basis_reduction_tab.c

   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 #endif /* USE_GMP_FOR_MP */
  49
  50 #ifdef USE_IMATH_FOR_MP
  51 #include <imrat.h>
  52
  53 #define GBR_type                            mp_rat
  54 #define GBR_init(v)                         v = mp_rat_alloc()
  55 #define GBR_clear(v)                        mp_rat_free(v)
  56 #define GBR_set(a,b)                        mp_rat_copy(b,a)
  57 #define GBR_set_ui(a,b)                     mp_rat_set_uvalue(a,b,1)
  58 #define GBR_mul(a,b,c)                      mp_rat_mul(b,c,a)
  59 #define GBR_lt(a,b)                         (mp_rat_compare(a,b) < 0)
  60 #define GBR_is_zero(a)                      (mp_rat_compare_zero(a) == 0)
  61 #define GBR_numref(a)                       mp_rat_numer_ref(a)
  62 #define GBR_denref(a)                       mp_rat_denom_ref(a)
  63 #define GBR_floor(a,b)                      impz_fdiv_q(a,GBR_numref(b),GBR_denref(b))
  64 #define GBR_ceil(a,b)                       impz_cdiv_q(a,GBR_numref(b),GBR_denref(b))
  65 #endif /* USE_IMATH_FOR_MP */
  66
  67 static struct tab_lp *init_lp(struct isl_tab *tab);
  68 static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim);
  69 static int solve_lp(struct tab_lp *lp);
  70 static void get_obj_val(struct tab_lp* lp, GBR_type *F);
  71 static void delete_lp(struct tab_lp *lp);
  72 static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim);
  73 static void get_alpha(struct tab_lp* lp, int row, GBR_type *alpha);
  74 static int del_lp_row(struct tab_lp *lp) WARN_UNUSED;
  75 static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row);
  76
  77 #define GBR_LP                              struct tab_lp
  78 #define GBR_lp_init(P)                      init_lp(P)
  79 #define GBR_lp_set_obj(lp, obj, dim)        set_lp_obj(lp, obj, dim)
  80 #define GBR_lp_solve(lp)                    solve_lp(lp)
  81 #define GBR_lp_get_obj_val(lp, F)           get_obj_val(lp, F)
  82 #define GBR_lp_delete(lp)                   delete_lp(lp)
  83 #define GBR_lp_next_row(lp)                 lp->neq
  84 #define GBR_lp_add_row(lp, row, dim)        add_lp_row(lp, row, dim)
  85 #define GBR_lp_get_alpha(lp, row, alpha)    get_alpha(lp, row, alpha)
  86 #define GBR_lp_del_row(lp)                  del_lp_row(lp)
  87 #define GBR_lp_is_fixed(lp)                 (lp)->is_fixed
  88 #define GBR_lp_cut(lp, obj)                 cut_lp_to_hyperplane(lp, obj)
  89 #include "basis_reduction_templ.c"
  90
  91 /* Set up a tableau for the Cartesian product of bset with itself.
  92  * This could be optimized by first setting up a tableau for bset
  93  * and then performing the Cartesian product on the tableau.
  94  */
  95 static struct isl_tab *gbr_tab(struct isl_tab *tab, struct isl_vec *row)
  96 {
  97         unsigned dim;
  98         struct isl_tab *prod;
  99
 100         if (!tab || !row)
 101                 return NULL;
 102
 103         dim = tab->n_var;
 104         prod = isl_tab_product(tab, tab);
 105         if (isl_tab_extend_cons(prod, 3 * dim + 1) < 0) {
 106                 isl_tab_free(prod);
 107                 return NULL;
 108         }
 109         return prod;
 110 }
 111
 112 static struct tab_lp *init_lp(struct isl_tab *tab)
 113 {
 114         struct tab_lp *lp = NULL;
 115
 116         if (!tab)
 117                 return NULL;
 118
 119         lp = isl_calloc_type(tab->mat->ctx, struct tab_lp);
 120         if (!lp)
 121                 return NULL;
 122
 123         isl_int_init(lp->opt);
 124         isl_int_init(lp->opt_denom);
 125         isl_int_init(lp->tmp);
 126         isl_int_init(lp->tmp2);
 127
 128         lp->dim = tab->n_var;
 129
 130         lp->ctx = tab->mat->ctx;
 131         isl_ctx_ref(lp->ctx);
 132
 133         lp->stack = isl_alloc_array(lp->ctx, struct isl_tab_undo *, lp->dim);
 134
 135         lp->row = isl_vec_alloc(lp->ctx, 1 + 2 * lp->dim);
 136         if (!lp->row)
 137                 goto error;
 138         lp->tab = gbr_tab(tab, lp->row);
 139         if (!lp->tab)
 140                 goto error;
 141         lp->con_offset = lp->tab->n_con;
 142         lp->obj = NULL;
 143         lp->neq = 0;
 144
 145         return lp;
 146 error:
 147         delete_lp(lp);
 148         return NULL;
 149 }
 150
 151 static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim)
