| File: | polly/lib/External/isl/isl_map_simplify.c |
| Warning: | line 743, column 41 Division by zero |
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| 1 | /* | ||||
| 2 | * Copyright 2008-2009 Katholieke Universiteit Leuven | ||||
| 3 | * Copyright 2012-2013 Ecole Normale Superieure | ||||
| 4 | * Copyright 2014-2015 INRIA Rocquencourt | ||||
| 5 | * Copyright 2016 Sven Verdoolaege | ||||
| 6 | * | ||||
| 7 | * Use of this software is governed by the MIT license | ||||
| 8 | * | ||||
| 9 | * Written by Sven Verdoolaege, K.U.Leuven, Departement | ||||
| 10 | * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium | ||||
| 11 | * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France | ||||
| 12 | * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt, | ||||
| 13 | * B.P. 105 - 78153 Le Chesnay, France | ||||
| 14 | */ | ||||
| 15 | |||||
| 16 | #include <isl_ctx_private.h> | ||||
| 17 | #include <isl_map_private.h> | ||||
| 18 | #include "isl_equalities.h" | ||||
| 19 | #include <isl/map.h> | ||||
| 20 | #include <isl_seq.h> | ||||
| 21 | #include "isl_tab.h" | ||||
| 22 | #include <isl_space_private.h> | ||||
| 23 | #include <isl_mat_private.h> | ||||
| 24 | #include <isl_vec_private.h> | ||||
| 25 | |||||
| 26 | #include <bset_to_bmap.c> | ||||
| 27 | #include <bset_from_bmap.c> | ||||
| 28 | #include <set_to_map.c> | ||||
| 29 | #include <set_from_map.c> | ||||
| 30 | |||||
| 31 | static void swap_equality(struct isl_basic_map *bmap, int a, int b) | ||||
| 32 | { | ||||
| 33 | isl_int *t = bmap->eq[a]; | ||||
| 34 | bmap->eq[a] = bmap->eq[b]; | ||||
| 35 | bmap->eq[b] = t; | ||||
| 36 | } | ||||
| 37 | |||||
| 38 | static void swap_inequality(struct isl_basic_map *bmap, int a, int b) | ||||
| 39 | { | ||||
| 40 | if (a != b) { | ||||
| 41 | isl_int *t = bmap->ineq[a]; | ||||
| 42 | bmap->ineq[a] = bmap->ineq[b]; | ||||
| 43 | bmap->ineq[b] = t; | ||||
| 44 | } | ||||
| 45 | } | ||||
| 46 | |||||
| 47 | __isl_give isl_basic_map *isl_basic_map_normalize_constraints( | ||||
| 48 | __isl_take isl_basic_map *bmap) | ||||
| 49 | { | ||||
| 50 | int i; | ||||
| 51 | isl_int gcd; | ||||
| 52 | isl_size total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 53 | |||||
| 54 | if (total < 0) | ||||
| 55 | return isl_basic_map_free(bmap); | ||||
| 56 | |||||
| 57 | isl_int_init(gcd)isl_sioimath_init((gcd)); | ||||
| 58 | for (i = bmap->n_eq - 1; i >= 0; --i) { | ||||
| 59 | isl_seq_gcd(bmap->eq[i]+1, total, &gcd); | ||||
| 60 | if (isl_int_is_zero(gcd)(isl_sioimath_sgn(*(gcd)) == 0)) { | ||||
| 61 | if (!isl_int_is_zero(bmap->eq[i][0])(isl_sioimath_sgn(*(bmap->eq[i][0])) == 0)) { | ||||
| 62 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
| 63 | break; | ||||
| 64 | } | ||||
| 65 | if (isl_basic_map_drop_equality(bmap, i) < 0) | ||||
| 66 | goto error; | ||||
| 67 | continue; | ||||
| 68 | } | ||||
| 69 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4))))) | ||||
| 70 | isl_int_gcd(gcd, gcd, bmap->eq[i][0])isl_sioimath_gcd((gcd), *(gcd), *(bmap->eq[i][0])); | ||||
| 71 | if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0)) | ||||
| 72 | continue; | ||||
| 73 | if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)isl_sioimath_is_divisible_by(*(bmap->eq[i][0]), *(gcd))) { | ||||
| 74 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
| 75 | break; | ||||
| 76 | } | ||||
| 77 | isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total); | ||||
| 78 | } | ||||
| 79 | |||||
| 80 | for (i = bmap->n_ineq - 1; i >= 0; --i) { | ||||
| 81 | isl_seq_gcd(bmap->ineq[i]+1, total, &gcd); | ||||
| 82 | if (isl_int_is_zero(gcd)(isl_sioimath_sgn(*(gcd)) == 0)) { | ||||
| 83 | if (isl_int_is_neg(bmap->ineq[i][0])(isl_sioimath_sgn(*(bmap->ineq[i][0])) < 0)) { | ||||
| 84 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
| 85 | break; | ||||
| 86 | } | ||||
| 87 | if (isl_basic_map_drop_inequality(bmap, i) < 0) | ||||
| 88 | goto error; | ||||
| 89 | continue; | ||||
| 90 | } | ||||
| 91 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4))))) | ||||
| 92 | isl_int_gcd(gcd, gcd, bmap->ineq[i][0])isl_sioimath_gcd((gcd), *(gcd), *(bmap->ineq[i][0])); | ||||
| 93 | if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0)) | ||||
| 94 | continue; | ||||
| 95 | isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd)isl_sioimath_fdiv_q((bmap->ineq[i][0]), *(bmap->ineq[i] [0]), *(gcd)); | ||||
| 96 | isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total); | ||||
| 97 | } | ||||
| 98 | isl_int_clear(gcd)isl_sioimath_clear((gcd)); | ||||
| 99 | |||||
| 100 | return bmap; | ||||
| 101 | error: | ||||
| 102 | isl_int_clear(gcd)isl_sioimath_clear((gcd)); | ||||
| 103 | isl_basic_map_free(bmap); | ||||
| 104 | return NULL((void*)0); | ||||
| 105 | } | ||||
| 106 | |||||
| 107 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_normalize_constraints( | ||||
| 108 | __isl_take isl_basic_setisl_basic_map *bset) | ||||
| 109 | { | ||||
| 110 | isl_basic_map *bmap = bset_to_bmap(bset); | ||||
| 111 | return bset_from_bmap(isl_basic_map_normalize_constraints(bmap)); | ||||
| 112 | } | ||||
| 113 | |||||
| 114 | /* Reduce the coefficient of the variable at position "pos" | ||||
| 115 | * in integer division "div", such that it lies in the half-open | ||||
| 116 | * interval (1/2,1/2], extracting any excess value from this integer division. | ||||
| 117 | * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0 | ||||
| 118 | * corresponds to the constant term. | ||||
| 119 | * | ||||
| 120 | * That is, the integer division is of the form | ||||
| 121 | * | ||||
| 122 | * floor((... + (c * d + r) * x_pos + ...)/d) | ||||
| 123 | * | ||||
| 124 | * with -d < 2 * r <= d. | ||||
| 125 | * Replace it by | ||||
| 126 | * | ||||
| 127 | * floor((... + r * x_pos + ...)/d) + c * x_pos | ||||
| 128 | * | ||||
| 129 | * If 2 * ((c * d + r) % d) <= d, then c = floor((c * d + r)/d). | ||||
| 130 | * Otherwise, c = floor((c * d + r)/d) + 1. | ||||
| 131 | * | ||||
| 132 | * This is the same normalization that is performed by isl_aff_floor. | ||||
| 133 | */ | ||||
| 134 | static __isl_give isl_basic_map *reduce_coefficient_in_div( | ||||
| 135 | __isl_take isl_basic_map *bmap, int div, int pos) | ||||
| 136 | { | ||||
| 137 | isl_int shift; | ||||
| 138 | int add_one; | ||||
| 139 | |||||
| 140 | isl_int_init(shift)isl_sioimath_init((shift)); | ||||
| 141 | isl_int_fdiv_r(shift, bmap->div[div][1 + pos], bmap->div[div][0])isl_sioimath_fdiv_r((shift), *(bmap->div[div][1 + pos]), * (bmap->div[div][0])); | ||||
| 142 | isl_int_mul_ui(shift, shift, 2)isl_sioimath_mul_ui((shift), *(shift), 2); | ||||
| 143 | add_one = isl_int_gt(shift, bmap->div[div][0])(isl_sioimath_cmp(*(shift), *(bmap->div[div][0])) > 0); | ||||
| 144 | isl_int_fdiv_q(shift, bmap->div[div][1 + pos], bmap->div[div][0])isl_sioimath_fdiv_q((shift), *(bmap->div[div][1 + pos]), * (bmap->div[div][0])); | ||||
| 145 | if (add_one) | ||||
| 146 | isl_int_add_ui(shift, shift, 1)isl_sioimath_add_ui((shift), *(shift), 1); | ||||
| 147 | isl_int_neg(shift, shift)isl_sioimath_neg((shift), *(shift)); | ||||
| 148 | bmap = isl_basic_map_shift_div(bmap, div, pos, shift); | ||||
| 149 | isl_int_clear(shift)isl_sioimath_clear((shift)); | ||||
| 150 | |||||
| 151 | return bmap; | ||||
| 152 | } | ||||
| 153 | |||||
| 154 | /* Does the coefficient of the variable at position "pos" | ||||
| 155 | * in integer division "div" need to be reduced? | ||||
| 156 | * That is, does it lie outside the half-open interval (1/2,1/2]? | ||||
| 157 | * The coefficient c/d lies outside this interval if abs(2 * c) >= d and | ||||
| 158 | * 2 * c != d. | ||||
| 159 | */ | ||||
| 160 | static isl_bool needs_reduction(__isl_keep isl_basic_map *bmap, int div, | ||||
| 161 | int pos) | ||||
| 162 | { | ||||
| 163 | isl_bool r; | ||||
| 164 | |||||
| 165 | if (isl_int_is_zero(bmap->div[div][1 + pos])(isl_sioimath_sgn(*(bmap->div[div][1 + pos])) == 0)) | ||||
| 166 | return isl_bool_false; | ||||
| 167 | |||||
| 168 | isl_int_mul_ui(bmap->div[div][1 + pos], bmap->div[div][1 + pos], 2)isl_sioimath_mul_ui((bmap->div[div][1 + pos]), *(bmap-> div[div][1 + pos]), 2); | ||||
| 169 | r = isl_int_abs_ge(bmap->div[div][1 + pos], bmap->div[div][0])(isl_sioimath_abs_cmp(*(bmap->div[div][1 + pos]), *(bmap-> div[div][0])) >= 0) && | ||||
| 170 | !isl_int_eq(bmap->div[div][1 + pos], bmap->div[div][0])(isl_sioimath_cmp(*(bmap->div[div][1 + pos]), *(bmap->div [div][0])) == 0); | ||||
| 171 | isl_int_divexact_ui(bmap->div[div][1 + pos],isl_sioimath_tdiv_q_ui((bmap->div[div][1 + pos]), *(bmap-> div[div][1 + pos]), 2) | ||||
| 172 | bmap->div[div][1 + pos], 2)isl_sioimath_tdiv_q_ui((bmap->div[div][1 + pos]), *(bmap-> div[div][1 + pos]), 2); | ||||
| 173 | |||||
| 174 | return r; | ||||
| 175 | } | ||||
| 176 | |||||
| 177 | /* Reduce the coefficients (including the constant term) of | ||||
| 178 | * integer division "div", if needed. | ||||
| 179 | * In particular, make sure all coefficients lie in | ||||
| 180 | * the half-open interval (1/2,1/2]. | ||||
| 181 | */ | ||||
| 182 | static __isl_give isl_basic_map *reduce_div_coefficients_of_div( | ||||
| 183 | __isl_take isl_basic_map *bmap, int div) | ||||
| 184 | { | ||||
| 185 | int i; | ||||
| 186 | isl_size total; | ||||
| 187 | |||||
| 188 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 189 | if (total < 0) | ||||
| 190 | return isl_basic_map_free(bmap); | ||||
| 191 | for (i = 0; i < 1 + total; ++i) { | ||||
| 192 | isl_bool reduce; | ||||
| 193 | |||||
| 194 | reduce = needs_reduction(bmap, div, i); | ||||
| 195 | if (reduce < 0) | ||||
| 196 | return isl_basic_map_free(bmap); | ||||
| 197 | if (!reduce) | ||||
| 198 | continue; | ||||
| 199 | bmap = reduce_coefficient_in_div(bmap, div, i); | ||||
| 200 | if (!bmap) | ||||
| 201 | break; | ||||
| 202 | } | ||||
| 203 | |||||
| 204 | return bmap; | ||||
| 205 | } | ||||
| 206 | |||||
| 207 | /* Reduce the coefficients (including the constant term) of | ||||
| 208 | * the known integer divisions, if needed | ||||
| 209 | * In particular, make sure all coefficients lie in | ||||
| 210 | * the half-open interval (1/2,1/2]. | ||||
| 211 | */ | ||||
| 212 | static __isl_give isl_basic_map *reduce_div_coefficients( | ||||
| 213 | __isl_take isl_basic_map *bmap) | ||||
| 214 | { | ||||
| 215 | int i; | ||||
| 216 | |||||
| 217 | if (!bmap) | ||||
| 218 | return NULL((void*)0); | ||||
| 219 | if (bmap->n_div == 0) | ||||
| 220 | return bmap; | ||||
| 221 | |||||
| 222 | for (i = 0; i < bmap->n_div; ++i) { | ||||
| 223 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
| 224 | continue; | ||||
| 225 | bmap = reduce_div_coefficients_of_div(bmap, i); | ||||
| 226 | if (!bmap) | ||||
| 227 | break; | ||||
| 228 | } | ||||
| 229 | |||||
| 230 | return bmap; | ||||
| 231 | } | ||||
| 232 | |||||
| 233 | /* Remove any common factor in numerator and denominator of the div expression, | ||||
| 234 | * not taking into account the constant term. | ||||
| 235 | * That is, if the div is of the form | ||||
| 236 | * | ||||
| 237 | * floor((a + m f(x))/(m d)) | ||||
| 238 | * | ||||
| 239 | * then replace it by | ||||
| 240 | * | ||||
| 241 | * floor((floor(a/m) + f(x))/d) | ||||
| 242 | * | ||||
| 243 | * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d | ||||
| 244 | * and can therefore not influence the result of the floor. | ||||
| 245 | */ | ||||
| 246 | static __isl_give isl_basic_map *normalize_div_expression( | ||||
| 247 | __isl_take isl_basic_map *bmap, int div) | ||||
| 248 | { | ||||
| 249 | isl_size total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 250 | isl_ctx *ctx = bmap->ctx; | ||||
| 251 | |||||
| 252 | if (total < 0) | ||||
| 253 | return isl_basic_map_free(bmap); | ||||
| 254 | if (isl_int_is_zero(bmap->div[div][0])(isl_sioimath_sgn(*(bmap->div[div][0])) == 0)) | ||||
| 255 | return bmap; | ||||
| 256 | isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd); | ||||
| 257 | isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, bmap->div[div][0])isl_sioimath_gcd((ctx->normalize_gcd), *(ctx->normalize_gcd ), *(bmap->div[div][0])); | ||||
| 258 | if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0)) | ||||
| 259 | return bmap; | ||||
| 260 | isl_int_fdiv_q(bmap->div[div][1], bmap->div[div][1],isl_sioimath_fdiv_q((bmap->div[div][1]), *(bmap->div[div ][1]), *(ctx->normalize_gcd)) | ||||
| 261 | ctx->normalize_gcd)isl_sioimath_fdiv_q((bmap->div[div][1]), *(bmap->div[div ][1]), *(ctx->normalize_gcd)); | ||||
| 262 | isl_int_divexact(bmap->div[div][0], bmap->div[div][0],isl_sioimath_tdiv_q((bmap->div[div][0]), *(bmap->div[div ][0]), *(ctx->normalize_gcd)) | ||||
| 263 | ctx->normalize_gcd)isl_sioimath_tdiv_q((bmap->div[div][0]), *(bmap->div[div ][0]), *(ctx->normalize_gcd)); | ||||
| 264 | isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2, | ||||
| 265 | ctx->normalize_gcd, total); | ||||
| 266 | |||||
| 267 | return bmap; | ||||
| 268 | } | ||||
| 269 | |||||
| 270 | /* Remove any common factor in numerator and denominator of a div expression, | ||||
| 271 | * not taking into account the constant term. | ||||
| 272 | * That is, look for any div of the form | ||||
| 273 | * | ||||
| 274 | * floor((a + m f(x))/(m d)) | ||||
| 275 | * | ||||
| 276 | * and replace it by | ||||
| 277 | * | ||||
| 278 | * floor((floor(a/m) + f(x))/d) | ||||
| 279 | * | ||||
| 280 | * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d | ||||
| 281 | * and can therefore not influence the result of the floor. | ||||
| 282 | */ | ||||
| 283 | static __isl_give isl_basic_map *normalize_div_expressions( | ||||
| 284 | __isl_take isl_basic_map *bmap) | ||||
| 285 | { | ||||
| 286 | int i; | ||||
| 287 | |||||
| 288 | if (!bmap) | ||||
| 289 | return NULL((void*)0); | ||||
| 290 | if (bmap->n_div == 0) | ||||
| 291 | return bmap; | ||||
| 292 | |||||
| 293 | for (i = 0; i < bmap->n_div; ++i) | ||||
| 294 | bmap = normalize_div_expression(bmap, i); | ||||
| 295 | |||||
| 296 | return bmap; | ||||
| 297 | } | ||||
| 298 | |||||
| 299 | /* Assumes divs have been ordered if keep_divs is set. | ||||
| 300 | */ | ||||
| 301 | static __isl_give isl_basic_map *eliminate_var_using_equality( | ||||
| 302 | __isl_take isl_basic_map *bmap, | ||||
| 303 | unsigned pos, isl_int *eq, int keep_divs, int *progress) | ||||
| 304 | { | ||||
| 305 | isl_size total; | ||||
| 306 | isl_size v_div; | ||||
| 307 | int k; | ||||
| 308 | int last_div; | ||||
| 309 | |||||
| 310 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 311 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 312 | if (total < 0 || v_div < 0) | ||||
| 313 | return isl_basic_map_free(bmap); | ||||
| 314 | last_div = isl_seq_last_non_zero(eq + 1 + v_div, bmap->n_div); | ||||
| 315 | for (k = 0; k < bmap->n_eq; ++k) { | ||||
| 316 | if (bmap->eq[k] == eq) | ||||
| 317 | continue; | ||||
| 318 | if (isl_int_is_zero(bmap->eq[k][1+pos])(isl_sioimath_sgn(*(bmap->eq[k][1+pos])) == 0)) | ||||
| 319 | continue; | ||||
| 320 | if (progress) | ||||
| 321 | *progress = 1; | ||||
| 322 | isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL((void*)0)); | ||||
| 323 | isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total); | ||||
| 324 | } | ||||
| 325 | |||||
| 326 | for (k = 0; k < bmap->n_ineq; ++k) { | ||||
| 327 | if (isl_int_is_zero(bmap->ineq[k][1+pos])(isl_sioimath_sgn(*(bmap->ineq[k][1+pos])) == 0)) | ||||
| 328 | continue; | ||||
| 329 | if (progress) | ||||
| 330 | *progress = 1; | ||||
| 331 | isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL((void*)0)); | ||||
| 332 | isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total); | ||||
| 333 | ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT)(((bmap)->flags) &= ~((1 << 3))); | ||||
| 334 | ISL_F_CLR(bmap, ISL_BASIC_MAP_SORTED)(((bmap)->flags) &= ~((1 << 5))); | ||||
| 335 | } | ||||
| 336 | |||||
| 337 | for (k = 0; k < bmap->n_div; ++k) { | ||||
| 338 | if (isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0)) | ||||
| 339 | continue; | ||||
| 340 | if (isl_int_is_zero(bmap->div[k][1+1+pos])(isl_sioimath_sgn(*(bmap->div[k][1+1+pos])) == 0)) | ||||
| 341 | continue; | ||||
| 342 | if (progress) | ||||
| 343 | *progress = 1; | ||||
| 344 | /* We need to be careful about circular definitions, | ||||
| 345 | * so for now we just remove the definition of div k | ||||
| 346 | * if the equality contains any divs. | ||||
| 347 | * If keep_divs is set, then the divs have been ordered | ||||
| 348 | * and we can keep the definition as long as the result | ||||
| 349 | * is still ordered. | ||||
| 350 | */ | ||||
| 351 | if (last_div == -1 || (keep_divs && last_div < k)) { | ||||
| 352 | isl_seq_elim(bmap->div[k]+1, eq, | ||||
| 353 | 1+pos, 1+total, &bmap->div[k][0]); | ||||
| 354 | bmap = normalize_div_expression(bmap, k); | ||||
| 355 | if (!bmap) | ||||
| 356 | return NULL((void*)0); | ||||
| 357 | } else | ||||
| 358 | isl_seq_clr(bmap->div[k], 1 + total); | ||||
| 359 | } | ||||
| 360 | |||||
| 361 | return bmap; | ||||
| 362 | } | ||||
| 363 | |||||
| 364 | /* Assumes divs have been ordered if keep_divs is set. | ||||
| 365 | */ | ||||
| 366 | static __isl_give isl_basic_map *eliminate_div(__isl_take isl_basic_map *bmap, | ||||
| 367 | isl_int *eq, unsigned div, int keep_divs) | ||||
| 368 | { | ||||
| 369 | isl_size v_div; | ||||
| 370 | unsigned pos; | ||||
| 371 | |||||
| 372 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 373 | if (v_div < 0) | ||||
| 374 | return isl_basic_map_free(bmap); | ||||
| 375 | pos = v_div + div; | ||||
| 376 | bmap = eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL((void*)0)); | ||||
| 377 | |||||
| 378 | bmap = isl_basic_map_drop_div(bmap, div); | ||||
| 379 | |||||
| 380 | return bmap; | ||||
| 381 | } | ||||
| 382 | |||||
| 383 | /* Check if elimination of div "div" using equality "eq" would not | ||||
| 384 | * result in a div depending on a later div. | ||||
| 385 | */ | ||||
| 386 | static isl_bool ok_to_eliminate_div(__isl_keep isl_basic_map *bmap, isl_int *eq, | ||||
| 387 | unsigned div) | ||||
| 388 | { | ||||
| 389 | int k; | ||||
| 390 | int last_div; | ||||
| 391 | isl_size v_div; | ||||
| 392 | unsigned pos; | ||||
| 393 | |||||
| 394 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 395 | if (v_div < 0) | ||||
| 396 | return isl_bool_error; | ||||
| 397 | pos = v_div + div; | ||||
| 398 | |||||
| 399 | last_div = isl_seq_last_non_zero(eq + 1 + v_div, bmap->n_div); | ||||
| 400 | if (last_div < 0 || last_div <= div) | ||||
| 401 | return isl_bool_true; | ||||
| 402 | |||||
| 403 | for (k = 0; k <= last_div; ++k) { | ||||
| 404 | if (isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0)) | ||||
| 405 | continue; | ||||
| 406 | if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos])(isl_sioimath_sgn(*(bmap->div[k][1 + 1 + pos])) == 0)) | ||||
| 407 | return isl_bool_false; | ||||
| 408 | } | ||||
| 409 | |||||
| 410 | return isl_bool_true; | ||||
| 411 | } | ||||
| 412 | |||||
| 413 | /* Eliminate divs based on equalities | ||||
| 414 | */ | ||||
| 415 | static __isl_give isl_basic_map *eliminate_divs_eq( | ||||
| 416 | __isl_take isl_basic_map *bmap, int *progress) | ||||
| 417 | { | ||||
| 418 | int d; | ||||
| 419 | int i; | ||||
| 420 | int modified = 0; | ||||
| 421 | unsigned off; | ||||
| 422 | |||||
| 423 | bmap = isl_basic_map_order_divs(bmap); | ||||
| 424 | |||||
| 425 | if (!bmap) | ||||
| 426 | return NULL((void*)0); | ||||
| 427 | |||||
| 428 | off = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 429 | |||||
| 430 | for (d = bmap->n_div - 1; d >= 0 ; --d) { | ||||
| 431 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
| 432 | isl_bool ok; | ||||
| 433 | |||||
| 434 | if (!isl_int_is_one(bmap->eq[i][off + d])(isl_sioimath_cmp_si(*(bmap->eq[i][off + d]), 1) == 0) && | ||||
| 435 | !isl_int_is_negone(bmap->eq[i][off + d])(isl_sioimath_cmp_si(*(bmap->eq[i][off + d]), -1) == 0)) | ||||
| 436 | continue; | ||||
| 437 | ok = ok_to_eliminate_div(bmap, bmap->eq[i], d); | ||||
| 438 | if (ok < 0) | ||||
| 439 | return isl_basic_map_free(bmap); | ||||
| 440 | if (!ok) | ||||
| 441 | continue; | ||||
| 442 | modified = 1; | ||||
| 443 | *progress = 1; | ||||
| 444 | bmap = eliminate_div(bmap, bmap->eq[i], d, 1); | ||||
| 445 | if (isl_basic_map_drop_equality(bmap, i) < 0) | ||||
| 446 | return isl_basic_map_free(bmap); | ||||
| 447 | break; | ||||
| 448 | } | ||||
| 449 | } | ||||
| 450 | if (modified) | ||||
| 451 | return eliminate_divs_eq(bmap, progress); | ||||
| 452 | return bmap; | ||||
| 453 | } | ||||
| 454 | |||||
| 455 | /* Eliminate divs based on inequalities | ||||
| 456 | */ | ||||
| 457 | static __isl_give isl_basic_map *eliminate_divs_ineq( | ||||
| 458 | __isl_take isl_basic_map *bmap, int *progress) | ||||
| 459 | { | ||||
| 460 | int d; | ||||
| 461 | int i; | ||||
| 462 | unsigned off; | ||||
| 463 | struct isl_ctx *ctx; | ||||
| 464 | |||||
| 465 | if (!bmap) | ||||
| 466 | return NULL((void*)0); | ||||
| 467 | |||||
| 468 | ctx = bmap->ctx; | ||||
| 469 | off = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 470 | |||||
| 471 | for (d = bmap->n_div - 1; d >= 0 ; --d) { | ||||
| 472 | for (i = 0; i < bmap->n_eq; ++i) | ||||
| 473 | if (!isl_int_is_zero(bmap->eq[i][off + d])(isl_sioimath_sgn(*(bmap->eq[i][off + d])) == 0)) | ||||
| 474 | break; | ||||
| 475 | if (i < bmap->n_eq) | ||||
| 476 | continue; | ||||
| 477 | for (i = 0; i < bmap->n_ineq; ++i) | ||||
| 478 | if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one)(isl_sioimath_abs_cmp(*(bmap->ineq[i][off + d]), *(ctx-> one)) > 0)) | ||||
| 479 | break; | ||||
| 480 | if (i < bmap->n_ineq) | ||||
| 481 | continue; | ||||
| 482 | *progress = 1; | ||||
| 483 | bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1); | ||||
| 484 | if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1))))) | ||||
| 485 | break; | ||||
| 486 | bmap = isl_basic_map_drop_div(bmap, d); | ||||
| 487 | if (!bmap) | ||||
| 488 | break; | ||||
| 489 | } | ||||
| 490 | return bmap; | ||||
| 491 | } | ||||
| 492 | |||||
| 493 | /* Does the equality constraint at position "eq" in "bmap" involve | ||||
| 494 | * any local variables in the range [first, first + n) | ||||
| 495 | * that are not marked as having an explicit representation? | ||||
| 496 | */ | ||||
| 497 | static isl_bool bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map *bmap, | ||||
| 498 | int eq, unsigned first, unsigned n) | ||||
| 499 | { | ||||
| 500 | unsigned o_div; | ||||
| 501 | int i; | ||||
| 502 | |||||
| 503 | if (!bmap) | ||||
| 504 | return isl_bool_error; | ||||
| 505 | |||||
| 506 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 507 | for (i = 0; i < n; ++i) { | ||||
| 508 | isl_bool unknown; | ||||
| 509 | |||||
| 510 | if (isl_int_is_zero(bmap->eq[eq][o_div + first + i])(isl_sioimath_sgn(*(bmap->eq[eq][o_div + first + i])) == 0 )) | ||||
| 511 | continue; | ||||
| 512 | unknown = isl_basic_map_div_is_marked_unknown(bmap, first + i); | ||||
| 513 | if (unknown < 0) | ||||
| 514 | return isl_bool_error; | ||||
| 515 | if (unknown) | ||||
| 516 | return isl_bool_true; | ||||
| 517 | } | ||||
| 518 | |||||
| 519 | return isl_bool_false; | ||||
| 520 | } | ||||
| 521 | |||||
| 522 | /* The last local variable involved in the equality constraint | ||||
| 523 | * at position "eq" in "bmap" is the local variable at position "div". | ||||
| 524 | * It can therefore be used to extract an explicit representation | ||||
| 525 | * for that variable. | ||||
| 526 | * Do so unless the local variable already has an explicit representation or | ||||
| 527 | * the explicit representation would involve any other local variables | ||||
| 528 | * that in turn do not have an explicit representation. | ||||
| 529 | * An equality constraint involving local variables without an explicit | ||||
| 530 | * representation can be used in isl_basic_map_drop_redundant_divs | ||||
| 531 | * to separate out an independent local variable. Introducing | ||||
| 532 | * an explicit representation here would block this transformation, | ||||
| 533 | * while the partial explicit representation in itself is not very useful. | ||||
| 534 | * Set *progress if anything is changed. | ||||
| 535 | * | ||||
| 536 | * The equality constraint is of the form | ||||
| 537 | * | ||||
| 538 | * f(x) + n e >= 0 | ||||
| 539 | * | ||||
| 540 | * with n a positive number. The explicit representation derived from | ||||
| 541 | * this constraint is | ||||
| 542 | * | ||||
| 543 | * floor((-f(x))/n) | ||||
| 544 | */ | ||||
| 545 | static __isl_give isl_basic_map *set_div_from_eq(__isl_take isl_basic_map *bmap, | ||||
| 546 | int div, int eq, int *progress) | ||||
| 547 | { | ||||
| 548 | isl_size total; | ||||
| 549 | unsigned o_div; | ||||
| 550 | isl_bool involves; | ||||
| 551 | |||||
| 552 | if (!bmap) | ||||
| 553 | return NULL((void*)0); | ||||
| 554 | |||||
| 555 | if (!isl_int_is_zero(bmap->div[div][0])(isl_sioimath_sgn(*(bmap->div[div][0])) == 0)) | ||||
| 556 | return bmap; | ||||
| 557 | |||||
| 558 | involves = bmap_eq_involves_unknown_divs(bmap, eq, 0, div); | ||||
| 559 | if (involves < 0) | ||||
| 560 | return isl_basic_map_free(bmap); | ||||
| 561 | if (involves) | ||||
| 562 | return bmap; | ||||
| 563 | |||||
| 564 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 565 | if (total < 0) | ||||
| 566 | return isl_basic_map_free(bmap); | ||||
| 567 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 568 | isl_seq_neg(bmap->div[div] + 1, bmap->eq[eq], 1 + total); | ||||
| 569 | isl_int_set_si(bmap->div[div][1 + o_div + div], 0)isl_sioimath_set_si((bmap->div[div][1 + o_div + div]), 0); | ||||
| 570 | isl_int_set(bmap->div[div][0], bmap->eq[eq][o_div + div])isl_sioimath_set((bmap->div[div][0]), *(bmap->eq[eq][o_div + div])); | ||||
| 571 | if (progress) | ||||
| 572 | *progress = 1; | ||||
| 573 | |||||
| 574 | return bmap; | ||||
| 575 | } | ||||
| 576 | |||||
| 577 | /* Perform fangcheng (Gaussian elimination) on the equality | ||||
| 578 | * constraints of "bmap". | ||||
| 579 | * That is, put them into row-echelon form, starting from the last column | ||||
| 580 | * backward and use them to eliminate the corresponding coefficients | ||||
| 581 | * from all constraints. | ||||
| 582 | * | ||||
| 583 | * If "progress" is not NULL, then it gets set if the elimination | ||||
| 584 | * result in any changes. | ||||
| 585 | * The elimination process may result in some equality constraints | ||||
| 586 | * getting interchanged or removed. | ||||
| 587 | * If "swap" or "drop" are not NULL, then they get called when | ||||
| 588 | * two equality constraints get interchanged or | ||||
| 589 | * when a number of final equality constraints get removed. | ||||
| 590 | * As a special case, if the input turns out to be empty, | ||||
| 591 | * then drop gets called with the number of removed equality | ||||
| 592 | * constraints set to the total number of equality constraints. | ||||
| 593 | * If "swap" or "drop" are not NULL, then the local variables (if any) | ||||
| 594 | * are assumed to be in a valid order. | ||||
| 595 | */ | ||||
| 596 | __isl_give isl_basic_map *isl_basic_map_gauss5(__isl_take isl_basic_map *bmap, | ||||
| 597 | int *progress, | ||||
| 598 | isl_stat (*swap)(unsigned a, unsigned b, void *user), | ||||
| 599 | isl_stat (*drop)(unsigned n, void *user), void *user) | ||||
| 600 | { | ||||
| 601 | int k; | ||||
| 602 | int done; | ||||
| 603 | int last_var; | ||||
| 604 | unsigned total_var; | ||||
| 605 | isl_size total; | ||||
| 606 | unsigned n_drop; | ||||
| 607 | |||||
| 608 | if (!swap && !drop) | ||||
| 609 | bmap = isl_basic_map_order_divs(bmap); | ||||
| 610 | |||||
| 611 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 612 | if (total < 0) | ||||
| 613 | return isl_basic_map_free(bmap); | ||||
| 614 | |||||
| 615 | total_var = total - bmap->n_div; | ||||
| 616 | |||||
| 617 | last_var = total - 1; | ||||
| 618 | for (done = 0; done < bmap->n_eq; ++done) { | ||||
| 619 | for (; last_var >= 0; --last_var) { | ||||
| 620 | for (k = done; k < bmap->n_eq; ++k) | ||||
| 621 | if (!isl_int_is_zero(bmap->eq[k][1+last_var])(isl_sioimath_sgn(*(bmap->eq[k][1+last_var])) == 0)) | ||||
| 622 | break; | ||||
| 623 | if (k < bmap->n_eq) | ||||
| 624 | break; | ||||
| 625 | } | ||||
| 626 | if (last_var < 0) | ||||
| 627 | break; | ||||
| 628 | if (k != done) { | ||||
| 629 | swap_equality(bmap, k, done); | ||||
| 630 | if (swap && swap(k, done, user) < 0) | ||||
| 631 | return isl_basic_map_free(bmap); | ||||
| 632 | } | ||||
| 633 | if (isl_int_is_neg(bmap->eq[done][1+last_var])(isl_sioimath_sgn(*(bmap->eq[done][1+last_var])) < 0)) | ||||
| 634 | isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total); | ||||
| 635 | |||||
| 636 | bmap = eliminate_var_using_equality(bmap, last_var, | ||||
| 637 | bmap->eq[done], 1, progress); | ||||
| 638 | |||||
| 639 | if (last_var >= total_var) | ||||
| 640 | bmap = set_div_from_eq(bmap, last_var - total_var, | ||||
| 641 | done, progress); | ||||
| 642 | if (!bmap) | ||||
| 643 | return NULL((void*)0); | ||||
| 644 | } | ||||
| 645 | if (done == bmap->n_eq) | ||||
| 646 | return bmap; | ||||
| 647 | for (k = done; k < bmap->n_eq; ++k) { | ||||
| 648 | if (isl_int_is_zero(bmap->eq[k][0])(isl_sioimath_sgn(*(bmap->eq[k][0])) == 0)) | ||||
| 649 | continue; | ||||
| 650 | if (drop && drop(bmap->n_eq, user) < 0) | ||||
| 651 | return isl_basic_map_free(bmap); | ||||
| 652 | return isl_basic_map_set_to_empty(bmap); | ||||
| 653 | } | ||||
| 654 | n_drop = bmap->n_eq - done; | ||||
| 655 | bmap = isl_basic_map_free_equality(bmap, n_drop); | ||||
| 656 | if (drop && drop(n_drop, user) < 0) | ||||
| 657 | return isl_basic_map_free(bmap); | ||||
| 658 | return bmap; | ||||
| 659 | } | ||||
| 660 | |||||
| 661 | __isl_give isl_basic_map *isl_basic_map_gauss(__isl_take isl_basic_map *bmap, | ||||
| 662 | int *progress) | ||||
| 663 | { | ||||
| 664 | return isl_basic_map_gauss5(bmap, progress, NULL((void*)0), NULL((void*)0), NULL((void*)0)); | ||||
| 665 | } | ||||
| 666 | |||||
| 667 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_gauss( | ||||
| 668 | __isl_take isl_basic_setisl_basic_map *bset, int *progress) | ||||
| 669 | { | ||||
| 670 | return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset), | ||||
| 671 | progress)); | ||||
| 672 | } | ||||
| 673 | |||||
| 674 | |||||
| 675 | static unsigned int round_up(unsigned int v) | ||||
| 676 | { | ||||
| 677 | int old_v = v; | ||||
| 678 | |||||
| 679 | while (v) { | ||||
| 680 | old_v = v; | ||||
| 681 | v ^= v & -v; | ||||
| 682 | } | ||||
| 683 | return old_v << 1; | ||||
| 684 | } | ||||
| 685 | |||||
| 686 | /* Hash table of inequalities in a basic map. | ||||
| 687 | * "index" is an array of addresses of inequalities in the basic map, some | ||||
| 688 | * of which are NULL. The inequalities are hashed on the coefficients | ||||
| 689 | * except the constant term. | ||||
| 690 | * "size" is the number of elements in the array and is always a power of two | ||||
| 691 | * "bits" is the number of bits need to represent an index into the array. | ||||
| 692 | * "total" is the total dimension of the basic map. | ||||
| 693 | */ | ||||
| 694 | struct isl_constraint_index { | ||||
| 695 | unsigned int size; | ||||
| 696 | int bits; | ||||
| 697 | isl_int ***index; | ||||
| 698 | isl_size total; | ||||
| 699 | }; | ||||
| 700 | |||||
| 701 | /* Fill in the "ci" data structure for holding the inequalities of "bmap". | ||||
| 702 | */ | ||||
| 703 | static isl_stat create_constraint_index(struct isl_constraint_index *ci, | ||||
| 704 | __isl_keep isl_basic_map *bmap) | ||||
| 705 | { | ||||
| 706 | isl_ctx *ctx; | ||||
| 707 | |||||
| 708 | ci->index = NULL((void*)0); | ||||
| 709 | if (!bmap
| ||||
| 710 | return isl_stat_error; | ||||
| 711 | ci->total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 712 | if (ci->total < 0) | ||||
| 713 | return isl_stat_error; | ||||
| 714 | if (bmap->n_ineq == 0) | ||||
| 715 | return isl_stat_ok; | ||||
| 716 | ci->size = round_up(4 * (bmap->n_ineq + 1) / 3 - 1); | ||||
| 717 | ci->bits = ffs(ci->size) - 1; | ||||
| 718 | ctx = isl_basic_map_get_ctx(bmap); | ||||
| 719 | ci->index = isl_calloc_array(ctx, isl_int **, ci->size)((isl_int ** *)isl_calloc_or_die(ctx, ci->size, sizeof(isl_int **))); | ||||
| 720 | if (!ci->index) | ||||
| 721 | return isl_stat_error; | ||||
| 722 | |||||
| 723 | return isl_stat_ok; | ||||
| 724 | } | ||||
| 725 | |||||
| 726 | /* Free the memory allocated by create_constraint_index. | ||||
| 727 | */ | ||||
| 728 | static void constraint_index_free(struct isl_constraint_index *ci) | ||||
| 729 | { | ||||
| 730 | free(ci->index); | ||||
| 731 | } | ||||
| 732 | |||||
| 733 | /* Return the position in ci->index that contains the address of | ||||
| 734 | * an inequality that is equal to *ineq up to the constant term, | ||||
| 735 | * provided this address is not identical to "ineq". | ||||
| 736 | * If there is no such inequality, then return the position where | ||||
| 737 | * such an inequality should be inserted. | ||||
| 738 | */ | ||||
| 739 | static int hash_index_ineq(struct isl_constraint_index *ci, isl_int **ineq) | ||||
| 740 | { | ||||
| 741 | int h; | ||||
| 742 | uint32_t hash = isl_seq_get_hash_bits((*ineq) + 1, ci->total, ci->bits); | ||||
| 743 | for (h = hash; ci->index[h]; h = (h+1) % ci->size) | ||||
| |||||
| 744 | if (ineq != ci->index[h] && | ||||
| 745 | isl_seq_eq((*ineq) + 1, ci->index[h][0]+1, ci->total)) | ||||
| 746 | break; | ||||
| 747 | return h; | ||||
| 748 | } | ||||
| 749 | |||||
| 750 | /* Return the position in ci->index that contains the address of | ||||
| 751 | * an inequality that is equal to the k'th inequality of "bmap" | ||||
| 752 | * up to the constant term, provided it does not point to the very | ||||
| 753 | * same inequality. | ||||
| 754 | * If there is no such inequality, then return the position where | ||||
| 755 | * such an inequality should be inserted. | ||||
| 756 | */ | ||||
| 757 | static int hash_index(struct isl_constraint_index *ci, | ||||
| 758 | __isl_keep isl_basic_map *bmap, int k) | ||||
| 759 | { | ||||
| 760 | return hash_index_ineq(ci, &bmap->ineq[k]); | ||||
| 761 | } | ||||
| 762 | |||||
| 763 | static int set_hash_index(struct isl_constraint_index *ci, | ||||
| 764 | __isl_keep isl_basic_setisl_basic_map *bset, int k) | ||||
| 765 | { | ||||
| 766 | return hash_index(ci, bset, k); | ||||
| 767 | } | ||||
| 768 | |||||
| 769 | /* Fill in the "ci" data structure with the inequalities of "bset". | ||||
| 770 | */ | ||||
| 771 | static isl_stat setup_constraint_index(struct isl_constraint_index *ci, | ||||
