| 1 | /* |
| 2 | * Copyright 2012-2013 Ecole Normale Superieure |
| 3 | * |
| 4 | * Use of this software is governed by the MIT license |
| 5 | * |
| 6 | * Written by Sven Verdoolaege, |
| 7 | * Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France |
| 8 | */ |
| 9 | |
| 10 | #include <isl/val.h> |
| 11 | #include <isl_map_private.h> |
| 12 | #include <isl_aff_private.h> |
| 13 | #include <isl/constraint.h> |
| 14 | #include <isl/set.h> |
| 15 | |
| 16 | /* Stride information about a specific set dimension. |
| 17 | * The values of the set dimension are equal to |
| 18 | * "offset" plus a multiple of "stride". |
| 19 | */ |
| 20 | struct isl_stride_info { |
| 21 | isl_val *stride; |
| 22 | isl_aff *offset; |
| 23 | }; |
| 24 | |
| 25 | /* Return the ctx to which "si" belongs. |
| 26 | */ |
| 27 | isl_ctx *isl_stride_info_get_ctx(__isl_keep isl_stride_info *si) |
| 28 | { |
| 29 | if (!si) |
| 30 | return NULL; |
| 31 | |
| 32 | return isl_val_get_ctx(val: si->stride); |
| 33 | } |
| 34 | |
| 35 | /* Free "si" and return NULL. |
| 36 | */ |
| 37 | __isl_null isl_stride_info *isl_stride_info_free( |
| 38 | __isl_take isl_stride_info *si) |
| 39 | { |
| 40 | if (!si) |
| 41 | return NULL; |
| 42 | isl_val_free(v: si->stride); |
| 43 | isl_aff_free(aff: si->offset); |
| 44 | free(ptr: si); |
| 45 | return NULL; |
| 46 | } |
| 47 | |
| 48 | /* Construct an isl_stride_info object with given offset and stride. |
| 49 | */ |
| 50 | __isl_give isl_stride_info *isl_stride_info_alloc( |
| 51 | __isl_take isl_val *stride, __isl_take isl_aff *offset) |
| 52 | { |
| 53 | struct isl_stride_info *si; |
| 54 | |
| 55 | if (!stride || !offset) |
| 56 | goto error; |
| 57 | si = isl_alloc_type(isl_val_get_ctx(stride), struct isl_stride_info); |
| 58 | if (!si) |
| 59 | goto error; |
| 60 | si->stride = stride; |
| 61 | si->offset = offset; |
| 62 | return si; |
| 63 | error: |
| 64 | isl_val_free(v: stride); |
| 65 | isl_aff_free(aff: offset); |
| 66 | return NULL; |
| 67 | } |
| 68 | |
| 69 | /* Make a copy of "si" and return it. |
| 70 | */ |
| 71 | __isl_give isl_stride_info *isl_stride_info_copy( |
| 72 | __isl_keep isl_stride_info *si) |
| 73 | { |
| 74 | if (!si) |
| 75 | return NULL; |
| 76 | |
| 77 | return isl_stride_info_alloc(stride: isl_val_copy(v: si->stride), |
| 78 | offset: isl_aff_copy(aff: si->offset)); |
| 79 | } |
| 80 | |
| 81 | /* Return the stride of "si". |
| 82 | */ |
| 83 | __isl_give isl_val *isl_stride_info_get_stride(__isl_keep isl_stride_info *si) |
| 84 | { |
| 85 | if (!si) |
| 86 | return NULL; |
| 87 | return isl_val_copy(v: si->stride); |
| 88 | } |
| 89 | |
| 90 | /* Return the offset of "si". |
| 91 | */ |
| 92 | __isl_give isl_aff *isl_stride_info_get_offset(__isl_keep isl_stride_info *si) |
| 93 | { |
| 94 | if (!si) |
| 95 | return NULL; |
| 96 | return isl_aff_copy(aff: si->offset); |
| 97 | } |
| 98 | |
| 99 | /* Information used inside detect_stride. |
| 100 | * |
| 101 | * "pos" is the set dimension at which the stride is being determined. |
| 102 | * "want_offset" is set if the offset should be computed. |
| 103 | * "found" is set if some stride was found already. |
| 104 | * "stride" and "offset" contain the (combined) stride and offset |
| 105 | * found so far and are NULL when "found" is not set. |
| 106 | * If "want_offset" is not set, then "offset" remains NULL. |
| 107 | */ |
| 108 | struct isl_detect_stride_data { |
| 109 | int pos; |
| 110 | int want_offset; |
| 111 | int found; |
