row vector and replace |
| * them with their product with "T". "T" is assumed to be a square matrix. |
| */ |
| static isl_stat preimage(isl_int *c, __isl_keep isl_mat *T) |
| { |
| int n; |
| isl_ctx *ctx; |
| isl_vec *v; |
| |
| if (!T) |
| return isl_stat_error; |
| n = isl_mat_rows(T); |
| if (isl_seq_first_non_zero(c, n) == -1) |
| return isl_stat_ok; |
| ctx = isl_mat_get_ctx(T); |
| v = isl_vec_alloc(ctx, n); |
| if (!v) |
| return isl_stat_error; |
| isl_seq_swp_or_cpy(v->el, c, n); |
| v = isl_vec_mat_product(v, isl_mat_copy(T)); |
| if (!v) |
| return isl_stat_error; |
| isl_seq_swp_or_cpy(c, v->el, n); |
| isl_vec_free(v); |
| |
| return isl_stat_ok; |
| } |
| |
| /* Plug in T for the variables in "bmap" starting at "pos". |
| * T is a linear unimodular matrix, i.e., without constant term. |
| */ |
| static __isl_give isl_basic_map *isl_basic_map_preimage_vars( |
| __isl_take isl_basic_map *bmap, unsigned pos, __isl_take isl_mat *T) |
| { |
| int i; |
| unsigned n, total; |
| |
| bmap = isl_basic_map_cow(bmap); |
| if (!bmap || !T) |
| goto error; |
| |
| n = isl_mat_cols(T); |
| if (n != isl_mat_rows(T)) |
| isl_die(isl_mat_get_ctx(T), isl_error_invalid, |
| "expecting square matrix", goto error); |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| if (pos + n > total || pos + n < pos) |
| isl_die(isl_mat_get_ctx(T), isl_error_invalid, |
| "invalid range", goto error); |
| |
| for (i = 0; i < bmap->n_eq; ++i) |
| if (preimage(bmap->eq[i] + 1 + pos, T) < 0) |
| goto error; |
| for (i = 0; i < bmap->n_ineq; ++i) |
| if (preimage(bmap->ineq[i] + 1 + pos, T) < 0) |
| goto error; |
| for (i = 0; i < bmap->n_div; ++i) { |
| if (isl_basic_map_div_is_marked_unknown(bmap, i)) |
| continue; |
| if (preimage(bmap->div[i] + 1 + 1 + pos, T) < 0) |
| goto error; |
| } |
| |
| isl_mat_free(T); |
| return bmap; |
| error: |
| isl_basic_map_free(bmap); |
| isl_mat_free(T); |
| return NULL; |
| } |
| |
| /* Remove divs that are not strictly needed. |
| * |
| * First look for an equality constraint involving two or more |
| * existentially quantified variables without an explicit |
| * representation. Replace the combination that appears |
| * in the equality constraint by a single existentially quantified |
| * variable such that the equality can be used to derive |
| * an explicit representation for the variable. |
| * If there are no more such equality constraints, then continue |
| * with isl_basic_map_drop_redundant_divs_ineq. |
| * |
| * In particular, if the equality constraint is of the form |
| * |
| * f(x) + \sum_i c_i a_i = 0 |
| * |
| * with a_i existentially quantified variable without explicit |
| * representation, then apply a transformation on the existentially |
| * quantified variables to turn the constraint into |
| * |
| * f(x) + g a_1' = 0 |
| * |
| * with g the gcd of the c_i. |
| * In order to easily identify which existentially quantified variables |
| * have a complete explicit representation, i.e., without being defined |
| * in terms of other existentially quantified variables without |
| * an explicit representation, the existentially quantified variables |
| * are first sorted. |
| * |
| * The variable transformation is computed by extending the row |
| * [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation |
| * |
| * [a_1'] [c_1/g ... c_n/g] [ a_1 ] |
| * [a_2'] [ a_2 ] |
| * ... = U .... |
| * [a_n'] [ a_n ] |
| * |
| * with [c_1/g ... c_n/g] representing the first row of U. |
| * The inverse of U is then plugged into the original constraints. |
| * The call to isl_basic_map_simplify makes sure the explicit |
| * representation for a_1' is extracted from the equality constraint. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs( |
| __isl_take isl_basic_map *bmap) |
| { |
| int first; |
| int i; |
| unsigned o_div, n_div; |
| int l; |
| isl_ctx *ctx; |
| isl_mat *T; |
| |
| if (!bmap) |
| return NULL; |
| if (isl_basic_map_divs_known(bmap)) |