| 772 | __isl_keep isl_basic_setisl_basic_map *bset) | ||||
| 773 | { | ||||
| 774 | int k, h; | ||||
| 775 | |||||
| 776 | if (create_constraint_index(ci, bset) < 0) | ||||
| 777 | return isl_stat_error; | ||||
| 778 | |||||
| 779 | for (k = 0; k < bset->n_ineq; ++k) { | ||||
| 780 | h = set_hash_index(ci, bset, k); | ||||
| 781 | ci->index[h] = &bset->ineq[k]; | ||||
| 782 | } | ||||
| 783 | |||||
| 784 | return isl_stat_ok; | ||||
| 785 | } | ||||
| 786 | |||||
| 787 | /* Is the inequality ineq (obviously) redundant with respect | ||||
| 788 | * to the constraints in "ci"? | ||||
| 789 | * | ||||
| 790 | * Look for an inequality in "ci" with the same coefficients and then | ||||
| 791 | * check if the contant term of "ineq" is greater than or equal | ||||
| 792 | * to the constant term of that inequality. If so, "ineq" is clearly | ||||
| 793 | * redundant. | ||||
| 794 | * | ||||
| 795 | * Note that hash_index_ineq ignores a stored constraint if it has | ||||
| 796 | * the same address as the passed inequality. It is ok to pass | ||||
| 797 | * the address of a local variable here since it will never be | ||||
| 798 | * the same as the address of a constraint in "ci". | ||||
| 799 | */ | ||||
| 800 | static isl_bool constraint_index_is_redundant(struct isl_constraint_index *ci, | ||||
| 801 | isl_int *ineq) | ||||
| 802 | { | ||||
| 803 | int h; | ||||
| 804 | |||||
| 805 | h = hash_index_ineq(ci, &ineq); | ||||
| 806 | if (!ci->index[h]) | ||||
| 807 | return isl_bool_false; | ||||
| 808 | return isl_int_ge(ineq[0], (*ci->index[h])[0])(isl_sioimath_cmp(*(ineq[0]), *((*ci->index[h])[0])) >= 0); | ||||
| 809 | } | ||||
| 810 | |||||
| 811 | /* If we can eliminate more than one div, then we need to make | ||||
| 812 | * sure we do it from last div to first div, in order not to | ||||
| 813 | * change the position of the other divs that still need to | ||||
| 814 | * be removed. | ||||
| 815 | */ | ||||
| 816 | static __isl_give isl_basic_map *remove_duplicate_divs( | ||||
| 817 | __isl_take isl_basic_map *bmap, int *progress) | ||||
| 818 | { | ||||
| 819 | unsigned int size; | ||||
| 820 | int *index; | ||||
| 821 | int *elim_for; | ||||
| 822 | int k, l, h; | ||||
| 823 | int bits; | ||||
| 824 | struct isl_blk eq; | ||||
| 825 | isl_size v_div; | ||||
| 826 | unsigned total; | ||||
| 827 | struct isl_ctx *ctx; | ||||
| 828 | |||||
| 829 | bmap = isl_basic_map_order_divs(bmap); | ||||
| 830 | if (!bmap || bmap->n_div <= 1) | ||||
| 831 | return bmap; | ||||
| 832 | |||||
| 833 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 834 | if (v_div < 0) | ||||
| 835 | return isl_basic_map_free(bmap); | ||||
| 836 | total = v_div + bmap->n_div; | ||||
| 837 | |||||
| 838 | ctx = bmap->ctx; | ||||
| 839 | for (k = bmap->n_div - 1; k >= 0; --k) | ||||
| 840 | if (!isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0)) | ||||
| 841 | break; | ||||
| 842 | if (k <= 0) | ||||
| 843 | return bmap; | ||||
| 844 | |||||
| 845 | size = round_up(4 * bmap->n_div / 3 - 1); | ||||
| 846 | if (size == 0) | ||||
| 847 | return bmap; | ||||
| 848 | elim_for = isl_calloc_array(ctx, int, bmap->n_div)((int *)isl_calloc_or_die(ctx, bmap->n_div, sizeof(int))); | ||||
| 849 | bits = ffs(size) - 1; | ||||
| 850 | index = isl_calloc_array(ctx, int, size)((int *)isl_calloc_or_die(ctx, size, sizeof(int))); | ||||
| 851 | if (!elim_for || !index) | ||||
| 852 | goto out; | ||||
| 853 | eq = isl_blk_alloc(ctx, 1+total); | ||||
| 854 | if (isl_blk_is_error(eq)) | ||||
| 855 | goto out; | ||||
| 856 | |||||
| 857 | isl_seq_clr(eq.data, 1+total); | ||||
| 858 | index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1; | ||||
| 859 | for (--k; k >= 0; --k) { | ||||
| 860 | uint32_t hash; | ||||
| 861 | |||||
| 862 | if (isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0)) | ||||
| 863 | continue; | ||||
| 864 | |||||
| 865 | hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits); | ||||
| 866 | for (h = hash; index[h]; h = (h+1) % size) | ||||
| 867 | if (isl_seq_eq(bmap->div[k], | ||||
| 868 | bmap->div[index[h]-1], 2+total)) | ||||
| 869 | break; | ||||
| 870 | if (index[h]) { | ||||
| 871 | *progress = 1; | ||||
| 872 | l = index[h] - 1; | ||||
| 873 | elim_for[l] = k + 1; | ||||
| 874 | } | ||||
| 875 | index[h] = k+1; | ||||
| 876 | } | ||||
| 877 | for (l = bmap->n_div - 1; l >= 0; --l) { | ||||
| 878 | if (!elim_for[l]) | ||||
| 879 | continue; | ||||
| 880 | k = elim_for[l] - 1; | ||||
| 881 | isl_int_set_si(eq.data[1 + v_div + k], -1)isl_sioimath_set_si((eq.data[1 + v_div + k]), -1); | ||||
| 882 | isl_int_set_si(eq.data[1 + v_div + l], 1)isl_sioimath_set_si((eq.data[1 + v_div + l]), 1); | ||||
| 883 | bmap = eliminate_div(bmap, eq.data, l, 1); | ||||
| 884 | if (!bmap) | ||||
| 885 | break; | ||||
| 886 | isl_int_set_si(eq.data[1 + v_div + k], 0)isl_sioimath_set_si((eq.data[1 + v_div + k]), 0); | ||||
| 887 | isl_int_set_si(eq.data[1 + v_div + l], 0)isl_sioimath_set_si((eq.data[1 + v_div + l]), 0); | ||||
| 888 | } | ||||
| 889 | |||||
| 890 | isl_blk_free(ctx, eq); | ||||
| 891 | out: | ||||
| 892 | free(index); | ||||
| 893 | free(elim_for); | ||||
| 894 | return bmap; | ||||
| 895 | } | ||||
| 896 | |||||
| 897 | static int n_pure_div_eq(struct isl_basic_map *bmap) | ||||
| 898 | { | ||||
| 899 | int i, j; | ||||
| 900 | isl_size v_div; | ||||
| 901 | |||||
| 902 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 903 | if (v_div < 0) | ||||
| 904 | return -1; | ||||
| 905 | for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) { | ||||
| 906 | while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + v_div + j])(isl_sioimath_sgn(*(bmap->eq[i][1 + v_div + j])) == 0)) | ||||
| 907 | --j; | ||||
| 908 | if (j < 0) | ||||
| 909 | break; | ||||
| 910 | if (isl_seq_first_non_zero(bmap->eq[i] + 1 + v_div, j) != -1) | ||||
| 911 | return 0; | ||||
| 912 | } | ||||
| 913 | return i; | ||||
| 914 | } | ||||
| 915 | |||||
| 916 | /* Normalize divs that appear in equalities. | ||||
| 917 | * | ||||
| 918 | * In particular, we assume that bmap contains some equalities | ||||
| 919 | * of the form | ||||
| 920 | * | ||||
| 921 | * a x = m * e_i | ||||
| 922 | * | ||||
| 923 | * and we want to replace the set of e_i by a minimal set and | ||||
| 924 | * such that the new e_i have a canonical representation in terms | ||||
| 925 | * of the vector x. | ||||
| 926 | * If any of the equalities involves more than one divs, then | ||||
| 927 | * we currently simply bail out. | ||||
| 928 | * | ||||
| 929 | * Let us first additionally assume that all equalities involve | ||||
| 930 | * a div. The equalities then express modulo constraints on the | ||||
| 931 | * remaining variables and we can use "parameter compression" | ||||
| 932 | * to find a minimal set of constraints. The result is a transformation | ||||
| 933 | * | ||||
| 934 | * x = T(x') = x_0 + G x' | ||||
| 935 | * | ||||
| 936 | * with G a lower-triangular matrix with all elements below the diagonal | ||||
| 937 | * non-negative and smaller than the diagonal element on the same row. | ||||
| 938 | * We first normalize x_0 by making the same property hold in the affine | ||||
| 939 | * T matrix. | ||||
| 940 | * The rows i of G with a 1 on the diagonal do not impose any modulo | ||||
| 941 | * constraint and simply express x_i = x'_i. | ||||
| 942 | * For each of the remaining rows i, we introduce a div and a corresponding | ||||
| 943 | * equality. In particular | ||||
| 944 | * | ||||
| 945 | * g_ii e_j = x_i - g_i(x') | ||||
| 946 | * | ||||
| 947 | * where each x'_k is replaced either by x_k (if g_kk = 1) or the | ||||
| 948 | * corresponding div (if g_kk != 1). | ||||
| 949 | * | ||||
| 950 | * If there are any equalities not involving any div, then we | ||||
| 951 | * first apply a variable compression on the variables x: | ||||
| 952 | * | ||||
| 953 | * x = C x'' x'' = C_2 x | ||||
| 954 | * | ||||
| 955 | * and perform the above parameter compression on A C instead of on A. | ||||
| 956 | * The resulting compression is then of the form | ||||
| 957 | * | ||||
| 958 | * x'' = T(x') = x_0 + G x' | ||||
| 959 | * | ||||
| 960 | * and in constructing the new divs and the corresponding equalities, | ||||
| 961 | * we have to replace each x'', i.e., the x'_k with (g_kk = 1), | ||||
| 962 | * by the corresponding row from C_2. | ||||
| 963 | */ | ||||
| 964 | static __isl_give isl_basic_map *normalize_divs(__isl_take isl_basic_map *bmap, | ||||
| 965 | int *progress) | ||||
| 966 | { | ||||
| 967 | int i, j, k; | ||||
| 968 | isl_size v_div; | ||||
| 969 | int div_eq; | ||||
| 970 | struct isl_mat *B; | ||||
| 971 | struct isl_vec *d; | ||||
| 972 | struct isl_mat *T = NULL((void*)0); | ||||
| 973 | struct isl_mat *C = NULL((void*)0); | ||||
| 974 | struct isl_mat *C2 = NULL((void*)0); | ||||
| 975 | isl_int v; | ||||
| 976 | int *pos = NULL((void*)0); | ||||
| 977 | int dropped, needed; | ||||
| 978 | |||||
| 979 | if (!bmap) | ||||
| 980 | return NULL((void*)0); | ||||
| 981 | |||||
| 982 | if (bmap->n_div == 0) | ||||
| 983 | return bmap; | ||||
| 984 | |||||
| 985 | if (bmap->n_eq == 0) | ||||
| 986 | return bmap; | ||||
| 987 | |||||
| 988 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS)(!!(((bmap)->flags) & ((1 << 6))))) | ||||
| 989 | return bmap; | ||||
| 990 | |||||
| 991 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 992 | div_eq = n_pure_div_eq(bmap); | ||||
| 993 | if (v_div < 0 || div_eq < 0) | ||||
| 994 | return isl_basic_map_free(bmap); | ||||
| 995 | if (div_eq == 0) | ||||
| 996 | return bmap; | ||||
| 997 | |||||
| 998 | if (div_eq < bmap->n_eq) { | ||||
| 999 | B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq, | ||||
| 1000 | bmap->n_eq - div_eq, 0, 1 + v_div); | ||||
| 1001 | C = isl_mat_variable_compression(B, &C2); | ||||
| 1002 | if (!C || !C2) | ||||
| 1003 | goto error; | ||||
| 1004 | if (C->n_col == 0) { | ||||
| 1005 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
| 1006 | isl_mat_free(C); | ||||
| 1007 | isl_mat_free(C2); | ||||
| 1008 | goto done; | ||||
| 1009 | } | ||||
| 1010 | } | ||||
| 1011 | |||||
| 1012 | d = isl_vec_alloc(bmap->ctx, div_eq); | ||||
| 1013 | if (!d) | ||||
| 1014 | goto error; | ||||
| 1015 | for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) { | ||||
| 1016 | while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + v_div + j])(isl_sioimath_sgn(*(bmap->eq[i][1 + v_div + j])) == 0)) | ||||
| 1017 | --j; | ||||
| 1018 | isl_int_set(d->block.data[i], bmap->eq[i][1 + v_div + j])isl_sioimath_set((d->block.data[i]), *(bmap->eq[i][1 + v_div + j])); | ||||
| 1019 | } | ||||
| 1020 | B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + v_div); | ||||
| 1021 | |||||
| 1022 | if (C) { | ||||
| 1023 | B = isl_mat_product(B, C); | ||||
| 1024 | C = NULL((void*)0); | ||||
| 1025 | } | ||||
| 1026 | |||||
| 1027 | T = isl_mat_parameter_compression(B, d); | ||||
| 1028 | if (!T) | ||||
| 1029 | goto error; | ||||
| 1030 | if (T->n_col == 0) { | ||||
| 1031 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
| 1032 | isl_mat_free(C2); | ||||
| 1033 | isl_mat_free(T); | ||||
| 1034 | goto done; | ||||
| 1035 | } | ||||
| 1036 | isl_int_init(v)isl_sioimath_init((v)); | ||||
| 1037 | for (i = 0; i < T->n_row - 1; ++i) { | ||||
| 1038 | isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i])isl_sioimath_fdiv_q((v), *(T->row[1 + i][0]), *(T->row[ 1 + i][1 + i])); | ||||
| 1039 | if (isl_int_is_zero(v)(isl_sioimath_sgn(*(v)) == 0)) | ||||
| 1040 | continue; | ||||
| 1041 | isl_mat_col_submul(T, 0, v, 1 + i); | ||||
| 1042 | } | ||||
| 1043 | isl_int_clear(v)isl_sioimath_clear((v)); | ||||
| 1044 | pos = isl_alloc_array(bmap->ctx, int, T->n_row)((int *)isl_malloc_or_die(bmap->ctx, (T->n_row)*sizeof( int))); | ||||
| 1045 | if (!pos) | ||||
| 1046 | goto error; | ||||
| 1047 | /* We have to be careful because dropping equalities may reorder them */ | ||||
| 1048 | dropped = 0; | ||||
| 1049 | for (j = bmap->n_div - 1; j >= 0; --j) { | ||||
| 1050 | for (i = 0; i < bmap->n_eq; ++i) | ||||
| 1051 | if (!isl_int_is_zero(bmap->eq[i][1 + v_div + j])(isl_sioimath_sgn(*(bmap->eq[i][1 + v_div + j])) == 0)) | ||||
| 1052 | break; | ||||
| 1053 | if (i < bmap->n_eq) { | ||||
| 1054 | bmap = isl_basic_map_drop_div(bmap, j); | ||||
| 1055 | if (isl_basic_map_drop_equality(bmap, i) < 0) | ||||
| 1056 | goto error; | ||||
| 1057 | ++dropped; | ||||
| 1058 | } | ||||
| 1059 | } | ||||
| 1060 | pos[0] = 0; | ||||
| 1061 | needed = 0; | ||||
| 1062 | for (i = 1; i < T->n_row; ++i) { | ||||
| 1063 | if (isl_int_is_one(T->row[i][i])(isl_sioimath_cmp_si(*(T->row[i][i]), 1) == 0)) | ||||
| 1064 | pos[i] = i; | ||||
| 1065 | else | ||||
| 1066 | needed++; | ||||
| 1067 | } | ||||
| 1068 | if (needed > dropped) { | ||||
| 1069 | bmap = isl_basic_map_extend(bmap, needed, needed, 0); | ||||
| 1070 | if (!bmap) | ||||
| 1071 | goto error; | ||||
| 1072 | } | ||||
| 1073 | for (i = 1; i < T->n_row; ++i) { | ||||
| 1074 | if (isl_int_is_one(T->row[i][i])(isl_sioimath_cmp_si(*(T->row[i][i]), 1) == 0)) | ||||
| 1075 | continue; | ||||
| 1076 | k = isl_basic_map_alloc_div(bmap); | ||||
| 1077 | pos[i] = 1 + v_div + k; | ||||
| 1078 | isl_seq_clr(bmap->div[k] + 1, 1 + v_div + bmap->n_div); | ||||
| 1079 | isl_int_set(bmap->div[k][0], T->row[i][i])isl_sioimath_set((bmap->div[k][0]), *(T->row[i][i])); | ||||
| 1080 | if (C2) | ||||
| 1081 | isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + v_div); | ||||
| 1082 | else | ||||
| 1083 | isl_int_set_si(bmap->div[k][1 + i], 1)isl_sioimath_set_si((bmap->div[k][1 + i]), 1); | ||||
| 1084 | for (j = 0; j < i; ++j) { | ||||
| 1085 | if (isl_int_is_zero(T->row[i][j])(isl_sioimath_sgn(*(T->row[i][j])) == 0)) | ||||
| 1086 | continue; | ||||
| 1087 | if (pos[j] < T->n_row && C2) | ||||
| 1088 | isl_seq_submul(bmap->div[k] + 1, T->row[i][j], | ||||
| 1089 | C2->row[pos[j]], 1 + v_div); | ||||
| 1090 | else | ||||
| 1091 | isl_int_neg(bmap->div[k][1 + pos[j]],isl_sioimath_neg((bmap->div[k][1 + pos[j]]), *(T->row[i ][j])) | ||||
| 1092 | T->row[i][j])isl_sioimath_neg((bmap->div[k][1 + pos[j]]), *(T->row[i ][j])); | ||||
| 1093 | } | ||||
| 1094 | j = isl_basic_map_alloc_equality(bmap); | ||||
| 1095 | isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+v_div+bmap->n_div); | ||||
| 1096 | isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0])isl_sioimath_set((bmap->eq[j][pos[i]]), *(bmap->div[k][ 0])); | ||||
| 1097 | } | ||||
| 1098 | free(pos); | ||||
| 1099 | isl_mat_free(C2); | ||||
| 1100 | isl_mat_free(T); | ||||
| 1101 | |||||
| 1102 | if (progress) | ||||
| 1103 | *progress = 1; | ||||
| 1104 | done: | ||||
| 1105 | ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS)(((bmap)->flags) |= ((1 << 6))); | ||||
| 1106 | |||||
| 1107 | return bmap; | ||||
| 1108 | error: | ||||
| 1109 | free(pos); | ||||
| 1110 | isl_mat_free(C); | ||||
| 1111 | isl_mat_free(C2); | ||||
| 1112 | isl_mat_free(T); | ||||
| 1113 | isl_basic_map_free(bmap); | ||||
| 1114 | return NULL((void*)0); | ||||
| 1115 | } | ||||
| 1116 | |||||
| 1117 | static __isl_give isl_basic_map *set_div_from_lower_bound( | ||||
| 1118 | __isl_take isl_basic_map *bmap, int div, int ineq) | ||||
| 1119 | { | ||||
| 1120 | unsigned total = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 1121 | |||||
| 1122 | isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div); | ||||
| 1123 | isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div])isl_sioimath_set((bmap->div[div][0]), *(bmap->ineq[ineq ][total + div])); | ||||
| 1124 | isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0])isl_sioimath_add((bmap->div[div][1]), *(bmap->div[div][ 1]), *(bmap->div[div][0])); | ||||
| 1125 | isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1)isl_sioimath_sub_ui((bmap->div[div][1]), *(bmap->div[div ][1]), 1); | ||||
| 1126 | isl_int_set_si(bmap->div[div][1 + total + div], 0)isl_sioimath_set_si((bmap->div[div][1 + total + div]), 0); | ||||
| 1127 | |||||
| 1128 | return bmap; | ||||
| 1129 | } | ||||
| 1130 | |||||
| 1131 | /* Check whether it is ok to define a div based on an inequality. | ||||
| 1132 | * To avoid the introduction of circular definitions of divs, we | ||||
| 1133 | * do not allow such a definition if the resulting expression would refer to | ||||
| 1134 | * any other undefined divs or if any known div is defined in | ||||
| 1135 | * terms of the unknown div. | ||||
| 1136 | */ | ||||
| 1137 | static isl_bool ok_to_set_div_from_bound(__isl_keep isl_basic_map *bmap, | ||||
| 1138 | int div, int ineq) | ||||
| 1139 | { | ||||
| 1140 | int j; | ||||
| 1141 | unsigned total = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 1142 | |||||
| 1143 | /* Not defined in terms of unknown divs */ | ||||
| 1144 | for (j = 0; j < bmap->n_div; ++j) { | ||||
| 1145 | if (div == j) | ||||
| 1146 | continue; | ||||
| 1147 | if (isl_int_is_zero(bmap->ineq[ineq][total + j])(isl_sioimath_sgn(*(bmap->ineq[ineq][total + j])) == 0)) | ||||
| 1148 | continue; | ||||
| 1149 | if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0)) | ||||
| 1150 | return isl_bool_false; | ||||
| 1151 | } | ||||
| 1152 | |||||
| 1153 | /* No other div defined in terms of this one => avoid loops */ | ||||
| 1154 | for (j = 0; j < bmap->n_div; ++j) { | ||||
| 1155 | if (div == j) | ||||
| 1156 | continue; | ||||
| 1157 | if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0)) | ||||
| 1158 | continue; | ||||
| 1159 | if (!isl_int_is_zero(bmap->div[j][1 + total + div])(isl_sioimath_sgn(*(bmap->div[j][1 + total + div])) == 0)) | ||||
| 1160 | return isl_bool_false; | ||||
| 1161 | } | ||||
| 1162 | |||||
| 1163 | return isl_bool_true; | ||||
| 1164 | } | ||||
| 1165 | |||||
| 1166 | /* Would an expression for div "div" based on inequality "ineq" of "bmap" | ||||
| 1167 | * be a better expression than the current one? | ||||
| 1168 | * | ||||
| 1169 | * If we do not have any expression yet, then any expression would be better. | ||||
| 1170 | * Otherwise we check if the last variable involved in the inequality | ||||
| 1171 | * (disregarding the div that it would define) is in an earlier position | ||||
| 1172 | * than the last variable involved in the current div expression. | ||||
| 1173 | */ | ||||
| 1174 | static isl_bool better_div_constraint(__isl_keep isl_basic_map *bmap, | ||||
| 1175 | int div, int ineq) | ||||
| 1176 | { | ||||
| 1177 | unsigned total = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 1178 | int last_div; | ||||
| 1179 | int last_ineq; | ||||
| 1180 | |||||
| 1181 | if (isl_int_is_zero(bmap->div[div][0])(isl_sioimath_sgn(*(bmap->div[div][0])) == 0)) | ||||
| 1182 | return isl_bool_true; | ||||
| 1183 | |||||
| 1184 | if (isl_seq_last_non_zero(bmap->ineq[ineq] + total + div + 1, | ||||
| 1185 | bmap->n_div - (div + 1)) >= 0) | ||||
| 1186 | return isl_bool_false; | ||||
| 1187 | |||||
| 1188 | last_ineq = isl_seq_last_non_zero(bmap->ineq[ineq], total + div); | ||||
| 1189 | last_div = isl_seq_last_non_zero(bmap->div[div] + 1, | ||||
| 1190 | total + bmap->n_div); | ||||
| 1191 | |||||
| 1192 | return last_ineq < last_div; | ||||
| 1193 | } | ||||
| 1194 | |||||
| 1195 | /* Given two constraints "k" and "l" that are opposite to each other, | ||||
| 1196 | * except for the constant term, check if we can use them | ||||
| 1197 | * to obtain an expression for one of the hitherto unknown divs or | ||||
| 1198 | * a "better" expression for a div for which we already have an expression. | ||||
| 1199 | * "sum" is the sum of the constant terms of the constraints. | ||||
| 1200 | * If this sum is strictly smaller than the coefficient of one | ||||
| 1201 | * of the divs, then this pair can be used define the div. | ||||
| 1202 | * To avoid the introduction of circular definitions of divs, we | ||||
| 1203 | * do not use the pair if the resulting expression would refer to | ||||
| 1204 | * any other undefined divs or if any known div is defined in | ||||
| 1205 | * terms of the unknown div. | ||||
| 1206 | */ | ||||
| 1207 | static __isl_give isl_basic_map *check_for_div_constraints( | ||||
| 1208 | __isl_take isl_basic_map *bmap, int k, int l, isl_int sum, | ||||
| 1209 | int *progress) | ||||
| 1210 | { | ||||
| 1211 | int i; | ||||
| 1212 | unsigned total = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 1213 | |||||
| 1214 | for (i = 0; i < bmap->n_div; ++i) { | ||||
| 1215 | isl_bool set_div; | ||||
| 1216 | |||||
| 1217 | if (isl_int_is_zero(bmap->ineq[k][total + i])(isl_sioimath_sgn(*(bmap->ineq[k][total + i])) == 0)) | ||||
| 1218 | continue; | ||||
| 1219 | if (isl_int_abs_ge(sum, bmap->ineq[k][total + i])(isl_sioimath_abs_cmp(*(sum), *(bmap->ineq[k][total + i])) >= 0)) | ||||
| 1220 | continue; | ||||
| 1221 | set_div = better_div_constraint(bmap, i, k); | ||||
| 1222 | if (set_div >= 0 && set_div) | ||||
| 1223 | set_div = ok_to_set_div_from_bound(bmap, i, k); | ||||
| 1224 | if (set_div < 0) | ||||
| 1225 | return isl_basic_map_free(bmap); | ||||
| 1226 | if (!set_div) | ||||
| 1227 | break; | ||||
| 1228 | if (isl_int_is_pos(bmap->ineq[k][total + i])(isl_sioimath_sgn(*(bmap->ineq[k][total + i])) > 0)) | ||||
| 1229 | bmap = set_div_from_lower_bound(bmap, i, k); | ||||
| 1230 | else | ||||
| 1231 | bmap = set_div_from_lower_bound(bmap, i, l); | ||||
| 1232 | if (progress) | ||||
| 1233 | *progress = 1; | ||||
| 1234 | break; | ||||
| 1235 | } | ||||
| 1236 | return bmap; | ||||
| 1237 | } | ||||
| 1238 | |||||
| 1239 | __isl_give isl_basic_map *isl_basic_map_remove_duplicate_constraints( | ||||
| 1240 | __isl_take isl_basic_map *bmap, int *progress, int detect_divs) | ||||
| 1241 | { | ||||
| 1242 | struct isl_constraint_index ci; | ||||
| 1243 | int k, l, h; | ||||
| 1244 | isl_size total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 1245 | isl_int sum; | ||||
| 1246 | |||||
| 1247 | if (total < 0 || bmap->n_ineq <= 1) | ||||
| 1248 | return bmap; | ||||
| 1249 | |||||
| 1250 | if (create_constraint_index(&ci, bmap) < 0) | ||||
| 1251 | return bmap; | ||||
| 1252 | |||||
| 1253 | h = isl_seq_get_hash_bits(bmap->ineq[0] + 1, total, ci.bits); | ||||
| 1254 | ci.index[h] = &bmap->ineq[0]; | ||||
| 1255 | for (k = 1; k < bmap->n_ineq; ++k) { | ||||
| 1256 | h = hash_index(&ci, bmap, k); | ||||
| 1257 | if (!ci.index[h]) { | ||||
| 1258 | ci.index[h] = &bmap->ineq[k]; | ||||
| 1259 | continue; | ||||
| 1260 | } | ||||
| 1261 | if (progress) | ||||
| 1262 | *progress = 1; | ||||
| 1263 | l = ci.index[h] - &bmap->ineq[0]; | ||||
| 1264 | if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0])(isl_sioimath_cmp(*(bmap->ineq[k][0]), *(bmap->ineq[l][ 0])) < 0)) | ||||
| 1265 | swap_inequality(bmap, k, l); | ||||
| 1266 | isl_basic_map_drop_inequality(bmap, k); | ||||
| 1267 | --k; | ||||
| 1268 | } | ||||
| 1269 | isl_int_init(sum)isl_sioimath_init((sum)); | ||||
| 1270 | for (k = 0; bmap && k < bmap->n_ineq-1; ++k) { | ||||
| 1271 | isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total); | ||||
| 1272 | h = hash_index(&ci, bmap, k); | ||||
| 1273 | isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total); | ||||
| 1274 | if (!ci.index[h]) | ||||
| 1275 | continue; | ||||
| 1276 | l = ci.index[h] - &bmap->ineq[0]; | ||||
| 1277 | isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0])isl_sioimath_add((sum), *(bmap->ineq[k][0]), *(bmap->ineq [l][0])); | ||||
| 1278 | if (isl_int_is_pos(sum)(isl_sioimath_sgn(*(sum)) > 0)) { | ||||
| 1279 | if (detect_divs) | ||||
| 1280 | bmap = check_for_div_constraints(bmap, k, l, | ||||
| 1281 | sum, progress); | ||||
| 1282 | continue; | ||||
| 1283 | } | ||||
| 1284 | if (isl_int_is_zero(sum)(isl_sioimath_sgn(*(sum)) == 0)) { | ||||
| 1285 | /* We need to break out of the loop after these | ||||
| 1286 | * changes since the contents of the hash | ||||
| 1287 | * will no longer be valid. | ||||
| 1288 | * Plus, we probably we want to regauss first. | ||||
| 1289 | */ | ||||
| 1290 | if (progress) | ||||
| 1291 | *progress = 1; | ||||
| 1292 | isl_basic_map_drop_inequality(bmap, l); | ||||
| 1293 | isl_basic_map_inequality_to_equality(bmap, k); | ||||
| 1294 | } else | ||||
| 1295 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
| 1296 | break; | ||||
| 1297 | } | ||||
| 1298 | isl_int_clear(sum)isl_sioimath_clear((sum)); | ||||
| 1299 | |||||
| 1300 | constraint_index_free(&ci); | ||||
| 1301 | return bmap; | ||||
| 1302 | } | ||||
| 1303 | |||||
| 1304 | /* Detect all pairs of inequalities that form an equality. | ||||
| 1305 | * | ||||
| 1306 | * isl_basic_map_remove_duplicate_constraints detects at most one such pair. | ||||
| 1307 | * Call it repeatedly while it is making progress. | ||||
| 1308 | */ | ||||
| 1309 | __isl_give isl_basic_map *isl_basic_map_detect_inequality_pairs( | ||||
| 1310 | __isl_take isl_basic_map *bmap, int *progress) | ||||
| 1311 | { | ||||
| 1312 | int duplicate; | ||||
| 1313 | |||||
| 1314 | do { | ||||
| 1315 | duplicate = 0; | ||||
| 1316 | bmap = isl_basic_map_remove_duplicate_constraints(bmap, | ||||
| 1317 | &duplicate, 0); | ||||
| 1318 | if (progress && duplicate) | ||||
| 1319 | *progress = 1; | ||||
| 1320 | } while (duplicate); | ||||
| 1321 | |||||
| 1322 | return bmap; | ||||
| 1323 | } | ||||
| 1324 | |||||
| 1325 | /* Eliminate knowns divs from constraints where they appear with | ||||
| 1326 | * a (positive or negative) unit coefficient. | ||||
| 1327 | * | ||||
| 1328 | * That is, replace | ||||
| 1329 | * | ||||
| 1330 | * floor(e/m) + f >= 0 | ||||
| 1331 | * | ||||
| 1332 | * by | ||||
| 1333 | * | ||||
| 1334 | * e + m f >= 0 | ||||
| 1335 | * | ||||
| 1336 | * and | ||||
| 1337 | * | ||||
| 1338 | * -floor(e/m) + f >= 0 | ||||
| 1339 | * | ||||
| 1340 | * by | ||||
| 1341 | * | ||||
| 1342 | * -e + m f + m - 1 >= 0 | ||||
| 1343 | * | ||||
| 1344 | * The first conversion is valid because floor(e/m) >= -f is equivalent | ||||
| 1345 | * to e/m >= -f because -f is an integral expression. | ||||
| 1346 | * The second conversion follows from the fact that | ||||
| 1347 | * | ||||
| 1348 | * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m) | ||||
| 1349 | * | ||||
| 1350 | * | ||||
| 1351 | * Note that one of the div constraints may have been eliminated | ||||
| 1352 | * due to being redundant with respect to the constraint that is | ||||
| 1353 | * being modified by this function. The modified constraint may | ||||
| 1354 | * no longer imply this div constraint, so we add it back to make | ||||
| 1355 | * sure we do not lose any information. | ||||
| 1356 | * | ||||
| 1357 | * We skip integral divs, i.e., those with denominator 1, as we would | ||||
| 1358 | * risk eliminating the div from the div constraints. We do not need | ||||
| 1359 | * to handle those divs here anyway since the div constraints will turn | ||||
| 1360 | * out to form an equality and this equality can then be used to eliminate | ||||
| 1361 | * the div from all constraints. | ||||
| 1362 | */ | ||||
| 1363 | static __isl_give isl_basic_map *eliminate_unit_divs( | ||||
| 1364 | __isl_take isl_basic_map *bmap, int *progress) | ||||
| 1365 | { | ||||
| 1366 | int i, j; | ||||
| 1367 | isl_ctx *ctx; | ||||
| 1368 | unsigned total; | ||||
| 1369 | |||||
| 1370 | if (!bmap) | ||||
| 1371 | return NULL((void*)0); | ||||
| 1372 | |||||
| 1373 | ctx = isl_basic_map_get_ctx(bmap); | ||||
| 1374 | total = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 1375 | |||||
| 1376 | for (i = 0; i < bmap->n_div; ++i) { | ||||
| 1377 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
| 1378 | continue; | ||||
| 1379 | if (isl_int_is_one(bmap->div[i][0])(isl_sioimath_cmp_si(*(bmap->div[i][0]), 1) == 0)) | ||||
| 1380 | continue; | ||||
| 1381 | for (j = 0; j < bmap->n_ineq; ++j) { | ||||
| 1382 | int s; | ||||
| 1383 | |||||
| 1384 | if (!isl_int_is_one(bmap->ineq[j][total + i])(isl_sioimath_cmp_si(*(bmap->ineq[j][total + i]), 1) == 0) && | ||||
| 1385 | !isl_int_is_negone(bmap->ineq[j][total + i])(isl_sioimath_cmp_si(*(bmap->ineq[j][total + i]), -1) == 0 )) | ||||
| 1386 | continue; | ||||
| 1387 | |||||
| 1388 | *progress = 1; | ||||
| 1389 | |||||
| 1390 | s = isl_int_sgn(bmap->ineq[j][total + i])isl_sioimath_sgn(*(bmap->ineq[j][total + i])); | ||||
| 1391 | isl_int_set_si(bmap->ineq[j][total + i], 0)isl_sioimath_set_si((bmap->ineq[j][total + i]), 0); | ||||
| 1392 | if (s < 0) | ||||
| 1393 | isl_seq_combine(bmap->ineq[j], | ||||
| 1394 | ctx->negone, bmap->div[i] + 1, | ||||
| 1395 | bmap->div[i][0], bmap->ineq[j], | ||||
| 1396 | total + bmap->n_div); | ||||
| 1397 | else | ||||
| 1398 | isl_seq_combine(bmap->ineq[j], | ||||
| 1399 | ctx->one, bmap->div[i] + 1, | ||||
| 1400 | bmap->div[i][0], bmap->ineq[j], | ||||
| 1401 | total + bmap->n_div); | ||||
| 1402 | if (s < 0) { | ||||
| 1403 | isl_int_add(bmap->ineq[j][0],isl_sioimath_add((bmap->ineq[j][0]), *(bmap->ineq[j][0] ), *(bmap->div[i][0])) | ||||
| 1404 | bmap->ineq[j][0], bmap->div[i][0])isl_sioimath_add((bmap->ineq[j][0]), *(bmap->ineq[j][0] ), *(bmap->div[i][0])); | ||||
| 1405 | isl_int_sub_ui(bmap->ineq[j][0],isl_sioimath_sub_ui((bmap->ineq[j][0]), *(bmap->ineq[j] [0]), 1) | ||||
| 1406 | bmap->ineq[j][0], 1)isl_sioimath_sub_ui((bmap->ineq[j][0]), *(bmap->ineq[j] [0]), 1); | ||||
| 1407 | } | ||||
| 1408 | |||||
| 1409 | bmap = isl_basic_map_extend_constraints(bmap, 0, 1); | ||||
| 1410 | bmap = isl_basic_map_add_div_constraint(bmap, i, s); | ||||
| 1411 | if (!bmap) | ||||
| 1412 | return NULL((void*)0); | ||||
| 1413 | } | ||||
| 1414 | } | ||||
| 1415 | |||||
| 1416 | return bmap; | ||||
| 1417 | } | ||||
| 1418 | |||||
| 1419 | __isl_give isl_basic_map *isl_basic_map_simplify(__isl_take isl_basic_map *bmap) | ||||
| 1420 | { | ||||
| 1421 | int progress = 1; | ||||
| 1422 | if (!bmap) | ||||
| 1423 | return NULL((void*)0); | ||||
| 1424 | while (progress) { | ||||
| 1425 | isl_bool empty; | ||||
| 1426 | |||||
| 1427 | progress = 0; | ||||
| 1428 | empty = isl_basic_map_plain_is_empty(bmap); | ||||
| 1429 | if (empty < 0) | ||||
| 1430 | return isl_basic_map_free(bmap); | ||||
| 1431 | if (empty) | ||||
| 1432 | break; | ||||
| 1433 | bmap = isl_basic_map_normalize_constraints(bmap); | ||||
| 1434 | bmap = reduce_div_coefficients(bmap); | ||||
| 1435 | bmap = normalize_div_expressions(bmap); | ||||
| 1436 | bmap = remove_duplicate_divs(bmap, &progress); | ||||
| 1437 | bmap = eliminate_unit_divs(bmap, &progress); | ||||
| 1438 | bmap = eliminate_divs_eq(bmap, &progress); | ||||
| 1439 | bmap = eliminate_divs_ineq(bmap, &progress); | ||||
| 1440 | bmap = isl_basic_map_gauss(bmap, &progress); | ||||
| 1441 | /* requires equalities in normal form */ | ||||
| 1442 | bmap = normalize_divs(bmap, &progress); | ||||
| 1443 | bmap = isl_basic_map_remove_duplicate_constraints(bmap, | ||||
| 1444 | &progress, 1); | ||||
| 1445 | if (bmap && progress) | ||||
| 1446 | ISL_F_CLR(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(((bmap)->flags) &= ~((1 << 8))); | ||||
| 1447 | } | ||||
| 1448 | return bmap; | ||||
| 1449 | } | ||||
| 1450 | |||||
| 1451 | struct isl_basic_setisl_basic_map *isl_basic_set_simplify(struct isl_basic_setisl_basic_map *bset) | ||||
| 1452 | { | ||||
| 1453 | return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset))); | ||||
| 1454 | } | ||||
| 1455 | |||||
| 1456 | |||||
| 1457 | isl_bool isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap, | ||||
| 1458 | isl_int *constraint, unsigned div) | ||||
| 1459 | { | ||||
| 1460 | unsigned pos; | ||||
| 1461 | |||||
| 1462 | if (!bmap) | ||||
| 1463 | return isl_bool_error; | ||||
| 1464 | |||||
| 1465 | pos = isl_basic_map_offset(bmap, isl_dim_div) + div; | ||||
| 1466 | |||||
| 1467 | if (isl_int_eq(constraint[pos], bmap->div[div][0])(isl_sioimath_cmp(*(constraint[pos]), *(bmap->div[div][0]) ) == 0)) { | ||||
| 1468 | int neg; | ||||
| 1469 | isl_int_sub(bmap->div[div][1],isl_sioimath_sub((bmap->div[div][1]), *(bmap->div[div][ 1]), *(bmap->div[div][0])) | ||||
| 1470 | bmap->div[div][1], bmap->div[div][0])isl_sioimath_sub((bmap->div[div][1]), *(bmap->div[div][ 1]), *(bmap->div[div][0])); | ||||
| 1471 | isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1)isl_sioimath_add_ui((bmap->div[div][1]), *(bmap->div[div ][1]), 1); | ||||
| 1472 | neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos); | ||||
| 1473 | isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1)isl_sioimath_sub_ui((bmap->div[div][1]), *(bmap->div[div ][1]), 1); | ||||
| 1474 | isl_int_add(bmap->div[div][1],isl_sioimath_add((bmap->div[div][1]), *(bmap->div[div][ 1]), *(bmap->div[div][0])) | ||||
| 1475 | bmap->div[div][1], bmap->div[div][0])isl_sioimath_add((bmap->div[div][1]), *(bmap->div[div][ 1]), *(bmap->div[div][0])); | ||||
| 1476 | if (!neg) | ||||
| 1477 | return isl_bool_false; | ||||
| 1478 | if (isl_seq_first_non_zero(constraint+pos+1, | ||||
| 1479 | bmap->n_div-div-1) != -1) | ||||
| 1480 | return isl_bool_false; | ||||
| 1481 | } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])(isl_sioimath_abs_cmp(*(constraint[pos]), *(bmap->div[div] [0])) == 0)) { | ||||
| 1482 | if (!isl_seq_eq(constraint, bmap->div[div]+1, pos)) | ||||
| 1483 | return isl_bool_false; | ||||
| 1484 | if (isl_seq_first_non_zero(constraint+pos+1, | ||||
| 1485 | bmap->n_div-div-1) != -1) | ||||
| 1486 | return isl_bool_false; | ||||
| 1487 | } else | ||||
| 1488 | return isl_bool_false; | ||||
| 1489 | |||||
| 1490 | return isl_bool_true; | ||||
| 1491 | } | ||||
| 1492 | |||||
| 1493 | isl_bool isl_basic_set_is_div_constraint(__isl_keep isl_basic_setisl_basic_map *bset, | ||||
| 1494 | isl_int *constraint, unsigned div) | ||||
| 1495 | { | ||||
| 1496 | return isl_basic_map_is_div_constraint(bset, constraint, div); | ||||
| 1497 | } | ||||
| 1498 | |||||
| 1499 | |||||
| 1500 | /* If the only constraints a div d=floor(f/m) | ||||
| 1501 | * appears in are its two defining constraints | ||||
| 1502 | * | ||||
| 1503 | * f - m d >=0 | ||||
| 1504 | * -(f - (m - 1)) + m d >= 0 | ||||
| 1505 | * | ||||
| 1506 | * then it can safely be removed. | ||||
| 1507 | */ | ||||
| 1508 | static isl_bool div_is_redundant(__isl_keep isl_basic_map *bmap, int div) | ||||
| 1509 | { | ||||
| 1510 | int i; | ||||
| 1511 | isl_size v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 1512 | unsigned pos = 1 + v_div + div; | ||||
| 1513 | |||||
| 1514 | if (v_div < 0) | ||||
| 1515 | return isl_bool_error; | ||||
| 1516 | |||||
| 1517 | for (i = 0; i < bmap->n_eq; ++i) | ||||
| 1518 | if (!isl_int_is_zero(bmap->eq[i][pos])(isl_sioimath_sgn(*(bmap->eq[i][pos])) == 0)) | ||||
| 1519 | return isl_bool_false; | ||||
| 1520 | |||||
