basis_reduction_tab.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 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_seq.h"
  12 #include "isl_tab.h"
  13
  14 struct tab_lp {
  15         struct isl_ctx  *ctx;
  16         struct isl_vec  *row;
  17         struct isl_tab  *tab;
  18         struct isl_tab_undo     **stack;
  19         isl_int         *obj;
  20         isl_int          opt;
  21         isl_int          opt_denom;
  22         isl_int          tmp;
  23         isl_int          tmp2;
  24         int              neq;
  25         unsigned         dim;
  26         /* number of constraints in initial product tableau */
  27         int              con_offset;
  28         /* objective function has fixed or no integer value */
  29         int              is_fixed;
  30 };
  31
  32 static struct tab_lp *init_lp(struct isl_tab *tab);
  33 static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim);
  34 static int solve_lp(struct tab_lp *lp);
  35 static void get_obj_val(struct tab_lp* lp, mpq_t *F);
  36 static void delete_lp(struct tab_lp *lp);
  37 static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim);
  38 static void get_alpha(struct tab_lp* lp, int row, mpq_t *alpha);
  39 static int del_lp_row(struct tab_lp *lp) WARN_UNUSED;
  40 static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row);
  41
  42 #define GBR_LP                              struct tab_lp
  43 #define GBR_type                            mpq_t
  44 #define GBR_init(v)                         mpq_init(v)
  45 #define GBR_clear(v)                        mpq_clear(v)
  46 #define GBR_set(a,b)                        mpq_set(a,b)
  47 #define GBR_set_ui(a,b)                     mpq_set_ui(a,b,1)
  48 #define GBR_mul(a,b,c)                      mpq_mul(a,b,c)
  49 #define GBR_lt(a,b)                         (mpq_cmp(a,b) < 0)
  50 #define GBR_is_zero(a)                      (mpq_sgn(a) == 0)
  51 #define GBR_floor(a,b)                      mpz_fdiv_q(a,mpq_numref(b),mpq_denref(b))
  52 #define GBR_ceil(a,b)                       mpz_cdiv_q(a,mpq_numref(b),mpq_denref(b))
  53 #define GBR_lp_init(P)                      init_lp(P)
  54 #define GBR_lp_set_obj(lp, obj, dim)        set_lp_obj(lp, obj, dim)
  55 #define GBR_lp_solve(lp)                    solve_lp(lp)
  56 #define GBR_lp_get_obj_val(lp, F)           get_obj_val(lp, F)
  57 #define GBR_lp_delete(lp)                   delete_lp(lp)
  58 #define GBR_lp_next_row(lp)                 lp->neq
  59 #define GBR_lp_add_row(lp, row, dim)        add_lp_row(lp, row, dim)
  60 #define GBR_lp_get_alpha(lp, row, alpha)    get_alpha(lp, row, alpha)
  61 #define GBR_lp_del_row(lp)                  del_lp_row(lp)
  62 #define GBR_lp_is_fixed(lp)                 (lp)->is_fixed
  63 #define GBR_lp_cut(lp, obj)                 cut_lp_to_hyperplane(lp, obj)
  64 #include "basis_reduction_templ.c"
  65
  66 /* Set up a tableau for the Cartesian product of bset with itself.
  67  * This could be optimized by first setting up a tableau for bset
  68  * and then performing the Cartesian product on the tableau.
  69  */
  70 static struct isl_tab *gbr_tab(struct isl_tab *tab, struct isl_vec *row)
  71 {
  72         unsigned dim;
  73         struct isl_tab *prod;
  74
  75         if (!tab || !row)
  76                 return NULL;
  77
  78         dim = tab->n_var;
  79         prod = isl_tab_product(tab, tab);
  80         if (isl_tab_extend_cons(prod, 3 * dim + 1) < 0) {
  81                 isl_tab_free(prod);
  82                 return NULL;
  83         }
  84         return prod;
  85 }
  86
  87 static struct tab_lp *init_lp(struct isl_tab *tab)
  88 {
  89         struct tab_lp *lp = NULL;
  90
  91         if (!tab)
  92                 return NULL;
  93
  94         lp = isl_calloc_type(tab->mat->ctx, struct tab_lp);
  95         if (!lp)
  96                 return NULL;
  97
  98         isl_int_init(lp->opt);
  99         isl_int_init(lp->opt_denom);
 100         isl_int_init(lp->tmp);
 101         isl_int_init(lp->tmp2);
 102
 103         lp->dim = tab->n_var;
 104
 105         lp->ctx = tab->mat->ctx;
 106         isl_ctx_ref(lp->ctx);
 107
 108         lp->stack = isl_alloc_array(lp->ctx, struct isl_tab_undo *, lp->dim);
 109
 110         lp->row = isl_vec_alloc(lp->ctx, 1 + 2 * lp->dim);
 111         if (!lp->row)
 112                 goto error;
 113         lp->tab = gbr_tab(tab, lp->row);
 114         if (!lp->tab)
