| 1 | /* |
| 2 | * Copyright 2008-2009 Katholieke Universiteit Leuven |
| 3 | * |
| 4 | * Use of this software is governed by the MIT license |
| 5 | * |
| 6 | * Written by Sven Verdoolaege, K.U.Leuven, Departement |
| 7 | * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium |
| 8 | */ |
| 9 | |
| 10 | #include <assert.h> |
| 11 | #include <isl_map_private.h> |
| 12 | #include <isl_seq.h> |
| 13 | #include "isl_tab.h" |
| 14 | #include <isl_int.h> |
| 15 | #include <isl_config.h> |
| 16 | |
| 17 | struct tab_lp { |
| 18 | struct isl_ctx *ctx; |
| 19 | struct isl_vec *row; |
| 20 | struct isl_tab *tab; |
| 21 | struct isl_tab_undo **stack; |
| 22 | isl_int *obj; |
| 23 | isl_int opt; |
| 24 | isl_int opt_denom; |
| 25 | isl_int tmp; |
| 26 | isl_int tmp2; |
| 27 | int neq; |
| 28 | unsigned dim; |
| 29 | /* number of constraints in initial product tableau */ |
| 30 | int con_offset; |
| 31 | /* objective function has fixed or no integer value */ |
| 32 | int is_fixed; |
| 33 | }; |
| 34 | |
| 35 | #ifdef USE_GMP_FOR_MP |
| 36 | #define GBR_type mpq_t |
| 37 | #define GBR_init(v) mpq_init(v) |
| 38 | #define GBR_clear(v) mpq_clear(v) |
| 39 | #define GBR_set(a,b) mpq_set(a,b) |
| 40 | #define GBR_set_ui(a,b) mpq_set_ui(a,b,1) |
| 41 | #define GBR_mul(a,b,c) mpq_mul(a,b,c) |
| 42 | #define GBR_lt(a,b) (mpq_cmp(a,b) < 0) |
| 43 | #define GBR_is_zero(a) (mpq_sgn(a) == 0) |
| 44 | #define GBR_numref(a) mpq_numref(a) |
| 45 | #define GBR_denref(a) mpq_denref(a) |
| 46 | #define GBR_floor(a,b) mpz_fdiv_q(a,GBR_numref(b),GBR_denref(b)) |
| 47 | #define GBR_ceil(a,b) mpz_cdiv_q(a,GBR_numref(b),GBR_denref(b)) |
| 48 | #define GBR_set_num_neg(a, b) mpz_neg(GBR_numref(*a), b); |
| 49 | #define GBR_set_den(a, b) mpz_set(GBR_denref(*a), b); |
| 50 | #endif /* USE_GMP_FOR_MP */ |
| 51 | |
| 52 | #ifdef USE_IMATH_FOR_MP |
| 53 | #include <imrat.h> |
| 54 | |
| 55 | #define GBR_type mp_rat |
| 56 | #define GBR_init(v) v = mp_rat_alloc() |
| 57 | #define GBR_clear(v) mp_rat_free(v) |
| 58 | #define GBR_set(a,b) mp_rat_copy(b,a) |
| 59 | #define GBR_set_ui(a,b) mp_rat_set_uvalue(a,b,1) |
| 60 | #define GBR_mul(a,b,c) mp_rat_mul(b,c,a) |
| 61 | #define GBR_lt(a,b) (mp_rat_compare(a,b) < 0) |
| 62 | #define GBR_is_zero(a) (mp_rat_compare_zero(a) == 0) |
| 63 | #ifdef USE_SMALL_INT_OPT |
| 64 | #define GBR_numref(a) isl_sioimath_encode_big(mp_rat_numer_ref(a)) |
| 65 | #define GBR_denref(a) isl_sioimath_encode_big(mp_rat_denom_ref(a)) |
| 66 | #define GBR_floor(a, b) isl_sioimath_fdiv_q((a), GBR_numref(b), GBR_denref(b)) |
| 67 | #define GBR_ceil(a, b) isl_sioimath_cdiv_q((a), GBR_numref(b), GBR_denref(b)) |
| 68 | #define GBR_set_num_neg(a, b) \ |
| 69 | do { \ |
| 70 | isl_sioimath_scratchspace_t scratch; \ |
| 71 | impz_neg(mp_rat_numer_ref(*a), \ |