| 1521 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
| 1522 | isl_bool red; | ||||
| 1523 | |||||
| 1524 | if (isl_int_is_zero(bmap->ineq[i][pos])(isl_sioimath_sgn(*(bmap->ineq[i][pos])) == 0)) | ||||
| 1525 | continue; | ||||
| 1526 | red = isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div); | ||||
| 1527 | if (red < 0 || !red) | ||||
| 1528 | return red; | ||||
| 1529 | } | ||||
| 1530 | |||||
| 1531 | for (i = 0; i < bmap->n_div; ++i) { | ||||
| 1532 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
| 1533 | continue; | ||||
| 1534 | if (!isl_int_is_zero(bmap->div[i][1+pos])(isl_sioimath_sgn(*(bmap->div[i][1+pos])) == 0)) | ||||
| 1535 | return isl_bool_false; | ||||
| 1536 | } | ||||
| 1537 | |||||
| 1538 | return isl_bool_true; | ||||
| 1539 | } | ||||
| 1540 | |||||
| 1541 | /* | ||||
| 1542 | * Remove divs that don't occur in any of the constraints or other divs. | ||||
| 1543 | * These can arise when dropping constraints from a basic map or | ||||
| 1544 | * when the divs of a basic map have been temporarily aligned | ||||
| 1545 | * with the divs of another basic map. | ||||
| 1546 | */ | ||||
| 1547 | static __isl_give isl_basic_map *remove_redundant_divs( | ||||
| 1548 | __isl_take isl_basic_map *bmap) | ||||
| 1549 | { | ||||
| 1550 | int i; | ||||
| 1551 | isl_size v_div; | ||||
| 1552 | |||||
| 1553 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 1554 | if (v_div < 0) | ||||
| 1555 | return isl_basic_map_free(bmap); | ||||
| 1556 | |||||
| 1557 | for (i = bmap->n_div-1; i >= 0; --i) { | ||||
| 1558 | isl_bool redundant; | ||||
| 1559 | |||||
| 1560 | redundant = div_is_redundant(bmap, i); | ||||
| 1561 | if (redundant < 0) | ||||
| 1562 | return isl_basic_map_free(bmap); | ||||
| 1563 | if (!redundant) | ||||
| 1564 | continue; | ||||
| 1565 | bmap = isl_basic_map_drop_constraints_involving(bmap, | ||||
| 1566 | v_div + i, 1); | ||||
| 1567 | bmap = isl_basic_map_drop_div(bmap, i); | ||||
| 1568 | } | ||||
| 1569 | return bmap; | ||||
| 1570 | } | ||||
| 1571 | |||||
| 1572 | /* Mark "bmap" as final, without checking for obviously redundant | ||||
| 1573 | * integer divisions. This function should be used when "bmap" | ||||
| 1574 | * is known not to involve any such integer divisions. | ||||
| 1575 | */ | ||||
| 1576 | __isl_give isl_basic_map *isl_basic_map_mark_final( | ||||
| 1577 | __isl_take isl_basic_map *bmap) | ||||
| 1578 | { | ||||
| 1579 | if (!bmap) | ||||
| 1580 | return NULL((void*)0); | ||||
| 1581 | ISL_F_SET(bmap, ISL_BASIC_SET_FINAL)(((bmap)->flags) |= ((1 << 0))); | ||||
| 1582 | return bmap; | ||||
| 1583 | } | ||||
| 1584 | |||||
| 1585 | /* Mark "bmap" as final, after removing obviously redundant integer divisions. | ||||
| 1586 | */ | ||||
| 1587 | __isl_give isl_basic_map *isl_basic_map_finalize(__isl_take isl_basic_map *bmap) | ||||
| 1588 | { | ||||
| 1589 | bmap = remove_redundant_divs(bmap); | ||||
| 1590 | bmap = isl_basic_map_mark_final(bmap); | ||||
| 1591 | return bmap; | ||||
| 1592 | } | ||||
| 1593 | |||||
| 1594 | struct isl_basic_setisl_basic_map *isl_basic_set_finalize(struct isl_basic_setisl_basic_map *bset) | ||||
| 1595 | { | ||||
| 1596 | return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset))); | ||||
| 1597 | } | ||||
| 1598 | |||||
| 1599 | /* Remove definition of any div that is defined in terms of the given variable. | ||||
| 1600 | * The div itself is not removed. Functions such as | ||||
| 1601 | * eliminate_divs_ineq depend on the other divs remaining in place. | ||||
| 1602 | */ | ||||
| 1603 | static __isl_give isl_basic_map *remove_dependent_vars( | ||||
| 1604 | __isl_take isl_basic_map *bmap, int pos) | ||||
| 1605 | { | ||||
| 1606 | int i; | ||||
| 1607 | |||||
| 1608 | if (!bmap) | ||||
| 1609 | return NULL((void*)0); | ||||
| 1610 | |||||
| 1611 | for (i = 0; i < bmap->n_div; ++i) { | ||||
| 1612 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
| 1613 | continue; | ||||
| 1614 | if (isl_int_is_zero(bmap->div[i][1+1+pos])(isl_sioimath_sgn(*(bmap->div[i][1+1+pos])) == 0)) | ||||
| 1615 | continue; | ||||
| 1616 | bmap = isl_basic_map_mark_div_unknown(bmap, i); | ||||
| 1617 | if (!bmap) | ||||
| 1618 | return NULL((void*)0); | ||||
| 1619 | } | ||||
| 1620 | return bmap; | ||||
| 1621 | } | ||||
| 1622 | |||||
| 1623 | /* Eliminate the specified variables from the constraints using | ||||
| 1624 | * Fourier-Motzkin. The variables themselves are not removed. | ||||
| 1625 | */ | ||||
| 1626 | __isl_give isl_basic_map *isl_basic_map_eliminate_vars( | ||||
| 1627 | __isl_take isl_basic_map *bmap, unsigned pos, unsigned n) | ||||
| 1628 | { | ||||
| 1629 | int d; | ||||
| 1630 | int i, j, k; | ||||
| 1631 | isl_size total; | ||||
| 1632 | int need_gauss = 0; | ||||
| 1633 | |||||
| 1634 | if (n == 0) | ||||
| 1635 | return bmap; | ||||
| 1636 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 1637 | if (total < 0) | ||||
| 1638 | return isl_basic_map_free(bmap); | ||||
| 1639 | |||||
| 1640 | bmap = isl_basic_map_cow(bmap); | ||||
| 1641 | for (d = pos + n - 1; d >= 0 && d >= pos; --d) | ||||
| 1642 | bmap = remove_dependent_vars(bmap, d); | ||||
| 1643 | if (!bmap) | ||||
| 1644 | return NULL((void*)0); | ||||
| 1645 | |||||
| 1646 | for (d = pos + n - 1; | ||||
| 1647 | d >= 0 && d >= total - bmap->n_div && d >= pos; --d) | ||||
| 1648 | isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total); | ||||
| 1649 | for (d = pos + n - 1; d >= 0 && d >= pos; --d) { | ||||
| 1650 | int n_lower, n_upper; | ||||
| 1651 | if (!bmap) | ||||
| 1652 | return NULL((void*)0); | ||||
| 1653 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
| 1654 | if (isl_int_is_zero(bmap->eq[i][1+d])(isl_sioimath_sgn(*(bmap->eq[i][1+d])) == 0)) | ||||
| 1655 | continue; | ||||
| 1656 | bmap = eliminate_var_using_equality(bmap, d, | ||||
| 1657 | bmap->eq[i], 0, NULL((void*)0)); | ||||
| 1658 | if (isl_basic_map_drop_equality(bmap, i) < 0) | ||||
| 1659 | return isl_basic_map_free(bmap); | ||||
| 1660 | need_gauss = 1; | ||||
| 1661 | break; | ||||
| 1662 | } | ||||
| 1663 | if (i < bmap->n_eq) | ||||
| 1664 | continue; | ||||
| 1665 | n_lower = 0; | ||||
| 1666 | n_upper = 0; | ||||
| 1667 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
| 1668 | if (isl_int_is_pos(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) > 0)) | ||||
| 1669 | n_lower++; | ||||
| 1670 | else if (isl_int_is_neg(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) < 0)) | ||||
| 1671 | n_upper++; | ||||
| 1672 | } | ||||
| 1673 | bmap = isl_basic_map_extend_constraints(bmap, | ||||
| 1674 | 0, n_lower * n_upper); | ||||
| 1675 | if (!bmap) | ||||
| 1676 | goto error; | ||||
| 1677 | for (i = bmap->n_ineq - 1; i >= 0; --i) { | ||||
| 1678 | int last; | ||||
| 1679 | if (isl_int_is_zero(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) == 0)) | ||||
| 1680 | continue; | ||||
| 1681 | last = -1; | ||||
| 1682 | for (j = 0; j < i; ++j) { | ||||
| 1683 | if (isl_int_is_zero(bmap->ineq[j][1+d])(isl_sioimath_sgn(*(bmap->ineq[j][1+d])) == 0)) | ||||
| 1684 | continue; | ||||
| 1685 | last = j; | ||||
| 1686 | if (isl_int_sgn(bmap->ineq[i][1+d])isl_sioimath_sgn(*(bmap->ineq[i][1+d])) == | ||||
| 1687 | isl_int_sgn(bmap->ineq[j][1+d])isl_sioimath_sgn(*(bmap->ineq[j][1+d]))) | ||||
| 1688 | continue; | ||||
| 1689 | k = isl_basic_map_alloc_inequality(bmap); | ||||
| 1690 | if (k < 0) | ||||
| 1691 | goto error; | ||||
| 1692 | isl_seq_cpy(bmap->ineq[k], bmap->ineq[i], | ||||
| 1693 | 1+total); | ||||
| 1694 | isl_seq_elim(bmap->ineq[k], bmap->ineq[j], | ||||
| 1695 | 1+d, 1+total, NULL((void*)0)); | ||||
| 1696 | } | ||||
| 1697 | isl_basic_map_drop_inequality(bmap, i); | ||||
| 1698 | i = last + 1; | ||||
| 1699 | } | ||||
| 1700 | if (n_lower > 0 && n_upper > 0) { | ||||
| 1701 | bmap = isl_basic_map_normalize_constraints(bmap); | ||||
| 1702 | bmap = isl_basic_map_remove_duplicate_constraints(bmap, | ||||
| 1703 | NULL((void*)0), 0); | ||||
| 1704 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
| 1705 | bmap = isl_basic_map_remove_redundancies(bmap); | ||||
| 1706 | need_gauss = 0; | ||||
| 1707 | if (!bmap) | ||||
| 1708 | goto error; | ||||
| 1709 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1))))) | ||||
| 1710 | break; | ||||
| 1711 | } | ||||
| 1712 | } | ||||
| 1713 | if (need_gauss) | ||||
| 1714 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
| 1715 | return bmap; | ||||
| 1716 | error: | ||||
| 1717 | isl_basic_map_free(bmap); | ||||
| 1718 | return NULL((void*)0); | ||||
| 1719 | } | ||||
| 1720 | |||||
| 1721 | struct isl_basic_setisl_basic_map *isl_basic_set_eliminate_vars( | ||||
| 1722 | struct isl_basic_setisl_basic_map *bset, unsigned pos, unsigned n) | ||||
| 1723 | { | ||||
| 1724 | return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset), | ||||
| 1725 | pos, n)); | ||||
| 1726 | } | ||||
| 1727 | |||||
| 1728 | /* Eliminate the specified n dimensions starting at first from the | ||||
| 1729 | * constraints, without removing the dimensions from the space. | ||||
| 1730 | * If the set is rational, the dimensions are eliminated using Fourier-Motzkin. | ||||
| 1731 | * Otherwise, they are projected out and the original space is restored. | ||||
| 1732 | */ | ||||
| 1733 | __isl_give isl_basic_map *isl_basic_map_eliminate( | ||||
| 1734 | __isl_take isl_basic_map *bmap, | ||||
| 1735 | enum isl_dim_type type, unsigned first, unsigned n) | ||||
| 1736 | { | ||||
| 1737 | isl_space *space; | ||||
| 1738 | |||||
| 1739 | if (!bmap) | ||||
| 1740 | return NULL((void*)0); | ||||
| 1741 | if (n == 0) | ||||
| 1742 | return bmap; | ||||
| 1743 | |||||
| 1744 | if (isl_basic_map_check_range(bmap, type, first, n) < 0) | ||||
| 1745 | return isl_basic_map_free(bmap); | ||||
| 1746 | |||||
| 1747 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4))))) { | ||||
| 1748 | first += isl_basic_map_offset(bmap, type) - 1; | ||||
| 1749 | bmap = isl_basic_map_eliminate_vars(bmap, first, n); | ||||
| 1750 | return isl_basic_map_finalize(bmap); | ||||
| 1751 | } | ||||
| 1752 | |||||
| 1753 | space = isl_basic_map_get_space(bmap); | ||||
| 1754 | bmap = isl_basic_map_project_out(bmap, type, first, n); | ||||
| 1755 | bmap = isl_basic_map_insert_dims(bmap, type, first, n); | ||||
| 1756 | bmap = isl_basic_map_reset_space(bmap, space); | ||||
| 1757 | return bmap; | ||||
| 1758 | } | ||||
| 1759 | |||||
| 1760 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_eliminate( | ||||
| 1761 | __isl_take isl_basic_setisl_basic_map *bset, | ||||
| 1762 | enum isl_dim_type type, unsigned first, unsigned n) | ||||
| 1763 | { | ||||
| 1764 | return isl_basic_map_eliminate(bset, type, first, n); | ||||
| 1765 | } | ||||
| 1766 | |||||
| 1767 | /* Remove all constraints from "bmap" that reference any unknown local | ||||
| 1768 | * variables (directly or indirectly). | ||||
| 1769 | * | ||||
| 1770 | * Dropping all constraints on a local variable will make it redundant, | ||||
| 1771 | * so it will get removed implicitly by | ||||
| 1772 | * isl_basic_map_drop_constraints_involving_dims. Some other local | ||||
| 1773 | * variables may also end up becoming redundant if they only appear | ||||
| 1774 | * in constraints together with the unknown local variable. | ||||
| 1775 | * Therefore, start over after calling | ||||
| 1776 | * isl_basic_map_drop_constraints_involving_dims. | ||||
| 1777 | */ | ||||
| 1778 | __isl_give isl_basic_map *isl_basic_map_drop_constraint_involving_unknown_divs( | ||||
| 1779 | __isl_take isl_basic_map *bmap) | ||||
| 1780 | { | ||||
| 1781 | isl_bool known; | ||||
| 1782 | isl_size n_div; | ||||
| 1783 | int i, o_div; | ||||
| 1784 | |||||
| 1785 | known = isl_basic_map_divs_known(bmap); | ||||
| 1786 | if (known < 0) | ||||
| 1787 | return isl_basic_map_free(bmap); | ||||
| 1788 | if (known) | ||||
| 1789 | return bmap; | ||||
| 1790 | |||||
| 1791 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 1792 | if (n_div < 0) | ||||
| 1793 | return isl_basic_map_free(bmap); | ||||
| 1794 | o_div = isl_basic_map_offset(bmap, isl_dim_div) - 1; | ||||
| 1795 | |||||
| 1796 | for (i = 0; i < n_div; ++i) { | ||||
| 1797 | known = isl_basic_map_div_is_known(bmap, i); | ||||
| 1798 | if (known < 0) | ||||
| 1799 | return isl_basic_map_free(bmap); | ||||
| 1800 | if (known) | ||||
| 1801 | continue; | ||||
| 1802 | bmap = remove_dependent_vars(bmap, o_div + i); | ||||
| 1803 | bmap = isl_basic_map_drop_constraints_involving_dims(bmap, | ||||
| 1804 | isl_dim_div, i, 1); | ||||
| 1805 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 1806 | if (n_div < 0) | ||||
| 1807 | return isl_basic_map_free(bmap); | ||||
| 1808 | i = -1; | ||||
| 1809 | } | ||||
| 1810 | |||||
| 1811 | return bmap; | ||||
| 1812 | } | ||||
| 1813 | |||||
| 1814 | /* Remove all constraints from "map" that reference any unknown local | ||||
| 1815 | * variables (directly or indirectly). | ||||
| 1816 | * | ||||
| 1817 | * Since constraints may get dropped from the basic maps, | ||||
| 1818 | * they may no longer be disjoint from each other. | ||||
| 1819 | */ | ||||
| 1820 | __isl_give isl_map *isl_map_drop_constraint_involving_unknown_divs( | ||||
| 1821 | __isl_take isl_map *map) | ||||
| 1822 | { | ||||
| 1823 | int i; | ||||
| 1824 | isl_bool known; | ||||
| 1825 | |||||
| 1826 | known = isl_map_divs_known(map); | ||||
| 1827 | if (known < 0) | ||||
| 1828 | return isl_map_free(map); | ||||
| 1829 | if (known) | ||||
| 1830 | return map; | ||||
| 1831 | |||||
| 1832 | map = isl_map_cow(map); | ||||
| 1833 | if (!map) | ||||
| 1834 | return NULL((void*)0); | ||||
| 1835 | |||||
| 1836 | for (i = 0; i < map->n; ++i) { | ||||
| 1837 | map->p[i] = | ||||
| 1838 | isl_basic_map_drop_constraint_involving_unknown_divs( | ||||
| 1839 | map->p[i]); | ||||
| 1840 | if (!map->p[i]) | ||||
| 1841 | return isl_map_free(map); | ||||
| 1842 | } | ||||
| 1843 | |||||
| 1844 | if (map->n > 1) | ||||
| 1845 | ISL_F_CLR(map, ISL_MAP_DISJOINT)(((map)->flags) &= ~((1 << 0))); | ||||
| 1846 | |||||
| 1847 | return map; | ||||
| 1848 | } | ||||
| 1849 | |||||
| 1850 | /* Don't assume equalities are in order, because align_divs | ||||
| 1851 | * may have changed the order of the divs. | ||||
| 1852 | */ | ||||
| 1853 | static void compute_elimination_index(__isl_keep isl_basic_map *bmap, int *elim) | ||||
| 1854 | { | ||||
| 1855 | int d, i; | ||||
| 1856 | unsigned total; | ||||
| 1857 | |||||
| 1858 | total = isl_space_dim(bmap->dim, isl_dim_all); | ||||
| 1859 | for (d = 0; d < total; ++d) | ||||
| 1860 | elim[d] = -1; | ||||
| 1861 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
| 1862 | for (d = total - 1; d >= 0; --d) { | ||||
| 1863 | if (isl_int_is_zero(bmap->eq[i][1+d])(isl_sioimath_sgn(*(bmap->eq[i][1+d])) == 0)) | ||||
| 1864 | continue; | ||||
| 1865 | elim[d] = i; | ||||
| 1866 | break; | ||||
| 1867 | } | ||||
| 1868 | } | ||||
| 1869 | } | ||||
| 1870 | |||||
| 1871 | static void set_compute_elimination_index(__isl_keep isl_basic_setisl_basic_map *bset, | ||||
| 1872 | int *elim) | ||||
| 1873 | { | ||||
| 1874 | compute_elimination_index(bset_to_bmap(bset), elim); | ||||
| 1875 | } | ||||
| 1876 | |||||
| 1877 | static int reduced_using_equalities(isl_int *dst, isl_int *src, | ||||
| 1878 | __isl_keep isl_basic_map *bmap, int *elim) | ||||
| 1879 | { | ||||
| 1880 | int d; | ||||
| 1881 | int copied = 0; | ||||
| 1882 | unsigned total; | ||||
| 1883 | |||||
| 1884 | total = isl_space_dim(bmap->dim, isl_dim_all); | ||||
| 1885 | for (d = total - 1; d >= 0; --d) { | ||||
| 1886 | if (isl_int_is_zero(src[1+d])(isl_sioimath_sgn(*(src[1+d])) == 0)) | ||||
| 1887 | continue; | ||||
| 1888 | if (elim[d] == -1) | ||||
| 1889 | continue; | ||||
| 1890 | if (!copied) { | ||||
| 1891 | isl_seq_cpy(dst, src, 1 + total); | ||||
| 1892 | copied = 1; | ||||
| 1893 | } | ||||
| 1894 | isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL((void*)0)); | ||||
| 1895 | } | ||||
| 1896 | return copied; | ||||
| 1897 | } | ||||
| 1898 | |||||
| 1899 | static int set_reduced_using_equalities(isl_int *dst, isl_int *src, | ||||
| 1900 | __isl_keep isl_basic_setisl_basic_map *bset, int *elim) | ||||
| 1901 | { | ||||
| 1902 | return reduced_using_equalities(dst, src, | ||||
| 1903 | bset_to_bmap(bset), elim); | ||||
| 1904 | } | ||||
| 1905 | |||||
| 1906 | static __isl_give isl_basic_setisl_basic_map *isl_basic_set_reduce_using_equalities( | ||||
| 1907 | __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context) | ||||
| 1908 | { | ||||
| 1909 | int i; | ||||
| 1910 | int *elim; | ||||
| 1911 | isl_size dim; | ||||
| 1912 | |||||
| 1913 | if (!bset || !context) | ||||
| 1914 | goto error; | ||||
| 1915 | |||||
| 1916 | if (context->n_eq == 0) { | ||||
| 1917 | isl_basic_set_free(context); | ||||
| 1918 | return bset; | ||||
| 1919 | } | ||||
| 1920 | |||||
| 1921 | bset = isl_basic_set_cow(bset); | ||||
| 1922 | dim = isl_basic_set_dim(bset, isl_dim_set); | ||||
| 1923 | if (dim < 0) | ||||
| 1924 | goto error; | ||||
| 1925 | |||||
| 1926 | elim = isl_alloc_array(bset->ctx, int, dim)((int *)isl_malloc_or_die(bset->ctx, (dim)*sizeof(int))); | ||||
| 1927 | if (!elim) | ||||
| 1928 | goto error; | ||||
| 1929 | set_compute_elimination_index(context, elim); | ||||
| 1930 | for (i = 0; i < bset->n_eq; ++i) | ||||
| 1931 | set_reduced_using_equalities(bset->eq[i], bset->eq[i], | ||||
| 1932 | context, elim); | ||||
| 1933 | for (i = 0; i < bset->n_ineq; ++i) | ||||
| 1934 | set_reduced_using_equalities(bset->ineq[i], bset->ineq[i], | ||||
| 1935 | context, elim); | ||||
| 1936 | isl_basic_set_free(context); | ||||
| 1937 | free(elim); | ||||
| 1938 | bset = isl_basic_set_simplify(bset); | ||||
| 1939 | bset = isl_basic_set_finalize(bset); | ||||
| 1940 | return bset; | ||||
| 1941 | error: | ||||
| 1942 | isl_basic_set_free(bset); | ||||
| 1943 | isl_basic_set_free(context); | ||||
| 1944 | return NULL((void*)0); | ||||
| 1945 | } | ||||
| 1946 | |||||
| 1947 | /* For each inequality in "ineq" that is a shifted (more relaxed) | ||||
| 1948 | * copy of an inequality in "context", mark the corresponding entry | ||||
| 1949 | * in "row" with -1. | ||||
| 1950 | * If an inequality only has a non-negative constant term, then | ||||
| 1951 | * mark it as well. | ||||
| 1952 | */ | ||||
| 1953 | static isl_stat mark_shifted_constraints(__isl_keep isl_mat *ineq, | ||||
| 1954 | __isl_keep isl_basic_setisl_basic_map *context, int *row) | ||||
| 1955 | { | ||||
| 1956 | struct isl_constraint_index ci; | ||||
| 1957 | isl_size n_ineq, cols; | ||||
| 1958 | unsigned total; | ||||
| 1959 | int k; | ||||
| 1960 | |||||
| 1961 | if (!ineq || !context) | ||||
| 1962 | return isl_stat_error; | ||||
| 1963 | if (context->n_ineq == 0) | ||||
| 1964 | return isl_stat_ok; | ||||
| 1965 | if (setup_constraint_index(&ci, context) < 0) | ||||
| 1966 | return isl_stat_error; | ||||
| 1967 | |||||
| 1968 | n_ineq = isl_mat_rows(ineq); | ||||
| 1969 | cols = isl_mat_cols(ineq); | ||||
| 1970 | if (n_ineq < 0 || cols < 0) | ||||
| 1971 | return isl_stat_error; | ||||
| 1972 | total = cols - 1; | ||||
| 1973 | for (k = 0; k < n_ineq; ++k) { | ||||
| 1974 | int l; | ||||
| 1975 | isl_bool redundant; | ||||
| 1976 | |||||
| 1977 | l = isl_seq_first_non_zero(ineq->row[k] + 1, total); | ||||
| 1978 | if (l < 0 && isl_int_is_nonneg(ineq->row[k][0])(isl_sioimath_sgn(*(ineq->row[k][0])) >= 0)) { | ||||
| 1979 | row[k] = -1; | ||||
| 1980 | continue; | ||||
| 1981 | } | ||||
| 1982 | redundant = constraint_index_is_redundant(&ci, ineq->row[k]); | ||||
| 1983 | if (redundant < 0) | ||||
| 1984 | goto error; | ||||
| 1985 | if (!redundant) | ||||
| 1986 | continue; | ||||
| 1987 | row[k] = -1; | ||||
| 1988 | } | ||||
| 1989 | constraint_index_free(&ci); | ||||
| 1990 | return isl_stat_ok; | ||||
| 1991 | error: | ||||
| 1992 | constraint_index_free(&ci); | ||||
| 1993 | return isl_stat_error; | ||||
| 1994 | } | ||||
| 1995 | |||||
| 1996 | static __isl_give isl_basic_setisl_basic_map *remove_shifted_constraints( | ||||
| 1997 | __isl_take isl_basic_setisl_basic_map *bset, __isl_keep isl_basic_setisl_basic_map *context) | ||||
| 1998 | { | ||||
| 1999 | struct isl_constraint_index ci; | ||||
| 2000 | int k; | ||||
| 2001 | |||||
| 2002 | if (!bset || !context) | ||||
| 2003 | return bset; | ||||
| 2004 | |||||
| 2005 | if (context->n_ineq == 0) | ||||
| 2006 | return bset; | ||||
| 2007 | if (setup_constraint_index(&ci, context) < 0) | ||||
| 2008 | return bset; | ||||
| 2009 | |||||
| 2010 | for (k = 0; k < bset->n_ineq; ++k) { | ||||
| 2011 | isl_bool redundant; | ||||
| 2012 | |||||
| 2013 | redundant = constraint_index_is_redundant(&ci, bset->ineq[k]); | ||||
| 2014 | if (redundant < 0) | ||||
| 2015 | goto error; | ||||
| 2016 | if (!redundant) | ||||
| 2017 | continue; | ||||
| 2018 | bset = isl_basic_set_cow(bset); | ||||
| 2019 | if (!bset) | ||||
| 2020 | goto error; | ||||
| 2021 | isl_basic_set_drop_inequality(bset, k); | ||||
| 2022 | --k; | ||||
| 2023 | } | ||||
| 2024 | constraint_index_free(&ci); | ||||
| 2025 | return bset; | ||||
| 2026 | error: | ||||
| 2027 | constraint_index_free(&ci); | ||||
| 2028 | return bset; | ||||
| 2029 | } | ||||
| 2030 | |||||
| 2031 | /* Remove constraints from "bmap" that are identical to constraints | ||||
| 2032 | * in "context" or that are more relaxed (greater constant term). | ||||
| 2033 | * | ||||
| 2034 | * We perform the test for shifted copies on the pure constraints | ||||
| 2035 | * in remove_shifted_constraints. | ||||
| 2036 | */ | ||||
| 2037 | static __isl_give isl_basic_map *isl_basic_map_remove_shifted_constraints( | ||||
| 2038 | __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context) | ||||
| 2039 | { | ||||
| 2040 | isl_basic_setisl_basic_map *bset, *bset_context; | ||||
| 2041 | |||||
| 2042 | if (!bmap || !context) | ||||
| 2043 | goto error; | ||||
| 2044 | |||||
| 2045 | if (bmap->n_ineq == 0 || context->n_ineq == 0) { | ||||
| 2046 | isl_basic_map_free(context); | ||||
| 2047 | return bmap; | ||||
| 2048 | } | ||||
| 2049 | |||||
| 2050 | context = isl_basic_map_align_divs(context, bmap); | ||||
| 2051 | bmap = isl_basic_map_align_divs(bmap, context); | ||||
| 2052 | |||||
| 2053 | bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap)); | ||||
| 2054 | bset_context = isl_basic_map_underlying_set(context); | ||||
| 2055 | bset = remove_shifted_constraints(bset, bset_context); | ||||
| 2056 | isl_basic_set_free(bset_context); | ||||
| 2057 | |||||
| 2058 | bmap = isl_basic_map_overlying_set(bset, bmap); | ||||
| 2059 | |||||
| 2060 | return bmap; | ||||
| 2061 | error: | ||||
| 2062 | isl_basic_map_free(bmap); | ||||
| 2063 | isl_basic_map_free(context); | ||||
| 2064 | return NULL((void*)0); | ||||
| 2065 | } | ||||
| 2066 | |||||
| 2067 | /* Does the (linear part of a) constraint "c" involve any of the "len" | ||||
| 2068 | * "relevant" dimensions? | ||||
| 2069 | */ | ||||
| 2070 | static int is_related(isl_int *c, int len, int *relevant) | ||||
| 2071 | { | ||||
| 2072 | int i; | ||||
| 2073 | |||||
| 2074 | for (i = 0; i < len; ++i) { | ||||
| 2075 | if (!relevant[i]) | ||||
| 2076 | continue; | ||||
| 2077 | if (!isl_int_is_zero(c[i])(isl_sioimath_sgn(*(c[i])) == 0)) | ||||
| 2078 | return 1; | ||||
| 2079 | } | ||||
| 2080 | |||||
| 2081 | return 0; | ||||
| 2082 | } | ||||
| 2083 | |||||
| 2084 | /* Drop constraints from "bmap" that do not involve any of | ||||
| 2085 | * the dimensions marked "relevant". | ||||
| 2086 | */ | ||||
| 2087 | static __isl_give isl_basic_map *drop_unrelated_constraints( | ||||
| 2088 | __isl_take isl_basic_map *bmap, int *relevant) | ||||
| 2089 | { | ||||
| 2090 | int i; | ||||
| 2091 | isl_size dim; | ||||
| 2092 | |||||
| 2093 | dim = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 2094 | if (dim < 0) | ||||
| 2095 | return isl_basic_map_free(bmap); | ||||
| 2096 | for (i = 0; i < dim; ++i) | ||||
| 2097 | if (!relevant[i]) | ||||
| 2098 | break; | ||||
| 2099 | if (i >= dim) | ||||
| 2100 | return bmap; | ||||
| 2101 | |||||
| 2102 | for (i = bmap->n_eq - 1; i >= 0; --i) | ||||
| 2103 | if (!is_related(bmap->eq[i] + 1, dim, relevant)) { | ||||
| 2104 | bmap = isl_basic_map_cow(bmap); | ||||
| 2105 | if (isl_basic_map_drop_equality(bmap, i) < 0) | ||||
| 2106 | return isl_basic_map_free(bmap); | ||||
| 2107 | } | ||||
| 2108 | |||||
| 2109 | for (i = bmap->n_ineq - 1; i >= 0; --i) | ||||
| 2110 | if (!is_related(bmap->ineq[i] + 1, dim, relevant)) { | ||||
| 2111 | bmap = isl_basic_map_cow(bmap); | ||||
| 2112 | if (isl_basic_map_drop_inequality(bmap, i) < 0) | ||||
| 2113 | return isl_basic_map_free(bmap); | ||||
| 2114 | } | ||||
| 2115 | |||||
| 2116 | return bmap; | ||||
| 2117 | } | ||||
| 2118 | |||||
| 2119 | /* Update the groups in "group" based on the (linear part of a) constraint "c". | ||||
| 2120 | * | ||||
| 2121 | * In particular, for any variable involved in the constraint, | ||||
| 2122 | * find the actual group id from before and replace the group | ||||
| 2123 | * of the corresponding variable by the minimal group of all | ||||
| 2124 | * the variables involved in the constraint considered so far | ||||
| 2125 | * (if this minimum is smaller) or replace the minimum by this group | ||||
| 2126 | * (if the minimum is larger). | ||||
| 2127 | * | ||||
| 2128 | * At the end, all the variables in "c" will (indirectly) point | ||||
| 2129 | * to the minimal of the groups that they referred to originally. | ||||
| 2130 | */ | ||||
| 2131 | static void update_groups(int dim, int *group, isl_int *c) | ||||
| 2132 | { | ||||
| 2133 | int j; | ||||
| 2134 | int min = dim; | ||||
| 2135 | |||||
| 2136 | for (j = 0; j < dim; ++j) { | ||||
| 2137 | if (isl_int_is_zero(c[j])(isl_sioimath_sgn(*(c[j])) == 0)) | ||||
| 2138 | continue; | ||||
| 2139 | while (group[j] >= 0 && group[group[j]] != group[j]) | ||||
| 2140 | group[j] = group[group[j]]; | ||||
| 2141 | if (group[j] == min) | ||||
| 2142 | continue; | ||||
| 2143 | if (group[j] < min) { | ||||
| 2144 | if (min >= 0 && min < dim) | ||||
| 2145 | group[min] = group[j]; | ||||
| 2146 | min = group[j]; | ||||
| 2147 | } else | ||||
| 2148 | group[group[j]] = min; | ||||
| 2149 | } | ||||
| 2150 | } | ||||
| 2151 | |||||
| 2152 | /* Allocate an array of groups of variables, one for each variable | ||||
| 2153 | * in "context", initialized to zero. | ||||
| 2154 | */ | ||||
| 2155 | static int *alloc_groups(__isl_keep isl_basic_setisl_basic_map *context) | ||||
| 2156 | { | ||||
| 2157 | isl_ctx *ctx; | ||||
| 2158 | isl_size dim; | ||||
| 2159 | |||||
| 2160 | dim = isl_basic_set_dim(context, isl_dim_set); | ||||
| 2161 | if (dim < 0) | ||||
| 2162 | return NULL((void*)0); | ||||
| 2163 | ctx = isl_basic_set_get_ctx(context); | ||||
| 2164 | return isl_calloc_array(ctx, int, dim)((int *)isl_calloc_or_die(ctx, dim, sizeof(int))); | ||||
| 2165 | } | ||||
| 2166 | |||||
| 2167 | /* Drop constraints from "bmap" that only involve variables that are | ||||
| 2168 | * not related to any of the variables marked with a "-1" in "group". | ||||
| 2169 | * | ||||
| 2170 | * We construct groups of variables that collect variables that | ||||
| 2171 | * (indirectly) appear in some common constraint of "bmap". | ||||
| 2172 | * Each group is identified by the first variable in the group, | ||||
| 2173 | * except for the special group of variables that was already identified | ||||
| 2174 | * in the input as -1 (or are related to those variables). | ||||
| 2175 | * If group[i] is equal to i (or -1), then the group of i is i (or -1), | ||||
| 2176 | * otherwise the group of i is the group of group[i]. | ||||
| 2177 | * | ||||
| 2178 | * We first initialize groups for the remaining variables. | ||||
| 2179 | * Then we iterate over the constraints of "bmap" and update the | ||||
| 2180 | * group of the variables in the constraint by the smallest group. | ||||
| 2181 | * Finally, we resolve indirect references to groups by running over | ||||
| 2182 | * the variables. | ||||
| 2183 | * | ||||
| 2184 | * After computing the groups, we drop constraints that do not involve | ||||
| 2185 | * any variables in the -1 group. | ||||
| 2186 | */ | ||||
| 2187 | __isl_give isl_basic_map *isl_basic_map_drop_unrelated_constraints( | ||||
| 2188 | __isl_take isl_basic_map *bmap, __isl_take int *group) | ||||
| 2189 | { | ||||
| 2190 | isl_size dim; | ||||
| 2191 | int i; | ||||
| 2192 | int last; | ||||
| 2193 | |||||
| 2194 | dim = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 2195 | if (dim < 0) | ||||
| 2196 | return isl_basic_map_free(bmap); | ||||
| 2197 | |||||
| 2198 | last = -1; | ||||
| 2199 | for (i = 0; i < dim; ++i) | ||||
| 2200 | if (group[i] >= 0) | ||||
| 2201 | last = group[i] = i; | ||||
| 2202 | if (last < 0) { | ||||
| 2203 | free(group); | ||||
| 2204 | return bmap; | ||||
| 2205 | } | ||||
| 2206 | |||||
| 2207 | for (i = 0; i < bmap->n_eq; ++i) | ||||
| 2208 | update_groups(dim, group, bmap->eq[i] + 1); | ||||
| 2209 | for (i = 0; i < bmap->n_ineq; ++i) | ||||
| 2210 | update_groups(dim, group, bmap->ineq[i] + 1); | ||||
| 2211 | |||||
| 2212 | for (i = 0; i < dim; ++i) | ||||
| 2213 | if (group[i] >= 0) | ||||
| 2214 | group[i] = group[group[i]]; | ||||
| 2215 | |||||
| 2216 | for (i = 0; i < dim; ++i) | ||||
| 2217 | group[i] = group[i] == -1; | ||||
| 2218 | |||||
| 2219 | bmap = drop_unrelated_constraints(bmap, group); | ||||
| 2220 | |||||
| 2221 | free(group); | ||||
| 2222 | return bmap; | ||||
| 2223 | } | ||||
| 2224 | |||||
| 2225 | /* Drop constraints from "context" that are irrelevant for computing | ||||
| 2226 | * the gist of "bset". | ||||
| 2227 | * | ||||
| 2228 | * In particular, drop constraints in variables that are not related | ||||
| 2229 | * to any of the variables involved in the constraints of "bset" | ||||
| 2230 | * in the sense that there is no sequence of constraints that connects them. | ||||
| 2231 | * | ||||
| 2232 | * We first mark all variables that appear in "bset" as belonging | ||||
| 2233 | * to a "-1" group and then continue with group_and_drop_irrelevant_constraints. | ||||
| 2234 | */ | ||||
| 2235 | static __isl_give isl_basic_setisl_basic_map *drop_irrelevant_constraints( | ||||
| 2236 | __isl_take isl_basic_setisl_basic_map *context, __isl_keep isl_basic_setisl_basic_map *bset) | ||||
| 2237 | { | ||||
| 2238 | int *group; | ||||
| 2239 | isl_size dim; | ||||
| 2240 | int i, j; | ||||
| 2241 | |||||
| 2242 | dim = isl_basic_set_dim(bset, isl_dim_set); | ||||
| 2243 | if (!context || dim < 0) | ||||
| 2244 | return isl_basic_set_free(context); | ||||
| 2245 | |||||
| 2246 | group = alloc_groups(context); | ||||
| 2247 | |||||
| 2248 | if (!group) | ||||
| 2249 | return isl_basic_set_free(context); | ||||
| 2250 | |||||
| 2251 | for (i = 0; i < dim; ++i) { | ||||
| 2252 | for (j = 0; j < bset->n_eq; ++j) | ||||
| 2253 | if (!isl_int_is_zero(bset->eq[j][1 + i])(isl_sioimath_sgn(*(bset->eq[j][1 + i])) == 0)) | ||||
| 2254 | break; | ||||
| 2255 | if (j < bset->n_eq) { | ||||
| 2256 | group[i] = -1; | ||||
| 2257 | continue; | ||||
| 2258 | } | ||||
| 2259 | for (j = 0; j < bset->n_ineq; ++j) | ||||
| 2260 | if (!isl_int_is_zero(bset->ineq[j][1 + i])(isl_sioimath_sgn(*(bset->ineq[j][1 + i])) == 0)) | ||||
| 2261 | break; | ||||
| 2262 | if (j < bset->n_ineq) | ||||
| 2263 | group[i] = -1; | ||||
| 2264 | } | ||||
| 2265 | |||||
| 2266 | return isl_basic_map_drop_unrelated_constraints(context, group); | ||||
| 2267 | } | ||||
| 2268 | |||||
| 2269 | /* Drop constraints from "context" that are irrelevant for computing | ||||
| 2270 | * the gist of the inequalities "ineq". | ||||
| 2271 | * Inequalities in "ineq" for which the corresponding element of row | ||||
| 2272 | * is set to -1 have already been marked for removal and should be ignored. | ||||
| 2273 | * | ||||
| 2274 | * In particular, drop constraints in variables that are not related | ||||
| 2275 | * to any of the variables involved in "ineq" | ||||
| 2276 | * in the sense that there is no sequence of constraints that connects them. | ||||
| 2277 | * | ||||
| 2278 | * We first mark all variables that appear in "bset" as belonging | ||||
| 2279 | * to a "-1" group and then continue with group_and_drop_irrelevant_constraints. | ||||
| 2280 | */ | ||||
| 2281 | static __isl_give isl_basic_setisl_basic_map *drop_irrelevant_constraints_marked( | ||||
| 2282 | __isl_take isl_basic_setisl_basic_map *context, __isl_keep isl_mat *ineq, int *row) | ||||
| 2283 | { | ||||
| 2284 | int *group; | ||||
| 2285 | isl_size dim; | ||||
| 2286 | int i, j; | ||||
| 2287 | isl_size n; | ||||
| 2288 | |||||
| 2289 | dim = isl_basic_set_dim(context, isl_dim_set); | ||||
| 2290 | n = isl_mat_rows(ineq); | ||||
| 2291 | if (dim < 0 || n < 0) | ||||
| 2292 | return isl_basic_set_free(context); | ||||
| 2293 | |||||
| 2294 | group = alloc_groups(context); | ||||
| 2295 | |||||
| 2296 | if (!group) | ||||
| 2297 | return isl_basic_set_free(context); | ||||
| 2298 | |||||
| 2299 | for (i = 0; i < dim; ++i) { | ||||
| 2300 | for (j = 0; j < n; ++j) { | ||||
| 2301 | if (row[j] < 0) | ||||
| 2302 | continue; | ||||
| 2303 | if (!isl_int_is_zero(ineq->row[j][1 + i])(isl_sioimath_sgn(*(ineq->row[j][1 + i])) == 0)) | ||||
| 2304 | break; | ||||
| 2305 | } | ||||
| 2306 | if (j < n) | ||||
| 2307 | group[i] = -1; | ||||
| 2308 | } | ||||
| 2309 | |||||
| 2310 | return isl_basic_map_drop_unrelated_constraints(context, group); | ||||
| 2311 | } | ||||
| 2312 | |||||
| 2313 | /* Do all "n" entries of "row" contain a negative value? | ||||
| 2314 | */ | ||||
| 2315 | static int all_neg(int *row, int n) | ||||
| 2316 | { | ||||
| 2317 | int i; | ||||
| 2318 | |||||
| 2319 | for (i = 0; i < n; ++i) | ||||
| 2320 | if (row[i] >= 0) | ||||
| 2321 | return 0; | ||||
| 2322 | |||||
| 2323 | return 1; | ||||
| 2324 | } | ||||
| 2325 | |||||
| 2326 | /* Update the inequalities in "bset" based on the information in "row" | ||||
| 2327 | * and "tab". | ||||
| 2328 | * | ||||
| 2329 | * In particular, the array "row" contains either -1, meaning that | ||||
| 2330 | * the corresponding inequality of "bset" is redundant, or the index | ||||
| 2331 | * of an inequality in "tab". | ||||
| 2332 | * | ||||
| 2333 | * If the row entry is -1, then drop the inequality. | ||||
| 2334 | * Otherwise, if the constraint is marked redundant in the tableau, | ||||
| 2335 | * then drop the inequality. Similarly, if it is marked as an equality | ||||
| 2336 | * in the tableau, then turn the inequality into an equality and | ||||
| 2337 | * perform Gaussian elimination. | ||||
| 2338 | */ | ||||