 152 {
 153         lp->obj = row;
 154 }
 155
 156 static int solve_lp(struct tab_lp *lp)
 157 {
 158         enum isl_lp_result res;
 159         unsigned flags = 0;
 160
 161         lp->is_fixed = 0;
 162
 163         isl_int_set_si(lp->row->el[0], 0);
 164         isl_seq_cpy(lp->row->el + 1, lp->obj, lp->dim);
 165         isl_seq_neg(lp->row->el + 1 + lp->dim, lp->obj, lp->dim);
 166         if (lp->neq)
 167                 flags = ISL_TAB_SAVE_DUAL;
 168         res = isl_tab_min(lp->tab, lp->row->el, lp->ctx->one,
 169                           &lp->opt, &lp->opt_denom, flags);
 170         isl_int_mul_ui(lp->opt_denom, lp->opt_denom, 2);
 171         if (isl_int_abs_lt(lp->opt, lp->opt_denom)) {
 172                 struct isl_vec *sample = isl_tab_get_sample_value(lp->tab);
 173                 if (!sample)
 174                         return -1;
 175                 isl_seq_inner_product(lp->obj, sample->el + 1, lp->dim, &lp->tmp);
 176                 isl_seq_inner_product(lp->obj, sample->el + 1 + lp->dim, lp->dim, &lp->tmp2);
 177                 isl_int_cdiv_q(lp->tmp, lp->tmp, sample->el[0]);
 178                 isl_int_fdiv_q(lp->tmp2, lp->tmp2, sample->el[0]);
 179                 if (isl_int_ge(lp->tmp, lp->tmp2))
 180                         lp->is_fixed = 1;
 181                 isl_vec_free(sample);
 182         }
 183         isl_int_divexact_ui(lp->opt_denom, lp->opt_denom, 2);
 184         if (res < 0)
 185                 return -1;
 186         if (res != isl_lp_ok)
 187                 isl_die(lp->ctx, isl_error_internal,
 188                         "unexpected missing (bounded) solution", return -1);
 189         return 0;
 190 }
 191
 192 /* The current objective function has a fixed (or no) integer value.
 193  * Cut the tableau to the hyperplane that fixes this value in
 194  * both halves of the tableau.
 195  * Return 1 if the resulting tableau is empty.
 196  */
 197 static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row)
 198 {
 199         enum isl_lp_result res;
 200
 201         isl_int_set_si(lp->row->el[0], 0);
 202         isl_seq_cpy(lp->row->el + 1, row, lp->dim);
 203         isl_seq_clr(lp->row->el + 1 + lp->dim, lp->dim);
 204         res = isl_tab_min(lp->tab, lp->row->el, lp->ctx->one,
 205                           &lp->tmp, NULL, 0);
 206         if (res != isl_lp_ok)
 207                 return -1;
 208
 209         isl_int_neg(lp->row->el[0], lp->tmp);
 210         if (isl_tab_add_eq(lp->tab, lp->row->el) < 0)
 211                 return -1;
 212
 213         isl_seq_cpy(lp->row->el + 1 + lp->dim, row, lp->dim);
 214         isl_seq_clr(lp->row->el + 1, lp->dim);
 215         if (isl_tab_add_eq(lp->tab, lp->row->el) < 0)
 216                 return -1;
 217
 218         lp->con_offset += 2;
 219
 220         return lp->tab->empty;
 221 }
 222
 223 static void get_obj_val(struct tab_lp* lp, GBR_type *F)
 224 {
 225         isl_int_neg(GBR_numref(*F), lp->opt);
 226         isl_int_set(GBR_denref(*F), lp->opt_denom);
 227 }
 228
 229 static void delete_lp(struct tab_lp *lp)
 230 {
 231         if (!lp)
 232                 return;
 233
 234         isl_int_clear(lp->opt);
 235         isl_int_clear(lp->opt_denom);
 236         isl_int_clear(lp->tmp);
 237         isl_int_clear(lp->tmp2);
 238         isl_vec_free(lp->row);
 239         free(lp->stack);
 240         isl_tab_free(lp->tab);
 241         isl_ctx_deref(lp->ctx);
 242         free(lp);
 243 }
 244
 245 static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim)
 246 {
 247         lp->stack[lp->neq] = isl_tab_snap(lp->tab);
 248
 249         isl_int_set_si(lp->row->el[0], 0);
 250         isl_seq_cpy(lp->row->el + 1, row, lp->dim);
 251         isl_seq_neg(lp->row->el + 1 + lp->dim, row, lp->dim);
 252
 253         if (isl_tab_add_valid_eq(lp->tab, lp->row->el) < 0)
 254                 return -1;
 255
 256         return lp->neq++;
 257 }
 258
 259 static void get_alpha(struct tab_lp* lp, int row, GBR_type *alpha)
 260 {
 261         row += lp->con_offset;
 262         isl_int_neg(GBR_numref(*alpha), lp->tab->dual->el[1 + row]);
 263         isl_int_set(GBR_denref(*alpha), lp->tab->dual->el[0]);
 264 }
 265
 266 static int del_lp_row(struct tab_lp *lp)
 267 {
 268         lp->neq--;
 269         return isl_tab_rollback(lp->tab, lp->stack[lp->neq]);
 270 }