| 72 | isl_sioimath_bigarg_src(*b, &scratch));\ |
| 73 | } while (0) |
| 74 | #define GBR_set_den(a, b) \ |
| 75 | do { \ |
| 76 | isl_sioimath_scratchspace_t scratch; \ |
| 77 | impz_set(mp_rat_denom_ref(*a), \ |
| 78 | isl_sioimath_bigarg_src(*b, &scratch));\ |
| 79 | } while (0) |
| 80 | #else /* USE_SMALL_INT_OPT */ |
| 81 | #define GBR_numref(a) mp_rat_numer_ref(a) |
| 82 | #define GBR_denref(a) mp_rat_denom_ref(a) |
| 83 | #define GBR_floor(a,b) impz_fdiv_q(a,GBR_numref(b),GBR_denref(b)) |
| 84 | #define GBR_ceil(a,b) impz_cdiv_q(a,GBR_numref(b),GBR_denref(b)) |
| 85 | #define GBR_set_num_neg(a, b) impz_neg(GBR_numref(*a), b) |
| 86 | #define GBR_set_den(a, b) impz_set(GBR_denref(*a), b) |
| 87 | #endif /* USE_SMALL_INT_OPT */ |
| 88 | #endif /* USE_IMATH_FOR_MP */ |
| 89 | |
| 90 | static struct tab_lp *init_lp(struct isl_tab *tab); |
| 91 | static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim); |
| 92 | static int solve_lp(struct tab_lp *lp); |
| 93 | static void get_obj_val(struct tab_lp* lp, GBR_type *F); |
| 94 | static void delete_lp(struct tab_lp *lp); |
| 95 | static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim); |
| 96 | static void get_alpha(struct tab_lp* lp, int row, GBR_type *alpha); |
| 97 | static int del_lp_row(struct tab_lp *lp) WARN_UNUSED; |
| 98 | static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row); |
| 99 | |
| 100 | #define GBR_LP struct tab_lp |
| 101 | #define GBR_lp_init(P) init_lp(P) |
| 102 | #define GBR_lp_set_obj(lp, obj, dim) set_lp_obj(lp, obj, dim) |
| 103 | #define GBR_lp_solve(lp) solve_lp(lp) |
| 104 | #define GBR_lp_get_obj_val(lp, F) get_obj_val(lp, F) |
| 105 | #define GBR_lp_delete(lp) delete_lp(lp) |
| 106 | #define GBR_lp_next_row(lp) lp->neq |
| 107 | #define GBR_lp_add_row(lp, row, dim) add_lp_row(lp, row, dim) |
| 108 | #define GBR_lp_get_alpha(lp, row, alpha) get_alpha(lp, row, alpha) |
| 109 | #define GBR_lp_del_row(lp) del_lp_row(lp) |
| 110 | #define GBR_lp_is_fixed(lp) (lp)->is_fixed |
| 111 | #define GBR_lp_cut(lp, obj) cut_lp_to_hyperplane(lp, obj) |
| 112 | #include "basis_reduction_templ.c" |
| 113 | |
| 114 | /* Set up a tableau for the Cartesian product of bset with itself. |
| 115 | * This could be optimized by first setting up a tableau for bset |
| 116 | * and then performing the Cartesian product on the tableau. |
| 117 | */ |
| 118 | static struct isl_tab *gbr_tab(struct isl_tab *tab, struct isl_vec *row) |
| 119 | { |
| 120 | unsigned dim; |
| 121 | struct isl_tab *prod; |
| 122 | |
| 123 | if (!tab || !row) |
| 124 | return NULL; |
| 125 | |
| 126 | dim = tab->n_var; |
| 127 | prod = isl_tab_product(tab1: tab, tab2: tab); |
| 128 | if (isl_tab_extend_cons(tab: prod, n_new: 3 * dim + 1) < 0) { |
| 129 | isl_tab_free(tab: prod); |
| 130 | return NULL; |
| 131 | } |