| 2339 | static __isl_give isl_basic_setisl_basic_map *update_ineq(__isl_take isl_basic_setisl_basic_map *bset, | ||||
| 2340 | __isl_keep int *row, struct isl_tab *tab) | ||||
| 2341 | { | ||||
| 2342 | int i; | ||||
| 2343 | unsigned n_ineq; | ||||
| 2344 | unsigned n_eq; | ||||
| 2345 | int found_equality = 0; | ||||
| 2346 | |||||
| 2347 | if (!bset) | ||||
| 2348 | return NULL((void*)0); | ||||
| 2349 | if (tab && tab->empty) | ||||
| 2350 | return isl_basic_set_set_to_empty(bset); | ||||
| 2351 | |||||
| 2352 | n_ineq = bset->n_ineq; | ||||
| 2353 | for (i = n_ineq - 1; i >= 0; --i) { | ||||
| 2354 | if (row[i] < 0) { | ||||
| 2355 | if (isl_basic_set_drop_inequality(bset, i) < 0) | ||||
| 2356 | return isl_basic_set_free(bset); | ||||
| 2357 | continue; | ||||
| 2358 | } | ||||
| 2359 | if (!tab) | ||||
| 2360 | continue; | ||||
| 2361 | n_eq = tab->n_eq; | ||||
| 2362 | if (isl_tab_is_equality(tab, n_eq + row[i])) { | ||||
| 2363 | isl_basic_map_inequality_to_equality(bset, i); | ||||
| 2364 | found_equality = 1; | ||||
| 2365 | } else if (isl_tab_is_redundant(tab, n_eq + row[i])) { | ||||
| 2366 | if (isl_basic_set_drop_inequality(bset, i) < 0) | ||||
| 2367 | return isl_basic_set_free(bset); | ||||
| 2368 | } | ||||
| 2369 | } | ||||
| 2370 | |||||
| 2371 | if (found_equality) | ||||
| 2372 | bset = isl_basic_set_gauss(bset, NULL((void*)0)); | ||||
| 2373 | bset = isl_basic_set_finalize(bset); | ||||
| 2374 | return bset; | ||||
| 2375 | } | ||||
| 2376 | |||||
| 2377 | /* Update the inequalities in "bset" based on the information in "row" | ||||
| 2378 | * and "tab" and free all arguments (other than "bset"). | ||||
| 2379 | */ | ||||
| 2380 | static __isl_give isl_basic_setisl_basic_map *update_ineq_free( | ||||
| 2381 | __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_mat *ineq, | ||||
| 2382 | __isl_take isl_basic_setisl_basic_map *context, __isl_take int *row, | ||||
| 2383 | struct isl_tab *tab) | ||||
| 2384 | { | ||||
| 2385 | isl_mat_free(ineq); | ||||
| 2386 | isl_basic_set_free(context); | ||||
| 2387 | |||||
| 2388 | bset = update_ineq(bset, row, tab); | ||||
| 2389 | |||||
| 2390 | free(row); | ||||
| 2391 | isl_tab_free(tab); | ||||
| 2392 | return bset; | ||||
| 2393 | } | ||||
| 2394 | |||||
| 2395 | /* Remove all information from bset that is redundant in the context | ||||
| 2396 | * of context. | ||||
| 2397 | * "ineq" contains the (possibly transformed) inequalities of "bset", | ||||
| 2398 | * in the same order. | ||||
| 2399 | * The (explicit) equalities of "bset" are assumed to have been taken | ||||
| 2400 | * into account by the transformation such that only the inequalities | ||||
| 2401 | * are relevant. | ||||
| 2402 | * "context" is assumed not to be empty. | ||||
| 2403 | * | ||||
| 2404 | * "row" keeps track of the constraint index of a "bset" inequality in "tab". | ||||
| 2405 | * A value of -1 means that the inequality is obviously redundant and may | ||||
| 2406 | * not even appear in "tab". | ||||
| 2407 | * | ||||
| 2408 | * We first mark the inequalities of "bset" | ||||
| 2409 | * that are obviously redundant with respect to some inequality in "context". | ||||
| 2410 | * Then we remove those constraints from "context" that have become | ||||
| 2411 | * irrelevant for computing the gist of "bset". | ||||
| 2412 | * Note that this removal of constraints cannot be replaced by | ||||
| 2413 | * a factorization because factors in "bset" may still be connected | ||||
| 2414 | * to each other through constraints in "context". | ||||
| 2415 | * | ||||
| 2416 | * If there are any inequalities left, we construct a tableau for | ||||
| 2417 | * the context and then add the inequalities of "bset". | ||||
| 2418 | * Before adding these inequalities, we freeze all constraints such that | ||||
| 2419 | * they won't be considered redundant in terms of the constraints of "bset". | ||||
| 2420 | * Then we detect all redundant constraints (among the | ||||
| 2421 | * constraints that weren't frozen), first by checking for redundancy in the | ||||
| 2422 | * the tableau and then by checking if replacing a constraint by its negation | ||||
| 2423 | * would lead to an empty set. This last step is fairly expensive | ||||
| 2424 | * and could be optimized by more reuse of the tableau. | ||||
| 2425 | * Finally, we update bset according to the results. | ||||
| 2426 | */ | ||||
| 2427 | static __isl_give isl_basic_setisl_basic_map *uset_gist_full(__isl_take isl_basic_setisl_basic_map *bset, | ||||
| 2428 | __isl_take isl_mat *ineq, __isl_take isl_basic_setisl_basic_map *context) | ||||
| 2429 | { | ||||
| 2430 | int i, r; | ||||
| 2431 | int *row = NULL((void*)0); | ||||
| 2432 | isl_ctx *ctx; | ||||
| 2433 | isl_basic_setisl_basic_map *combined = NULL((void*)0); | ||||
| 2434 | struct isl_tab *tab = NULL((void*)0); | ||||
| 2435 | unsigned n_eq, context_ineq; | ||||
| 2436 | |||||
| 2437 | if (!bset || !ineq || !context) | ||||
| 2438 | goto error; | ||||
| 2439 | |||||
| 2440 | if (bset->n_ineq == 0 || isl_basic_set_plain_is_universe(context)) { | ||||
| 2441 | isl_basic_set_free(context); | ||||
| 2442 | isl_mat_free(ineq); | ||||
| 2443 | return bset; | ||||
| 2444 | } | ||||
| 2445 | |||||
| 2446 | ctx = isl_basic_set_get_ctx(context); | ||||
| 2447 | row = isl_calloc_array(ctx, int, bset->n_ineq)((int *)isl_calloc_or_die(ctx, bset->n_ineq, sizeof(int))); | ||||
| 2448 | if (!row) | ||||
| 2449 | goto error; | ||||
| 2450 | |||||
| 2451 | if (mark_shifted_constraints(ineq, context, row) < 0) | ||||
| 2452 | goto error; | ||||
| 2453 | if (all_neg(row, bset->n_ineq)) | ||||
| 2454 | return update_ineq_free(bset, ineq, context, row, NULL((void*)0)); | ||||
| 2455 | |||||
| 2456 | context = drop_irrelevant_constraints_marked(context, ineq, row); | ||||
| 2457 | if (!context) | ||||
| 2458 | goto error; | ||||
| 2459 | if (isl_basic_set_plain_is_universe(context)) | ||||
| 2460 | return update_ineq_free(bset, ineq, context, row, NULL((void*)0)); | ||||
| 2461 | |||||
| 2462 | n_eq = context->n_eq; | ||||
| 2463 | context_ineq = context->n_ineq; | ||||
| 2464 | combined = isl_basic_set_cow(isl_basic_set_copy(context)); | ||||
| 2465 | combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq); | ||||
| 2466 | tab = isl_tab_from_basic_set(combined, 0); | ||||
| 2467 | for (i = 0; i < context_ineq; ++i) | ||||
| 2468 | if (isl_tab_freeze_constraint(tab, n_eq + i) < 0) | ||||
| 2469 | goto error; | ||||
| 2470 | if (isl_tab_extend_cons(tab, bset->n_ineq) < 0) | ||||
| 2471 | goto error; | ||||
| 2472 | r = context_ineq; | ||||
| 2473 | for (i = 0; i < bset->n_ineq; ++i) { | ||||
| 2474 | if (row[i] < 0) | ||||
| 2475 | continue; | ||||
| 2476 | combined = isl_basic_set_add_ineq(combined, ineq->row[i]); | ||||
| 2477 | if (isl_tab_add_ineq(tab, ineq->row[i]) < 0) | ||||
| 2478 | goto error; | ||||
| 2479 | row[i] = r++; | ||||
| 2480 | } | ||||
| 2481 | if (isl_tab_detect_implicit_equalities(tab) < 0) | ||||
| 2482 | goto error; | ||||
| 2483 | if (isl_tab_detect_redundant(tab) < 0) | ||||
| 2484 | goto error; | ||||
| 2485 | for (i = bset->n_ineq - 1; i >= 0; --i) { | ||||
| 2486 | isl_basic_setisl_basic_map *test; | ||||
| 2487 | int is_empty; | ||||
| 2488 | |||||
| 2489 | if (row[i] < 0) | ||||
| 2490 | continue; | ||||
| 2491 | r = row[i]; | ||||
| 2492 | if (tab->con[n_eq + r].is_redundant) | ||||
| 2493 | continue; | ||||
| 2494 | test = isl_basic_set_dup(combined); | ||||
| 2495 | test = isl_inequality_negate(test, r); | ||||
| 2496 | test = isl_basic_set_update_from_tab(test, tab); | ||||
| 2497 | is_empty = isl_basic_set_is_empty(test); | ||||
| 2498 | isl_basic_set_free(test); | ||||
| 2499 | if (is_empty < 0) | ||||
| 2500 | goto error; | ||||
| 2501 | if (is_empty) | ||||
| 2502 | tab->con[n_eq + r].is_redundant = 1; | ||||
| 2503 | } | ||||
| 2504 | bset = update_ineq_free(bset, ineq, context, row, tab); | ||||
| 2505 | if (bset) { | ||||
| 2506 | ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) |= ((1 << 2))); | ||||
| 2507 | ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT)(((bset)->flags) |= ((1 << 3))); | ||||
| 2508 | } | ||||
| 2509 | |||||
| 2510 | isl_basic_set_free(combined); | ||||
| 2511 | return bset; | ||||
| 2512 | error: | ||||
| 2513 | free(row); | ||||
| 2514 | isl_mat_free(ineq); | ||||
| 2515 | isl_tab_free(tab); | ||||
| 2516 | isl_basic_set_free(combined); | ||||
| 2517 | isl_basic_set_free(context); | ||||
| 2518 | isl_basic_set_free(bset); | ||||
| 2519 | return NULL((void*)0); | ||||
| 2520 | } | ||||
| 2521 | |||||
| 2522 | /* Extract the inequalities of "bset" as an isl_mat. | ||||
| 2523 | */ | ||||
| 2524 | static __isl_give isl_mat *extract_ineq(__isl_keep isl_basic_setisl_basic_map *bset) | ||||
| 2525 | { | ||||
| 2526 | isl_size total; | ||||
| 2527 | isl_ctx *ctx; | ||||
| 2528 | isl_mat *ineq; | ||||
| 2529 | |||||
| 2530 | total = isl_basic_set_dim(bset, isl_dim_all); | ||||
| 2531 | if (total < 0) | ||||
| 2532 | return NULL((void*)0); | ||||
| 2533 | |||||
| 2534 | ctx = isl_basic_set_get_ctx(bset); | ||||
| 2535 | ineq = isl_mat_sub_alloc6(ctx, bset->ineq, 0, bset->n_ineq, | ||||
| 2536 | 0, 1 + total); | ||||
| 2537 | |||||
| 2538 | return ineq; | ||||
| 2539 | } | ||||
| 2540 | |||||
| 2541 | /* Remove all information from "bset" that is redundant in the context | ||||
| 2542 | * of "context", for the case where both "bset" and "context" are | ||||
| 2543 | * full-dimensional. | ||||
| 2544 | */ | ||||
| 2545 | static __isl_give isl_basic_setisl_basic_map *uset_gist_uncompressed( | ||||
| 2546 | __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context) | ||||
| 2547 | { | ||||
| 2548 | isl_mat *ineq; | ||||
| 2549 | |||||
| 2550 | ineq = extract_ineq(bset); | ||||
| 2551 | return uset_gist_full(bset, ineq, context); | ||||
| 2552 | } | ||||
| 2553 | |||||
| 2554 | /* Remove all information from "bset" that is redundant in the context | ||||
| 2555 | * of "context", for the case where the combined equalities of | ||||
| 2556 | * "bset" and "context" allow for a compression that can be obtained | ||||
| 2557 | * by preapplication of "T". | ||||
| 2558 | * | ||||
| 2559 | * "bset" itself is not transformed by "T". Instead, the inequalities | ||||
| 2560 | * are extracted from "bset" and those are transformed by "T". | ||||
| 2561 | * uset_gist_full then determines which of the transformed inequalities | ||||
| 2562 | * are redundant with respect to the transformed "context" and removes | ||||
| 2563 | * the corresponding inequalities from "bset". | ||||
| 2564 | * | ||||
| 2565 | * After preapplying "T" to the inequalities, any common factor is | ||||
| 2566 | * removed from the coefficients. If this results in a tightening | ||||
| 2567 | * of the constant term, then the same tightening is applied to | ||||
| 2568 | * the corresponding untransformed inequality in "bset". | ||||
| 2569 | * That is, if after plugging in T, a constraint f(x) >= 0 is of the form | ||||
| 2570 | * | ||||
| 2571 | * g f'(x) + r >= 0 | ||||
| 2572 | * | ||||
| 2573 | * with 0 <= r < g, then it is equivalent to | ||||
| 2574 | * | ||||
| 2575 | * f'(x) >= 0 | ||||
| 2576 | * | ||||
| 2577 | * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine | ||||
| 2578 | * subspace compressed by T since the latter would be transformed to | ||||
| 2579 | * | ||||
| 2580 | * g f'(x) >= 0 | ||||
| 2581 | */ | ||||
| 2582 | static __isl_give isl_basic_setisl_basic_map *uset_gist_compressed( | ||||
| 2583 | __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context, | ||||
| 2584 | __isl_take isl_mat *T) | ||||
| 2585 | { | ||||
| 2586 | isl_ctx *ctx; | ||||
| 2587 | isl_mat *ineq; | ||||
| 2588 | int i; | ||||
| 2589 | isl_size n_row, n_col; | ||||
| 2590 | isl_int rem; | ||||
| 2591 | |||||
| 2592 | ineq = extract_ineq(bset); | ||||
| 2593 | ineq = isl_mat_product(ineq, isl_mat_copy(T)); | ||||
| 2594 | context = isl_basic_set_preimage(context, T); | ||||
| 2595 | |||||
| 2596 | if (!ineq || !context) | ||||
| 2597 | goto error; | ||||
| 2598 | if (isl_basic_set_plain_is_empty(context)) { | ||||
| 2599 | isl_mat_free(ineq); | ||||
| 2600 | isl_basic_set_free(context); | ||||
| 2601 | return isl_basic_set_set_to_empty(bset); | ||||
| 2602 | } | ||||
| 2603 | |||||
| 2604 | ctx = isl_mat_get_ctx(ineq); | ||||
| 2605 | n_row = isl_mat_rows(ineq); | ||||
| 2606 | n_col = isl_mat_cols(ineq); | ||||
| 2607 | if (n_row < 0 || n_col < 0) | ||||
| 2608 | goto error; | ||||
| 2609 | isl_int_init(rem)isl_sioimath_init((rem)); | ||||
| 2610 | for (i = 0; i < n_row; ++i) { | ||||
| 2611 | isl_seq_gcd(ineq->row[i] + 1, n_col - 1, &ctx->normalize_gcd); | ||||
| 2612 | if (isl_int_is_zero(ctx->normalize_gcd)(isl_sioimath_sgn(*(ctx->normalize_gcd)) == 0)) | ||||
| 2613 | continue; | ||||
| 2614 | if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0)) | ||||
| 2615 | continue; | ||||
| 2616 | isl_seq_scale_down(ineq->row[i] + 1, ineq->row[i] + 1, | ||||
| 2617 | ctx->normalize_gcd, n_col - 1); | ||||
| 2618 | isl_int_fdiv_r(rem, ineq->row[i][0], ctx->normalize_gcd)isl_sioimath_fdiv_r((rem), *(ineq->row[i][0]), *(ctx->normalize_gcd )); | ||||
| 2619 | isl_int_fdiv_q(ineq->row[i][0],isl_sioimath_fdiv_q((ineq->row[i][0]), *(ineq->row[i][0 ]), *(ctx->normalize_gcd)) | ||||
| 2620 | ineq->row[i][0], ctx->normalize_gcd)isl_sioimath_fdiv_q((ineq->row[i][0]), *(ineq->row[i][0 ]), *(ctx->normalize_gcd)); | ||||
| 2621 | if (isl_int_is_zero(rem)(isl_sioimath_sgn(*(rem)) == 0)) | ||||
| 2622 | continue; | ||||
| 2623 | bset = isl_basic_set_cow(bset); | ||||
| 2624 | if (!bset) | ||||
| 2625 | break; | ||||
| 2626 | isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], rem)isl_sioimath_sub((bset->ineq[i][0]), *(bset->ineq[i][0] ), *(rem)); | ||||
| 2627 | } | ||||
| 2628 | isl_int_clear(rem)isl_sioimath_clear((rem)); | ||||
| 2629 | |||||
| 2630 | return uset_gist_full(bset, ineq, context); | ||||
| 2631 | error: | ||||
| 2632 | isl_mat_free(ineq); | ||||
| 2633 | isl_basic_set_free(context); | ||||
| 2634 | isl_basic_set_free(bset); | ||||
| 2635 | return NULL((void*)0); | ||||
| 2636 | } | ||||
| 2637 | |||||
| 2638 | /* Project "bset" onto the variables that are involved in "template". | ||||
| 2639 | */ | ||||
| 2640 | static __isl_give isl_basic_setisl_basic_map *project_onto_involved( | ||||
| 2641 | __isl_take isl_basic_setisl_basic_map *bset, __isl_keep isl_basic_setisl_basic_map *template) | ||||
| 2642 | { | ||||
| 2643 | int i; | ||||
| 2644 | isl_size n; | ||||
| 2645 | |||||
| 2646 | n = isl_basic_set_dim(template, isl_dim_set); | ||||
| 2647 | if (n < 0 || !template) | ||||
| 2648 | return isl_basic_set_free(bset); | ||||
| 2649 | |||||
| 2650 | for (i = 0; i < n; ++i) { | ||||
| 2651 | isl_bool involved; | ||||
| 2652 | |||||
| 2653 | involved = isl_basic_set_involves_dims(template, | ||||
| 2654 | isl_dim_set, i, 1); | ||||
| 2655 | if (involved < 0) | ||||
| 2656 | return isl_basic_set_free(bset); | ||||
| 2657 | if (involved) | ||||
| 2658 | continue; | ||||
| 2659 | bset = isl_basic_set_eliminate_vars(bset, i, 1); | ||||
| 2660 | } | ||||
| 2661 | |||||
| 2662 | return bset; | ||||
| 2663 | } | ||||
| 2664 | |||||
| 2665 | /* Remove all information from bset that is redundant in the context | ||||
| 2666 | * of context. In particular, equalities that are linear combinations | ||||
| 2667 | * of those in context are removed. Then the inequalities that are | ||||
| 2668 | * redundant in the context of the equalities and inequalities of | ||||
| 2669 | * context are removed. | ||||
| 2670 | * | ||||
| 2671 | * First of all, we drop those constraints from "context" | ||||
| 2672 | * that are irrelevant for computing the gist of "bset". | ||||
| 2673 | * Alternatively, we could factorize the intersection of "context" and "bset". | ||||
| 2674 | * | ||||
| 2675 | * We first compute the intersection of the integer affine hulls | ||||
| 2676 | * of "bset" and "context", | ||||
| 2677 | * compute the gist inside this intersection and then reduce | ||||
| 2678 | * the constraints with respect to the equalities of the context | ||||
| 2679 | * that only involve variables already involved in the input. | ||||
| 2680 | * | ||||
| 2681 | * If two constraints are mutually redundant, then uset_gist_full | ||||
| 2682 | * will remove the second of those constraints. We therefore first | ||||
| 2683 | * sort the constraints so that constraints not involving existentially | ||||
| 2684 | * quantified variables are given precedence over those that do. | ||||
| 2685 | * We have to perform this sorting before the variable compression, | ||||
| 2686 | * because that may effect the order of the variables. | ||||
| 2687 | */ | ||||
| 2688 | static __isl_give isl_basic_setisl_basic_map *uset_gist(__isl_take isl_basic_setisl_basic_map *bset, | ||||
| 2689 | __isl_take isl_basic_setisl_basic_map *context) | ||||
| 2690 | { | ||||
| 2691 | isl_mat *eq; | ||||
| 2692 | isl_mat *T; | ||||
| 2693 | isl_basic_setisl_basic_map *aff; | ||||
| 2694 | isl_basic_setisl_basic_map *aff_context; | ||||
| 2695 | isl_size total; | ||||
| 2696 | |||||
| 2697 | total = isl_basic_set_dim(bset, isl_dim_all); | ||||
| 2698 | if (total < 0 || !context) | ||||
| 2699 | goto error; | ||||
| 2700 | |||||
| 2701 | context = drop_irrelevant_constraints(context, bset); | ||||
| 2702 | |||||
| 2703 | bset = isl_basic_set_detect_equalities(bset); | ||||
| 2704 | aff = isl_basic_set_copy(bset); | ||||
| 2705 | aff = isl_basic_set_plain_affine_hull(aff); | ||||
| 2706 | context = isl_basic_set_detect_equalities(context); | ||||
| 2707 | aff_context = isl_basic_set_copy(context); | ||||
| 2708 | aff_context = isl_basic_set_plain_affine_hull(aff_context); | ||||
| 2709 | aff = isl_basic_set_intersect(aff, aff_context); | ||||
| 2710 | if (!aff) | ||||
| 2711 | goto error; | ||||
| 2712 | if (isl_basic_set_plain_is_empty(aff)) { | ||||
| 2713 | isl_basic_set_free(bset); | ||||
| 2714 | isl_basic_set_free(context); | ||||
| 2715 | return aff; | ||||
| 2716 | } | ||||
| 2717 | bset = isl_basic_set_sort_constraints(bset); | ||||
| 2718 | if (aff->n_eq == 0) { | ||||
| 2719 | isl_basic_set_free(aff); | ||||
| 2720 | return uset_gist_uncompressed(bset, context); | ||||
| 2721 | } | ||||
| 2722 | eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total); | ||||
| 2723 | eq = isl_mat_cow(eq); | ||||
| 2724 | T = isl_mat_variable_compression(eq, NULL((void*)0)); | ||||
| 2725 | isl_basic_set_free(aff); | ||||
| 2726 | if (T && T->n_col == 0) { | ||||
| 2727 | isl_mat_free(T); | ||||
| 2728 | isl_basic_set_free(context); | ||||
| 2729 | return isl_basic_set_set_to_empty(bset); | ||||
| 2730 | } | ||||
| 2731 | |||||
| 2732 | aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context)); | ||||
| 2733 | aff_context = project_onto_involved(aff_context, bset); | ||||
| 2734 | |||||
| 2735 | bset = uset_gist_compressed(bset, context, T); | ||||
| 2736 | bset = isl_basic_set_reduce_using_equalities(bset, aff_context); | ||||
| 2737 | |||||
| 2738 | if (bset) { | ||||
| 2739 | ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) |= ((1 << 2))); | ||||
| 2740 | ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT)(((bset)->flags) |= ((1 << 3))); | ||||
| 2741 | } | ||||
| 2742 | |||||
| 2743 | return bset; | ||||
| 2744 | error: | ||||
| 2745 | isl_basic_set_free(bset); | ||||
| 2746 | isl_basic_set_free(context); | ||||
| 2747 | return NULL((void*)0); | ||||
| 2748 | } | ||||
| 2749 | |||||
| 2750 | /* Return the number of equality constraints in "bmap" that involve | ||||
| 2751 | * local variables. This function assumes that Gaussian elimination | ||||
| 2752 | * has been applied to the equality constraints. | ||||
| 2753 | */ | ||||
| 2754 | static int n_div_eq(__isl_keep isl_basic_map *bmap) | ||||
| 2755 | { | ||||
| 2756 | int i; | ||||
| 2757 | isl_size total, n_div; | ||||
| 2758 | |||||
| 2759 | if (!bmap) | ||||
| 2760 | return -1; | ||||
| 2761 | |||||
| 2762 | if (bmap->n_eq == 0) | ||||
| 2763 | return 0; | ||||
| 2764 | |||||
| 2765 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 2766 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 2767 | if (total < 0 || n_div < 0) | ||||
| 2768 | return -1; | ||||
| 2769 | total -= n_div; | ||||
| 2770 | |||||
| 2771 | for (i = 0; i < bmap->n_eq; ++i) | ||||
| 2772 | if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, | ||||
| 2773 | n_div) == -1) | ||||
| 2774 | return i; | ||||
| 2775 | |||||
| 2776 | return bmap->n_eq; | ||||
| 2777 | } | ||||
| 2778 | |||||
| 2779 | /* Construct a basic map in "space" defined by the equality constraints in "eq". | ||||
| 2780 | * The constraints are assumed not to involve any local variables. | ||||
| 2781 | */ | ||||
| 2782 | static __isl_give isl_basic_map *basic_map_from_equalities( | ||||
| 2783 | __isl_take isl_space *space, __isl_take isl_mat *eq) | ||||
| 2784 | { | ||||
| 2785 | int i, k; | ||||
| 2786 | isl_size total; | ||||
| 2787 | isl_basic_map *bmap = NULL((void*)0); | ||||
| 2788 | |||||
| 2789 | total = isl_space_dim(space, isl_dim_all); | ||||
| 2790 | if (total < 0 || !eq) | ||||
| 2791 | goto error; | ||||
| 2792 | |||||
| 2793 | if (1 + total != eq->n_col) | ||||
| 2794 | isl_die(isl_space_get_ctx(space), isl_error_internal,do { isl_handle_error(isl_space_get_ctx(space), isl_error_internal , "unexpected number of columns", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 2795); goto error; } while (0) | ||||
| 2795 | "unexpected number of columns", goto error)do { isl_handle_error(isl_space_get_ctx(space), isl_error_internal , "unexpected number of columns", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 2795); goto error; } while (0); | ||||
| 2796 | |||||
| 2797 | bmap = isl_basic_map_alloc_space(isl_space_copy(space), | ||||
| 2798 | 0, eq->n_row, 0); | ||||
| 2799 | for (i = 0; i < eq->n_row; ++i) { | ||||
| 2800 | k = isl_basic_map_alloc_equality(bmap); | ||||
| 2801 | if (k < 0) | ||||
| 2802 | goto error; | ||||
| 2803 | isl_seq_cpy(bmap->eq[k], eq->row[i], eq->n_col); | ||||
| 2804 | } | ||||
| 2805 | |||||
| 2806 | isl_space_free(space); | ||||
| 2807 | isl_mat_free(eq); | ||||
| 2808 | return bmap; | ||||
| 2809 | error: | ||||
| 2810 | isl_space_free(space); | ||||
| 2811 | isl_mat_free(eq); | ||||
| 2812 | isl_basic_map_free(bmap); | ||||
| 2813 | return NULL((void*)0); | ||||
| 2814 | } | ||||
| 2815 | |||||
| 2816 | /* Construct and return a variable compression based on the equality | ||||
| 2817 | * constraints in "bmap1" and "bmap2" that do not involve the local variables. | ||||
| 2818 | * "n1" is the number of (initial) equality constraints in "bmap1" | ||||
| 2819 | * that do involve local variables. | ||||
| 2820 | * "n2" is the number of (initial) equality constraints in "bmap2" | ||||
| 2821 | * that do involve local variables. | ||||
| 2822 | * "total" is the total number of other variables. | ||||
| 2823 | * This function assumes that Gaussian elimination | ||||
| 2824 | * has been applied to the equality constraints in both "bmap1" and "bmap2" | ||||
| 2825 | * such that the equality constraints not involving local variables | ||||
| 2826 | * are those that start at "n1" or "n2". | ||||
| 2827 | * | ||||
| 2828 | * If either of "bmap1" and "bmap2" does not have such equality constraints, | ||||
| 2829 | * then simply compute the compression based on the equality constraints | ||||
| 2830 | * in the other basic map. | ||||
| 2831 | * Otherwise, combine the equality constraints from both into a new | ||||
| 2832 | * basic map such that Gaussian elimination can be applied to this combination | ||||
| 2833 | * and then construct a variable compression from the resulting | ||||
| 2834 | * equality constraints. | ||||
| 2835 | */ | ||||
| 2836 | static __isl_give isl_mat *combined_variable_compression( | ||||
| 2837 | __isl_keep isl_basic_map *bmap1, int n1, | ||||
| 2838 | __isl_keep isl_basic_map *bmap2, int n2, int total) | ||||
| 2839 | { | ||||
| 2840 | isl_ctx *ctx; | ||||
| 2841 | isl_mat *E1, *E2, *V; | ||||
| 2842 | isl_basic_map *bmap; | ||||
| 2843 | |||||
| 2844 | ctx = isl_basic_map_get_ctx(bmap1); | ||||
| 2845 | if (bmap1->n_eq == n1) { | ||||
| 2846 | E2 = isl_mat_sub_alloc6(ctx, bmap2->eq, | ||||
| 2847 | n2, bmap2->n_eq - n2, 0, 1 + total); | ||||
| 2848 | return isl_mat_variable_compression(E2, NULL((void*)0)); | ||||
| 2849 | } | ||||
| 2850 | if (bmap2->n_eq == n2) { | ||||
| 2851 | E1 = isl_mat_sub_alloc6(ctx, bmap1->eq, | ||||
| 2852 | n1, bmap1->n_eq - n1, 0, 1 + total); | ||||
| 2853 | return isl_mat_variable_compression(E1, NULL((void*)0)); | ||||
| 2854 | } | ||||
| 2855 | E1 = isl_mat_sub_alloc6(ctx, bmap1->eq, | ||||
| 2856 | n1, bmap1->n_eq - n1, 0, 1 + total); | ||||
| 2857 | E2 = isl_mat_sub_alloc6(ctx, bmap2->eq, | ||||
| 2858 | n2, bmap2->n_eq - n2, 0, 1 + total); | ||||
| 2859 | E1 = isl_mat_concat(E1, E2); | ||||
| 2860 | bmap = basic_map_from_equalities(isl_basic_map_get_space(bmap1), E1); | ||||
| 2861 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
| 2862 | if (!bmap) | ||||
| 2863 | return NULL((void*)0); | ||||
| 2864 | E1 = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total); | ||||
| 2865 | V = isl_mat_variable_compression(E1, NULL((void*)0)); | ||||
| 2866 | isl_basic_map_free(bmap); | ||||
| 2867 | |||||
| 2868 | return V; | ||||
| 2869 | } | ||||
| 2870 | |||||
| 2871 | /* Extract the stride constraints from "bmap", compressed | ||||
| 2872 | * with respect to both the stride constraints in "context" and | ||||
| 2873 | * the remaining equality constraints in both "bmap" and "context". | ||||
| 2874 | * "bmap_n_eq" is the number of (initial) stride constraints in "bmap". | ||||
| 2875 | * "context_n_eq" is the number of (initial) stride constraints in "context". | ||||
| 2876 | * | ||||
| 2877 | * Let x be all variables in "bmap" (and "context") other than the local | ||||
| 2878 | * variables. First compute a variable compression | ||||
| 2879 | * | ||||
| 2880 | * x = V x' | ||||
| 2881 | * | ||||
| 2882 | * based on the non-stride equality constraints in "bmap" and "context". | ||||
| 2883 | * Consider the stride constraints of "context", | ||||
| 2884 | * | ||||
| 2885 | * A(x) + B(y) = 0 | ||||
| 2886 | * | ||||
| 2887 | * with y the local variables and plug in the variable compression, | ||||
| 2888 | * resulting in | ||||
| 2889 | * | ||||
| 2890 | * A(V x') + B(y) = 0 | ||||
| 2891 | * | ||||
| 2892 | * Use these constraints to compute a parameter compression on x' | ||||
| 2893 | * | ||||
| 2894 | * x' = T x'' | ||||
| 2895 | * | ||||
| 2896 | * Now consider the stride constraints of "bmap" | ||||
| 2897 | * | ||||
| 2898 | * C(x) + D(y) = 0 | ||||
| 2899 | * | ||||
| 2900 | * and plug in x = V*T x''. | ||||
| 2901 | * That is, return A = [C*V*T D]. | ||||
| 2902 | */ | ||||
| 2903 | static __isl_give isl_mat *extract_compressed_stride_constraints( | ||||
| 2904 | __isl_keep isl_basic_map *bmap, int bmap_n_eq, | ||||
| 2905 | __isl_keep isl_basic_map *context, int context_n_eq) | ||||
| 2906 | { | ||||
| 2907 | isl_size total, n_div; | ||||
| 2908 | isl_ctx *ctx; | ||||
| 2909 | isl_mat *A, *B, *T, *V; | ||||
| 2910 | |||||
| 2911 | total = isl_basic_map_dim(context, isl_dim_all); | ||||
| 2912 | n_div = isl_basic_map_dim(context, isl_dim_div); | ||||
| 2913 | if (total < 0 || n_div < 0) | ||||
| 2914 | return NULL((void*)0); | ||||
| 2915 | total -= n_div; | ||||
| 2916 | |||||
| 2917 | ctx = isl_basic_map_get_ctx(bmap); | ||||
| 2918 | |||||
| 2919 | V = combined_variable_compression(bmap, bmap_n_eq, | ||||
| 2920 | context, context_n_eq, total); | ||||
| 2921 | |||||
| 2922 | A = isl_mat_sub_alloc6(ctx, context->eq, 0, context_n_eq, 0, 1 + total); | ||||
| 2923 | B = isl_mat_sub_alloc6(ctx, context->eq, | ||||
| 2924 | 0, context_n_eq, 1 + total, n_div); | ||||
| 2925 | A = isl_mat_product(A, isl_mat_copy(V)); | ||||
| 2926 | T = isl_mat_parameter_compression_ext(A, B); | ||||
| 2927 | T = isl_mat_product(V, T); | ||||
| 2928 | |||||
| 2929 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 2930 | if (n_div < 0) | ||||
| 2931 | T = isl_mat_free(T); | ||||
| 2932 | else | ||||
| 2933 | T = isl_mat_diagonal(T, isl_mat_identity(ctx, n_div)); | ||||
| 2934 | |||||
| 2935 | A = isl_mat_sub_alloc6(ctx, bmap->eq, | ||||
| 2936 | 0, bmap_n_eq, 0, 1 + total + n_div); | ||||
| 2937 | A = isl_mat_product(A, T); | ||||
| 2938 | |||||
| 2939 | return A; | ||||
| 2940 | } | ||||
| 2941 | |||||
| 2942 | /* Remove the prime factors from *g that have an exponent that | ||||
| 2943 | * is strictly smaller than the exponent in "c". | ||||
| 2944 | * All exponents in *g are known to be smaller than or equal | ||||
| 2945 | * to those in "c". | ||||
| 2946 | * | ||||
| 2947 | * That is, if *g is equal to | ||||
| 2948 | * | ||||
| 2949 | * p_1^{e_1} p_2^{e_2} ... p_n^{e_n} | ||||
| 2950 | * | ||||
| 2951 | * and "c" is equal to | ||||
| 2952 | * | ||||
| 2953 | * p_1^{f_1} p_2^{f_2} ... p_n^{f_n} | ||||
| 2954 | * | ||||
| 2955 | * then update *g to | ||||
| 2956 | * | ||||
| 2957 | * p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ... | ||||
| 2958 | * p_n^{e_n * (e_n = f_n)} | ||||
| 2959 | * | ||||
| 2960 | * If e_i = f_i, then c / *g does not have any p_i factors and therefore | ||||
| 2961 | * neither does the gcd of *g and c / *g. | ||||
| 2962 | * If e_i < f_i, then the gcd of *g and c / *g has a positive | ||||
| 2963 | * power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors. | ||||
| 2964 | * Dividing *g by this gcd therefore strictly reduces the exponent | ||||
| 2965 | * of the prime factors that need to be removed, while leaving the | ||||
| 2966 | * other prime factors untouched. | ||||
| 2967 | * Repeating this process until gcd(*g, c / *g) = 1 therefore | ||||
| 2968 | * removes all undesired factors, without removing any others. | ||||
| 2969 | */ | ||||
| 2970 | static void remove_incomplete_powers(isl_int *g, isl_int c) | ||||
| 2971 | { | ||||
| 2972 | isl_int t; | ||||
| 2973 | |||||
| 2974 | isl_int_init(t)isl_sioimath_init((t)); | ||||
| 2975 | for (;;) { | ||||
| 2976 | isl_int_divexact(t, c, *g)isl_sioimath_tdiv_q((t), *(c), *(*g)); | ||||
| 2977 | isl_int_gcd(t, t, *g)isl_sioimath_gcd((t), *(t), *(*g)); | ||||
| 2978 | if (isl_int_is_one(t)(isl_sioimath_cmp_si(*(t), 1) == 0)) | ||||
| 2979 | break; | ||||
| 2980 | isl_int_divexact(*g, *g, t)isl_sioimath_tdiv_q((*g), *(*g), *(t)); | ||||
| 2981 | } | ||||
| 2982 | isl_int_clear(t)isl_sioimath_clear((t)); | ||||
| 2983 | } | ||||
| 2984 | |||||
| 2985 | /* Reduce the "n" stride constraints in "bmap" based on a copy "A" | ||||
| 2986 | * of the same stride constraints in a compressed space that exploits | ||||
| 2987 | * all equalities in the context and the other equalities in "bmap". | ||||
| 2988 | * | ||||
| 2989 | * If the stride constraints of "bmap" are of the form | ||||
| 2990 | * | ||||
| 2991 | * C(x) + D(y) = 0 | ||||
| 2992 | * | ||||
| 2993 | * then A is of the form | ||||
| 2994 | * | ||||
| 2995 | * B(x') + D(y) = 0 | ||||
| 2996 | * | ||||
| 2997 | * If any of these constraints involves only a single local variable y, | ||||
| 2998 | * then the constraint appears as | ||||
| 2999 | * | ||||
| 3000 | * f(x) + m y_i = 0 | ||||
| 3001 | * | ||||
| 3002 | * in "bmap" and as | ||||
| 3003 | * | ||||
| 3004 | * h(x') + m y_i = 0 | ||||
| 3005 | * | ||||
| 3006 | * in "A". | ||||
| 3007 | * | ||||
| 3008 | * Let g be the gcd of m and the coefficients of h. | ||||
| 3009 | * Then, in particular, g is a divisor of the coefficients of h and | ||||
| 3010 | * | ||||
| 3011 | * f(x) = h(x') | ||||
| 3012 | * | ||||
| 3013 | * is known to be a multiple of g. | ||||
| 3014 | * If some prime factor in m appears with the same exponent in g, | ||||
| 3015 | * then it can be removed from m because f(x) is already known | ||||
| 3016 | * to be a multiple of g and therefore in particular of this power | ||||
| 3017 | * of the prime factors. | ||||
| 3018 | * Prime factors that appear with a smaller exponent in g cannot | ||||
| 3019 | * be removed from m. | ||||
| 3020 | * Let g' be the divisor of g containing all prime factors that | ||||
| 3021 | * appear with the same exponent in m and g, then | ||||
| 3022 | * | ||||
| 3023 | * f(x) + m y_i = 0 | ||||
| 3024 | * | ||||
| 3025 | * can be replaced by | ||||
| 3026 | * | ||||
| 3027 | * f(x) + m/g' y_i' = 0 | ||||
| 3028 | * | ||||
| 3029 | * Note that (if g' != 1) this changes the explicit representation | ||||
| 3030 | * of y_i to that of y_i', so the integer division at position i | ||||
| 3031 | * is marked unknown and later recomputed by a call to | ||||
| 3032 | * isl_basic_map_gauss. | ||||
| 3033 | */ | ||||
| 3034 | static __isl_give isl_basic_map *reduce_stride_constraints( | ||||
| 3035 | __isl_take isl_basic_map *bmap, int n, __isl_keep isl_mat *A) | ||||
| 3036 | { | ||||
| 3037 | int i; | ||||
| 3038 | isl_size total, n_div; | ||||
| 3039 | int any = 0; | ||||
| 3040 | isl_int gcd; | ||||
| 3041 | |||||
| 3042 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 3043 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 3044 | if (total < 0 || n_div < 0 || !A) | ||||
| 3045 | return isl_basic_map_free(bmap); | ||||
| 3046 | total -= n_div; | ||||
| 3047 | |||||
| 3048 | isl_int_init(gcd)isl_sioimath_init((gcd)); | ||||
| 3049 | for (i = 0; i < n; ++i) { | ||||
| 3050 | int div; | ||||
| 3051 | |||||
| 3052 | div = isl_seq_first_non_zero(bmap->eq[i] + 1 + total, n_div); | ||||
| 3053 | if (div < 0) | ||||
| 3054 | isl_die(isl_basic_map_get_ctx(bmap), isl_error_internal,do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_internal , "equality constraints modified unexpectedly", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 3056); goto error; } while (0) | ||||
| 3055 | "equality constraints modified unexpectedly",do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_internal , "equality constraints modified unexpectedly", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 3056); goto error; } while (0) | ||||
| 3056 | goto error)do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_internal , "equality constraints modified unexpectedly", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 3056); goto error; } while (0); | ||||
| 3057 | if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total + div + 1, | ||||
| 3058 | n_div - div - 1) != -1) | ||||
| 3059 | continue; | ||||
| 3060 | if (isl_mat_row_gcd(A, i, &gcd) < 0) | ||||
| 3061 | goto error; | ||||
| 3062 | if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0)) | ||||
| 3063 | continue; | ||||
| 3064 | remove_incomplete_powers(&gcd, bmap->eq[i][1 + total + div]); | ||||