| return isl_basic_map_drop_redundant_divs_ineq(bmap); |
| if (bmap->n_eq == 0) |
| return isl_basic_map_drop_redundant_divs_ineq(bmap); |
| bmap = isl_basic_map_sort_divs(bmap); |
| if (!bmap) |
| return NULL; |
| |
| first = isl_basic_map_first_unknown_div(bmap); |
| if (first < 0) |
| return isl_basic_map_free(bmap); |
| |
| o_div = isl_basic_map_offset(bmap, isl_dim_div); |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| |
| for (i = 0; i < bmap->n_eq; ++i) { |
| l = isl_seq_first_non_zero(bmap->eq[i] + o_div + first, |
| n_div - (first)); |
| if (l < 0) |
| continue; |
| l += first; |
| if (isl_seq_first_non_zero(bmap->eq[i] + o_div + l + 1, |
| n_div - (l + 1)) == -1) |
| continue; |
| break; |
| } |
| if (i >= bmap->n_eq) |
| return isl_basic_map_drop_redundant_divs_ineq(bmap); |
| |
| ctx = isl_basic_map_get_ctx(bmap); |
| T = isl_mat_alloc(ctx, n_div - l, n_div - l); |
| if (!T) |
| return isl_basic_map_free(bmap); |
| isl_seq_cpy(T->row[0], bmap->eq[i] + o_div + l, n_div - l); |
| T = isl_mat_normalize_row(T, 0); |
| T = isl_mat_unimodular_complete(T, 1); |
| T = isl_mat_right_inverse(T); |
| |
| for (i = l; i < n_div; ++i) |
| bmap = isl_basic_map_mark_div_unknown(bmap, i); |
| bmap = isl_basic_map_preimage_vars(bmap, o_div - 1 + l, T); |
| bmap = isl_basic_map_simplify(bmap); |
| |
| return isl_basic_map_drop_redundant_divs(bmap); |
| } |
| |
| /* Does "bmap" satisfy any equality that involves more than 2 variables |
| * and/or has coefficients different from -1 and 1? |
| */ |
| static int has_multiple_var_equality(__isl_keep isl_basic_map *bmap) |
| { |
| int i; |
| unsigned total; |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| |
| for (i = 0; i < bmap->n_eq; ++i) { |
| int j, k; |
| |
| j = isl_seq_first_non_zero(bmap->eq[i] + 1, total); |
| if (j < 0) |
| continue; |
| if (!isl_int_is_one(bmap->eq[i][1 + j]) && |
| !isl_int_is_negone(bmap->eq[i][1 + j])) |
| return 1; |
| |
| j += 1; |
| k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j); |
| if (k < 0) |
| continue; |
| j += k; |
| if (!isl_int_is_one(bmap->eq[i][1 + j]) && |
| !isl_int_is_negone(bmap->eq[i][1 + j])) |
| return 1; |
| |
| j += 1; |
| k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j); |
| if (k >= 0) |
| return 1; |
| } |
| |
| return 0; |
| } |
| |
| /* Remove any common factor g from the constraint coefficients in "v". |
| * The constant term is stored in the first position and is replaced |
| * by floor(c/g). If any common factor is removed and if this results |
| * in a tightening of the constraint, then set *tightened. |
| */ |
| static __isl_give isl_vec *normalize_constraint(__isl_take isl_vec *v, |
| int *tightened) |
| { |
| isl_ctx *ctx; |
| |
| 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)) |
| return v; |
| if (isl_int_is_one(ctx->normalize_gcd)) |
| return v; |
| v = isl_vec_cow(v); |
| if (!v) |
| return NULL; |
| if (tightened && !isl_int_is_divisible_by(v->el[0], ctx->normalize_gcd)) |
| *tightened = 1; |
| isl_int_fdiv_q(v->el[0], v->el[0], ctx->normalize_gcd); |
| isl_seq_scale_down(v->el + 1, v->el + 1, ctx->normalize_gcd, |
| v->size - 1); |
| return v; |
| } |
| |
| /* If "bmap" is an integer set that satisfies any equality involving |
| * more than 2 variables and/or has coefficients different from -1 and 1, |
| * then use variable compression to reduce the coefficients by removing |
| * any (hidden) common factor. |
| * In particular, apply the variable compression to each constraint, |
| * factor out any common factor in the non-constant coefficients and |
| * then apply the inverse of the compression. |
| * At the end, we mark the basic map as having reduced constants. |
| * If this flag is still set on the next invocation of this function, |
| * then we skip the computation. |
| * |
| * Removing a common factor may result in a tightening of some of |
| * the constraints. If this happens, then we may end up with two |
| * opposite inequalities that can be replaced by an equality. |