| 132 | return prod; |
| 133 | } |
| 134 | |
| 135 | static struct tab_lp *init_lp(struct isl_tab *tab) |
| 136 | { |
| 137 | struct tab_lp *lp = NULL; |
| 138 | |
| 139 | if (!tab) |
| 140 | return NULL; |
| 141 | |
| 142 | lp = isl_calloc_type(tab->mat->ctx, struct tab_lp); |
| 143 | if (!lp) |
| 144 | return NULL; |
| 145 | |
| 146 | isl_int_init(lp->opt); |
| 147 | isl_int_init(lp->opt_denom); |
| 148 | isl_int_init(lp->tmp); |
| 149 | isl_int_init(lp->tmp2); |
| 150 | |
| 151 | lp->dim = tab->n_var; |
| 152 | |
| 153 | lp->ctx = tab->mat->ctx; |
| 154 | isl_ctx_ref(ctx: lp->ctx); |
| 155 | |
| 156 | lp->stack = isl_alloc_array(lp->ctx, struct isl_tab_undo *, lp->dim); |
| 157 | |
| 158 | lp->row = isl_vec_alloc(ctx: lp->ctx, size: 1 + 2 * lp->dim); |
| 159 | if (!lp->row) |
| 160 | goto error; |
| 161 | lp->tab = gbr_tab(tab, row: lp->row); |
| 162 | if (!lp->tab) |
| 163 | goto error; |
| 164 | lp->con_offset = lp->tab->n_con; |
| 165 | lp->obj = NULL; |
| 166 | lp->neq = 0; |
| 167 | |
| 168 | return lp; |
| 169 | error: |
| 170 | delete_lp(lp); |
| 171 | return NULL; |
| 172 | } |
| 173 | |
| 174 | static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim) |
| 175 | { |
| 176 | lp->obj = row; |
| 177 | } |
| 178 | |
| 179 | static int solve_lp(struct tab_lp *lp) |
| 180 | { |
| 181 | enum isl_lp_result res; |
| 182 | unsigned flags = 0; |
| 183 | |
| 184 | lp->is_fixed = 0; |
| 185 | |
| 186 | isl_int_set_si(lp->row->el[0], 0); |
| 187 | isl_seq_cpy(dst: lp->row->el + 1, src: lp->obj, len: lp->dim); |
| 188 | isl_seq_neg(dst: lp->row->el + 1 + lp->dim, src: lp->obj, len: lp->dim); |
| 189 | if (lp->neq) |
| 190 | flags = ISL_TAB_SAVE_DUAL; |
| 191 | res = isl_tab_min(tab: lp->tab, f: lp->row->el, denom: lp->ctx->one, |
| 192 | opt: &lp->opt, opt_denom: &lp->opt_denom, flags); |
| 193 | isl_int_mul_ui(lp->opt_denom, lp->opt_denom, 2); |
| 194 | if (isl_int_abs_lt(lp->opt, lp->opt_denom)) { |
| 195 | struct isl_vec *sample = isl_tab_get_sample_value(tab: lp->tab); |
| 196 | if (!sample) |
| 197 | return -1; |
| 198 | isl_seq_inner_product(p1: lp->obj, p2: sample->el + 1, len: lp->dim, prod: &lp->tmp); |
| 199 | isl_seq_inner_product(p1: lp->obj, p2: sample->el + 1 + lp->dim, len: lp->dim, prod: &lp->tmp2); |
| 200 | isl_int_cdiv_q(lp->tmp, lp->tmp, sample->el[0]); |
| 201 | isl_int_fdiv_q(lp->tmp2, lp->tmp2, sample->el[0]); |
| 202 | if (isl_int_ge(lp->tmp, lp->tmp2)) |
| 203 | lp->is_fixed = 1; |
| 204 | isl_vec_free(vec: sample); |
| 205 | } |
| 206 | isl_int_divexact_ui(lp->opt_denom, lp->opt_denom, 2); |
| 207 | if (res < 0) |
| 208 | return -1; |
| 209 | if (res != isl_lp_ok) |
| 210 | isl_die(lp->ctx, isl_error_internal, |
| 211 | "unexpected missing (bounded) solution" , return -1); |
| 212 | return 0; |
| 213 | } |
| 214 | |