| 3065 | if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0)) | ||||
| 3066 | continue; | ||||
| 3067 | isl_int_divexact(bmap->eq[i][1 + total + div],isl_sioimath_tdiv_q((bmap->eq[i][1 + total + div]), *(bmap ->eq[i][1 + total + div]), *(gcd)) | ||||
| 3068 | bmap->eq[i][1 + total + div], gcd)isl_sioimath_tdiv_q((bmap->eq[i][1 + total + div]), *(bmap ->eq[i][1 + total + div]), *(gcd)); | ||||
| 3069 | bmap = isl_basic_map_mark_div_unknown(bmap, div); | ||||
| 3070 | if (!bmap) | ||||
| 3071 | goto error; | ||||
| 3072 | any = 1; | ||||
| 3073 | } | ||||
| 3074 | isl_int_clear(gcd)isl_sioimath_clear((gcd)); | ||||
| 3075 | |||||
| 3076 | if (any) | ||||
| 3077 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
| 3078 | |||||
| 3079 | return bmap; | ||||
| 3080 | error: | ||||
| 3081 | isl_int_clear(gcd)isl_sioimath_clear((gcd)); | ||||
| 3082 | isl_basic_map_free(bmap); | ||||
| 3083 | return NULL((void*)0); | ||||
| 3084 | } | ||||
| 3085 | |||||
| 3086 | /* Simplify the stride constraints in "bmap" based on | ||||
| 3087 | * the remaining equality constraints in "bmap" and all equality | ||||
| 3088 | * constraints in "context". | ||||
| 3089 | * Only do this if both "bmap" and "context" have stride constraints. | ||||
| 3090 | * | ||||
| 3091 | * First extract a copy of the stride constraints in "bmap" in a compressed | ||||
| 3092 | * space exploiting all the other equality constraints and then | ||||
| 3093 | * use this compressed copy to simplify the original stride constraints. | ||||
| 3094 | */ | ||||
| 3095 | static __isl_give isl_basic_map *gist_strides(__isl_take isl_basic_map *bmap, | ||||
| 3096 | __isl_keep isl_basic_map *context) | ||||
| 3097 | { | ||||
| 3098 | int bmap_n_eq, context_n_eq; | ||||
| 3099 | isl_mat *A; | ||||
| 3100 | |||||
| 3101 | if (!bmap || !context) | ||||
| 3102 | return isl_basic_map_free(bmap); | ||||
| 3103 | |||||
| 3104 | bmap_n_eq = n_div_eq(bmap); | ||||
| 3105 | context_n_eq = n_div_eq(context); | ||||
| 3106 | |||||
| 3107 | if (bmap_n_eq < 0 || context_n_eq < 0) | ||||
| 3108 | return isl_basic_map_free(bmap); | ||||
| 3109 | if (bmap_n_eq == 0 || context_n_eq == 0) | ||||
| 3110 | return bmap; | ||||
| 3111 | |||||
| 3112 | A = extract_compressed_stride_constraints(bmap, bmap_n_eq, | ||||
| 3113 | context, context_n_eq); | ||||
| 3114 | bmap = reduce_stride_constraints(bmap, bmap_n_eq, A); | ||||
| 3115 | |||||
| 3116 | isl_mat_free(A); | ||||
| 3117 | |||||
| 3118 | return bmap; | ||||
| 3119 | } | ||||
| 3120 | |||||
| 3121 | /* Return a basic map that has the same intersection with "context" as "bmap" | ||||
| 3122 | * and that is as "simple" as possible. | ||||
| 3123 | * | ||||
| 3124 | * The core computation is performed on the pure constraints. | ||||
| 3125 | * When we add back the meaning of the integer divisions, we need | ||||
| 3126 | * to (re)introduce the div constraints. If we happen to have | ||||
| 3127 | * discovered that some of these integer divisions are equal to | ||||
| 3128 | * some affine combination of other variables, then these div | ||||
| 3129 | * constraints may end up getting simplified in terms of the equalities, | ||||
| 3130 | * resulting in extra inequalities on the other variables that | ||||
| 3131 | * may have been removed already or that may not even have been | ||||
| 3132 | * part of the input. We try and remove those constraints of | ||||
| 3133 | * this form that are most obviously redundant with respect to | ||||
| 3134 | * the context. We also remove those div constraints that are | ||||
| 3135 | * redundant with respect to the other constraints in the result. | ||||
| 3136 | * | ||||
| 3137 | * The stride constraints among the equality constraints in "bmap" are | ||||
| 3138 | * also simplified with respecting to the other equality constraints | ||||
| 3139 | * in "bmap" and with respect to all equality constraints in "context". | ||||
| 3140 | */ | ||||
| 3141 | __isl_give isl_basic_map *isl_basic_map_gist(__isl_take isl_basic_map *bmap, | ||||
| 3142 | __isl_take isl_basic_map *context) | ||||
| 3143 | { | ||||
| 3144 | isl_basic_setisl_basic_map *bset, *eq; | ||||
| 3145 | isl_basic_map *eq_bmap; | ||||
| 3146 | isl_size total, n_div, n_div_bmap; | ||||
| 3147 | unsigned extra, n_eq, n_ineq; | ||||
| 3148 | |||||
| 3149 | if (!bmap || !context) | ||||
| 3150 | goto error; | ||||
| 3151 | |||||
| 3152 | if (isl_basic_map_plain_is_universe(bmap)) { | ||||
| 3153 | isl_basic_map_free(context); | ||||
| 3154 | return bmap; | ||||
| 3155 | } | ||||
| 3156 | if (isl_basic_map_plain_is_empty(context)) { | ||||
| 3157 | isl_space *space = isl_basic_map_get_space(bmap); | ||||
| 3158 | isl_basic_map_free(bmap); | ||||
| 3159 | isl_basic_map_free(context); | ||||
| 3160 | return isl_basic_map_universe(space); | ||||
| 3161 | } | ||||
| 3162 | if (isl_basic_map_plain_is_empty(bmap)) { | ||||
| 3163 | isl_basic_map_free(context); | ||||
| 3164 | return bmap; | ||||
| 3165 | } | ||||
| 3166 | |||||
| 3167 | bmap = isl_basic_map_remove_redundancies(bmap); | ||||
| 3168 | context = isl_basic_map_remove_redundancies(context); | ||||
| 3169 | context = isl_basic_map_align_divs(context, bmap); | ||||
| 3170 | |||||
| 3171 | n_div = isl_basic_map_dim(context, isl_dim_div); | ||||
| 3172 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 3173 | n_div_bmap = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 3174 | if (n_div < 0 || total < 0 || n_div_bmap < 0) | ||||
| 3175 | goto error; | ||||
| 3176 | extra = n_div - n_div_bmap; | ||||
| 3177 | |||||
| 3178 | bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap)); | ||||
| 3179 | bset = isl_basic_set_add_dims(bset, isl_dim_set, extra); | ||||
| 3180 | bset = uset_gist(bset, | ||||
| 3181 | isl_basic_map_underlying_set(isl_basic_map_copy(context))); | ||||
| 3182 | bset = isl_basic_set_project_out(bset, isl_dim_set, total, extra); | ||||
| 3183 | |||||
| 3184 | if (!bset || bset->n_eq == 0 || n_div == 0 || | ||||
| 3185 | isl_basic_set_plain_is_empty(bset)) { | ||||
| 3186 | isl_basic_map_free(context); | ||||
| 3187 | return isl_basic_map_overlying_set(bset, bmap); | ||||
| 3188 | } | ||||
| 3189 | |||||
| 3190 | n_eq = bset->n_eq; | ||||
| 3191 | n_ineq = bset->n_ineq; | ||||
| 3192 | eq = isl_basic_set_copy(bset); | ||||
| 3193 | eq = isl_basic_set_cow(eq); | ||||
| 3194 | eq = isl_basic_set_free_inequality(eq, n_ineq); | ||||
| 3195 | bset = isl_basic_set_free_equality(bset, n_eq); | ||||
| 3196 | |||||
| 3197 | eq_bmap = isl_basic_map_overlying_set(eq, isl_basic_map_copy(bmap)); | ||||
| 3198 | eq_bmap = gist_strides(eq_bmap, context); | ||||
| 3199 | eq_bmap = isl_basic_map_remove_shifted_constraints(eq_bmap, context); | ||||
| 3200 | bmap = isl_basic_map_overlying_set(bset, bmap); | ||||
| 3201 | bmap = isl_basic_map_intersect(bmap, eq_bmap); | ||||
| 3202 | bmap = isl_basic_map_remove_redundancies(bmap); | ||||
| 3203 | |||||
| 3204 | return bmap; | ||||
| 3205 | error: | ||||
| 3206 | isl_basic_map_free(bmap); | ||||
| 3207 | isl_basic_map_free(context); | ||||
| 3208 | return NULL((void*)0); | ||||
| 3209 | } | ||||
| 3210 | |||||
| 3211 | /* | ||||
| 3212 | * Assumes context has no implicit divs. | ||||
| 3213 | */ | ||||
| 3214 | __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map, | ||||
| 3215 | __isl_take isl_basic_map *context) | ||||
| 3216 | { | ||||
| 3217 | int i; | ||||
| 3218 | |||||
| 3219 | if (!map || !context) | ||||
| 3220 | goto error; | ||||
| 3221 | |||||
| 3222 | if (isl_basic_map_plain_is_empty(context)) { | ||||
| 3223 | isl_space *space = isl_map_get_space(map); | ||||
| 3224 | isl_map_free(map); | ||||
| 3225 | isl_basic_map_free(context); | ||||
| 3226 | return isl_map_universe(space); | ||||
| 3227 | } | ||||
| 3228 | |||||
| 3229 | context = isl_basic_map_remove_redundancies(context); | ||||
| 3230 | map = isl_map_cow(map); | ||||
| 3231 | if (isl_map_basic_map_check_equal_space(map, context) < 0) | ||||
| 3232 | goto error; | ||||
| 3233 | map = isl_map_compute_divs(map); | ||||
| 3234 | if (!map) | ||||
| 3235 | goto error; | ||||
| 3236 | for (i = map->n - 1; i >= 0; --i) { | ||||
| 3237 | map->p[i] = isl_basic_map_gist(map->p[i], | ||||
| 3238 | isl_basic_map_copy(context)); | ||||
| 3239 | if (!map->p[i]) | ||||
| 3240 | goto error; | ||||
| 3241 | if (isl_basic_map_plain_is_empty(map->p[i])) { | ||||
| 3242 | isl_basic_map_free(map->p[i]); | ||||
| 3243 | if (i != map->n - 1) | ||||
| 3244 | map->p[i] = map->p[map->n - 1]; | ||||
| 3245 | map->n--; | ||||
| 3246 | } | ||||
| 3247 | } | ||||
| 3248 | isl_basic_map_free(context); | ||||
| 3249 | ISL_F_CLR(map, ISL_MAP_NORMALIZED)(((map)->flags) &= ~((1 << 1))); | ||||
| 3250 | return map; | ||||
| 3251 | error: | ||||
| 3252 | isl_map_free(map); | ||||
| 3253 | isl_basic_map_free(context); | ||||
| 3254 | return NULL((void*)0); | ||||
| 3255 | } | ||||
| 3256 | |||||
| 3257 | /* Drop all inequalities from "bmap" that also appear in "context". | ||||
| 3258 | * "context" is assumed to have only known local variables and | ||||
| 3259 | * the initial local variables of "bmap" are assumed to be the same | ||||
| 3260 | * as those of "context". | ||||
| 3261 | * The constraints of both "bmap" and "context" are assumed | ||||
| 3262 | * to have been sorted using isl_basic_map_sort_constraints. | ||||
| 3263 | * | ||||
| 3264 | * Run through the inequality constraints of "bmap" and "context" | ||||
| 3265 | * in sorted order. | ||||
| 3266 | * If a constraint of "bmap" involves variables not in "context", | ||||
| 3267 | * then it cannot appear in "context". | ||||
| 3268 | * If a matching constraint is found, it is removed from "bmap". | ||||
| 3269 | */ | ||||
| 3270 | static __isl_give isl_basic_map *drop_inequalities( | ||||
| 3271 | __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context) | ||||
| 3272 | { | ||||
| 3273 | int i1, i2; | ||||
| 3274 | isl_size total, bmap_total; | ||||
| 3275 | unsigned extra; | ||||
| 3276 | |||||
| 3277 | total = isl_basic_map_dim(context, isl_dim_all); | ||||
| 3278 | bmap_total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 3279 | if (total < 0 || bmap_total < 0) | ||||
| 3280 | return isl_basic_map_free(bmap); | ||||
| 3281 | |||||
| 3282 | extra = bmap_total - total; | ||||
| 3283 | |||||
| 3284 | i1 = bmap->n_ineq - 1; | ||||
| 3285 | i2 = context->n_ineq - 1; | ||||
| 3286 | while (bmap && i1 >= 0 && i2 >= 0) { | ||||
| 3287 | int cmp; | ||||
| 3288 | |||||
| 3289 | if (isl_seq_first_non_zero(bmap->ineq[i1] + 1 + total, | ||||
| 3290 | extra) != -1) { | ||||
| 3291 | --i1; | ||||
| 3292 | continue; | ||||
| 3293 | } | ||||
| 3294 | cmp = isl_basic_map_constraint_cmp(context, bmap->ineq[i1], | ||||
| 3295 | context->ineq[i2]); | ||||
| 3296 | if (cmp < 0) { | ||||
| 3297 | --i2; | ||||
| 3298 | continue; | ||||
| 3299 | } | ||||
| 3300 | if (cmp > 0) { | ||||
| 3301 | --i1; | ||||
| 3302 | continue; | ||||
| 3303 | } | ||||
| 3304 | if (isl_int_eq(bmap->ineq[i1][0], context->ineq[i2][0])(isl_sioimath_cmp(*(bmap->ineq[i1][0]), *(context->ineq [i2][0])) == 0)) { | ||||
| 3305 | bmap = isl_basic_map_cow(bmap); | ||||
| 3306 | if (isl_basic_map_drop_inequality(bmap, i1) < 0) | ||||
| 3307 | bmap = isl_basic_map_free(bmap); | ||||
| 3308 | } | ||||
| 3309 | --i1; | ||||
| 3310 | --i2; | ||||
| 3311 | } | ||||
| 3312 | |||||
| 3313 | return bmap; | ||||
| 3314 | } | ||||
| 3315 | |||||
| 3316 | /* Drop all equalities from "bmap" that also appear in "context". | ||||
| 3317 | * "context" is assumed to have only known local variables and | ||||
| 3318 | * the initial local variables of "bmap" are assumed to be the same | ||||
| 3319 | * as those of "context". | ||||
| 3320 | * | ||||
| 3321 | * Run through the equality constraints of "bmap" and "context" | ||||
| 3322 | * in sorted order. | ||||
| 3323 | * If a constraint of "bmap" involves variables not in "context", | ||||
| 3324 | * then it cannot appear in "context". | ||||
| 3325 | * If a matching constraint is found, it is removed from "bmap". | ||||
| 3326 | */ | ||||
| 3327 | static __isl_give isl_basic_map *drop_equalities( | ||||
| 3328 | __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context) | ||||
| 3329 | { | ||||
| 3330 | int i1, i2; | ||||
| 3331 | isl_size total, bmap_total; | ||||
| 3332 | unsigned extra; | ||||
| 3333 | |||||
| 3334 | total = isl_basic_map_dim(context, isl_dim_all); | ||||
| 3335 | bmap_total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 3336 | if (total < 0 || bmap_total < 0) | ||||
| 3337 | return isl_basic_map_free(bmap); | ||||
| 3338 | |||||
| 3339 | extra = bmap_total - total; | ||||
| 3340 | |||||
| 3341 | i1 = bmap->n_eq - 1; | ||||
| 3342 | i2 = context->n_eq - 1; | ||||
| 3343 | |||||
| 3344 | while (bmap && i1 >= 0 && i2 >= 0) { | ||||
| 3345 | int last1, last2; | ||||
| 3346 | |||||
| 3347 | if (isl_seq_first_non_zero(bmap->eq[i1] + 1 + total, | ||||
| 3348 | extra) != -1) | ||||
| 3349 | break; | ||||
| 3350 | last1 = isl_seq_last_non_zero(bmap->eq[i1] + 1, total); | ||||
| 3351 | last2 = isl_seq_last_non_zero(context->eq[i2] + 1, total); | ||||
| 3352 | if (last1 > last2) { | ||||
| 3353 | --i2; | ||||
| 3354 | continue; | ||||
| 3355 | } | ||||
| 3356 | if (last1 < last2) { | ||||
| 3357 | --i1; | ||||
| 3358 | continue; | ||||
| 3359 | } | ||||
| 3360 | if (isl_seq_eq(bmap->eq[i1], context->eq[i2], 1 + total)) { | ||||
| 3361 | bmap = isl_basic_map_cow(bmap); | ||||
| 3362 | if (isl_basic_map_drop_equality(bmap, i1) < 0) | ||||
| 3363 | bmap = isl_basic_map_free(bmap); | ||||
| 3364 | } | ||||
| 3365 | --i1; | ||||
| 3366 | --i2; | ||||
| 3367 | } | ||||
| 3368 | |||||
| 3369 | return bmap; | ||||
| 3370 | } | ||||
| 3371 | |||||
| 3372 | /* Remove the constraints in "context" from "bmap". | ||||
| 3373 | * "context" is assumed to have explicit representations | ||||
| 3374 | * for all local variables. | ||||
| 3375 | * | ||||
| 3376 | * First align the divs of "bmap" to those of "context" and | ||||
| 3377 | * sort the constraints. Then drop all constraints from "bmap" | ||||
| 3378 | * that appear in "context". | ||||
| 3379 | */ | ||||
| 3380 | __isl_give isl_basic_map *isl_basic_map_plain_gist( | ||||
| 3381 | __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context) | ||||
| 3382 | { | ||||
| 3383 | isl_bool done, known; | ||||
| 3384 | |||||
| 3385 | done = isl_basic_map_plain_is_universe(context); | ||||
| 3386 | if (done == isl_bool_false) | ||||
| 3387 | done = isl_basic_map_plain_is_universe(bmap); | ||||
| 3388 | if (done == isl_bool_false) | ||||
| 3389 | done = isl_basic_map_plain_is_empty(context); | ||||
| 3390 | if (done == isl_bool_false) | ||||
| 3391 | done = isl_basic_map_plain_is_empty(bmap); | ||||
| 3392 | if (done < 0) | ||||
| 3393 | goto error; | ||||
| 3394 | if (done) { | ||||
| 3395 | isl_basic_map_free(context); | ||||
| 3396 | return bmap; | ||||
| 3397 | } | ||||
| 3398 | known = isl_basic_map_divs_known(context); | ||||
| 3399 | if (known < 0) | ||||
| 3400 | goto error; | ||||
| 3401 | if (!known) | ||||
| 3402 | isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_invalid , "context has unknown divs", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 3403); goto error; } while (0) | ||||
| 3403 | "context has unknown divs", goto error)do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_invalid , "context has unknown divs", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 3403); goto error; } while (0); | ||||
| 3404 | |||||
| 3405 | bmap = isl_basic_map_align_divs(bmap, context); | ||||
| 3406 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
| 3407 | bmap = isl_basic_map_sort_constraints(bmap); | ||||
| 3408 | context = isl_basic_map_sort_constraints(context); | ||||
| 3409 | |||||
| 3410 | bmap = drop_inequalities(bmap, context); | ||||
| 3411 | bmap = drop_equalities(bmap, context); | ||||
| 3412 | |||||
| 3413 | isl_basic_map_free(context); | ||||
| 3414 | bmap = isl_basic_map_finalize(bmap); | ||||
| 3415 | return bmap; | ||||
| 3416 | error: | ||||
| 3417 | isl_basic_map_free(bmap); | ||||
| 3418 | isl_basic_map_free(context); | ||||
| 3419 | return NULL((void*)0); | ||||
| 3420 | } | ||||
| 3421 | |||||
| 3422 | /* Replace "map" by the disjunct at position "pos" and free "context". | ||||
| 3423 | */ | ||||
| 3424 | static __isl_give isl_map *replace_by_disjunct(__isl_take isl_map *map, | ||||
| 3425 | int pos, __isl_take isl_basic_map *context) | ||||
| 3426 | { | ||||
| 3427 | isl_basic_map *bmap; | ||||
| 3428 | |||||
| 3429 | bmap = isl_basic_map_copy(map->p[pos]); | ||||
| 3430 | isl_map_free(map); | ||||
| 3431 | isl_basic_map_free(context); | ||||
| 3432 | return isl_map_from_basic_map(bmap); | ||||
| 3433 | } | ||||
| 3434 | |||||
| 3435 | /* Remove the constraints in "context" from "map". | ||||
| 3436 | * If any of the disjuncts in the result turns out to be the universe, | ||||
| 3437 | * then return this universe. | ||||
| 3438 | * "context" is assumed to have explicit representations | ||||
| 3439 | * for all local variables. | ||||
| 3440 | */ | ||||
| 3441 | __isl_give isl_map *isl_map_plain_gist_basic_map(__isl_take isl_map *map, | ||||
| 3442 | __isl_take isl_basic_map *context) | ||||
| 3443 | { | ||||
| 3444 | int i; | ||||
| 3445 | isl_bool univ, known; | ||||
| 3446 | |||||
| 3447 | univ = isl_basic_map_plain_is_universe(context); | ||||
| 3448 | if (univ < 0) | ||||
| 3449 | goto error; | ||||
| 3450 | if (univ) { | ||||
| 3451 | isl_basic_map_free(context); | ||||
| 3452 | return map; | ||||
| 3453 | } | ||||
| 3454 | known = isl_basic_map_divs_known(context); | ||||
| 3455 | if (known < 0) | ||||
| 3456 | goto error; | ||||
| 3457 | if (!known) | ||||
| 3458 | isl_die(isl_map_get_ctx(map), isl_error_invalid,do { isl_handle_error(isl_map_get_ctx(map), isl_error_invalid , "context has unknown divs", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 3459); goto error; } while (0) | ||||
| 3459 | "context has unknown divs", goto error)do { isl_handle_error(isl_map_get_ctx(map), isl_error_invalid , "context has unknown divs", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 3459); goto error; } while (0); | ||||
| 3460 | |||||
| 3461 | map = isl_map_cow(map); | ||||
| 3462 | if (!map) | ||||
| 3463 | goto error; | ||||
| 3464 | for (i = 0; i < map->n; ++i) { | ||||
| 3465 | map->p[i] = isl_basic_map_plain_gist(map->p[i], | ||||
| 3466 | isl_basic_map_copy(context)); | ||||
| 3467 | univ = isl_basic_map_plain_is_universe(map->p[i]); | ||||
| 3468 | if (univ < 0) | ||||
| 3469 | goto error; | ||||
| 3470 | if (univ && map->n > 1) | ||||
| 3471 | return replace_by_disjunct(map, i, context); | ||||
| 3472 | } | ||||
| 3473 | |||||
| 3474 | isl_basic_map_free(context); | ||||
| 3475 | ISL_F_CLR(map, ISL_MAP_NORMALIZED)(((map)->flags) &= ~((1 << 1))); | ||||
| 3476 | if (map->n > 1) | ||||
| 3477 | ISL_F_CLR(map, ISL_MAP_DISJOINT)(((map)->flags) &= ~((1 << 0))); | ||||
| 3478 | return map; | ||||
| 3479 | error: | ||||
| 3480 | isl_map_free(map); | ||||
| 3481 | isl_basic_map_free(context); | ||||
| 3482 | return NULL((void*)0); | ||||
| 3483 | } | ||||
| 3484 | |||||
| 3485 | /* Remove the constraints in "context" from "set". | ||||
| 3486 | * If any of the disjuncts in the result turns out to be the universe, | ||||
| 3487 | * then return this universe. | ||||
| 3488 | * "context" is assumed to have explicit representations | ||||
| 3489 | * for all local variables. | ||||
| 3490 | */ | ||||
| 3491 | __isl_give isl_setisl_map *isl_set_plain_gist_basic_set(__isl_take isl_setisl_map *set, | ||||
| 3492 | __isl_take isl_basic_setisl_basic_map *context) | ||||
| 3493 | { | ||||
| 3494 | return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set), | ||||
| 3495 | bset_to_bmap(context))); | ||||
| 3496 | } | ||||
| 3497 | |||||
| 3498 | /* Remove the constraints in "context" from "map". | ||||
| 3499 | * If any of the disjuncts in the result turns out to be the universe, | ||||
| 3500 | * then return this universe. | ||||
| 3501 | * "context" is assumed to consist of a single disjunct and | ||||
| 3502 | * to have explicit representations for all local variables. | ||||
| 3503 | */ | ||||
| 3504 | __isl_give isl_map *isl_map_plain_gist(__isl_take isl_map *map, | ||||
| 3505 | __isl_take isl_map *context) | ||||
| 3506 | { | ||||
| 3507 | isl_basic_map *hull; | ||||
| 3508 | |||||
| 3509 | hull = isl_map_unshifted_simple_hull(context); | ||||
| 3510 | return isl_map_plain_gist_basic_map(map, hull); | ||||
| 3511 | } | ||||
| 3512 | |||||
| 3513 | /* Replace "map" by a universe map in the same space and free "drop". | ||||
| 3514 | */ | ||||
| 3515 | static __isl_give isl_map *replace_by_universe(__isl_take isl_map *map, | ||||
| 3516 | __isl_take isl_map *drop) | ||||
| 3517 | { | ||||
| 3518 | isl_map *res; | ||||
| 3519 | |||||
| 3520 | res = isl_map_universe(isl_map_get_space(map)); | ||||
| 3521 | isl_map_free(map); | ||||
| 3522 | isl_map_free(drop); | ||||
| 3523 | return res; | ||||
| 3524 | } | ||||
| 3525 | |||||
| 3526 | /* Return a map that has the same intersection with "context" as "map" | ||||
| 3527 | * and that is as "simple" as possible. | ||||
| 3528 | * | ||||
| 3529 | * If "map" is already the universe, then we cannot make it any simpler. | ||||
| 3530 | * Similarly, if "context" is the universe, then we cannot exploit it | ||||
| 3531 | * to simplify "map" | ||||
| 3532 | * If "map" and "context" are identical to each other, then we can | ||||
| 3533 | * return the corresponding universe. | ||||
| 3534 | * | ||||
| 3535 | * If either "map" or "context" consists of multiple disjuncts, | ||||
| 3536 | * then check if "context" happens to be a subset of "map", | ||||
| 3537 | * in which case all constraints can be removed. | ||||
| 3538 | * In case of multiple disjuncts, the standard procedure | ||||
| 3539 | * may not be able to detect that all constraints can be removed. | ||||
| 3540 | * | ||||
| 3541 | * If none of these cases apply, we have to work a bit harder. | ||||
| 3542 | * During this computation, we make use of a single disjunct context, | ||||
| 3543 | * so if the original context consists of more than one disjunct | ||||
| 3544 | * then we need to approximate the context by a single disjunct set. | ||||
| 3545 | * Simply taking the simple hull may drop constraints that are | ||||
| 3546 | * only implicitly available in each disjunct. We therefore also | ||||
| 3547 | * look for constraints among those defining "map" that are valid | ||||
| 3548 | * for the context. These can then be used to simplify away | ||||
| 3549 | * the corresponding constraints in "map". | ||||
| 3550 | */ | ||||
| 3551 | __isl_give isl_map *isl_map_gist(__isl_take isl_map *map, | ||||
| 3552 | __isl_take isl_map *context) | ||||
| 3553 | { | ||||
| 3554 | int equal; | ||||
| 3555 | int is_universe; | ||||
| 3556 | isl_size n_disjunct_map, n_disjunct_context; | ||||
| 3557 | isl_bool subset; | ||||
| 3558 | isl_basic_map *hull; | ||||
| 3559 | |||||
| 3560 | is_universe = isl_map_plain_is_universe(map); | ||||
| 3561 | if (is_universe >= 0 && !is_universe) | ||||
| 3562 | is_universe = isl_map_plain_is_universe(context); | ||||
| 3563 | if (is_universe < 0) | ||||
| 3564 | goto error; | ||||
| 3565 | if (is_universe) { | ||||
| 3566 | isl_map_free(context); | ||||
| 3567 | return map; | ||||
| 3568 | } | ||||
| 3569 | |||||
| 3570 | isl_map_align_params_bin(&map, &context); | ||||
| 3571 | equal = isl_map_plain_is_equal(map, context); | ||||
| 3572 | if (equal < 0) | ||||
| 3573 | goto error; | ||||
| 3574 | if (equal) | ||||
| 3575 | return replace_by_universe(map, context); | ||||
| 3576 | |||||
| 3577 | n_disjunct_map = isl_map_n_basic_map(map); | ||||
| 3578 | n_disjunct_context = isl_map_n_basic_map(context); | ||||
| 3579 | if (n_disjunct_map < 0 || n_disjunct_context < 0) | ||||
| 3580 | goto error; | ||||
| 3581 | if (n_disjunct_map != 1 || n_disjunct_context != 1) { | ||||
| 3582 | subset = isl_map_is_subset(context, map); | ||||
| 3583 | if (subset < 0) | ||||
| 3584 | goto error; | ||||
| 3585 | if (subset) | ||||
| 3586 | return replace_by_universe(map, context); | ||||
| 3587 | } | ||||
| 3588 | |||||
| 3589 | context = isl_map_compute_divs(context); | ||||
| 3590 | if (!context) | ||||
| 3591 | goto error; | ||||
| 3592 | if (n_disjunct_context == 1) { | ||||
| 3593 | hull = isl_map_simple_hull(context); | ||||
| 3594 | } else { | ||||
| 3595 | isl_ctx *ctx; | ||||
| 3596 | isl_map_list *list; | ||||
| 3597 | |||||
| 3598 | ctx = isl_map_get_ctx(map); | ||||
| 3599 | list = isl_map_list_alloc(ctx, 2); | ||||
| 3600 | list = isl_map_list_add(list, isl_map_copy(context)); | ||||
| 3601 | list = isl_map_list_add(list, isl_map_copy(map)); | ||||
| 3602 | hull = isl_map_unshifted_simple_hull_from_map_list(context, | ||||
| 3603 | list); | ||||
| 3604 | } | ||||
| 3605 | return isl_map_gist_basic_map(map, hull); | ||||
| 3606 | error: | ||||
| 3607 | isl_map_free(map); | ||||
| 3608 | isl_map_free(context); | ||||
| 3609 | return NULL((void*)0); | ||||
| 3610 | } | ||||
| 3611 | |||||
| 3612 | struct isl_basic_setisl_basic_map *isl_basic_set_gist(struct isl_basic_setisl_basic_map *bset, | ||||
| 3613 | struct isl_basic_setisl_basic_map *context) | ||||
| 3614 | { | ||||
| 3615 | return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset), | ||||
| 3616 | bset_to_bmap(context))); | ||||
| 3617 | } | ||||
| 3618 | |||||
| 3619 | __isl_give isl_setisl_map *isl_set_gist_basic_set(__isl_take isl_setisl_map *set, | ||||
| 3620 | __isl_take isl_basic_setisl_basic_map *context) | ||||
| 3621 | { | ||||
| 3622 | return set_from_map(isl_map_gist_basic_map(set_to_map(set), | ||||
| 3623 | bset_to_bmap(context))); | ||||
| 3624 | } | ||||
| 3625 | |||||
| 3626 | __isl_give isl_setisl_map *isl_set_gist_params_basic_set(__isl_take isl_setisl_map *set, | ||||
| 3627 | __isl_take isl_basic_setisl_basic_map *context) | ||||
| 3628 | { | ||||
| 3629 | isl_space *space = isl_set_get_space(set); | ||||
| 3630 | isl_basic_setisl_basic_map *dom_context = isl_basic_set_universe(space); | ||||
| 3631 | dom_context = isl_basic_set_intersect_params(dom_context, context); | ||||
| 3632 | return isl_set_gist_basic_set(set, dom_context); | ||||
| 3633 | } | ||||
| 3634 | |||||
| 3635 | __isl_give isl_setisl_map *isl_set_gist(__isl_take isl_setisl_map *set, | ||||
| 3636 | __isl_take isl_setisl_map *context) | ||||
| 3637 | { | ||||
| 3638 | return set_from_map(isl_map_gist(set_to_map(set), set_to_map(context))); | ||||
| 3639 | } | ||||
| 3640 | |||||
| 3641 | /* Compute the gist of "bmap" with respect to the constraints "context" | ||||
| 3642 | * on the domain. | ||||
| 3643 | */ | ||||
| 3644 | __isl_give isl_basic_map *isl_basic_map_gist_domain( | ||||
| 3645 | __isl_take isl_basic_map *bmap, __isl_take isl_basic_setisl_basic_map *context) | ||||
| 3646 | { | ||||
| 3647 | isl_space *space = isl_basic_map_get_space(bmap); | ||||
| 3648 | isl_basic_map *bmap_context = isl_basic_map_universe(space); | ||||
| 3649 | |||||
| 3650 | bmap_context = isl_basic_map_intersect_domain(bmap_context, context); | ||||
| 3651 | return isl_basic_map_gist(bmap, bmap_context); | ||||
| 3652 | } | ||||
| 3653 | |||||
| 3654 | __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map, | ||||
| 3655 | __isl_take isl_setisl_map *context) | ||||
| 3656 | { | ||||
| 3657 | isl_map *map_context = isl_map_universe(isl_map_get_space(map)); | ||||
| 3658 | map_context = isl_map_intersect_domain(map_context, context); | ||||
| 3659 | return isl_map_gist(map, map_context); | ||||
| 3660 | } | ||||
| 3661 | |||||
| 3662 | __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map, | ||||
| 3663 | __isl_take isl_setisl_map *context) | ||||
| 3664 | { | ||||
| 3665 | isl_map *map_context = isl_map_universe(isl_map_get_space(map)); | ||||
| 3666 | map_context = isl_map_intersect_range(map_context, context); | ||||
| 3667 | return isl_map_gist(map, map_context); | ||||
| 3668 | } | ||||
| 3669 | |||||
| 3670 | __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map, | ||||
| 3671 | __isl_take isl_setisl_map *context) | ||||
| 3672 | { | ||||
| 3673 | isl_map *map_context = isl_map_universe(isl_map_get_space(map)); | ||||
| 3674 | map_context = isl_map_intersect_params(map_context, context); | ||||
| 3675 | return isl_map_gist(map, map_context); | ||||
| 3676 | } | ||||
| 3677 | |||||
| 3678 | __isl_give isl_setisl_map *isl_set_gist_params(__isl_take isl_setisl_map *set, | ||||
| 3679 | __isl_take isl_setisl_map *context) | ||||
| 3680 | { | ||||
| 3681 | return isl_map_gist_params(set, context); | ||||
| 3682 | } | ||||
| 3683 | |||||
| 3684 | /* Quick check to see if two basic maps are disjoint. | ||||
| 3685 | * In particular, we reduce the equalities and inequalities of | ||||
| 3686 | * one basic map in the context of the equalities of the other | ||||
| 3687 | * basic map and check if we get a contradiction. | ||||
| 3688 | */ | ||||
| 3689 | isl_bool isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1, | ||||
| 3690 | __isl_keep isl_basic_map *bmap2) | ||||
| 3691 | { | ||||
| 3692 | struct isl_vec *v = NULL((void*)0); | ||||
| 3693 | int *elim = NULL((void*)0); | ||||
| 3694 | isl_size total; | ||||
| 3695 | int i; | ||||
| 3696 | |||||
| 3697 | if (isl_basic_map_check_equal_space(bmap1, bmap2) < 0) | ||||
| 3698 | return isl_bool_error; | ||||
| 3699 | if (bmap1->n_div || bmap2->n_div) | ||||
| 3700 | return isl_bool_false; | ||||
| 3701 | if (!bmap1->n_eq && !bmap2->n_eq) | ||||
| 3702 | return isl_bool_false; | ||||
| 3703 | |||||
| 3704 | total = isl_space_dim(bmap1->dim, isl_dim_all); | ||||
| 3705 | if (total < 0) | ||||
| 3706 | return isl_bool_error; | ||||
| 3707 | if (total == 0) | ||||
| 3708 | return isl_bool_false; | ||||
| 3709 | v = isl_vec_alloc(bmap1->ctx, 1 + total); | ||||
| 3710 | if (!v) | ||||
| 3711 | goto error; | ||||
| 3712 | elim = isl_alloc_array(bmap1->ctx, int, total)((int *)isl_malloc_or_die(bmap1->ctx, (total)*sizeof(int)) ); | ||||
| 3713 | if (!elim) | ||||
| 3714 | goto error; | ||||
| 3715 | compute_elimination_index(bmap1, elim); | ||||
| 3716 | for (i = 0; i < bmap2->n_eq; ++i) { | ||||
| 3717 | int reduced; | ||||
| 3718 | reduced = reduced_using_equalities(v->block.data, bmap2->eq[i], | ||||
| 3719 | bmap1, elim); | ||||
| 3720 | if (reduced && !isl_int_is_zero(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) == 0) && | ||||
| 3721 | isl_seq_first_non_zero(v->block.data + 1, total) == -1) | ||||
| 3722 | goto disjoint; | ||||
| 3723 | } | ||||
| 3724 | for (i = 0; i < bmap2->n_ineq; ++i) { | ||||
| 3725 | int reduced; | ||||
| 3726 | reduced = reduced_using_equalities(v->block.data, | ||||
| 3727 | bmap2->ineq[i], bmap1, elim); | ||||
| 3728 | if (reduced && isl_int_is_neg(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) < 0) && | ||||
| 3729 | isl_seq_first_non_zero(v->block.data + 1, total) == -1) | ||||
| 3730 | goto disjoint; | ||||
| 3731 | } | ||||
| 3732 | compute_elimination_index(bmap2, elim); | ||||
| 3733 | for (i = 0; i < bmap1->n_ineq; ++i) { | ||||
| 3734 | int reduced; | ||||
| 3735 | reduced = reduced_using_equalities(v->block.data, | ||||
| 3736 | bmap1->ineq[i], bmap2, elim); | ||||
| 3737 | if (reduced && isl_int_is_neg(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) < 0) && | ||||
| 3738 | isl_seq_first_non_zero(v->block.data + 1, total) == -1) | ||||
| 3739 | goto disjoint; | ||||
| 3740 | } | ||||
| 3741 | isl_vec_free(v); | ||||
| 3742 | free(elim); | ||||
| 3743 | return isl_bool_false; | ||||
| 3744 | disjoint: | ||||
| 3745 | isl_vec_free(v); | ||||
| 3746 | free(elim); | ||||
| 3747 | return isl_bool_true; | ||||
| 3748 | error: | ||||
| 3749 | isl_vec_free(v); | ||||
| 3750 | free(elim); | ||||
| 3751 | return isl_bool_error; | ||||
| 3752 | } | ||||
| 3753 | |||||
| 3754 | int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_setisl_basic_map *bset1, | ||||
| 3755 | __isl_keep isl_basic_setisl_basic_map *bset2) | ||||
| 3756 | { | ||||
| 3757 | return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1), | ||||
| 3758 | bset_to_bmap(bset2)); | ||||
| 3759 | } | ||||
| 3760 | |||||
| 3761 | /* Does "test" hold for all pairs of basic maps in "map1" and "map2"? | ||||
| 3762 | */ | ||||
| 3763 | static isl_bool all_pairs(__isl_keep isl_map *map1, __isl_keep isl_map *map2, | ||||
| 3764 | isl_bool (*test)(__isl_keep isl_basic_map *bmap1, | ||||
| 3765 | __isl_keep isl_basic_map *bmap2)) | ||||
| 3766 | { | ||||
| 3767 | int i, j; | ||||
| 3768 | |||||
| 3769 | if (!map1 || !map2) | ||||
| 3770 | return isl_bool_error; | ||||
| 3771 | |||||
| 3772 | for (i = 0; i < map1->n; ++i) { | ||||
| 3773 | for (j = 0; j < map2->n; ++j) { | ||||
| 3774 | isl_bool d = test(map1->p[i], map2->p[j]); | ||||
| 3775 | if (d != isl_bool_true) | ||||
| 3776 | return d; | ||||
| 3777 | } | ||||
| 3778 | } | ||||
| 3779 | |||||
| 3780 | return isl_bool_true; | ||||
| 3781 | } | ||||
| 3782 | |||||
| 3783 | /* Are "map1" and "map2" obviously disjoint, based on information | ||||
| 3784 | * that can be derived without looking at the individual basic maps? | ||||
| 3785 | * | ||||
| 3786 | * In particular, if one of them is empty or if they live in different spaces | ||||
| 3787 | * (ignoring parameters), then they are clearly disjoint. | ||||
| 3788 | */ | ||||
| 3789 | static isl_bool isl_map_plain_is_disjoint_global(__isl_keep isl_map *map1, | ||||
| 3790 | __isl_keep isl_map *map2) | ||||
| 3791 | { | ||||
| 3792 | isl_bool disjoint; | ||||
| 3793 | isl_bool match; | ||||
| 3794 | |||||
| 3795 | if (!map1 || !map2) | ||||
| 3796 | return isl_bool_error; | ||||
| 3797 | |||||
| 3798 | disjoint = isl_map_plain_is_empty(map1); | ||||
| 3799 | if (disjoint < 0 || disjoint) | ||||
| 3800 | return disjoint; | ||||
| 3801 | |||||
| 3802 | disjoint = isl_map_plain_is_empty(map2); | ||||
| 3803 | if (disjoint < 0 || disjoint) | ||||
| 3804 | return disjoint; | ||||
| 3805 | |||||
| 3806 | match = isl_space_tuple_is_equal(map1->dim, isl_dim_in, | ||||
| 3807 | map2->dim, isl_dim_in); | ||||
| 3808 | if (match < 0 || !match) | ||||
| 3809 | return match < 0 ? isl_bool_error : isl_bool_true; | ||||
| 3810 | |||||
| 3811 | match = isl_space_tuple_is_equal(map1->dim, isl_dim_out, | ||||
| 3812 | map2->dim, isl_dim_out); | ||||
| 3813 | if (match < 0 || !match) | ||||
| 3814 | return match < 0 ? isl_bool_error : isl_bool_true; | ||||
| 3815 | |||||
| 3816 | return isl_bool_false; | ||||
| 3817 | } | ||||
| 3818 | |||||
| 3819 | /* Are "map1" and "map2" obviously disjoint? | ||||
| 3820 | * | ||||