| * We therefore call isl_basic_map_detect_inequality_pairs, |
| * which checks for such pairs of inequalities as well as eliminate_divs_eq |
| * and isl_basic_map_gauss if such a pair was found. |
| * |
| * Note that this function may leave the result in an inconsistent state. |
| * In particular, the constraints may not be gaussed. |
| * Unfortunately, isl_map_coalesce actually depends on this inconsistent state |
| * for some of the test cases to pass successfully. |
| * Any potential modification of the representation is therefore only |
| * performed on a single copy of the basic map. |
| */ |
| __isl_give isl_basic_map *isl_basic_map_reduce_coefficients( |
| __isl_take isl_basic_map *bmap) |
| { |
| unsigned total; |
| isl_ctx *ctx; |
| isl_vec *v; |
| isl_mat *eq, *T, *T2; |
| int i; |
| int tightened; |
| |
| if (!bmap) |
| return NULL; |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)) |
| return bmap; |
| if (isl_basic_map_is_rational(bmap)) |
| return bmap; |
| if (bmap->n_eq == 0) |
| return bmap; |
| if (!has_multiple_var_equality(bmap)) |
| return bmap; |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| ctx = isl_basic_map_get_ctx(bmap); |
| v = isl_vec_alloc(ctx, 1 + total); |
| if (!v) |
| return isl_basic_map_free(bmap); |
| |
| eq = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total); |
| T = isl_mat_variable_compression(eq, &T2); |
| if (!T || !T2) |
| goto error; |
| if (T->n_col == 0) { |
| isl_mat_free(T); |
| isl_mat_free(T2); |
| isl_vec_free(v); |
| return isl_basic_map_set_to_empty(bmap); |
| } |
| |
| bmap = isl_basic_map_cow(bmap); |
| if (!bmap) |
| goto error; |
| |
| tightened = 0; |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| isl_seq_cpy(v->el, bmap->ineq[i], 1 + total); |
| v = isl_vec_mat_product(v, isl_mat_copy(T)); |
| v = normalize_constraint(v, &tightened); |
| v = isl_vec_mat_product(v, isl_mat_copy(T2)); |
| if (!v) |
| goto error; |
| isl_seq_cpy(bmap->ineq[i], v->el, 1 + total); |
| } |
| |
| isl_mat_free(T); |
| isl_mat_free(T2); |
| isl_vec_free(v); |
| |
| ISL_F_SET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS); |
| |
| if (tightened) { |
| int progress = 0; |
| |
| bmap = isl_basic_map_detect_inequality_pairs(bmap, &progress); |
| if (progress) { |
| bmap = eliminate_divs_eq(bmap, &progress); |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| } |
| } |
| |
| return bmap; |
| error: |
| isl_mat_free(T); |
| isl_mat_free(T2); |
| isl_vec_free(v); |
| return isl_basic_map_free(bmap); |
| } |
| |
| /* Shift the integer division at position "div" of "bmap" |
| * by "shift" times the variable at position "pos". |
| * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0 |
| * corresponds to the constant term. |
| * |
| * That is, if the integer division has the form |
| * |
| * floor(f(x)/d) |
| * |
| * then replace it by |
| * |
| * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos |
| */ |
| __isl_give isl_basic_map *isl_basic_map_shift_div( |
| __isl_take isl_basic_map *bmap, int div, int pos, isl_int shift) |
| { |
| int i; |
| unsigned total; |
| |
| if (isl_int_is_zero(shift)) |
| return bmap; |
| if (!bmap) |
| return NULL; |
| |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| total -= isl_basic_map_dim(bmap, isl_dim_div); |
| |
| isl_int_addmul(bmap->div[div][1 + pos], shift, bmap->div[div][0]); |
| |
| for (i = 0; i < bmap->n_eq; ++i) { |
| if (isl_int_is_zero(bmap->eq[i][1 + total + div])) |
| continue; |
| isl_int_submul(bmap->eq[i][pos], |
| shift, bmap->eq[i][1 + total + div]); |
| } |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| if (isl_int_is_zero(bmap->ineq[i][1 + total + div])) |
| continue; |
| isl_int_submul(bmap->ineq[i][pos], |
| shift, bmap->ineq[i][1 + total + div]); |
| } |
| 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 + total + div])) |
| continue; |
| isl_int_submul(bmap->div[i][1 + pos], |
| shift, bmap->div[i][1 + 1 + total + div]); |
| } |
| |
| return bmap; |
| } |