| 215 | /* The current objective function has a fixed (or no) integer value. |
| 216 | * Cut the tableau to the hyperplane that fixes this value in |
| 217 | * both halves of the tableau. |
| 218 | * Return 1 if the resulting tableau is empty. |
| 219 | */ |
| 220 | static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row) |
| 221 | { |
| 222 | enum isl_lp_result res; |
| 223 | |
| 224 | isl_int_set_si(lp->row->el[0], 0); |
| 225 | isl_seq_cpy(dst: lp->row->el + 1, src: row, len: lp->dim); |
| 226 | isl_seq_clr(p: lp->row->el + 1 + lp->dim, len: lp->dim); |
| 227 | res = isl_tab_min(tab: lp->tab, f: lp->row->el, denom: lp->ctx->one, |
| 228 | opt: &lp->tmp, NULL, flags: 0); |
| 229 | if (res != isl_lp_ok) |
| 230 | return -1; |
| 231 | |
| 232 | isl_int_neg(lp->row->el[0], lp->tmp); |
| 233 | if (isl_tab_add_eq(tab: lp->tab, eq: lp->row->el) < 0) |
| 234 | return -1; |
| 235 | |
| 236 | isl_seq_cpy(dst: lp->row->el + 1 + lp->dim, src: row, len: lp->dim); |
| 237 | isl_seq_clr(p: lp->row->el + 1, len: lp->dim); |
| 238 | if (isl_tab_add_eq(tab: lp->tab, eq: lp->row->el) < 0) |
| 239 | return -1; |
| 240 | |
| 241 | lp->con_offset += 2; |
| 242 | |
| 243 | return lp->tab->empty; |
| 244 | } |
| 245 | |
| 246 | static void get_obj_val(struct tab_lp* lp, GBR_type *F) |
| 247 | { |
| 248 | GBR_set_num_neg(F, lp->opt); |
| 249 | GBR_set_den(F, lp->opt_denom); |
| 250 | } |
| 251 | |
| 252 | static void delete_lp(struct tab_lp *lp) |
| 253 | { |
| 254 | if (!lp) |
| 255 | return; |
| 256 | |
| 257 | isl_int_clear(lp->opt); |
| 258 | isl_int_clear(lp->opt_denom); |
| 259 | isl_int_clear(lp->tmp); |
| 260 | isl_int_clear(lp->tmp2); |
| 261 | isl_vec_free(vec: lp->row); |
| 262 | free(ptr: lp->stack); |
| 263 | isl_tab_free(tab: lp->tab); |
| 264 | isl_ctx_deref(ctx: lp->ctx); |
| 265 | free(ptr: lp); |
| 266 | } |
| 267 | |
| 268 | static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim) |
| 269 | { |
| 270 | lp->stack[lp->neq] = isl_tab_snap(tab: lp->tab); |
| 271 | |
| 272 | isl_int_set_si(lp->row->el[0], 0); |
| 273 | isl_seq_cpy(dst: lp->row->el + 1, src: row, len: lp->dim); |
| 274 | isl_seq_neg(dst: lp->row->el + 1 + lp->dim, src: row, len: lp->dim); |
| 275 | |
| 276 | if (isl_tab_add_valid_eq(tab: lp->tab, eq: lp->row->el) < 0) |
| 277 | return -1; |
| 278 | |
| 279 | return lp->neq++; |
| 280 | } |
| 281 | |
| 282 | static void get_alpha(struct tab_lp* lp, int row, GBR_type *alpha) |
| 283 | { |
| 284 | row += lp->con_offset; |
| 285 | GBR_set_num_neg(alpha, lp->tab->dual->el[1 + row]); |
| 286 | GBR_set_den(alpha, lp->tab->dual->el[0]); |
| 287 | } |
| 288 | |
| 289 | static int del_lp_row(struct tab_lp *lp) |
| 290 | { |
| 291 | lp->neq--; |
| 292 | return isl_tab_rollback(tab: lp->tab, snap: lp->stack[lp->neq]); |
| 293 | } |
| 294 | |