| 3821 | * If one of them is empty or if they live in different spaces (ignoring | ||||
| 3822 | * parameters), then they are clearly disjoint. | ||||
| 3823 | * This is checked by isl_map_plain_is_disjoint_global. | ||||
| 3824 | * | ||||
| 3825 | * If they have different parameters, then we skip any further tests. | ||||
| 3826 | * | ||||
| 3827 | * If they are obviously equal, but not obviously empty, then we will | ||||
| 3828 | * not be able to detect if they are disjoint. | ||||
| 3829 | * | ||||
| 3830 | * Otherwise we check if each basic map in "map1" is obviously disjoint | ||||
| 3831 | * from each basic map in "map2". | ||||
| 3832 | */ | ||||
| 3833 | isl_bool isl_map_plain_is_disjoint(__isl_keep isl_map *map1, | ||||
| 3834 | __isl_keep isl_map *map2) | ||||
| 3835 | { | ||||
| 3836 | isl_bool disjoint; | ||||
| 3837 | isl_bool intersect; | ||||
| 3838 | isl_bool match; | ||||
| 3839 | |||||
| 3840 | disjoint = isl_map_plain_is_disjoint_global(map1, map2); | ||||
| 3841 | if (disjoint < 0 || disjoint) | ||||
| 3842 | return disjoint; | ||||
| 3843 | |||||
| 3844 | match = isl_map_has_equal_params(map1, map2); | ||||
| 3845 | if (match < 0 || !match) | ||||
| 3846 | return match < 0 ? isl_bool_error : isl_bool_false; | ||||
| 3847 | |||||
| 3848 | intersect = isl_map_plain_is_equal(map1, map2); | ||||
| 3849 | if (intersect < 0 || intersect) | ||||
| 3850 | return intersect < 0 ? isl_bool_error : isl_bool_false; | ||||
| 3851 | |||||
| 3852 | return all_pairs(map1, map2, &isl_basic_map_plain_is_disjoint); | ||||
| 3853 | } | ||||
| 3854 | |||||
| 3855 | /* Are "map1" and "map2" disjoint? | ||||
| 3856 | * The parameters are assumed to have been aligned. | ||||
| 3857 | * | ||||
| 3858 | * In particular, check whether all pairs of basic maps are disjoint. | ||||
| 3859 | */ | ||||
| 3860 | static isl_bool isl_map_is_disjoint_aligned(__isl_keep isl_map *map1, | ||||
| 3861 | __isl_keep isl_map *map2) | ||||
| 3862 | { | ||||
| 3863 | return all_pairs(map1, map2, &isl_basic_map_is_disjoint); | ||||
| 3864 | } | ||||
| 3865 | |||||
| 3866 | /* Are "map1" and "map2" disjoint? | ||||
| 3867 | * | ||||
| 3868 | * They are disjoint if they are "obviously disjoint" or if one of them | ||||
| 3869 | * is empty. Otherwise, they are not disjoint if one of them is universal. | ||||
| 3870 | * If the two inputs are (obviously) equal and not empty, then they are | ||||
| 3871 | * not disjoint. | ||||
| 3872 | * If none of these cases apply, then check if all pairs of basic maps | ||||
| 3873 | * are disjoint after aligning the parameters. | ||||
| 3874 | */ | ||||
| 3875 | isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2) | ||||
| 3876 | { | ||||
| 3877 | isl_bool disjoint; | ||||
| 3878 | isl_bool intersect; | ||||
| 3879 | |||||
| 3880 | disjoint = isl_map_plain_is_disjoint_global(map1, map2); | ||||
| 3881 | if (disjoint < 0 || disjoint) | ||||
| 3882 | return disjoint; | ||||
| 3883 | |||||
| 3884 | disjoint = isl_map_is_empty(map1); | ||||
| 3885 | if (disjoint < 0 || disjoint) | ||||
| 3886 | return disjoint; | ||||
| 3887 | |||||
| 3888 | disjoint = isl_map_is_empty(map2); | ||||
| 3889 | if (disjoint < 0 || disjoint) | ||||
| 3890 | return disjoint; | ||||
| 3891 | |||||
| 3892 | intersect = isl_map_plain_is_universe(map1); | ||||
| 3893 | if (intersect < 0 || intersect) | ||||
| 3894 | return isl_bool_not(intersect); | ||||
| 3895 | |||||
| 3896 | intersect = isl_map_plain_is_universe(map2); | ||||
| 3897 | if (intersect < 0 || intersect) | ||||
| 3898 | return isl_bool_not(intersect); | ||||
| 3899 | |||||
| 3900 | intersect = isl_map_plain_is_equal(map1, map2); | ||||
| 3901 | if (intersect < 0 || intersect) | ||||
| 3902 | return isl_bool_not(intersect); | ||||
| 3903 | |||||
| 3904 | return isl_map_align_params_map_map_and_test(map1, map2, | ||||
| 3905 | &isl_map_is_disjoint_aligned); | ||||
| 3906 | } | ||||
| 3907 | |||||
| 3908 | /* Are "bmap1" and "bmap2" disjoint? | ||||
| 3909 | * | ||||
| 3910 | * They are disjoint if they are "obviously disjoint" or if one of them | ||||
| 3911 | * is empty. Otherwise, they are not disjoint if one of them is universal. | ||||
| 3912 | * If none of these cases apply, we compute the intersection and see if | ||||
| 3913 | * the result is empty. | ||||
| 3914 | */ | ||||
| 3915 | isl_bool isl_basic_map_is_disjoint(__isl_keep isl_basic_map *bmap1, | ||||
| 3916 | __isl_keep isl_basic_map *bmap2) | ||||
| 3917 | { | ||||
| 3918 | isl_bool disjoint; | ||||
| 3919 | isl_bool intersect; | ||||
| 3920 | isl_basic_map *test; | ||||
| 3921 | |||||
| 3922 | disjoint = isl_basic_map_plain_is_disjoint(bmap1, bmap2); | ||||
| 3923 | if (disjoint < 0 || disjoint) | ||||
| 3924 | return disjoint; | ||||
| 3925 | |||||
| 3926 | disjoint = isl_basic_map_is_empty(bmap1); | ||||
| 3927 | if (disjoint < 0 || disjoint) | ||||
| 3928 | return disjoint; | ||||
| 3929 | |||||
| 3930 | disjoint = isl_basic_map_is_empty(bmap2); | ||||
| 3931 | if (disjoint < 0 || disjoint) | ||||
| 3932 | return disjoint; | ||||
| 3933 | |||||
| 3934 | intersect = isl_basic_map_plain_is_universe(bmap1); | ||||
| 3935 | if (intersect < 0 || intersect) | ||||
| 3936 | return isl_bool_not(intersect); | ||||
| 3937 | |||||
| 3938 | intersect = isl_basic_map_plain_is_universe(bmap2); | ||||
| 3939 | if (intersect < 0 || intersect) | ||||
| 3940 | return isl_bool_not(intersect); | ||||
| 3941 | |||||
| 3942 | test = isl_basic_map_intersect(isl_basic_map_copy(bmap1), | ||||
| 3943 | isl_basic_map_copy(bmap2)); | ||||
| 3944 | disjoint = isl_basic_map_is_empty(test); | ||||
| 3945 | isl_basic_map_free(test); | ||||
| 3946 | |||||
| 3947 | return disjoint; | ||||
| 3948 | } | ||||
| 3949 | |||||
| 3950 | /* Are "bset1" and "bset2" disjoint? | ||||
| 3951 | */ | ||||
| 3952 | isl_bool isl_basic_set_is_disjoint(__isl_keep isl_basic_setisl_basic_map *bset1, | ||||
| 3953 | __isl_keep isl_basic_setisl_basic_map *bset2) | ||||
| 3954 | { | ||||
| 3955 | return isl_basic_map_is_disjoint(bset1, bset2); | ||||
| 3956 | } | ||||
| 3957 | |||||
| 3958 | isl_bool isl_set_plain_is_disjoint(__isl_keep isl_setisl_map *set1, | ||||
| 3959 | __isl_keep isl_setisl_map *set2) | ||||
| 3960 | { | ||||
| 3961 | return isl_map_plain_is_disjoint(set_to_map(set1), set_to_map(set2)); | ||||
| 3962 | } | ||||
| 3963 | |||||
| 3964 | /* Are "set1" and "set2" disjoint? | ||||
| 3965 | */ | ||||
| 3966 | isl_bool isl_set_is_disjoint(__isl_keep isl_setisl_map *set1, __isl_keep isl_setisl_map *set2) | ||||
| 3967 | { | ||||
| 3968 | return isl_map_is_disjoint(set1, set2); | ||||
| 3969 | } | ||||
| 3970 | |||||
| 3971 | /* Is "v" equal to 0, 1 or -1? | ||||
| 3972 | */ | ||||
| 3973 | static int is_zero_or_one(isl_int v) | ||||
| 3974 | { | ||||
| 3975 | return isl_int_is_zero(v)(isl_sioimath_sgn(*(v)) == 0) || isl_int_is_one(v)(isl_sioimath_cmp_si(*(v), 1) == 0) || isl_int_is_negone(v)(isl_sioimath_cmp_si(*(v), -1) == 0); | ||||
| 3976 | } | ||||
| 3977 | |||||
| 3978 | /* Are the "n" coefficients starting at "first" of inequality constraints | ||||
| 3979 | * "i" and "j" of "bmap" opposite to each other? | ||||
| 3980 | */ | ||||
| 3981 | static int is_opposite_part(__isl_keep isl_basic_map *bmap, int i, int j, | ||||
| 3982 | int first, int n) | ||||
| 3983 | { | ||||
| 3984 | return isl_seq_is_neg(bmap->ineq[i] + first, bmap->ineq[j] + first, n); | ||||
| 3985 | } | ||||
| 3986 | |||||
| 3987 | /* Are inequality constraints "i" and "j" of "bmap" opposite to each other, | ||||
| 3988 | * apart from the constant term? | ||||
| 3989 | */ | ||||
| 3990 | static isl_bool is_opposite(__isl_keep isl_basic_map *bmap, int i, int j) | ||||
| 3991 | { | ||||
| 3992 | isl_size total; | ||||
| 3993 | |||||
| 3994 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 3995 | if (total < 0) | ||||
| 3996 | return isl_bool_error; | ||||
| 3997 | return is_opposite_part(bmap, i, j, 1, total); | ||||
| 3998 | } | ||||
| 3999 | |||||
| 4000 | /* Check if we can combine a given div with lower bound l and upper | ||||
| 4001 | * bound u with some other div and if so return that other div. | ||||
| 4002 | * Otherwise, return a position beyond the integer divisions. | ||||
| 4003 | * Return -1 on error. | ||||
| 4004 | * | ||||
| 4005 | * We first check that | ||||
| 4006 | * - the bounds are opposites of each other (except for the constant | ||||
| 4007 | * term) | ||||
| 4008 | * - the bounds do not reference any other div | ||||
| 4009 | * - no div is defined in terms of this div | ||||
| 4010 | * | ||||
| 4011 | * Let m be the size of the range allowed on the div by the bounds. | ||||
| 4012 | * That is, the bounds are of the form | ||||
| 4013 | * | ||||
| 4014 | * e <= a <= e + m - 1 | ||||
| 4015 | * | ||||
| 4016 | * with e some expression in the other variables. | ||||
| 4017 | * We look for another div b such that no third div is defined in terms | ||||
| 4018 | * of this second div b and such that in any constraint that contains | ||||
| 4019 | * a (except for the given lower and upper bound), also contains b | ||||
| 4020 | * with a coefficient that is m times that of b. | ||||
| 4021 | * That is, all constraints (except for the lower and upper bound) | ||||
| 4022 | * are of the form | ||||
| 4023 | * | ||||
| 4024 | * e + f (a + m b) >= 0 | ||||
| 4025 | * | ||||
| 4026 | * Furthermore, in the constraints that only contain b, the coefficient | ||||
| 4027 | * of b should be equal to 1 or -1. | ||||
| 4028 | * If so, we return b so that "a + m b" can be replaced by | ||||
| 4029 | * a single div "c = a + m b". | ||||
| 4030 | */ | ||||
| 4031 | static int div_find_coalesce(__isl_keep isl_basic_map *bmap, int *pairs, | ||||
| 4032 | unsigned div, unsigned l, unsigned u) | ||||
| 4033 | { | ||||
| 4034 | int i, j; | ||||
| 4035 | unsigned n_div; | ||||
| 4036 | isl_size v_div; | ||||
| 4037 | int coalesce; | ||||
| 4038 | isl_bool opp; | ||||
| 4039 | |||||
| 4040 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 4041 | if (n_div <= 1) | ||||
| 4042 | return n_div; | ||||
| 4043 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 4044 | if (v_div < 0) | ||||
| 4045 | return -1; | ||||
| 4046 | if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + v_div, div) != -1) | ||||
| 4047 | return n_div; | ||||
| 4048 | if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + v_div + div + 1, | ||||
| 4049 | n_div - div - 1) != -1) | ||||
| 4050 | return n_div; | ||||
| 4051 | opp = is_opposite(bmap, l, u); | ||||
| 4052 | if (opp < 0 || !opp) | ||||
| 4053 | return opp < 0 ? -1 : n_div; | ||||
| 4054 | |||||
| 4055 | for (i = 0; i < n_div; ++i) { | ||||
| 4056 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
| 4057 | continue; | ||||
| 4058 | if (!isl_int_is_zero(bmap->div[i][1 + 1 + v_div + div])(isl_sioimath_sgn(*(bmap->div[i][1 + 1 + v_div + div])) == 0)) | ||||
| 4059 | return n_div; | ||||
| 4060 | } | ||||
| 4061 | |||||
| 4062 | isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_add((bmap->ineq[l][0]), *(bmap->ineq[l][0] ), *(bmap->ineq[u][0])); | ||||
| 4063 | if (isl_int_is_neg(bmap->ineq[l][0])(isl_sioimath_sgn(*(bmap->ineq[l][0])) < 0)) { | ||||
| 4064 | isl_int_sub(bmap->ineq[l][0],isl_sioimath_sub((bmap->ineq[l][0]), *(bmap->ineq[l][0] ), *(bmap->ineq[u][0])) | ||||
| 4065 | bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_sub((bmap->ineq[l][0]), *(bmap->ineq[l][0] ), *(bmap->ineq[u][0])); | ||||
| 4066 | bmap = isl_basic_map_copy(bmap); | ||||
| 4067 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
| 4068 | isl_basic_map_free(bmap); | ||||
| 4069 | return n_div; | ||||
| 4070 | } | ||||
| 4071 | isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1)isl_sioimath_add_ui((bmap->ineq[l][0]), *(bmap->ineq[l] [0]), 1); | ||||
| 4072 | coalesce = n_div; | ||||
| 4073 | for (i = 0; i < n_div; ++i) { | ||||
| 4074 | if (i == div) | ||||
| 4075 | continue; | ||||
| 4076 | if (!pairs[i]) | ||||
| 4077 | continue; | ||||
| 4078 | for (j = 0; j < n_div; ++j) { | ||||
| 4079 | if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0)) | ||||
| 4080 | continue; | ||||
| 4081 | if (!isl_int_is_zero(bmap->div[j][1 + 1 + v_div + i])(isl_sioimath_sgn(*(bmap->div[j][1 + 1 + v_div + i])) == 0 )) | ||||
| 4082 | break; | ||||
| 4083 | } | ||||
| 4084 | if (j < n_div) | ||||
| 4085 | continue; | ||||
| 4086 | for (j = 0; j < bmap->n_ineq; ++j) { | ||||
| 4087 | int valid; | ||||
| 4088 | if (j == l || j == u) | ||||
| 4089 | continue; | ||||
| 4090 | if (isl_int_is_zero(bmap->ineq[j][1 + v_div + div])(isl_sioimath_sgn(*(bmap->ineq[j][1 + v_div + div])) == 0)) { | ||||
| 4091 | if (is_zero_or_one(bmap->ineq[j][1 + v_div + i])) | ||||
| 4092 | continue; | ||||
| 4093 | break; | ||||
| 4094 | } | ||||
| 4095 | if (isl_int_is_zero(bmap->ineq[j][1 + v_div + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + v_div + i])) == 0)) | ||||
| 4096 | break; | ||||
| 4097 | isl_int_mul(bmap->ineq[j][1 + v_div + div],isl_sioimath_mul((bmap->ineq[j][1 + v_div + div]), *(bmap-> ineq[j][1 + v_div + div]), *(bmap->ineq[l][0])) | ||||
| 4098 | bmap->ineq[j][1 + v_div + div],isl_sioimath_mul((bmap->ineq[j][1 + v_div + div]), *(bmap-> ineq[j][1 + v_div + div]), *(bmap->ineq[l][0])) | ||||
| 4099 | bmap->ineq[l][0])isl_sioimath_mul((bmap->ineq[j][1 + v_div + div]), *(bmap-> ineq[j][1 + v_div + div]), *(bmap->ineq[l][0])); | ||||
| 4100 | valid = isl_int_eq(bmap->ineq[j][1 + v_div + div],(isl_sioimath_cmp(*(bmap->ineq[j][1 + v_div + div]), *(bmap ->ineq[j][1 + v_div + i])) == 0) | ||||
| 4101 | bmap->ineq[j][1 + v_div + i])(isl_sioimath_cmp(*(bmap->ineq[j][1 + v_div + div]), *(bmap ->ineq[j][1 + v_div + i])) == 0); | ||||
| 4102 | isl_int_divexact(bmap->ineq[j][1 + v_div + div],isl_sioimath_tdiv_q((bmap->ineq[j][1 + v_div + div]), *(bmap ->ineq[j][1 + v_div + div]), *(bmap->ineq[l][0])) | ||||
| 4103 | bmap->ineq[j][1 + v_div + div],isl_sioimath_tdiv_q((bmap->ineq[j][1 + v_div + div]), *(bmap ->ineq[j][1 + v_div + div]), *(bmap->ineq[l][0])) | ||||
| 4104 | bmap->ineq[l][0])isl_sioimath_tdiv_q((bmap->ineq[j][1 + v_div + div]), *(bmap ->ineq[j][1 + v_div + div]), *(bmap->ineq[l][0])); | ||||
| 4105 | if (!valid) | ||||
| 4106 | break; | ||||
| 4107 | } | ||||
| 4108 | if (j < bmap->n_ineq) | ||||
| 4109 | continue; | ||||
| 4110 | coalesce = i; | ||||
| 4111 | break; | ||||
| 4112 | } | ||||
| 4113 | isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1)isl_sioimath_sub_ui((bmap->ineq[l][0]), *(bmap->ineq[l] [0]), 1); | ||||
| 4114 | isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_sub((bmap->ineq[l][0]), *(bmap->ineq[l][0] ), *(bmap->ineq[u][0])); | ||||
| 4115 | return coalesce; | ||||
| 4116 | } | ||||
| 4117 | |||||
| 4118 | /* Internal data structure used during the construction and/or evaluation of | ||||
| 4119 | * an inequality that ensures that a pair of bounds always allows | ||||
| 4120 | * for an integer value. | ||||
| 4121 | * | ||||
| 4122 | * "tab" is the tableau in which the inequality is evaluated. It may | ||||
| 4123 | * be NULL until it is actually needed. | ||||
| 4124 | * "v" contains the inequality coefficients. | ||||
| 4125 | * "g", "fl" and "fu" are temporary scalars used during the construction and | ||||
| 4126 | * evaluation. | ||||
| 4127 | */ | ||||
| 4128 | struct test_ineq_data { | ||||
| 4129 | struct isl_tab *tab; | ||||
| 4130 | isl_vec *v; | ||||
| 4131 | isl_int g; | ||||
| 4132 | isl_int fl; | ||||
| 4133 | isl_int fu; | ||||
| 4134 | }; | ||||
| 4135 | |||||
| 4136 | /* Free all the memory allocated by the fields of "data". | ||||
| 4137 | */ | ||||
| 4138 | static void test_ineq_data_clear(struct test_ineq_data *data) | ||||
| 4139 | { | ||||
| 4140 | isl_tab_free(data->tab); | ||||
| 4141 | isl_vec_free(data->v); | ||||
| 4142 | isl_int_clear(data->g)isl_sioimath_clear((data->g)); | ||||
| 4143 | isl_int_clear(data->fl)isl_sioimath_clear((data->fl)); | ||||
| 4144 | isl_int_clear(data->fu)isl_sioimath_clear((data->fu)); | ||||
| 4145 | } | ||||
| 4146 | |||||
| 4147 | /* Is the inequality stored in data->v satisfied by "bmap"? | ||||
| 4148 | * That is, does it only attain non-negative values? | ||||
| 4149 | * data->tab is a tableau corresponding to "bmap". | ||||
| 4150 | */ | ||||
| 4151 | static isl_bool test_ineq_is_satisfied(__isl_keep isl_basic_map *bmap, | ||||
| 4152 | struct test_ineq_data *data) | ||||
| 4153 | { | ||||
| 4154 | isl_ctx *ctx; | ||||
| 4155 | enum isl_lp_result res; | ||||
| 4156 | |||||
| 4157 | ctx = isl_basic_map_get_ctx(bmap); | ||||
| 4158 | if (!data->tab) | ||||
| 4159 | data->tab = isl_tab_from_basic_map(bmap, 0); | ||||
| 4160 | res = isl_tab_min(data->tab, data->v->el, ctx->one, &data->g, NULL((void*)0), 0); | ||||
| 4161 | if (res == isl_lp_error) | ||||
| 4162 | return isl_bool_error; | ||||
| 4163 | return res == isl_lp_ok && isl_int_is_nonneg(data->g)(isl_sioimath_sgn(*(data->g)) >= 0); | ||||
| 4164 | } | ||||
| 4165 | |||||
| 4166 | /* Given a lower and an upper bound on div i, do they always allow | ||||
| 4167 | * for an integer value of the given div? | ||||
| 4168 | * Determine this property by constructing an inequality | ||||
| 4169 | * such that the property is guaranteed when the inequality is nonnegative. | ||||
| 4170 | * The lower bound is inequality l, while the upper bound is inequality u. | ||||
| 4171 | * The constructed inequality is stored in data->v. | ||||
| 4172 | * | ||||
| 4173 | * Let the upper bound be | ||||
| 4174 | * | ||||
| 4175 | * -n_u a + e_u >= 0 | ||||
| 4176 | * | ||||
| 4177 | * and the lower bound | ||||
| 4178 | * | ||||
| 4179 | * n_l a + e_l >= 0 | ||||
| 4180 | * | ||||
| 4181 | * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l). | ||||
| 4182 | * We have | ||||
| 4183 | * | ||||
| 4184 | * - f_u e_l <= f_u f_l g a <= f_l e_u | ||||
| 4185 | * | ||||
| 4186 | * Since all variables are integer valued, this is equivalent to | ||||
| 4187 | * | ||||
| 4188 | * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1) | ||||
| 4189 | * | ||||
| 4190 | * If this interval is at least f_u f_l g, then it contains at least | ||||
| 4191 | * one integer value for a. | ||||
| 4192 | * That is, the test constraint is | ||||
| 4193 | * | ||||
| 4194 | * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g | ||||
| 4195 | * | ||||
| 4196 | * or | ||||
| 4197 | * | ||||
| 4198 | * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0 | ||||
| 4199 | * | ||||
| 4200 | * If the coefficients of f_l e_u + f_u e_l have a common divisor g', | ||||
| 4201 | * then the constraint can be scaled down by a factor g', | ||||
| 4202 | * with the constant term replaced by | ||||
| 4203 | * floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g'). | ||||
| 4204 | * Note that the result of applying Fourier-Motzkin to this pair | ||||
| 4205 | * of constraints is | ||||
| 4206 | * | ||||
| 4207 | * f_l e_u + f_u e_l >= 0 | ||||
| 4208 | * | ||||
| 4209 | * If the constant term of the scaled down version of this constraint, | ||||
| 4210 | * i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant | ||||
| 4211 | * term of the scaled down test constraint, then the test constraint | ||||
| 4212 | * is known to hold and no explicit evaluation is required. | ||||
| 4213 | * This is essentially the Omega test. | ||||
| 4214 | * | ||||
| 4215 | * If the test constraint consists of only a constant term, then | ||||
| 4216 | * it is sufficient to look at the sign of this constant term. | ||||
| 4217 | */ | ||||
| 4218 | static isl_bool int_between_bounds(__isl_keep isl_basic_map *bmap, int i, | ||||
| 4219 | int l, int u, struct test_ineq_data *data) | ||||
| 4220 | { | ||||
| 4221 | unsigned offset; | ||||
| 4222 | isl_size n_div; | ||||
| 4223 | |||||
| 4224 | offset = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 4225 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 4226 | if (n_div < 0) | ||||
| 4227 | return isl_bool_error; | ||||
| 4228 | |||||
| 4229 | isl_int_gcd(data->g,isl_sioimath_gcd((data->g), *(bmap->ineq[l][offset + i] ), *(bmap->ineq[u][offset + i])) | ||||
| 4230 | bmap->ineq[l][offset + i], bmap->ineq[u][offset + i])isl_sioimath_gcd((data->g), *(bmap->ineq[l][offset + i] ), *(bmap->ineq[u][offset + i])); | ||||
| 4231 | isl_int_divexact(data->fl, bmap->ineq[l][offset + i], data->g)isl_sioimath_tdiv_q((data->fl), *(bmap->ineq[l][offset + i]), *(data->g)); | ||||
| 4232 | isl_int_divexact(data->fu, bmap->ineq[u][offset + i], data->g)isl_sioimath_tdiv_q((data->fu), *(bmap->ineq[u][offset + i]), *(data->g)); | ||||
| 4233 | isl_int_neg(data->fu, data->fu)isl_sioimath_neg((data->fu), *(data->fu)); | ||||
| 4234 | isl_seq_combine(data->v->el, data->fl, bmap->ineq[u], | ||||
| 4235 | data->fu, bmap->ineq[l], offset + n_div); | ||||
| 4236 | isl_int_mul(data->g, data->g, data->fl)isl_sioimath_mul((data->g), *(data->g), *(data->fl)); | ||||
| 4237 | isl_int_mul(data->g, data->g, data->fu)isl_sioimath_mul((data->g), *(data->g), *(data->fu)); | ||||
| 4238 | isl_int_sub(data->g, data->g, data->fl)isl_sioimath_sub((data->g), *(data->g), *(data->fl)); | ||||
| 4239 | isl_int_sub(data->g, data->g, data->fu)isl_sioimath_sub((data->g), *(data->g), *(data->fu)); | ||||
| 4240 | isl_int_add_ui(data->g, data->g, 1)isl_sioimath_add_ui((data->g), *(data->g), 1); | ||||
| 4241 | isl_int_sub(data->fl, data->v->el[0], data->g)isl_sioimath_sub((data->fl), *(data->v->el[0]), *(data ->g)); | ||||
| 4242 | |||||
| 4243 | isl_seq_gcd(data->v->el + 1, offset - 1 + n_div, &data->g); | ||||
| 4244 | if (isl_int_is_zero(data->g)(isl_sioimath_sgn(*(data->g)) == 0)) | ||||
| 4245 | return isl_int_is_nonneg(data->fl)(isl_sioimath_sgn(*(data->fl)) >= 0); | ||||
| 4246 | if (isl_int_is_one(data->g)(isl_sioimath_cmp_si(*(data->g), 1) == 0)) { | ||||
| 4247 | isl_int_set(data->v->el[0], data->fl)isl_sioimath_set((data->v->el[0]), *(data->fl)); | ||||
| 4248 | return test_ineq_is_satisfied(bmap, data); | ||||
| 4249 | } | ||||
| 4250 | isl_int_fdiv_q(data->fl, data->fl, data->g)isl_sioimath_fdiv_q((data->fl), *(data->fl), *(data-> g)); | ||||
| 4251 | isl_int_fdiv_q(data->v->el[0], data->v->el[0], data->g)isl_sioimath_fdiv_q((data->v->el[0]), *(data->v-> el[0]), *(data->g)); | ||||
| 4252 | if (isl_int_eq(data->fl, data->v->el[0])(isl_sioimath_cmp(*(data->fl), *(data->v->el[0])) == 0)) | ||||
| 4253 | return isl_bool_true; | ||||
| 4254 | isl_int_set(data->v->el[0], data->fl)isl_sioimath_set((data->v->el[0]), *(data->fl)); | ||||
| 4255 | isl_seq_scale_down(data->v->el + 1, data->v->el + 1, data->g, | ||||
| 4256 | offset - 1 + n_div); | ||||
| 4257 | |||||
| 4258 | return test_ineq_is_satisfied(bmap, data); | ||||
| 4259 | } | ||||
| 4260 | |||||
| 4261 | /* Remove more kinds of divs that are not strictly needed. | ||||
| 4262 | * In particular, if all pairs of lower and upper bounds on a div | ||||
| 4263 | * are such that they allow at least one integer value of the div, | ||||
| 4264 | * then we can eliminate the div using Fourier-Motzkin without | ||||
| 4265 | * introducing any spurious solutions. | ||||
| 4266 | * | ||||
| 4267 | * If at least one of the two constraints has a unit coefficient for the div, | ||||
| 4268 | * then the presence of such a value is guaranteed so there is no need to check. | ||||
| 4269 | * In particular, the value attained by the bound with unit coefficient | ||||
| 4270 | * can serve as this intermediate value. | ||||
| 4271 | */ | ||||
| 4272 | static __isl_give isl_basic_map *drop_more_redundant_divs( | ||||
| 4273 | __isl_take isl_basic_map *bmap, __isl_take int *pairs, int n) | ||||
| 4274 | { | ||||
| 4275 | isl_ctx *ctx; | ||||
| 4276 | struct test_ineq_data data = { NULL((void*)0), NULL((void*)0) }; | ||||
| 4277 | unsigned off; | ||||
| 4278 | isl_size n_div; | ||||
| 4279 | int remove = -1; | ||||
| 4280 | |||||
| 4281 | isl_int_init(data.g)isl_sioimath_init((data.g)); | ||||
| 4282 | isl_int_init(data.fl)isl_sioimath_init((data.fl)); | ||||
| 4283 | isl_int_init(data.fu)isl_sioimath_init((data.fu)); | ||||
| 4284 | |||||
| 4285 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 4286 | if (n_div < 0) | ||||
| 4287 | goto error; | ||||
| 4288 | |||||
| 4289 | ctx = isl_basic_map_get_ctx(bmap); | ||||
| 4290 | off = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 4291 | data.v = isl_vec_alloc(ctx, off + n_div); | ||||
| 4292 | if (!data.v) | ||||
| 4293 | goto error; | ||||
| 4294 | |||||
| 4295 | while (n > 0) { | ||||
| 4296 | int i, l, u; | ||||
| 4297 | int best = -1; | ||||
| 4298 | isl_bool has_int; | ||||
| 4299 | |||||
| 4300 | for (i = 0; i < n_div; ++i) { | ||||
| 4301 | if (!pairs[i]) | ||||
| 4302 | continue; | ||||
| 4303 | if (best >= 0 && pairs[best] <= pairs[i]) | ||||
| 4304 | continue; | ||||
| 4305 | best = i; | ||||
| 4306 | } | ||||
| 4307 | |||||
| 4308 | i = best; | ||||
| 4309 | for (l = 0; l < bmap->n_ineq; ++l) { | ||||
| 4310 | if (!isl_int_is_pos(bmap->ineq[l][off + i])(isl_sioimath_sgn(*(bmap->ineq[l][off + i])) > 0)) | ||||
| 4311 | continue; | ||||
| 4312 | if (isl_int_is_one(bmap->ineq[l][off + i])(isl_sioimath_cmp_si(*(bmap->ineq[l][off + i]), 1) == 0)) | ||||
| 4313 | continue; | ||||
| 4314 | for (u = 0; u < bmap->n_ineq; ++u) { | ||||
| 4315 | if (!isl_int_is_neg(bmap->ineq[u][off + i])(isl_sioimath_sgn(*(bmap->ineq[u][off + i])) < 0)) | ||||
| 4316 | continue; | ||||
| 4317 | if (isl_int_is_negone(bmap->ineq[u][off + i])(isl_sioimath_cmp_si(*(bmap->ineq[u][off + i]), -1) == 0)) | ||||
| 4318 | continue; | ||||
| 4319 | has_int = int_between_bounds(bmap, i, l, u, | ||||
| 4320 | &data); | ||||
| 4321 | if (has_int < 0) | ||||
| 4322 | goto error; | ||||
| 4323 | if (data.tab && data.tab->empty) | ||||
| 4324 | break; | ||||
| 4325 | if (!has_int) | ||||
| 4326 | break; | ||||
| 4327 | } | ||||
| 4328 | if (u < bmap->n_ineq) | ||||
| 4329 | break; | ||||
| 4330 | } | ||||
| 4331 | if (data.tab && data.tab->empty) { | ||||
| 4332 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
| 4333 | break; | ||||
| 4334 | } | ||||
| 4335 | if (l == bmap->n_ineq) { | ||||
| 4336 | remove = i; | ||||
| 4337 | break; | ||||
| 4338 | } | ||||
| 4339 | pairs[i] = 0; | ||||
| 4340 | --n; | ||||
| 4341 | } | ||||
| 4342 | |||||
| 4343 | test_ineq_data_clear(&data); | ||||
| 4344 | |||||
| 4345 | free(pairs); | ||||
| 4346 | |||||
| 4347 | if (remove < 0) | ||||
| 4348 | return bmap; | ||||
| 4349 | |||||
| 4350 | bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1); | ||||
| 4351 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
| 4352 | error: | ||||
| 4353 | free(pairs); | ||||
| 4354 | isl_basic_map_free(bmap); | ||||
| 4355 | test_ineq_data_clear(&data); | ||||
| 4356 | return NULL((void*)0); | ||||
| 4357 | } | ||||
| 4358 | |||||
| 4359 | /* Given a pair of divs div1 and div2 such that, except for the lower bound l | ||||
| 4360 | * and the upper bound u, div1 always occurs together with div2 in the form | ||||
| 4361 | * (div1 + m div2), where m is the constant range on the variable div1 | ||||
| 4362 | * allowed by l and u, replace the pair div1 and div2 by a single | ||||
| 4363 | * div that is equal to div1 + m div2. | ||||
| 4364 | * | ||||
| 4365 | * The new div will appear in the location that contains div2. | ||||
| 4366 | * We need to modify all constraints that contain | ||||
| 4367 | * div2 = (div - div1) / m | ||||
| 4368 | * The coefficient of div2 is known to be equal to 1 or -1. | ||||
| 4369 | * (If a constraint does not contain div2, it will also not contain div1.) | ||||
| 4370 | * If the constraint also contains div1, then we know they appear | ||||
| 4371 | * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div, | ||||
| 4372 | * i.e., the coefficient of div is f. | ||||
| 4373 | * | ||||
| 4374 | * Otherwise, we first need to introduce div1 into the constraint. | ||||
| 4375 | * Let l be | ||||
| 4376 | * | ||||
| 4377 | * div1 + f >=0 | ||||
| 4378 | * | ||||
| 4379 | * and u | ||||
| 4380 | * | ||||
| 4381 | * -div1 + f' >= 0 | ||||
| 4382 | * | ||||
| 4383 | * A lower bound on div2 | ||||
| 4384 | * | ||||
| 4385 | * div2 + t >= 0 | ||||
| 4386 | * | ||||
| 4387 | * can be replaced by | ||||
| 4388 | * | ||||
| 4389 | * m div2 + div1 + m t + f >= 0 | ||||
| 4390 | * | ||||
| 4391 | * An upper bound | ||||
| 4392 | * | ||||
| 4393 | * -div2 + t >= 0 | ||||
| 4394 | * | ||||
| 4395 | * can be replaced by | ||||
| 4396 | * | ||||
| 4397 | * -(m div2 + div1) + m t + f' >= 0 | ||||
| 4398 | * | ||||
| 4399 | * These constraint are those that we would obtain from eliminating | ||||
| 4400 | * div1 using Fourier-Motzkin. | ||||
| 4401 | * | ||||
| 4402 | * After all constraints have been modified, we drop the lower and upper | ||||
| 4403 | * bound and then drop div1. | ||||
| 4404 | * Since the new div is only placed in the same location that used | ||||
| 4405 | * to store div2, but otherwise has a different meaning, any possible | ||||
| 4406 | * explicit representation of the original div2 is removed. | ||||
| 4407 | */ | ||||
| 4408 | static __isl_give isl_basic_map *coalesce_divs(__isl_take isl_basic_map *bmap, | ||||
| 4409 | unsigned div1, unsigned div2, unsigned l, unsigned u) | ||||
| 4410 | { | ||||
| 4411 | isl_ctx *ctx; | ||||
| 4412 | isl_int m; | ||||
| 4413 | isl_size v_div; | ||||
| 4414 | unsigned total; | ||||
| 4415 | int i; | ||||
| 4416 | |||||
| 4417 | ctx = isl_basic_map_get_ctx(bmap); | ||||
| 4418 | |||||
| 4419 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 4420 | if (v_div < 0) | ||||
| 4421 | return isl_basic_map_free(bmap); | ||||
| 4422 | total = 1 + v_div + bmap->n_div; | ||||
| 4423 | |||||
| 4424 | isl_int_init(m)isl_sioimath_init((m)); | ||||
| 4425 | isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_add((m), *(bmap->ineq[l][0]), *(bmap->ineq [u][0])); | ||||
| 4426 | isl_int_add_ui(m, m, 1)isl_sioimath_add_ui((m), *(m), 1); | ||||
| 4427 | |||||
| 4428 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
| 4429 | if (i == l || i == u) | ||||
| 4430 | continue; | ||||
| 4431 | if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div2])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div2])) == 0 )) | ||||
| 4432 | continue; | ||||
| 4433 | if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div1])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div1])) == 0 )) { | ||||
| 4434 | if (isl_int_is_pos(bmap->ineq[i][1 + v_div + div2])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div2])) > 0)) | ||||
| 4435 | isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i], | ||||
| 4436 | ctx->one, bmap->ineq[l], total); | ||||
| 4437 | else | ||||
| 4438 | isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i], | ||||
| 4439 | ctx->one, bmap->ineq[u], total); | ||||
| 4440 | } | ||||
| 4441 | isl_int_set(bmap->ineq[i][1 + v_div + div2],isl_sioimath_set((bmap->ineq[i][1 + v_div + div2]), *(bmap ->ineq[i][1 + v_div + div1])) | ||||
| 4442 | bmap->ineq[i][1 + v_div + div1])isl_sioimath_set((bmap->ineq[i][1 + v_div + div2]), *(bmap ->ineq[i][1 + v_div + div1])); | ||||
| 4443 | isl_int_set_si(bmap->ineq[i][1 + v_div + div1], 0)isl_sioimath_set_si((bmap->ineq[i][1 + v_div + div1]), 0); | ||||
| 4444 | } | ||||
| 4445 | |||||
| 4446 | isl_int_clear(m)isl_sioimath_clear((m)); | ||||
| 4447 | if (l > u) { | ||||
| 4448 | isl_basic_map_drop_inequality(bmap, l); | ||||
| 4449 | isl_basic_map_drop_inequality(bmap, u); | ||||
| 4450 | } else { | ||||
| 4451 | isl_basic_map_drop_inequality(bmap, u); | ||||
| 4452 | isl_basic_map_drop_inequality(bmap, l); | ||||
| 4453 | } | ||||
| 4454 | bmap = isl_basic_map_mark_div_unknown(bmap, div2); | ||||
| 4455 | bmap = isl_basic_map_drop_div(bmap, div1); | ||||
| 4456 | return bmap; | ||||
| 4457 | } | ||||
| 4458 | |||||
| 4459 | /* First check if we can coalesce any pair of divs and | ||||
| 4460 | * then continue with dropping more redundant divs. | ||||
| 4461 | * | ||||
| 4462 | * We loop over all pairs of lower and upper bounds on a div | ||||
| 4463 | * with coefficient 1 and -1, respectively, check if there | ||||
| 4464 | * is any other div "c" with which we can coalesce the div | ||||
| 4465 | * and if so, perform the coalescing. | ||||
| 4466 | */ | ||||
| 4467 | static __isl_give isl_basic_map *coalesce_or_drop_more_redundant_divs( | ||||
| 4468 | __isl_take isl_basic_map *bmap, int *pairs, int n) | ||||
| 4469 | { | ||||
| 4470 | int i, l, u; | ||||
| 4471 | isl_size v_div; | ||||
| 4472 | isl_size n_div; | ||||
| 4473 | |||||
| 4474 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 4475 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 4476 | if (v_div < 0 || n_div < 0) | ||||
| 4477 | return isl_basic_map_free(bmap); | ||||
| 4478 | |||||
| 4479 | for (i = 0; i < n_div; ++i) { | ||||
| 4480 | if (!pairs[i]) | ||||
| 4481 | continue; | ||||
| 4482 | for (l = 0; l < bmap->n_ineq; ++l) { | ||||
| 4483 | if (!isl_int_is_one(bmap->ineq[l][1 + v_div + i])(isl_sioimath_cmp_si(*(bmap->ineq[l][1 + v_div + i]), 1) == 0)) | ||||
| 4484 | continue; | ||||
| 4485 | for (u = 0; u < bmap->n_ineq; ++u) { | ||||
| 4486 | int c; | ||||
| 4487 | |||||
| 4488 | if (!isl_int_is_negone(bmap->ineq[u][1+v_div+i])(isl_sioimath_cmp_si(*(bmap->ineq[u][1+v_div+i]), -1) == 0 )) | ||||
| 4489 | continue; | ||||
| 4490 | c = div_find_coalesce(bmap, pairs, i, l, u); | ||||
| 4491 | if (c < 0) | ||||
| 4492 | goto error; | ||||
| 4493 | if (c >= n_div) | ||||
| 4494 | continue; | ||||
| 4495 | free(pairs); | ||||
| 4496 | bmap = coalesce_divs(bmap, i, c, l, u); | ||||
| 4497 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
| 4498 | } | ||||
| 4499 | } | ||||
| 4500 | } | ||||
| 4501 | |||||
| 4502 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1))))) { | ||||
| 4503 | free(pairs); | ||||
| 4504 | return bmap; | ||||
| 4505 | } | ||||
| 4506 | |||||
| 4507 | return drop_more_redundant_divs(bmap, pairs, n); | ||||
| 4508 | error: | ||||
| 4509 | free(pairs); | ||||
| 4510 | isl_basic_map_free(bmap); | ||||
| 4511 | return NULL((void*)0); | ||||
| 4512 | } | ||||
| 4513 | |||||
| 4514 | /* Are the "n" coefficients starting at "first" of inequality constraints | ||||
| 4515 | * "i" and "j" of "bmap" equal to each other? | ||||
| 4516 | */ | ||||
| 4517 | static int is_parallel_part(__isl_keep isl_basic_map *bmap, int i, int j, | ||||
| 4518 | int first, int n) | ||||
| 4519 | { | ||||
| 4520 | return isl_seq_eq(bmap->ineq[i] + first, bmap->ineq[j] + first, n); | ||||
| 4521 | } | ||||
| 4522 | |||||
| 4523 | /* Are inequality constraints "i" and "j" of "bmap" equal to each other, | ||||
| 4524 | * apart from the constant term and the coefficient at position "pos"? | ||||
| 4525 | */ | ||||