 115                 goto error;
 116         lp->con_offset = lp->tab->n_con;
 117         lp->obj = NULL;
 118         lp->neq = 0;
 119
 120         return lp;
 121 error:
 122         delete_lp(lp);
 123         return NULL;
 124 }
 125
 126 static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim)
 127 {
 128         lp->obj = row;
 129 }
 130
 131 static int solve_lp(struct tab_lp *lp)
 132 {
 133         enum isl_lp_result res;
 134         unsigned flags = 0;
 135
 136         lp->is_fixed = 0;
 137
 138         isl_int_set_si(lp->row->el[0], 0);
 139         isl_seq_cpy(lp->row->el + 1, lp->obj, lp->dim);
 140         isl_seq_neg(lp->row->el + 1 + lp->dim, lp->obj, lp->dim);
 141         if (lp->neq)
 142                 flags = ISL_TAB_SAVE_DUAL;
 143         res = isl_tab_min(lp->tab, lp->row->el, lp->ctx->one,
 144                           &lp->opt, &lp->opt_denom, flags);
 145         isl_int_mul_ui(lp->opt_denom, lp->opt_denom, 2);
 146         if (isl_int_abs_lt(lp->opt, lp->opt_denom)) {
 147                 struct isl_vec *sample = isl_tab_get_sample_value(lp->tab);
 148                 if (!sample)
 149                         return -1;
 150                 isl_seq_inner_product(lp->obj, sample->el + 1, lp->dim, &lp->tmp);
 151                 isl_seq_inner_product(lp->obj, sample->el + 1 + lp->dim, lp->dim, &lp->tmp2);
 152                 isl_int_cdiv_q(lp->tmp, lp->tmp, sample->el[0]);
 153                 isl_int_fdiv_q(lp->tmp2, lp->tmp2, sample->el[0]);
 154                 if (isl_int_ge(lp->tmp, lp->tmp2))
 155                         lp->is_fixed = 1;
 156                 isl_vec_free(sample);
 157         }
 158         isl_int_divexact_ui(lp->opt_denom, lp->opt_denom, 2);
 159         if (res != isl_lp_ok)
 160                 return -1;
 161         return 0;
 162 }
 163
 164 /* The current objective function has a fixed (or no) integer value.
 165  * Cut the tableau to the hyperplane that fixes this value in
 166  * both halves of the tableau.
 167  * Return 1 if the resulting tableau is empty.
 168  */
 169 static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row)
 170 {
 171         enum isl_lp_result res;
 172
 173         isl_int_set_si(lp->row->el[0], 0);
 174         isl_seq_cpy(lp->row->el + 1, row, lp->dim);
 175         isl_seq_clr(lp->row->el + 1 + lp->dim, lp->dim);
 176         res = isl_tab_min(lp->tab, lp->row->el, lp->ctx->one,
 177                           &lp->tmp, NULL, 0);
 178         if (res != isl_lp_ok)
 179                 return -1;
 180
 181         isl_int_neg(lp->row->el[0], lp->tmp);
 182         if (isl_tab_add_eq(lp->tab, lp->row->el) < 0)
 183                 return -1;
 184
 185         isl_seq_cpy(lp->row->el + 1 + lp->dim, row, lp->dim);
 186         isl_seq_clr(lp->row->el + 1, lp->dim);
 187         if (isl_tab_add_eq(lp->tab, lp->row->el) < 0)
 188                 return -1;
 189
 190         lp->con_offset += 2;
 191
 192         return lp->tab->empty;
 193 }
 194
 195 static void get_obj_val(struct tab_lp* lp, mpq_t *F)
 196 {
 197         isl_int_neg(mpq_numref(*F), lp->opt);
 198         isl_int_set(mpq_denref(*F), lp->opt_denom);
 199 }
 200
 201 static void delete_lp(struct tab_lp *lp)
 202 {
 203         if (!lp)
 204                 return;
 205
 206         isl_int_clear(lp->opt);
 207         isl_int_clear(lp->opt_denom);
 208         isl_int_clear(lp->tmp);
 209         isl_int_clear(lp->tmp2);
 210         isl_vec_free(lp->row);
 211         free(lp->stack);
 212         isl_tab_free(lp->tab);
 213         isl_ctx_deref(lp->ctx);
 214         free(lp);
 215 }
 216
 217 static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim)
 218 {
 219         lp->stack[lp->neq] = isl_tab_snap(lp->tab);
 220
 221         isl_int_set_si(lp->row->el[0], 0);
 222         isl_seq_cpy(lp->row->el + 1, row, lp->dim);
 223         isl_seq_neg(lp->row->el + 1 + lp->dim, row, lp->dim);
 224
 225         if (isl_tab_add_valid_eq(lp->tab, lp->row->el) < 0)
 226                 return -1;
 227
 228         return lp->neq++;
 229 }
 230
 231 static void get_alpha(struct tab_lp* lp, int row, mpq_t *alpha)
 232 {
 233         row += lp->con_offset;
 234         isl_int_neg(mpq_numref(*alpha), lp->tab->dual->el[1 + row]);
 235         isl_int_set(mpq_denref(*alpha), lp->tab->dual->el[0]);
 236 }
 237
 238 static int del_lp_row(struct tab_lp *lp)
 239 {
 240         lp->neq--;
 241         return isl_tab_rollback(lp->tab, lp->stack[lp->neq]);
 242 }