| 4526 | static isl_bool is_parallel_except(__isl_keep isl_basic_map *bmap, int i, int j, | ||||
| 4527 | int pos) | ||||
| 4528 | { | ||||
| 4529 | isl_size total; | ||||
| 4530 | |||||
| 4531 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 4532 | if (total < 0) | ||||
| 4533 | return isl_bool_error; | ||||
| 4534 | return is_parallel_part(bmap, i, j, 1, pos - 1) && | ||||
| 4535 | is_parallel_part(bmap, i, j, pos + 1, total - pos); | ||||
| 4536 | } | ||||
| 4537 | |||||
| 4538 | /* Are inequality constraints "i" and "j" of "bmap" opposite to each other, | ||||
| 4539 | * apart from the constant term and the coefficient at position "pos"? | ||||
| 4540 | */ | ||||
| 4541 | static isl_bool is_opposite_except(__isl_keep isl_basic_map *bmap, int i, int j, | ||||
| 4542 | int pos) | ||||
| 4543 | { | ||||
| 4544 | isl_size total; | ||||
| 4545 | |||||
| 4546 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 4547 | if (total < 0) | ||||
| 4548 | return isl_bool_error; | ||||
| 4549 | return is_opposite_part(bmap, i, j, 1, pos - 1) && | ||||
| 4550 | is_opposite_part(bmap, i, j, pos + 1, total - pos); | ||||
| 4551 | } | ||||
| 4552 | |||||
| 4553 | /* Restart isl_basic_map_drop_redundant_divs after "bmap" has | ||||
| 4554 | * been modified, simplying it if "simplify" is set. | ||||
| 4555 | * Free the temporary data structure "pairs" that was associated | ||||
| 4556 | * to the old version of "bmap". | ||||
| 4557 | */ | ||||
| 4558 | static __isl_give isl_basic_map *drop_redundant_divs_again( | ||||
| 4559 | __isl_take isl_basic_map *bmap, __isl_take int *pairs, int simplify) | ||||
| 4560 | { | ||||
| 4561 | if (simplify) | ||||
| 4562 | bmap = isl_basic_map_simplify(bmap); | ||||
| 4563 | free(pairs); | ||||
| 4564 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
| 4565 | } | ||||
| 4566 | |||||
| 4567 | /* Is "div" the single unknown existentially quantified variable | ||||
| 4568 | * in inequality constraint "ineq" of "bmap"? | ||||
| 4569 | * "div" is known to have a non-zero coefficient in "ineq". | ||||
| 4570 | */ | ||||
| 4571 | static isl_bool single_unknown(__isl_keep isl_basic_map *bmap, int ineq, | ||||
| 4572 | int div) | ||||
| 4573 | { | ||||
| 4574 | int i; | ||||
| 4575 | isl_size n_div; | ||||
| 4576 | unsigned o_div; | ||||
| 4577 | isl_bool known; | ||||
| 4578 | |||||
| 4579 | known = isl_basic_map_div_is_known(bmap, div); | ||||
| 4580 | if (known < 0 || known) | ||||
| 4581 | return isl_bool_not(known); | ||||
| 4582 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 4583 | if (n_div < 0) | ||||
| 4584 | return isl_bool_error; | ||||
| 4585 | if (n_div == 1) | ||||
| 4586 | return isl_bool_true; | ||||
| 4587 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 4588 | for (i = 0; i < n_div; ++i) { | ||||
| 4589 | isl_bool known; | ||||
| 4590 | |||||
| 4591 | if (i == div) | ||||
| 4592 | continue; | ||||
| 4593 | if (isl_int_is_zero(bmap->ineq[ineq][o_div + i])(isl_sioimath_sgn(*(bmap->ineq[ineq][o_div + i])) == 0)) | ||||
| 4594 | continue; | ||||
| 4595 | known = isl_basic_map_div_is_known(bmap, i); | ||||
| 4596 | if (known < 0 || !known) | ||||
| 4597 | return known; | ||||
| 4598 | } | ||||
| 4599 | |||||
| 4600 | return isl_bool_true; | ||||
| 4601 | } | ||||
| 4602 | |||||
| 4603 | /* Does integer division "div" have coefficient 1 in inequality constraint | ||||
| 4604 | * "ineq" of "map"? | ||||
| 4605 | */ | ||||
| 4606 | static isl_bool has_coef_one(__isl_keep isl_basic_map *bmap, int div, int ineq) | ||||
| 4607 | { | ||||
| 4608 | unsigned o_div; | ||||
| 4609 | |||||
| 4610 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 4611 | if (isl_int_is_one(bmap->ineq[ineq][o_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[ineq][o_div + div]), 1) == 0)) | ||||
| 4612 | return isl_bool_true; | ||||
| 4613 | |||||
| 4614 | return isl_bool_false; | ||||
| 4615 | } | ||||
| 4616 | |||||
| 4617 | /* Turn inequality constraint "ineq" of "bmap" into an equality and | ||||
| 4618 | * then try and drop redundant divs again, | ||||
| 4619 | * freeing the temporary data structure "pairs" that was associated | ||||
| 4620 | * to the old version of "bmap". | ||||
| 4621 | */ | ||||
| 4622 | static __isl_give isl_basic_map *set_eq_and_try_again( | ||||
| 4623 | __isl_take isl_basic_map *bmap, int ineq, __isl_take int *pairs) | ||||
| 4624 | { | ||||
| 4625 | bmap = isl_basic_map_cow(bmap); | ||||
| 4626 | isl_basic_map_inequality_to_equality(bmap, ineq); | ||||
| 4627 | return drop_redundant_divs_again(bmap, pairs, 1); | ||||
| 4628 | } | ||||
| 4629 | |||||
| 4630 | /* Drop the integer division at position "div", along with the two | ||||
| 4631 | * inequality constraints "ineq1" and "ineq2" in which it appears | ||||
| 4632 | * from "bmap" and then try and drop redundant divs again, | ||||
| 4633 | * freeing the temporary data structure "pairs" that was associated | ||||
| 4634 | * to the old version of "bmap". | ||||
| 4635 | */ | ||||
| 4636 | static __isl_give isl_basic_map *drop_div_and_try_again( | ||||
| 4637 | __isl_take isl_basic_map *bmap, int div, int ineq1, int ineq2, | ||||
| 4638 | __isl_take int *pairs) | ||||
| 4639 | { | ||||
| 4640 | if (ineq1 > ineq2) { | ||||
| 4641 | isl_basic_map_drop_inequality(bmap, ineq1); | ||||
| 4642 | isl_basic_map_drop_inequality(bmap, ineq2); | ||||
| 4643 | } else { | ||||
| 4644 | isl_basic_map_drop_inequality(bmap, ineq2); | ||||
| 4645 | isl_basic_map_drop_inequality(bmap, ineq1); | ||||
| 4646 | } | ||||
| 4647 | bmap = isl_basic_map_drop_div(bmap, div); | ||||
| 4648 | return drop_redundant_divs_again(bmap, pairs, 0); | ||||
| 4649 | } | ||||
| 4650 | |||||
| 4651 | /* Given two inequality constraints | ||||
| 4652 | * | ||||
| 4653 | * f(x) + n d + c >= 0, (ineq) | ||||
| 4654 | * | ||||
| 4655 | * with d the variable at position "pos", and | ||||
| 4656 | * | ||||
| 4657 | * f(x) + c0 >= 0, (lower) | ||||
| 4658 | * | ||||
| 4659 | * compute the maximal value of the lower bound ceil((-f(x) - c)/n) | ||||
| 4660 | * determined by the first constraint. | ||||
| 4661 | * That is, store | ||||
| 4662 | * | ||||
| 4663 | * ceil((c0 - c)/n) | ||||
| 4664 | * | ||||
| 4665 | * in *l. | ||||
| 4666 | */ | ||||
| 4667 | static void lower_bound_from_parallel(__isl_keep isl_basic_map *bmap, | ||||
| 4668 | int ineq, int lower, int pos, isl_int *l) | ||||
| 4669 | { | ||||
| 4670 | isl_int_neg(*l, bmap->ineq[ineq][0])isl_sioimath_neg((*l), *(bmap->ineq[ineq][0])); | ||||
| 4671 | isl_int_add(*l, *l, bmap->ineq[lower][0])isl_sioimath_add((*l), *(*l), *(bmap->ineq[lower][0])); | ||||
| 4672 | isl_int_cdiv_q(*l, *l, bmap->ineq[ineq][pos])isl_sioimath_cdiv_q((*l), *(*l), *(bmap->ineq[ineq][pos])); | ||||
| 4673 | } | ||||
| 4674 | |||||
| 4675 | /* Given two inequality constraints | ||||
| 4676 | * | ||||
| 4677 | * f(x) + n d + c >= 0, (ineq) | ||||
| 4678 | * | ||||
| 4679 | * with d the variable at position "pos", and | ||||
| 4680 | * | ||||
| 4681 | * -f(x) - c0 >= 0, (upper) | ||||
| 4682 | * | ||||
| 4683 | * compute the minimal value of the lower bound ceil((-f(x) - c)/n) | ||||
| 4684 | * determined by the first constraint. | ||||
| 4685 | * That is, store | ||||
| 4686 | * | ||||
| 4687 | * ceil((-c1 - c)/n) | ||||
| 4688 | * | ||||
| 4689 | * in *u. | ||||
| 4690 | */ | ||||
| 4691 | static void lower_bound_from_opposite(__isl_keep isl_basic_map *bmap, | ||||
| 4692 | int ineq, int upper, int pos, isl_int *u) | ||||
| 4693 | { | ||||
| 4694 | isl_int_neg(*u, bmap->ineq[ineq][0])isl_sioimath_neg((*u), *(bmap->ineq[ineq][0])); | ||||
| 4695 | isl_int_sub(*u, *u, bmap->ineq[upper][0])isl_sioimath_sub((*u), *(*u), *(bmap->ineq[upper][0])); | ||||
| 4696 | isl_int_cdiv_q(*u, *u, bmap->ineq[ineq][pos])isl_sioimath_cdiv_q((*u), *(*u), *(bmap->ineq[ineq][pos])); | ||||
| 4697 | } | ||||
| 4698 | |||||
| 4699 | /* Given a lower bound constraint "ineq" on "div" in "bmap", | ||||
| 4700 | * does the corresponding lower bound have a fixed value in "bmap"? | ||||
| 4701 | * | ||||
| 4702 | * In particular, "ineq" is of the form | ||||
| 4703 | * | ||||
| 4704 | * f(x) + n d + c >= 0 | ||||
| 4705 | * | ||||
| 4706 | * with n > 0, c the constant term and | ||||
| 4707 | * d the existentially quantified variable "div". | ||||
| 4708 | * That is, the lower bound is | ||||
| 4709 | * | ||||
| 4710 | * ceil((-f(x) - c)/n) | ||||
| 4711 | * | ||||
| 4712 | * Look for a pair of constraints | ||||
| 4713 | * | ||||
| 4714 | * f(x) + c0 >= 0 | ||||
| 4715 | * -f(x) + c1 >= 0 | ||||
| 4716 | * | ||||
| 4717 | * i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value. | ||||
| 4718 | * That is, check that | ||||
| 4719 | * | ||||
| 4720 | * ceil((-c1 - c)/n) = ceil((c0 - c)/n) | ||||
| 4721 | * | ||||
| 4722 | * If so, return the index of inequality f(x) + c0 >= 0. | ||||
| 4723 | * Otherwise, return bmap->n_ineq. | ||||
| 4724 | * Return -1 on error. | ||||
| 4725 | */ | ||||
| 4726 | static int lower_bound_is_cst(__isl_keep isl_basic_map *bmap, int div, int ineq) | ||||
| 4727 | { | ||||
| 4728 | int i; | ||||
| 4729 | int lower = -1, upper = -1; | ||||
| 4730 | unsigned o_div; | ||||
| 4731 | isl_int l, u; | ||||
| 4732 | int equal; | ||||
| 4733 | |||||
| 4734 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 4735 | for (i = 0; i < bmap->n_ineq && (lower < 0 || upper < 0); ++i) { | ||||
| 4736 | isl_bool par, opp; | ||||
| 4737 | |||||
| 4738 | if (i == ineq) | ||||
| 4739 | continue; | ||||
| 4740 | if (!isl_int_is_zero(bmap->ineq[i][o_div + div])(isl_sioimath_sgn(*(bmap->ineq[i][o_div + div])) == 0)) | ||||
| 4741 | continue; | ||||
| 4742 | par = isl_bool_false; | ||||
| 4743 | if (lower < 0) | ||||
| 4744 | par = is_parallel_except(bmap, ineq, i, o_div + div); | ||||
| 4745 | if (par < 0) | ||||
| 4746 | return -1; | ||||
| 4747 | if (par) { | ||||
| 4748 | lower = i; | ||||
| 4749 | continue; | ||||
| 4750 | } | ||||
| 4751 | opp = isl_bool_false; | ||||
| 4752 | if (upper < 0) | ||||
| 4753 | opp = is_opposite_except(bmap, ineq, i, o_div + div); | ||||
| 4754 | if (opp < 0) | ||||
| 4755 | return -1; | ||||
| 4756 | if (opp) | ||||
| 4757 | upper = i; | ||||
| 4758 | } | ||||
| 4759 | |||||
| 4760 | if (lower < 0 || upper < 0) | ||||
| 4761 | return bmap->n_ineq; | ||||
| 4762 | |||||
| 4763 | isl_int_init(l)isl_sioimath_init((l)); | ||||
| 4764 | isl_int_init(u)isl_sioimath_init((u)); | ||||
| 4765 | |||||
| 4766 | lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &l); | ||||
| 4767 | lower_bound_from_opposite(bmap, ineq, upper, o_div + div, &u); | ||||
| 4768 | |||||
| 4769 | equal = isl_int_eq(l, u)(isl_sioimath_cmp(*(l), *(u)) == 0); | ||||
| 4770 | |||||
| 4771 | isl_int_clear(l)isl_sioimath_clear((l)); | ||||
| 4772 | isl_int_clear(u)isl_sioimath_clear((u)); | ||||
| 4773 | |||||
| 4774 | return equal ? lower : bmap->n_ineq; | ||||
| 4775 | } | ||||
| 4776 | |||||
| 4777 | /* Given a lower bound constraint "ineq" on the existentially quantified | ||||
| 4778 | * variable "div", such that the corresponding lower bound has | ||||
| 4779 | * a fixed value in "bmap", assign this fixed value to the variable and | ||||
| 4780 | * then try and drop redundant divs again, | ||||
| 4781 | * freeing the temporary data structure "pairs" that was associated | ||||
| 4782 | * to the old version of "bmap". | ||||
| 4783 | * "lower" determines the constant value for the lower bound. | ||||
| 4784 | * | ||||
| 4785 | * In particular, "ineq" is of the form | ||||
| 4786 | * | ||||
| 4787 | * f(x) + n d + c >= 0, | ||||
| 4788 | * | ||||
| 4789 | * while "lower" is of the form | ||||
| 4790 | * | ||||
| 4791 | * f(x) + c0 >= 0 | ||||
| 4792 | * | ||||
| 4793 | * The lower bound is ceil((-f(x) - c)/n) and its constant value | ||||
| 4794 | * is ceil((c0 - c)/n). | ||||
| 4795 | */ | ||||
| 4796 | static __isl_give isl_basic_map *fix_cst_lower(__isl_take isl_basic_map *bmap, | ||||
| 4797 | int div, int ineq, int lower, int *pairs) | ||||
| 4798 | { | ||||
| 4799 | isl_int c; | ||||
| 4800 | unsigned o_div; | ||||
| 4801 | |||||
| 4802 | isl_int_init(c)isl_sioimath_init((c)); | ||||
| 4803 | |||||
| 4804 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 4805 | lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &c); | ||||
| 4806 | bmap = isl_basic_map_fix(bmap, isl_dim_div, div, c); | ||||
| 4807 | free(pairs); | ||||
| 4808 | |||||
| 4809 | isl_int_clear(c)isl_sioimath_clear((c)); | ||||
| 4810 | |||||
| 4811 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
| 4812 | } | ||||
| 4813 | |||||
| 4814 | /* Remove divs that are not strictly needed based on the inequality | ||||
| 4815 | * constraints. | ||||
| 4816 | * In particular, if a div only occurs positively (or negatively) | ||||
| 4817 | * in constraints, then it can simply be dropped. | ||||
| 4818 | * Also, if a div occurs in only two constraints and if moreover | ||||
| 4819 | * those two constraints are opposite to each other, except for the constant | ||||
| 4820 | * term and if the sum of the constant terms is such that for any value | ||||
| 4821 | * of the other values, there is always at least one integer value of the | ||||
| 4822 | * div, i.e., if one plus this sum is greater than or equal to | ||||
| 4823 | * the (absolute value) of the coefficient of the div in the constraints, | ||||
| 4824 | * then we can also simply drop the div. | ||||
| 4825 | * | ||||
| 4826 | * If an existentially quantified variable does not have an explicit | ||||
| 4827 | * representation, appears in only a single lower bound that does not | ||||
| 4828 | * involve any other such existentially quantified variables and appears | ||||
| 4829 | * in this lower bound with coefficient 1, | ||||
| 4830 | * then fix the variable to the value of the lower bound. That is, | ||||
| 4831 | * turn the inequality into an equality. | ||||
| 4832 | * If for any value of the other variables, there is any value | ||||
| 4833 | * for the existentially quantified variable satisfying the constraints, | ||||
| 4834 | * then this lower bound also satisfies the constraints. | ||||
| 4835 | * It is therefore safe to pick this lower bound. | ||||
| 4836 | * | ||||
| 4837 | * The same reasoning holds even if the coefficient is not one. | ||||
| 4838 | * However, fixing the variable to the value of the lower bound may | ||||
| 4839 | * in general introduce an extra integer division, in which case | ||||
| 4840 | * it may be better to pick another value. | ||||
| 4841 | * If this integer division has a known constant value, then plugging | ||||
| 4842 | * in this constant value removes the existentially quantified variable | ||||
| 4843 | * completely. In particular, if the lower bound is of the form | ||||
| 4844 | * ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and | ||||
| 4845 | * -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n), | ||||
| 4846 | * then the existentially quantified variable can be assigned this | ||||
| 4847 | * shared value. | ||||
| 4848 | * | ||||
| 4849 | * We skip divs that appear in equalities or in the definition of other divs. | ||||
| 4850 | * Divs that appear in the definition of other divs usually occur in at least | ||||
| 4851 | * 4 constraints, but the constraints may have been simplified. | ||||
| 4852 | * | ||||
| 4853 | * If any divs are left after these simple checks then we move on | ||||
| 4854 | * to more complicated cases in drop_more_redundant_divs. | ||||
| 4855 | */ | ||||
| 4856 | static __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs_ineq( | ||||
| 4857 | __isl_take isl_basic_map *bmap) | ||||
| 4858 | { | ||||
| 4859 | int i, j; | ||||
| 4860 | isl_size off; | ||||
| 4861 | int *pairs = NULL((void*)0); | ||||
| 4862 | int n = 0; | ||||
| 4863 | int n_ineq; | ||||
| 4864 | |||||
| 4865 | if (!bmap) | ||||
| 4866 | goto error; | ||||
| 4867 | if (bmap->n_div == 0) | ||||
| 4868 | return bmap; | ||||
| 4869 | |||||
| 4870 | off = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
| 4871 | if (off < 0) | ||||
| 4872 | return isl_basic_map_free(bmap); | ||||
| 4873 | pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div)((int *)isl_calloc_or_die(bmap->ctx, bmap->n_div, sizeof (int))); | ||||
| 4874 | if (!pairs) | ||||
| 4875 | goto error; | ||||
| 4876 | |||||
| 4877 | n_ineq = isl_basic_map_n_inequality(bmap); | ||||
| 4878 | for (i = 0; i < bmap->n_div; ++i) { | ||||
| 4879 | int pos, neg; | ||||
| 4880 | int last_pos, last_neg; | ||||
| 4881 | int redundant; | ||||
| 4882 | int defined; | ||||
| 4883 | isl_bool opp, set_div; | ||||
| 4884 | |||||
| 4885 | defined = !isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0); | ||||
| 4886 | for (j = i; j < bmap->n_div; ++j) | ||||
| 4887 | if (!isl_int_is_zero(bmap->div[j][1 + 1 + off + i])(isl_sioimath_sgn(*(bmap->div[j][1 + 1 + off + i])) == 0)) | ||||
| 4888 | break; | ||||
| 4889 | if (j < bmap->n_div) | ||||
| 4890 | continue; | ||||
| 4891 | for (j = 0; j < bmap->n_eq; ++j) | ||||
| 4892 | if (!isl_int_is_zero(bmap->eq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->eq[j][1 + off + i])) == 0)) | ||||
| 4893 | break; | ||||
| 4894 | if (j < bmap->n_eq) | ||||
| 4895 | continue; | ||||
| 4896 | ++n; | ||||
| 4897 | pos = neg = 0; | ||||
| 4898 | for (j = 0; j < bmap->n_ineq; ++j) { | ||||
| 4899 | if (isl_int_is_pos(bmap->ineq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + off + i])) > 0)) { | ||||
| 4900 | last_pos = j; | ||||
| 4901 | ++pos; | ||||
| 4902 | } | ||||
| 4903 | if (isl_int_is_neg(bmap->ineq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + off + i])) < 0)) { | ||||
| 4904 | last_neg = j; | ||||
| 4905 | ++neg; | ||||
| 4906 | } | ||||
| 4907 | } | ||||
| 4908 | pairs[i] = pos * neg; | ||||
| 4909 | if (pairs[i] == 0) { | ||||
| 4910 | for (j = bmap->n_ineq - 1; j >= 0; --j) | ||||
| 4911 | if (!isl_int_is_zero(bmap->ineq[j][1+off+i])(isl_sioimath_sgn(*(bmap->ineq[j][1+off+i])) == 0)) | ||||
| 4912 | isl_basic_map_drop_inequality(bmap, j); | ||||
| 4913 | bmap = isl_basic_map_drop_div(bmap, i); | ||||
| 4914 | return drop_redundant_divs_again(bmap, pairs, 0); | ||||
| 4915 | } | ||||
| 4916 | if (pairs[i] != 1) | ||||
| 4917 | opp = isl_bool_false; | ||||
| 4918 | else | ||||
| 4919 | opp = is_opposite(bmap, last_pos, last_neg); | ||||
| 4920 | if (opp < 0) | ||||
| 4921 | goto error; | ||||
| 4922 | if (!opp) { | ||||
| 4923 | int lower; | ||||
| 4924 | isl_bool single, one; | ||||
| 4925 | |||||
| 4926 | if (pos != 1) | ||||
| 4927 | continue; | ||||
| 4928 | single = single_unknown(bmap, last_pos, i); | ||||
| 4929 | if (single < 0) | ||||
| 4930 | goto error; | ||||
| 4931 | if (!single) | ||||
| 4932 | continue; | ||||
| 4933 | one = has_coef_one(bmap, i, last_pos); | ||||
| 4934 | if (one < 0) | ||||
| 4935 | goto error; | ||||
| 4936 | if (one) | ||||
| 4937 | return set_eq_and_try_again(bmap, last_pos, | ||||
| 4938 | pairs); | ||||
| 4939 | lower = lower_bound_is_cst(bmap, i, last_pos); | ||||
| 4940 | if (lower < 0) | ||||
| 4941 | goto error; | ||||
| 4942 | if (lower < n_ineq) | ||||
| 4943 | return fix_cst_lower(bmap, i, last_pos, lower, | ||||
| 4944 | pairs); | ||||
| 4945 | continue; | ||||
| 4946 | } | ||||
| 4947 | |||||
| 4948 | isl_int_add(bmap->ineq[last_pos][0],isl_sioimath_add((bmap->ineq[last_pos][0]), *(bmap->ineq [last_pos][0]), *(bmap->ineq[last_neg][0])) | ||||
| 4949 | bmap->ineq[last_pos][0], bmap->ineq[last_neg][0])isl_sioimath_add((bmap->ineq[last_pos][0]), *(bmap->ineq [last_pos][0]), *(bmap->ineq[last_neg][0])); | ||||
| 4950 | isl_int_add_ui(bmap->ineq[last_pos][0],isl_sioimath_add_ui((bmap->ineq[last_pos][0]), *(bmap-> ineq[last_pos][0]), 1) | ||||
| 4951 | bmap->ineq[last_pos][0], 1)isl_sioimath_add_ui((bmap->ineq[last_pos][0]), *(bmap-> ineq[last_pos][0]), 1); | ||||
| 4952 | redundant = isl_int_ge(bmap->ineq[last_pos][0],(isl_sioimath_cmp(*(bmap->ineq[last_pos][0]), *(bmap->ineq [last_pos][1+off+i])) >= 0) | ||||
| 4953 | bmap->ineq[last_pos][1+off+i])(isl_sioimath_cmp(*(bmap->ineq[last_pos][0]), *(bmap->ineq [last_pos][1+off+i])) >= 0); | ||||
| 4954 | isl_int_sub_ui(bmap->ineq[last_pos][0],isl_sioimath_sub_ui((bmap->ineq[last_pos][0]), *(bmap-> ineq[last_pos][0]), 1) | ||||
| 4955 | bmap->ineq[last_pos][0], 1)isl_sioimath_sub_ui((bmap->ineq[last_pos][0]), *(bmap-> ineq[last_pos][0]), 1); | ||||
| 4956 | isl_int_sub(bmap->ineq[last_pos][0],isl_sioimath_sub((bmap->ineq[last_pos][0]), *(bmap->ineq [last_pos][0]), *(bmap->ineq[last_neg][0])) | ||||
| 4957 | bmap->ineq[last_pos][0], bmap->ineq[last_neg][0])isl_sioimath_sub((bmap->ineq[last_pos][0]), *(bmap->ineq [last_pos][0]), *(bmap->ineq[last_neg][0])); | ||||
| 4958 | if (redundant) | ||||
| 4959 | return drop_div_and_try_again(bmap, i, | ||||
| 4960 | last_pos, last_neg, pairs); | ||||
| 4961 | if (defined) | ||||
| 4962 | set_div = isl_bool_false; | ||||
| 4963 | else | ||||
| 4964 | set_div = ok_to_set_div_from_bound(bmap, i, last_pos); | ||||
| 4965 | if (set_div < 0) | ||||
| 4966 | return isl_basic_map_free(bmap); | ||||
| 4967 | if (set_div) { | ||||
| 4968 | bmap = set_div_from_lower_bound(bmap, i, last_pos); | ||||
| 4969 | return drop_redundant_divs_again(bmap, pairs, 1); | ||||
| 4970 | } | ||||
| 4971 | pairs[i] = 0; | ||||
| 4972 | --n; | ||||
| 4973 | } | ||||
| 4974 | |||||
| 4975 | if (n > 0) | ||||
| 4976 | return coalesce_or_drop_more_redundant_divs(bmap, pairs, n); | ||||
| 4977 | |||||
| 4978 | free(pairs); | ||||
| 4979 | return bmap; | ||||
| 4980 | error: | ||||
| 4981 | free(pairs); | ||||
| 4982 | isl_basic_map_free(bmap); | ||||
| 4983 | return NULL((void*)0); | ||||
| 4984 | } | ||||
| 4985 | |||||
| 4986 | /* Consider the coefficients at "c" as a row vector and replace | ||||
| 4987 | * them with their product with "T". "T" is assumed to be a square matrix. | ||||
| 4988 | */ | ||||
| 4989 | static isl_stat preimage(isl_int *c, __isl_keep isl_mat *T) | ||||
| 4990 | { | ||||
| 4991 | isl_size n; | ||||
| 4992 | isl_ctx *ctx; | ||||
| 4993 | isl_vec *v; | ||||
| 4994 | |||||
| 4995 | n = isl_mat_rows(T); | ||||
| 4996 | if (n < 0) | ||||
| 4997 | return isl_stat_error; | ||||
| 4998 | if (isl_seq_first_non_zero(c, n) == -1) | ||||
| 4999 | return isl_stat_ok; | ||||
| 5000 | ctx = isl_mat_get_ctx(T); | ||||
| 5001 | v = isl_vec_alloc(ctx, n); | ||||
| 5002 | if (!v) | ||||
| 5003 | return isl_stat_error; | ||||
| 5004 | isl_seq_swp_or_cpy(v->el, c, n); | ||||
| 5005 | v = isl_vec_mat_product(v, isl_mat_copy(T)); | ||||
| 5006 | if (!v) | ||||
| 5007 | return isl_stat_error; | ||||
| 5008 | isl_seq_swp_or_cpy(c, v->el, n); | ||||
| 5009 | isl_vec_free(v); | ||||
| 5010 | |||||
| 5011 | return isl_stat_ok; | ||||
| 5012 | } | ||||
| 5013 | |||||
| 5014 | /* Plug in T for the variables in "bmap" starting at "pos". | ||||
| 5015 | * T is a linear unimodular matrix, i.e., without constant term. | ||||
| 5016 | */ | ||||
| 5017 | static __isl_give isl_basic_map *isl_basic_map_preimage_vars( | ||||
| 5018 | __isl_take isl_basic_map *bmap, unsigned pos, __isl_take isl_mat *T) | ||||
| 5019 | { | ||||
| 5020 | int i; | ||||
| 5021 | isl_size n_row, n_col; | ||||
| 5022 | |||||
| 5023 | bmap = isl_basic_map_cow(bmap); | ||||
| 5024 | n_row = isl_mat_rows(T); | ||||
| 5025 | n_col = isl_mat_cols(T); | ||||
| 5026 | if (!bmap || n_row < 0 || n_col < 0) | ||||
| 5027 | goto error; | ||||
| 5028 | |||||
| 5029 | if (n_col != n_row) | ||||
| 5030 | isl_die(isl_mat_get_ctx(T), isl_error_invalid,do { isl_handle_error(isl_mat_get_ctx(T), isl_error_invalid, "expecting square matrix" , "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 5031); goto error; } while (0) | ||||
| 5031 | "expecting square matrix", goto error)do { isl_handle_error(isl_mat_get_ctx(T), isl_error_invalid, "expecting square matrix" , "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/polly/lib/External/isl/isl_map_simplify.c" , 5031); goto error; } while (0); | ||||
| 5032 | |||||
| 5033 | if (isl_basic_map_check_range(bmap, isl_dim_all, pos, n_col) < 0) | ||||
| 5034 | goto error; | ||||
| 5035 | |||||
| 5036 | for (i = 0; i < bmap->n_eq; ++i) | ||||
| 5037 | if (preimage(bmap->eq[i] + 1 + pos, T) < 0) | ||||
| 5038 | goto error; | ||||
| 5039 | for (i = 0; i < bmap->n_ineq; ++i) | ||||
| 5040 | if (preimage(bmap->ineq[i] + 1 + pos, T) < 0) | ||||
| 5041 | goto error; | ||||
| 5042 | for (i = 0; i < bmap->n_div; ++i) { | ||||
| 5043 | if (isl_basic_map_div_is_marked_unknown(bmap, i)) | ||||
| 5044 | continue; | ||||
| 5045 | if (preimage(bmap->div[i] + 1 + 1 + pos, T) < 0) | ||||
| 5046 | goto error; | ||||
| 5047 | } | ||||
| 5048 | |||||
| 5049 | isl_mat_free(T); | ||||
| 5050 | return bmap; | ||||
| 5051 | error: | ||||
| 5052 | isl_basic_map_free(bmap); | ||||
| 5053 | isl_mat_free(T); | ||||
| 5054 | return NULL((void*)0); | ||||
| 5055 | } | ||||
| 5056 | |||||
| 5057 | /* Remove divs that are not strictly needed. | ||||
| 5058 | * | ||||
| 5059 | * First look for an equality constraint involving two or more | ||||
| 5060 | * existentially quantified variables without an explicit | ||||
| 5061 | * representation. Replace the combination that appears | ||||
| 5062 | * in the equality constraint by a single existentially quantified | ||||
| 5063 | * variable such that the equality can be used to derive | ||||
| 5064 | * an explicit representation for the variable. | ||||
| 5065 | * If there are no more such equality constraints, then continue | ||||
| 5066 | * with isl_basic_map_drop_redundant_divs_ineq. | ||||
| 5067 | * | ||||
| 5068 | * In particular, if the equality constraint is of the form | ||||
| 5069 | * | ||||
| 5070 | * f(x) + \sum_i c_i a_i = 0 | ||||
| 5071 | * | ||||
| 5072 | * with a_i existentially quantified variable without explicit | ||||
| 5073 | * representation, then apply a transformation on the existentially | ||||
| 5074 | * quantified variables to turn the constraint into | ||||
| 5075 | * | ||||
| 5076 | * f(x) + g a_1' = 0 | ||||
| 5077 | * | ||||
| 5078 | * with g the gcd of the c_i. | ||||
| 5079 | * In order to easily identify which existentially quantified variables | ||||
| 5080 | * have a complete explicit representation, i.e., without being defined | ||||
| 5081 | * in terms of other existentially quantified variables without | ||||
| 5082 | * an explicit representation, the existentially quantified variables | ||||
| 5083 | * are first sorted. | ||||
| 5084 | * | ||||
| 5085 | * The variable transformation is computed by extending the row | ||||
| 5086 | * [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation | ||||
| 5087 | * | ||||
| 5088 | * [a_1'] [c_1/g ... c_n/g] [ a_1 ] | ||||
| 5089 | * [a_2'] [ a_2 ] | ||||
| 5090 | * ... = U .... | ||||
| 5091 | * [a_n'] [ a_n ] | ||||
| 5092 | * | ||||
| 5093 | * with [c_1/g ... c_n/g] representing the first row of U. | ||||
| 5094 | * The inverse of U is then plugged into the original constraints. | ||||
| 5095 | * The call to isl_basic_map_simplify makes sure the explicit | ||||
| 5096 | * representation for a_1' is extracted from the equality constraint. | ||||
| 5097 | */ | ||||
| 5098 | __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs( | ||||
| 5099 | __isl_take isl_basic_map *bmap) | ||||
| 5100 | { | ||||
| 5101 | int first; | ||||
| 5102 | int i; | ||||
| 5103 | unsigned o_div; | ||||
| 5104 | isl_size n_div; | ||||
| 5105 | int l; | ||||
| 5106 | isl_ctx *ctx; | ||||
| 5107 | isl_mat *T; | ||||
| 5108 | |||||
| 5109 | if (!bmap) | ||||
| 5110 | return NULL((void*)0); | ||||
| 5111 | if (isl_basic_map_divs_known(bmap)) | ||||
| 5112 | return isl_basic_map_drop_redundant_divs_ineq(bmap); | ||||
| 5113 | if (bmap->n_eq == 0) | ||||
| 5114 | return isl_basic_map_drop_redundant_divs_ineq(bmap); | ||||
| 5115 | bmap = isl_basic_map_sort_divs(bmap); | ||||
| 5116 | if (!bmap) | ||||
| 5117 | return NULL((void*)0); | ||||
| 5118 | |||||
| 5119 | first = isl_basic_map_first_unknown_div(bmap); | ||||
| 5120 | if (first < 0) | ||||
| 5121 | return isl_basic_map_free(bmap); | ||||
| 5122 | |||||
| 5123 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
| 5124 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 5125 | if (n_div < 0) | ||||
| 5126 | return isl_basic_map_free(bmap); | ||||
| 5127 | |||||
| 5128 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
| 5129 | l = isl_seq_first_non_zero(bmap->eq[i] + o_div + first, | ||||
| 5130 | n_div - (first)); | ||||
| 5131 | if (l < 0) | ||||
| 5132 | continue; | ||||
| 5133 | l += first; | ||||
| 5134 | if (isl_seq_first_non_zero(bmap->eq[i] + o_div + l + 1, | ||||
| 5135 | n_div - (l + 1)) == -1) | ||||
| 5136 | continue; | ||||
| 5137 | break; | ||||
| 5138 | } | ||||
| 5139 | if (i >= bmap->n_eq) | ||||
| 5140 | return isl_basic_map_drop_redundant_divs_ineq(bmap); | ||||
| 5141 | |||||
| 5142 | ctx = isl_basic_map_get_ctx(bmap); | ||||
| 5143 | T = isl_mat_alloc(ctx, n_div - l, n_div - l); | ||||
| 5144 | if (!T) | ||||
| 5145 | return isl_basic_map_free(bmap); | ||||
| 5146 | isl_seq_cpy(T->row[0], bmap->eq[i] + o_div + l, n_div - l); | ||||
| 5147 | T = isl_mat_normalize_row(T, 0); | ||||
| 5148 | T = isl_mat_unimodular_complete(T, 1); | ||||
| 5149 | T = isl_mat_right_inverse(T); | ||||
| 5150 | |||||
| 5151 | for (i = l; i < n_div; ++i) | ||||
| 5152 | bmap = isl_basic_map_mark_div_unknown(bmap, i); | ||||
| 5153 | bmap = isl_basic_map_preimage_vars(bmap, o_div - 1 + l, T); | ||||
| 5154 | bmap = isl_basic_map_simplify(bmap); | ||||
| 5155 | |||||
| 5156 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
| 5157 | } | ||||
| 5158 | |||||
| 5159 | /* Does "bmap" satisfy any equality that involves more than 2 variables | ||||
| 5160 | * and/or has coefficients different from -1 and 1? | ||||
| 5161 | */ | ||||
| 5162 | static isl_bool has_multiple_var_equality(__isl_keep isl_basic_map *bmap) | ||||
| 5163 | { | ||||
| 5164 | int i; | ||||
| 5165 | isl_size total; | ||||
| 5166 | |||||
| 5167 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 5168 | if (total < 0) | ||||
| 5169 | return isl_bool_error; | ||||
| 5170 | |||||
| 5171 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
| 5172 | int j, k; | ||||
| 5173 | |||||
| 5174 | j = isl_seq_first_non_zero(bmap->eq[i] + 1, total); | ||||
| 5175 | if (j < 0) | ||||
| 5176 | continue; | ||||
| 5177 | if (!isl_int_is_one(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), 1) == 0) && | ||||
| 5178 | !isl_int_is_negone(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), -1) == 0)) | ||||
| 5179 | return isl_bool_true; | ||||
| 5180 | |||||
| 5181 | j += 1; | ||||
| 5182 | k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j); | ||||
| 5183 | if (k < 0) | ||||
| 5184 | continue; | ||||
| 5185 | j += k; | ||||
| 5186 | if (!isl_int_is_one(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), 1) == 0) && | ||||
| 5187 | !isl_int_is_negone(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), -1) == 0)) | ||||
| 5188 | return isl_bool_true; | ||||
| 5189 | |||||
| 5190 | j += 1; | ||||
| 5191 | k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j); | ||||
| 5192 | if (k >= 0) | ||||
| 5193 | return isl_bool_true; | ||||
| 5194 | } | ||||
| 5195 | |||||
| 5196 | return isl_bool_false; | ||||
| 5197 | } | ||||
| 5198 | |||||
| 5199 | /* Remove any common factor g from the constraint coefficients in "v". | ||||
| 5200 | * The constant term is stored in the first position and is replaced | ||||
| 5201 | * by floor(c/g). If any common factor is removed and if this results | ||||
| 5202 | * in a tightening of the constraint, then set *tightened. | ||||
| 5203 | */ | ||||
| 5204 | static __isl_give isl_vec *normalize_constraint(__isl_take isl_vec *v, | ||||
| 5205 | int *tightened) | ||||
| 5206 | { | ||||
| 5207 | isl_ctx *ctx; | ||||
| 5208 | |||||
| 5209 | if (!v) | ||||
| 5210 | return NULL((void*)0); | ||||
| 5211 | ctx = isl_vec_get_ctx(v); | ||||
| 5212 | isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd); | ||||
| 5213 | if (isl_int_is_zero(ctx->normalize_gcd)(isl_sioimath_sgn(*(ctx->normalize_gcd)) == 0)) | ||||
| 5214 | return v; | ||||
| 5215 | if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0)) | ||||
| 5216 | return v; | ||||
| 5217 | v = isl_vec_cow(v); | ||||
| 5218 | if (!v) | ||||
| 5219 | return NULL((void*)0); | ||||
| 5220 | if (tightened
))) | ||||
| 5221 | *tightened = 1; | ||||
| 5222 | isl_int_fdiv_q(v->el[0], v->el[0], ctx->normalize_gcd)isl_sioimath_fdiv_q((v->el[0]), *(v->el[0]), *(ctx-> normalize_gcd)); | ||||
| 5223 | isl_seq_scale_down(v->el + 1, v->el + 1, ctx->normalize_gcd, | ||||
| 5224 | v->size - 1); | ||||
| 5225 | return v; | ||||
| 5226 | } | ||||
| 5227 | |||||
| 5228 | /* If "bmap" is an integer set that satisfies any equality involving | ||||
| 5229 | * more than 2 variables and/or has coefficients different from -1 and 1, | ||||
| 5230 | * then use variable compression to reduce the coefficients by removing | ||||
| 5231 | * any (hidden) common factor. | ||||
| 5232 | * In particular, apply the variable compression to each constraint, | ||||
| 5233 | * factor out any common factor in the non-constant coefficients and | ||||
| 5234 | * then apply the inverse of the compression. | ||||
| 5235 | * At the end, we mark the basic map as having reduced constants. | ||||
| 5236 | * If this flag is still set on the next invocation of this function, | ||||
| 5237 | * then we skip the computation. | ||||
| 5238 | * | ||||
| 5239 | * Removing a common factor may result in a tightening of some of | ||||
| 5240 | * the constraints. If this happens, then we may end up with two | ||||
| 5241 | * opposite inequalities that can be replaced by an equality. | ||||
| 5242 | * We therefore call isl_basic_map_detect_inequality_pairs, | ||||
| 5243 | * which checks for such pairs of inequalities as well as eliminate_divs_eq | ||||
| 5244 | * and isl_basic_map_gauss if such a pair was found. | ||||
| 5245 | * | ||||
| 5246 | * Tightening may also result in some other constraints becoming | ||||
| 5247 | * (rationally) redundant with respect to the tightened constraint | ||||
| 5248 | * (in combination with other constraints). The basic map may | ||||
| 5249 | * therefore no longer be assumed to have no redundant constraints. | ||||
| 5250 | * | ||||
| 5251 | * Note that this function may leave the result in an inconsistent state. | ||||
| 5252 | * In particular, the constraints may not be gaussed. | ||||
| 5253 | * Unfortunately, isl_map_coalesce actually depends on this inconsistent state | ||||
| 5254 | * for some of the test cases to pass successfully. | ||||
| 5255 | * Any potential modification of the representation is therefore only | ||||
| 5256 | * performed on a single copy of the basic map. | ||||
| 5257 | */ | ||||
| 5258 | __isl_give isl_basic_map *isl_basic_map_reduce_coefficients( | ||||
| 5259 | __isl_take isl_basic_map *bmap) | ||||
| 5260 | { | ||||
| 5261 | isl_size total; | ||||
| 5262 | isl_bool multi; | ||||
| 5263 | isl_ctx *ctx; | ||||
| 5264 | isl_vec *v; | ||||
| 5265 | isl_mat *eq, *T, *T2; | ||||
| 5266 | int i; | ||||
| 5267 | int tightened; | ||||
| 5268 | |||||
| 5269 | if (!bmap) | ||||
| |||||
| 5270 | return NULL((void*)0); | ||||
| 5271 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(!!(((bmap)->flags) & ((1 << 8))))) | ||||
| 5272 | return bmap; | ||||
| 5273 | if (isl_basic_map_is_rational(bmap)) | ||||
| 5274 | return bmap; | ||||
| 5275 | if (bmap->n_eq == 0) | ||||
| 5276 | return bmap; | ||||
| 5277 | multi = has_multiple_var_equality(bmap); | ||||
| 5278 | if (multi
| ||||
| 5279 | return isl_basic_map_free(bmap); | ||||
| 5280 | if (!multi
| ||||
| 5281 | return bmap; | ||||
| 5282 | |||||
| 5283 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 5284 | if (total < 0) | ||||
| 5285 | return isl_basic_map_free(bmap); | ||||
| 5286 | ctx = isl_basic_map_get_ctx(bmap); | ||||
| 5287 | v = isl_vec_alloc(ctx, 1 + total); | ||||
| 5288 | if (!v) | ||||
| 5289 | return isl_basic_map_free(bmap); | ||||
| 5290 | |||||
| 5291 | eq = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total); | ||||
| 5292 | T = isl_mat_variable_compression(eq, &T2); | ||||
| 5293 | if (!T || !T2) | ||||
| 5294 | goto error; | ||||
| 5295 | if (T->n_col == 0) { | ||||
| 5296 | isl_mat_free(T); | ||||
| 5297 | isl_mat_free(T2); | ||||
| 5298 | isl_vec_free(v); | ||||
| 5299 | return isl_basic_map_set_to_empty(bmap); | ||||
| 5300 | } | ||||
| 5301 | |||||
| 5302 | bmap = isl_basic_map_cow(bmap); | ||||
| 5303 | if (!bmap) | ||||
| 5304 | goto error; | ||||
| 5305 | |||||
| 5306 | tightened = 0; | ||||
| 5307 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
| 5308 | isl_seq_cpy(v->el, bmap->ineq[i], 1 + total); | ||||
| 5309 | v = isl_vec_mat_product(v, isl_mat_copy(T)); | ||||
| 5310 | v = normalize_constraint(v, &tightened); | ||||
| 5311 | v = isl_vec_mat_product(v, isl_mat_copy(T2)); | ||||
| 5312 | if (!v) | ||||
| 5313 | goto error; | ||||
| 5314 | isl_seq_cpy(bmap->ineq[i], v->el, 1 + total); | ||||
| 5315 | } | ||||
| 5316 | |||||
| 5317 | isl_mat_free(T); | ||||
| 5318 | isl_mat_free(T2); | ||||
| 5319 | isl_vec_free(v); | ||||
| 5320 | |||||
| 5321 | ISL_F_SET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(((bmap)->flags) |= ((1 << 8))); | ||||
| 5322 | |||||
| 5323 | if (tightened
| ||||
| 5324 | int progress = 0; | ||||
| 5325 | |||||
| 5326 | ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT)(((bmap)->flags) &= ~((1 << 3))); | ||||
| 5327 | bmap = isl_basic_map_detect_inequality_pairs(bmap, &progress); | ||||
| 5328 | if (progress) { | ||||
| 5329 | bmap = eliminate_divs_eq(bmap, &progress); | ||||
| 5330 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
| 5331 | } | ||||
| 5332 | } | ||||
| 5333 | |||||
| 5334 | return bmap; | ||||
| 5335 | error: | ||||
| 5336 | isl_mat_free(T); | ||||
| 5337 | isl_mat_free(T2); | ||||
| 5338 | isl_vec_free(v); | ||||
| 5339 | return isl_basic_map_free(bmap); | ||||
| 5340 | } | ||||
| 5341 | |||||
| 5342 | /* Shift the integer division at position "div" of "bmap" | ||||
| 5343 | * by "shift" times the variable at position "pos". | ||||
| 5344 | * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0 | ||||
| 5345 | * corresponds to the constant term. | ||||
| 5346 | * | ||||
| 5347 | * That is, if the integer division has the form | ||||
| 5348 | * | ||||
| 5349 | * floor(f(x)/d) | ||||
| 5350 | * | ||||
| 5351 | * then replace it by | ||||
| 5352 | * | ||||
| 5353 | * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos | ||||
| 5354 | */ | ||||
| 5355 | __isl_give isl_basic_map *isl_basic_map_shift_div( | ||||
| 5356 | __isl_take isl_basic_map *bmap, int div, int pos, isl_int shift) | ||||
| 5357 | { | ||||
| 5358 | int i; | ||||
| 5359 | isl_size total, n_div; | ||||
| 5360 | |||||
| 5361 | if (isl_int_is_zero(shift)(isl_sioimath_sgn(*(shift)) == 0)) | ||||
| 5362 | return bmap; | ||||
| 5363 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
| 5364 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
| 5365 | total -= n_div; | ||||
| 5366 | if (total < 0 || n_div < 0) | ||||
| 5367 | return isl_basic_map_free(bmap); | ||||
| 5368 | |||||
| 5369 | isl_int_addmul(bmap->div[div][1 + pos], shift, bmap->div[div][0])isl_sioimath_addmul((bmap->div[div][1 + pos]), *(shift), * (bmap->div[div][0])); | ||||
| 5370 | |||||
| 5371 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
| 5372 | if (isl_int_is_zero(bmap->eq[i][1 + total + div])(isl_sioimath_sgn(*(bmap->eq[i][1 + total + div])) == 0)) | ||||
| 5373 | continue; | ||||
| 5374 | isl_int_submul(bmap->eq[i][pos],isl_sioimath_submul((bmap->eq[i][pos]), *(shift), *(bmap-> eq[i][1 + total + div])) | ||||
| 5375 | shift, bmap->eq[i][1 + total + div])isl_sioimath_submul((bmap->eq[i][pos]), *(shift), *(bmap-> eq[i][1 + total + div])); | ||||
| 5376 | } | ||||
| 5377 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
| 5378 | if (isl_int_is_zero(bmap->ineq[i][1 + total + div])(isl_sioimath_sgn(*(bmap->ineq[i][1 + total + div])) == 0)) | ||||
| 5379 | continue; | ||||
| 5380 | isl_int_submul(bmap->ineq[i][pos],isl_sioimath_submul((bmap->ineq[i][pos]), *(shift), *(bmap ->ineq[i][1 + total + div])) | ||||
| 5381 | shift, bmap->ineq[i][1 + total + div])isl_sioimath_submul((bmap->ineq[i][pos]), *(shift), *(bmap ->ineq[i][1 + total + div])); | ||||
| 5382 | } | ||||
| 5383 | for (i = 0; i < bmap->n_div; ++i) { | ||||
| 5384 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
| 5385 | continue; | ||||
| 5386 | if (isl_int_is_zero(bmap->div[i][1 + 1 + total + div])(isl_sioimath_sgn(*(bmap->div[i][1 + 1 + total + div])) == 0)) | ||||
| 5387 | continue; | ||||
| 5388 | isl_int_submul(bmap->div[i][1 + pos],isl_sioimath_submul((bmap->div[i][1 + pos]), *(shift), *(bmap ->div[i][1 + 1 + total + div])) | ||||
| 5389 | shift, bmap->div[i][1 + 1 + total + div])isl_sioimath_submul((bmap->div[i][1 + pos]), *(shift), *(bmap ->div[i][1 + 1 + total + div])); | ||||
| 5390 | } | ||||
| 5391 | |||||
| 5392 | return bmap; | ||||
| 5393 | } |
| 1 | /* |
| 2 | * Copyright 2015 INRIA Paris-Rocquencourt |
| 3 | * |
| 4 | * Use of this software is governed by the MIT license |
| 5 | * |
| 6 | * Written by Michael Kruse, INRIA Paris-Rocquencourt, |
| 7 | * Domaine de Voluceau, Rocquenqourt, B.P. 105, |
| 8 | * 78153 Le Chesnay Cedex France |
| 9 | */ |
| 10 | #ifndef ISL_INT_SIOIMATH_H |
| 11 | #define ISL_INT_SIOIMATH_H |
| 12 | |
| 13 | #include <inttypes.h> |
| 14 | #include <limits.h> |
| 15 | #include <stdint.h> |
| 16 | #include <stdlib.h> |
| 17 | |
| 18 | #include <isl_imath.h> |
| 19 | #include <isl/hash.h> |
| 20 | |
| 21 | #define ARRAY_SIZE(array)(sizeof(array)/sizeof(*array)) (sizeof(array)/sizeof(*array)) |
| 22 | |
| 23 | /* Visual Studio before VS2015 does not support the inline keyword when |
| 24 | * compiling in C mode because it was introduced in C99 which it does not |
| 25 | * officially support. Instead, it has a proprietary extension using __inline. |
| 26 | */ |
| 27 | #if defined(_MSC_VER) && (_MSC_VER < 1900) |
| 28 | #define inline __inline |
| 29 | #endif |
| 30 | |
| 31 | /* The type to represent integers optimized for small values. It is either a |
| 32 | * pointer to an mp_int ( = mpz_t*; big representation) or an int32_t (small |
| 33 | * represenation) with a discriminator at the least significant bit. In big |
| 34 | * representation it will be always zero because of heap alignment. It is set |
| 35 | * to 1 for small representation and use the 32 most significant bits for the |
| 36 | * int32_t. |
| 37 | * |
| 38 | * Structure on 64 bit machines, with 8-byte aligment (3 bits): |
| 39 | * |
| 40 | * Big representation: |
| 41 | * MSB LSB |
| 42 | * |------------------------------------------------------------000 |
| 43 | * | mpz_t* | |
| 44 | * | != NULL | |
| 45 | * |
| 46 | * Small representation: |
| 47 | * MSB 32 LSB |
| 48 | * |------------------------------|00000000000000000000000000000001 |
| 49 | * | int32_t | |
| 50 | * | 2147483647 ... -2147483647 | |
| 51 | * ^ |
| 52 | * | |
| 53 | * discriminator bit |
| 54 | * |
| 55 | * On 32 bit machines isl_sioimath type is blown up to 8 bytes, i.e. |
| 56 | * isl_sioimath is guaranteed to be at least 8 bytes. This is to ensure the |
| 57 | * int32_t can be hidden in that type without data loss. In the future we might |
| 58 | * optimize this to use 31 hidden bits in a 32 bit pointer. We may also use 63 |
| 59 | * bits on 64 bit machines, but this comes with the cost of additional overflow |
| 60 | * checks because there is no standardized 128 bit integer we could expand to. |
| 61 | * |
| 62 | * We use native integer types and avoid union structures to avoid assumptions |
| 63 | * on the machine's endianness. |
| 64 | * |
| 65 | * This implementation makes the following assumptions: |
| 66 | * - long can represent any int32_t |
| 67 | * - mp_small is signed long |
| 68 | * - mp_usmall is unsigned long |
| 69 | * - adresses returned by malloc are aligned to 2-byte boundaries (leastmost |
| 70 | * bit is zero) |
| 71 | */ |
| 72 | #if UINT64_MAX(18446744073709551615UL) > UINTPTR_MAX(18446744073709551615UL) |
| 73 | typedef uint64_t isl_sioimath; |
| 74 | #else |
| 75 | typedef uintptr_t isl_sioimath; |
| 76 | #endif |
| 77 | |
| 78 | /* The negation of the smallest possible number in int32_t, INT32_MIN |
| 79 | * (0x80000000u, -2147483648), cannot be represented in an int32_t, therefore |
| 80 | * every operation that may produce this value needs to special-case it. |
| 81 | * The operations are: |
| 82 | * abs(INT32_MIN) |
| 83 | * -INT32_MIN (negation) |
| 84 | * -1 * INT32_MIN (multiplication) |
| 85 | * INT32_MIN/-1 (any division: divexact, fdiv, cdiv, tdiv) |
| 86 | * To avoid checking these cases, we exclude INT32_MIN from small |
| 87 | * representation. |
| 88 | */ |
| 89 | #define ISL_SIOIMATH_SMALL_MIN(-(2147483647)) (-INT32_MAX(2147483647)) |
| 90 | |
| 91 | /* Largest possible number in small representation */ |
| 92 | #define ISL_SIOIMATH_SMALL_MAX(2147483647) INT32_MAX(2147483647) |
| 93 | |
| 94 | /* Used for function parameters the function modifies. */ |
| 95 | typedef isl_sioimath *isl_sioimath_ptr; |
| 96 | |
| 97 | /* Used for function parameters that are read-only. */ |
| 98 | typedef isl_sioimath isl_sioimath_src; |
| 99 | |
| 100 | /* Return whether the argument is stored in small representation. |
| 101 | */ |
| 102 | inline int isl_sioimath_is_small(isl_sioimath val) |
| 103 | { |
| 104 | return val & 0x00000001; |
| 105 | } |
| 106 | |
| 107 | /* Return whether the argument is stored in big representation. |
| 108 | */ |
| 109 | inline int isl_sioimath_is_big(isl_sioimath val) |
| 110 | { |
| 111 | return !isl_sioimath_is_small(val); |
| 112 | } |
| 113 | |
| 114 | /* Get the number of an isl_int in small representation. Result is undefined if |
| 115 | * val is not stored in that format. |
| 116 | */ |
| 117 | inline int32_t isl_sioimath_get_small(isl_sioimath val) |
| 118 | { |
| 119 | return val >> 32; |
| 120 | } |
| 121 | |
| 122 | /* Get the number of an in isl_int in big representation. Result is undefined if |
| 123 | * val is not stored in that format. |
| 124 | */ |
| 125 | inline mp_int isl_sioimath_get_big(isl_sioimath val) |
| 126 | { |
| 127 | return (mp_int)(uintptr_t) val; |
| 128 | } |
| 129 | |
| 130 | /* Return 1 if val is stored in small representation and store its value to |
| 131 | * small. We rely on the compiler to optimize the isl_sioimath_get_small such |
| 132 | * that the shift is moved into the branch that executes in case of small |
| 133 | * representation. If there is no such branch, then a single shift is still |
| 134 | * cheaper than introducing branching code. |
| 135 | */ |
| 136 | inline int isl_sioimath_decode_small(isl_sioimath val, int32_t *small) |
| 137 | { |
| 138 | *small = isl_sioimath_get_small(val); |
| 139 | return isl_sioimath_is_small(val); |
| 140 | } |
| 141 | |
| 142 | /* Return 1 if val is stored in big representation and store its value to big. |
| 143 | */ |
| 144 | inline int isl_sioimath_decode_big(isl_sioimath val, mp_int *big) |
| 145 | { |
| 146 | *big = isl_sioimath_get_big(val); |
| 147 | return isl_sioimath_is_big(val); |
| 148 | } |
| 149 | |
| 150 | /* Encode a small representation into an isl_int. |
| 151 | */ |
| 152 | inline isl_sioimath isl_sioimath_encode_small(int32_t val) |
| 153 | { |
| 154 | return ((isl_sioimath) val) << 32 | 0x00000001; |
| 155 | } |
| 156 | |
| 157 | /* Encode a big representation. |
| 158 | */ |
| 159 | inline isl_sioimath isl_sioimath_encode_big(mp_int val) |
| 160 | { |
| 161 | return (isl_sioimath)(uintptr_t) val; |
| 162 | } |
| 163 | |
| 164 | /* A common situation is to call an IMath function with at least one argument |
| 165 | * that is currently in small representation or an integer parameter, i.e. a big |
| 166 | * representation of the same number is required. Promoting the original |
| 167 | * argument comes with multiple problems, such as modifying a read-only |
| 168 | * argument, the responsibility of deallocation and the execution cost. Instead, |
| 169 | * we make a copy by 'faking' the IMath internal structure. |
| 170 | * |
| 171 | * We reserve the maximum number of required digits on the stack to avoid heap |
| 172 | * allocations. |
| 173 | * |
| 174 | * mp_digit can be uint32_t or uint16_t. This code must work for little and big |
| 175 | * endian digits. The structure for an uint64_t argument and 32-bit mp_digits is |
| 176 | * sketched below. |
| 177 | * |
| 178 | * |----------------------------| |
| 179 | * uint64_t |
| 180 | * |
| 181 | * |-------------||-------------| |
| 182 | * mp_digit mp_digit |
| 183 | * digits[1] digits[0] |
| 184 | * Most sig digit Least sig digit |
| 185 | */ |
| 186 | typedef struct { |
| 187 | mpz_t big; |
| 188 | mp_digit digits[(sizeof(uintmax_t) + sizeof(mp_digit) - 1) / |
| 189 | sizeof(mp_digit)]; |
| 190 | } isl_sioimath_scratchspace_t; |
| 191 | |
| 192 | /* Convert a native integer to IMath's digit representation. A native integer |
| 193 | * might be big- or little endian, but IMath always stores the least significant |
| 194 | * digit in the lowest array indices. memcpy therefore is not possible. |
| 195 | * |
| 196 | * We also have to consider that long and mp_digit can be of different sizes, |
| 197 | * depending on the compiler (LP64, LLP64) and IMath's USE_64BIT_WORDS. This |
| 198 | * macro should work for all of them. |
| 199 | * |
| 200 | * "used" is set to the number of written digits. It must be minimal (IMath |
| 201 | * checks zeroness using the used field), but always at least one. Also note |
| 202 | * that the result of num>>(sizeof(num)*CHAR_BIT) is undefined. |
| 203 | */ |
| 204 | #define ISL_SIOIMATH_TO_DIGITS(num, digits, used)do { int i = 0; do { (digits)[i] = ((num) >> (sizeof(mp_digit ) * 8 * i)); i += 1; if (i >= (sizeof(num) + sizeof(mp_digit ) - 1) / sizeof(mp_digit)) break; if (((num) >> (sizeof (mp_digit) * 8 * i)) == 0) break; } while (1); (used) = i; } while (0) \ |
| 205 | do { \ |
| 206 | int i = 0; \ |
| 207 | do { \ |
| 208 | (digits)[i] = \ |
| 209 | ((num) >> (sizeof(mp_digit) * CHAR_BIT8 * i)); \ |
| 210 | i += 1; \ |
| 211 | if (i >= (sizeof(num) + sizeof(mp_digit) - 1) / \ |
| 212 | sizeof(mp_digit)) \ |
| 213 | break; \ |
| 214 | if (((num) >> (sizeof(mp_digit) * CHAR_BIT8 * i)) == 0) \ |
| 215 | break; \ |
| 216 | } while (1); \ |
| 217 | (used) = i; \ |
| 218 | } while (0) |
| 219 | |
| 220 | inline void isl_siomath_uint32_to_digits(uint32_t num, mp_digit *digits, |
| 221 | mp_size *used) |
| 222 | { |
| 223 | ISL_SIOIMATH_TO_DIGITS(num, digits, *used)do { int i = 0; do { (digits)[i] = ((num) >> (sizeof(mp_digit ) * 8 * i)); i += 1; if (i >= (sizeof(num) + sizeof(mp_digit ) - 1) / sizeof(mp_digit)) break; if (((num) >> (sizeof (mp_digit) * 8 * i)) == 0) break; } while (1); (*used) = i; } while (0); |
| 224 | } |
| 225 | |
| 226 | inline void isl_siomath_ulong_to_digits(unsigned long num, mp_digit *digits, |
| 227 | mp_size *used) |
| 228 | { |
| 229 | ISL_SIOIMATH_TO_DIGITS(num, digits, *used)do { int i = 0; do { (digits)[i] = ((num) >> (sizeof(mp_digit ) * 8 * i)); i += 1; if (i >= (sizeof(num) + sizeof(mp_digit ) - 1) / sizeof(mp_digit)) break; if (((num) >> (sizeof (mp_digit) * 8 * i)) == 0) break; } while (1); (*used) = i; } while (0); |
| 230 | } |
| 231 | |
| 232 | inline void isl_siomath_uint64_to_digits(uint64_t num, mp_digit *digits, |
| 233 | mp_size *used) |
| 234 | { |
| 235 | ISL_SIOIMATH_TO_DIGITS(num, digits, *used)do { int i = 0; do { (digits)[i] = ((num) >> (sizeof(mp_digit ) * 8 * i)); i += 1; if (i >= (sizeof(num) + sizeof(mp_digit ) - 1) / sizeof(mp_digit)) break; if (((num) >> (sizeof (mp_digit) * 8 * i)) == 0) break; } while (1); (*used) = i; } while (0); |
| 236 | } |
| 237 | |
| 238 | /* Get the IMath representation of an isl_int without modifying it. |
| 239 | * For the case it is not in big representation yet, pass some scratch space we |
| 240 | * can use to store the big representation in. |
| 241 | * In order to avoid requiring init and free on the scratch space, we directly |
| 242 | * modify the internal representation. |
| 243 | * |
| 244 | * The name derives from its indented use: getting the big representation of an |
| 245 | * input (src) argument. |
| 246 | */ |
| 247 | inline mp_int isl_sioimath_bigarg_src(isl_sioimath arg, |
| 248 | isl_sioimath_scratchspace_t *scratch) |
| 249 | { |
| 250 | mp_int big; |
| 251 | int32_t small; |
| 252 | uint32_t num; |
| 253 | |
| 254 | if (isl_sioimath_decode_big(arg, &big)) |
| 255 | return big; |
| 256 | |
| 257 | small = isl_sioimath_get_small(arg); |
| 258 | scratch->big.digits = scratch->digits; |
| 259 | scratch->big.alloc = ARRAY_SIZE(scratch->digits)(sizeof(scratch->digits)/sizeof(*scratch->digits)); |
| 260 | if (small >= 0) { |
| 261 | scratch->big.sign = MP_ZPOS; |
| 262 | num = small; |
| 263 | } else { |
| 264 | scratch->big.sign = MP_NEG; |
| 265 | num = -small; |
| 266 | } |
| 267 | |
| 268 | isl_siomath_uint32_to_digits(num, scratch->digits, &scratch->big.used); |
| 269 | return &scratch->big; |
| 270 | } |
| 271 | |
| 272 | /* Create a temporary IMath mp_int for a signed long. |
| 273 | */ |
| 274 | inline mp_int isl_sioimath_siarg_src(signed long arg, |
| 275 | isl_sioimath_scratchspace_t *scratch) |
| 276 | { |
| 277 | unsigned long num; |
| 278 | |
| 279 | scratch->big.digits = scratch->digits; |
| 280 | scratch->big.alloc = ARRAY_SIZE(scratch->digits)(sizeof(scratch->digits)/sizeof(*scratch->digits)); |
| 281 | if (arg >= 0) { |
| 282 | scratch->big.sign = MP_ZPOS; |
| 283 | num = arg; |
| 284 | } else { |
| 285 | scratch->big.sign = MP_NEG; |
| 286 | num = (arg == LONG_MIN(-9223372036854775807L -1L)) ? ((unsigned long) LONG_MAX9223372036854775807L) + 1 : -arg; |
| 287 | } |
| 288 | |
| 289 | isl_siomath_ulong_to_digits(num, scratch->digits, &scratch->big.used); |
| 290 | return &scratch->big; |
| 291 | } |
| 292 | |
| 293 | /* Create a temporary IMath mp_int for an int64_t. |
| 294 | */ |
| 295 | inline mp_int isl_sioimath_si64arg_src(int64_t arg, |
| 296 | isl_sioimath_scratchspace_t *scratch) |
| 297 | { |
| 298 | uint64_t num; |
| 299 | |
| 300 | scratch->big.digits = scratch->digits; |
| 301 | scratch->big.alloc = ARRAY_SIZE(scratch->digits)(sizeof(scratch->digits)/sizeof(*scratch->digits)); |
| 302 | if (arg >= 0) { |
| 303 | scratch->big.sign = MP_ZPOS; |
| 304 | num = arg; |
| 305 | } else { |
| 306 | scratch->big.sign = MP_NEG; |
| 307 | num = (arg == INT64_MIN(-9223372036854775807L -1)) ? ((uint64_t) INT64_MAX(9223372036854775807L)) + 1 : -arg; |
| 308 | } |
| 309 | |
| 310 | isl_siomath_uint64_to_digits(num, scratch->digits, &scratch->big.used); |
| 311 | return &scratch->big; |
| 312 | } |
| 313 | |
| 314 | /* Create a temporary IMath mp_int for an unsigned long. |
| 315 | */ |
| 316 | inline mp_int isl_sioimath_uiarg_src(unsigned long arg, |
| 317 | isl_sioimath_scratchspace_t *scratch) |
| 318 | { |
| 319 | scratch->big.digits = scratch->digits; |
| 320 | scratch->big.alloc = ARRAY_SIZE(scratch->digits)(sizeof(scratch->digits)/sizeof(*scratch->digits)); |
| 321 | scratch->big.sign = MP_ZPOS; |
| 322 | |
| 323 | isl_siomath_ulong_to_digits(arg, scratch->digits, &scratch->big.used); |
| 324 | return &scratch->big; |
| 325 | } |
| 326 | |
| 327 | /* Ensure big representation. Does not preserve the current number. |
| 328 | * Callers may use the fact that the value _is_ preserved if the presentation |
| 329 | * was big before. |
| 330 | */ |
| 331 | inline mp_int isl_sioimath_reinit_big(isl_sioimath_ptr ptr) |
| 332 | { |
| 333 | if (isl_sioimath_is_small(*ptr)) |
| 334 | *ptr = isl_sioimath_encode_big(mp_int_alloc()); |
| 335 | return isl_sioimath_get_big(*ptr); |
| 336 | } |
| 337 | |
| 338 | /* Set ptr to a number in small representation. |
| 339 | */ |
| 340 | inline void isl_sioimath_set_small(isl_sioimath_ptr ptr, int32_t val) |
| 341 | { |
| 342 | if (isl_sioimath_is_big(*ptr)) |
| 343 | mp_int_free(isl_sioimath_get_big(*ptr)); |
| 344 | *ptr = isl_sioimath_encode_small(val); |
| 345 | } |
| 346 | |
| 347 | /* Set ptr to val, choosing small representation if possible. |
| 348 | */ |
| 349 | inline void isl_sioimath_set_int32(isl_sioimath_ptr ptr, int32_t val) |
| 350 | { |
| 351 | if (ISL_SIOIMATH_SMALL_MIN(-(2147483647)) <= val && val <= ISL_SIOIMATH_SMALL_MAX(2147483647)) { |
| 352 | isl_sioimath_set_small(ptr, val); |
| 353 | return; |
| 354 | } |
| 355 | |
| 356 | mp_int_init_value(isl_sioimath_reinit_big(ptr), val); |
| 357 | } |
| 358 | |
| 359 | /* Assign an int64_t number using small representation if possible. |
| 360 | */ |
| 361 | inline void isl_sioimath_set_int64(isl_sioimath_ptr ptr, int64_t val) |
| 362 | { |
| 363 | if (ISL_SIOIMATH_SMALL_MIN(-(2147483647)) <= val && val <= ISL_SIOIMATH_SMALL_MAX(2147483647)) { |
| 364 | isl_sioimath_set_small(ptr, val); |
| 365 | return; |
| 366 | } |
| 367 | |
| 368 | isl_sioimath_scratchspace_t scratch; |
| 369 | mp_int_copy(isl_sioimath_si64arg_src(val, &scratch), |
| 370 | isl_sioimath_reinit_big(ptr)); |
| 371 | } |
| 372 | |
| 373 | /* Convert to big representation while preserving the current number. |
| 374 | */ |
| 375 | inline void isl_sioimath_promote(isl_sioimath_ptr dst) |
| 376 | { |
| 377 | int32_t small; |
| 378 | |
| 379 | if (isl_sioimath_is_big(*dst)) |
| 380 | return; |
| 381 | |
| 382 | small = isl_sioimath_get_small(*dst); |
| 383 | mp_int_set_value(isl_sioimath_reinit_big(dst), small); |
| 384 | } |
| 385 | |
| 386 | /* Convert to small representation while preserving the current number. Does |
| 387 | * nothing if dst doesn't fit small representation. |
| 388 | */ |
| 389 | inline void isl_sioimath_try_demote(isl_sioimath_ptr dst) |
| 390 | { |
| 391 | mp_small small; |
| 392 | |
| 393 | if (isl_sioimath_is_small(*dst)) |
| 394 | return; |
| 395 | |
| 396 | if (mp_int_to_int(isl_sioimath_get_big(*dst), &small) != MP_OK) |
| 397 | return; |
| 398 | |
| 399 | if (ISL_SIOIMATH_SMALL_MIN(-(2147483647)) <= small && small <= ISL_SIOIMATH_SMALL_MAX(2147483647)) |
| 400 | isl_sioimath_set_small(dst, small); |
| 401 | } |
| 402 | |
| 403 | /* Initialize an isl_int. The implicit value is 0 in small representation. |
| 404 | */ |
| 405 | inline void isl_sioimath_init(isl_sioimath_ptr dst) |
| 406 | { |
| 407 | *dst = isl_sioimath_encode_small(0); |
| 408 | } |
| 409 | |
| 410 | /* Free the resources taken by an isl_int. |
| 411 | */ |
| 412 | inline void isl_sioimath_clear(isl_sioimath_ptr dst) |
| 413 | { |
| 414 | if (isl_sioimath_is_small(*dst)) |
| 415 | return; |
| 416 | |
| 417 | mp_int_free(isl_sioimath_get_big(*dst)); |
| 418 | } |
| 419 | |
| 420 | /* Copy the value of one isl_int to another. |
| 421 | */ |
| 422 | inline void isl_sioimath_set(isl_sioimath_ptr dst, isl_sioimath_src val) |
| 423 | { |
| 424 | if (isl_sioimath_is_small(val)) { |
| 425 | isl_sioimath_set_small(dst, isl_sioimath_get_small(val)); |
| 426 | return; |
| 427 | } |
| 428 | |
| 429 | mp_int_copy(isl_sioimath_get_big(val), isl_sioimath_reinit_big(dst)); |
| 430 | } |
| 431 | |
| 432 | /* Store a signed long into an isl_int. |
| 433 | */ |
| 434 | inline void isl_sioimath_set_si(isl_sioimath_ptr dst, long val) |
| 435 | { |
| 436 | if (ISL_SIOIMATH_SMALL_MIN(-(2147483647)) <= val && val <= ISL_SIOIMATH_SMALL_MAX(2147483647)) { |
| 437 | isl_sioimath_set_small(dst, val); |
| 438 | return; |
| 439 | } |
| 440 | |
| 441 | mp_int_set_value(isl_sioimath_reinit_big(dst), val); |
| 442 | } |
| 443 | |
| 444 | /* Store an unsigned long into an isl_int. |
| 445 | */ |
| 446 | inline void isl_sioimath_set_ui(isl_sioimath_ptr dst, unsigned long val) |
| 447 | { |
| 448 | if (val <= ISL_SIOIMATH_SMALL_MAX(2147483647)) { |
| 449 | isl_sioimath_set_small(dst, val); |
| 450 | return; |
| 451 | } |
| 452 | |
| 453 | mp_int_set_uvalue(isl_sioimath_reinit_big(dst), val); |
| 454 | } |
| 455 | |
| 456 | /* Return whether a number can be represented by a signed long. |
| 457 | */ |
| 458 | inline int isl_sioimath_fits_slong(isl_sioimath_src val) |
| 459 | { |
| 460 | mp_small dummy; |
| 461 | |
| 462 | if (isl_sioimath_is_small(val)) |
| 463 | return 1; |
| 464 | |
| 465 | return mp_int_to_int(isl_sioimath_get_big(val), &dummy) == MP_OK; |
| 466 | } |
| 467 | |
| 468 | /* Return a number as signed long. Result is undefined if the number cannot be |
| 469 | * represented as long. |
| 470 | */ |
| 471 | inline long isl_sioimath_get_si(isl_sioimath_src val) |
| 472 | { |
| 473 | mp_small result; |
| 474 | |
| 475 | if (isl_sioimath_is_small(val)) |
| 476 | return isl_sioimath_get_small(val); |
| 477 | |
| 478 | mp_int_to_int(isl_sioimath_get_big(val), &result); |
| 479 | return result; |
| 480 | } |
| 481 | |
| 482 | /* Return whether a number can be represented as unsigned long. |
| 483 | */ |
| 484 | inline int isl_sioimath_fits_ulong(isl_sioimath_src val) |
| 485 | { |
| 486 | mp_usmall dummy; |
| 487 | |
| 488 | if (isl_sioimath_is_small(val)) |
| 489 | return isl_sioimath_get_small(val) >= 0; |
| 490 | |
| 491 | return mp_int_to_uint(isl_sioimath_get_big(val), &dummy) == MP_OK; |
| 492 | } |
| 493 | |
| 494 | /* Return a number as unsigned long. Result is undefined if the number cannot be |
| 495 | * represented as unsigned long. |
| 496 | */ |
| 497 | inline unsigned long isl_sioimath_get_ui(isl_sioimath_src val) |
| 498 | { |
| 499 | mp_usmall result; |
| 500 | |
| 501 | if (isl_sioimath_is_small(val)) |
| 502 | return isl_sioimath_get_small(val); |
| 503 | |
| 504 | mp_int_to_uint(isl_sioimath_get_big(val), &result); |
| 505 | return result; |
| 506 | } |
| 507 | |
| 508 | /* Return a number as floating point value. |
| 509 | */ |
| 510 | inline double isl_sioimath_get_d(isl_sioimath_src val) |
| 511 | { |
| 512 | mp_int big; |
| 513 | double result = 0; |
| 514 | int i; |
| 515 | |
| 516 | if (isl_sioimath_is_small(val)) |
| 517 | return isl_sioimath_get_small(val); |
| 518 | |
| 519 | big = isl_sioimath_get_big(val); |
| 520 | for (i = 0; i < big->used; ++i) |
| 521 | result = result * (double) ((uintmax_t) MP_DIGIT_MAX((4294967295U) * 1UL) + 1) + |
| 522 | (double) big->digits[i]; |
| 523 | |
| 524 | if (big->sign == MP_NEG) |
| 525 | result = -result; |
| 526 | |
| 527 | return result; |
| 528 | } |
| 529 | |
| 530 | /* Format a number as decimal string. |
| 531 | * |
| 532 | * The largest possible string from small representation is 12 characters |
| 533 | * ("-2147483647"). |
| 534 | */ |
| 535 | inline char *isl_sioimath_get_str(isl_sioimath_src val) |
| 536 | { |
| 537 | char *result; |
| 538 | |
| 539 | if (isl_sioimath_is_small(val)) { |
| 540 | result = malloc(12); |
| 541 | snprintf(result, 12, "%" PRIi32"i", isl_sioimath_get_small(val)); |
| 542 | return result; |
| 543 | } |
| 544 | |
| 545 | return impz_get_str(NULL((void*)0), 10, isl_sioimath_get_big(val)); |
| 546 | } |
| 547 | |
| 548 | /* Return the absolute value. |
| 549 | */ |
| 550 | inline void isl_sioimath_abs(isl_sioimath_ptr dst, isl_sioimath_src arg) |
| 551 | { |
| 552 | if (isl_sioimath_is_small(arg)) { |
| 553 | isl_sioimath_set_small(dst, labs(isl_sioimath_get_small(arg))); |
| 554 | return; |
| 555 | } |
| 556 | |
| 557 | mp_int_abs(isl_sioimath_get_big(arg), isl_sioimath_reinit_big(dst)); |
| 558 | } |
| 559 | |
| 560 | /* Return the negation of a number. |
| 561 | */ |
| 562 | inline void isl_sioimath_neg(isl_sioimath_ptr dst, isl_sioimath_src arg) |
| 563 | { |
| 564 | if (isl_sioimath_is_small(arg)) { |
| 565 | isl_sioimath_set_small(dst, -isl_sioimath_get_small(arg)); |
| 566 | return; |
| 567 | } |
| 568 | |
| 569 | mp_int_neg(isl_sioimath_get_big(arg), isl_sioimath_reinit_big(dst)); |
| 570 | } |
| 571 | |
| 572 | /* Swap two isl_ints. |
| 573 | * |
| 574 | * isl_sioimath can be copied bytewise; nothing depends on its address. It can |
| 575 | * also be stored in a CPU register. |
| 576 | */ |
| 577 | inline void isl_sioimath_swap(isl_sioimath_ptr lhs, isl_sioimath_ptr rhs) |
| 578 | { |
| 579 | isl_sioimath tmp = *lhs; |
| 580 | *lhs = *rhs; |
| 581 | *rhs = tmp; |
| 582 | } |
| 583 | |
| 584 | /* Add an unsigned long to the number. |
| 585 | * |
| 586 | * On LP64 unsigned long exceeds the range of an int64_t, therefore we check in |
| 587 | * advance whether small representation possibly overflows. |
| 588 | */ |
| 589 | inline void isl_sioimath_add_ui(isl_sioimath_ptr dst, isl_sioimath lhs, |
| 590 | unsigned long rhs) |
| 591 | { |
| 592 | int32_t smalllhs; |
| 593 | isl_sioimath_scratchspace_t lhsscratch; |
| 594 | |
| 595 | if (isl_sioimath_decode_small(lhs, &smalllhs) && |
| 596 | (rhs <= (uint64_t) INT64_MAX(9223372036854775807L) - (uint64_t) ISL_SIOIMATH_SMALL_MAX(2147483647))) { |
| 597 | isl_sioimath_set_int64(dst, (int64_t) smalllhs + rhs); |
| 598 | return; |
| 599 | } |
| 600 | |
| 601 | impz_add_ui(isl_sioimath_reinit_big(dst), |
| 602 | isl_sioimath_bigarg_src(lhs, &lhsscratch), rhs); |
| 603 | isl_sioimath_try_demote(dst); |
| 604 | } |
| 605 | |
| 606 | /* Subtract an unsigned long. |
| 607 | * |
| 608 | * On LP64 unsigned long exceeds the range of an int64_t. If |
| 609 | * ISL_SIOIMATH_SMALL_MIN-rhs>=INT64_MIN we can do the calculation using int64_t |
| 610 | * without risking an overflow. |
| 611 | */ |
| 612 | inline void isl_sioimath_sub_ui(isl_sioimath_ptr dst, isl_sioimath lhs, |
| 613 | unsigned long rhs) |
| 614 | { |
| 615 | int32_t smalllhs; |
| 616 | isl_sioimath_scratchspace_t lhsscratch; |
| 617 | |
| 618 | if (isl_sioimath_decode_small(lhs, &smalllhs) && |
| 619 | (rhs < (uint64_t) INT64_MIN(-9223372036854775807L -1) - (uint64_t) ISL_SIOIMATH_SMALL_MIN(-(2147483647)))) { |
| 620 | isl_sioimath_set_int64(dst, (int64_t) smalllhs - rhs); |
| 621 | return; |
| 622 | } |
| 623 | |
| 624 | impz_sub_ui(isl_sioimath_reinit_big(dst), |
| 625 | isl_sioimath_bigarg_src(lhs, &lhsscratch), rhs); |
| 626 | isl_sioimath_try_demote(dst); |
| 627 | } |
| 628 | |
| 629 | /* Sum of two isl_ints. |
| 630 | */ |
| 631 | inline void isl_sioimath_add(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 632 | isl_sioimath_src rhs) |
| 633 | { |
| 634 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 635 | int32_t smalllhs, smallrhs; |
| 636 | |
| 637 | if (isl_sioimath_decode_small(lhs, &smalllhs) && |
| 638 | isl_sioimath_decode_small(rhs, &smallrhs)) { |
| 639 | isl_sioimath_set_int64( |
| 640 | dst, (int64_t) smalllhs + (int64_t) smallrhs); |
| 641 | return; |
| 642 | } |
| 643 | |
| 644 | mp_int_add(isl_sioimath_bigarg_src(lhs, &scratchlhs), |
| 645 | isl_sioimath_bigarg_src(rhs, &scratchrhs), |
| 646 | isl_sioimath_reinit_big(dst)); |
| 647 | isl_sioimath_try_demote(dst); |
| 648 | } |
| 649 | |
| 650 | /* Subtract two isl_ints. |
| 651 | */ |
| 652 | inline void isl_sioimath_sub(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 653 | isl_sioimath_src rhs) |
| 654 | { |
| 655 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 656 | int32_t smalllhs, smallrhs; |
| 657 | |
| 658 | if (isl_sioimath_decode_small(lhs, &smalllhs) && |
| 659 | isl_sioimath_decode_small(rhs, &smallrhs)) { |
| 660 | isl_sioimath_set_int64( |
| 661 | dst, (int64_t) smalllhs - (int64_t) smallrhs); |
| 662 | return; |
| 663 | } |
| 664 | |
| 665 | mp_int_sub(isl_sioimath_bigarg_src(lhs, &scratchlhs), |
| 666 | isl_sioimath_bigarg_src(rhs, &scratchrhs), |
| 667 | isl_sioimath_reinit_big(dst)); |
| 668 | isl_sioimath_try_demote(dst); |
| 669 | } |
| 670 | |
| 671 | /* Multiply two isl_ints. |
| 672 | */ |
| 673 | inline void isl_sioimath_mul(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 674 | isl_sioimath_src rhs) |
| 675 | { |
| 676 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 677 | int32_t smalllhs, smallrhs; |
| 678 | |
| 679 | if (isl_sioimath_decode_small(lhs, &smalllhs) && |
| 680 | isl_sioimath_decode_small(rhs, &smallrhs)) { |
| 681 | isl_sioimath_set_int64( |
| 682 | dst, (int64_t) smalllhs * (int64_t) smallrhs); |
| 683 | return; |
| 684 | } |
| 685 | |
| 686 | mp_int_mul(isl_sioimath_bigarg_src(lhs, &scratchlhs), |
| 687 | isl_sioimath_bigarg_src(rhs, &scratchrhs), |
| 688 | isl_sioimath_reinit_big(dst)); |
| 689 | isl_sioimath_try_demote(dst); |
| 690 | } |
| 691 | |
| 692 | /* Shift lhs by rhs bits to the left and store the result in dst. Effectively, |
| 693 | * this operation computes 'lhs * 2^rhs'. |
| 694 | */ |
| 695 | inline void isl_sioimath_mul_2exp(isl_sioimath_ptr dst, isl_sioimath lhs, |
| 696 | unsigned long rhs) |
| 697 | { |
| 698 | isl_sioimath_scratchspace_t scratchlhs; |
| 699 | int32_t smalllhs; |
| 700 | |
| 701 | if (isl_sioimath_decode_small(lhs, &smalllhs) && (rhs <= 32ul)) { |
| 702 | isl_sioimath_set_int64(dst, ((int64_t) smalllhs) << rhs); |
| 703 | return; |
| 704 | } |
| 705 | |
| 706 | mp_int_mul_pow2(isl_sioimath_bigarg_src(lhs, &scratchlhs), rhs, |
| 707 | isl_sioimath_reinit_big(dst)); |
| 708 | } |
| 709 | |
| 710 | /* Multiply an isl_int and a signed long. |
| 711 | */ |
| 712 | inline void isl_sioimath_mul_si(isl_sioimath_ptr dst, isl_sioimath lhs, |
| 713 | signed long rhs) |
| 714 | { |
| 715 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 716 | int32_t smalllhs; |
| 717 | |
| 718 | if (isl_sioimath_decode_small(lhs, &smalllhs) && (rhs > LONG_MIN(-9223372036854775807L -1L)) && |
| 719 | (labs(rhs) <= UINT32_MAX(4294967295U))) { |
| 720 | isl_sioimath_set_int64(dst, (int64_t) smalllhs * (int64_t) rhs) |