| 112 | isl_val *stride; |
| 113 | isl_aff *offset; |
| 114 | }; |
| 115 | |
| 116 | /* Set the stride and offset of data->pos to the given |
| 117 | * value and expression. |
| 118 | * |
| 119 | * If we had already found a stride before, then the two strides |
| 120 | * are combined into a single stride. |
| 121 | * |
| 122 | * In particular, if the new stride information is of the form |
| 123 | * |
| 124 | * i = f + s (...) |
| 125 | * |
| 126 | * and the old stride information is of the form |
| 127 | * |
| 128 | * i = f2 + s2 (...) |
| 129 | * |
| 130 | * then we compute the extended gcd of s and s2 |
| 131 | * |
| 132 | * a s + b s2 = g, |
| 133 | * |
| 134 | * with g = gcd(s,s2), multiply the first equation with t1 = b s2/g |
| 135 | * and the second with t2 = a s1/g. |
| 136 | * This results in |
| 137 | * |
| 138 | * i = (b s2 + a s1)/g i = t1 f + t2 f2 + (s s2)/g (...) |
| 139 | * |
| 140 | * so that t1 f + t2 f2 is the combined offset and (s s2)/g = lcm(s,s2) |
| 141 | * is the combined stride. |
| 142 | */ |
| 143 | static isl_stat set_stride(struct isl_detect_stride_data *data, |
| 144 | __isl_take isl_val *stride, __isl_take isl_aff *offset) |
| 145 | { |
| 146 | if (!stride || !offset) |
| 147 | goto error; |
| 148 | |
| 149 | if (data->found) { |
| 150 | isl_val *stride2, *a, *b, *g; |
| 151 | isl_aff *offset2; |
| 152 | |
| 153 | stride2 = data->stride; |
| 154 | g = isl_val_gcdext(v1: isl_val_copy(v: stride), v2: isl_val_copy(v: stride2), |
| 155 | x: &a, y: &b); |
| 156 | a = isl_val_mul(v1: a, v2: isl_val_copy(v: stride)); |
| 157 | a = isl_val_div(v1: a, v2: isl_val_copy(v: g)); |
| 158 | stride2 = isl_val_div(v1: stride2, v2: g); |
| 159 | b = isl_val_mul(v1: b, v2: isl_val_copy(v: stride2)); |
| 160 | stride = isl_val_mul(v1: stride, v2: stride2); |
| 161 | |
| 162 | if (!data->want_offset) { |
| 163 | isl_val_free(v: a); |
| 164 | isl_val_free(v: b); |
| 165 | } else { |
| 166 | offset2 = data->offset; |
| 167 | offset2 = isl_aff_scale_val(aff: offset2, v: a); |
| 168 | offset = isl_aff_scale_val(aff: offset, v: b); |
| 169 | offset = isl_aff_add(aff1: offset, aff2: offset2); |
| 170 | } |
| 171 | } |
| 172 | |
| 173 | data->found = 1; |
| 174 | data->stride = stride; |
| 175 | if (data->want_offset) |
| 176 | data->offset = offset; |
| 177 | else |
| 178 | isl_aff_free(aff: offset); |
| 179 | if (!data->stride || (data->want_offset && !data->offset)) |
| 180 | return isl_stat_error; |
| 181 | |
| 182 | return isl_stat_ok; |
| 183 | error: |
| 184 | isl_val_free(v: stride); |
| 185 | isl_aff_free(aff: offset); |
| 186 | return isl_stat_error; |
| 187 | } |
| 188 | |
| 189 | /* Check if constraint "c" imposes any stride on dimension data->pos |
| 190 | * and, if so, update the stride information in "data". |
| 191 | * |
| 192 | * In order to impose a stride on the dimension, "c" needs to be an equality |
| 193 | * and it needs to involve the dimension. Note that "c" may also be |
| 194 | * a div constraint and thus an inequality that we cannot use. |
| 195 | * |
| 196 | * Let c be of the form |
| 197 | * |
| 198 | * h(p) + g * v * i + g * stride * f(alpha) = 0 |
| 199 | * |
| 200 | * with h(p) an expression in terms of the parameters and other dimensions |
| 201 | * and f(alpha) an expression in terms of the existentially quantified |
| 202 | * variables. |
| 203 | * |
| 204 | * If "stride" is not zero and not one, then it represents a non-trivial stride |
| 205 | * on "i". We compute a and b such that |
| 206 | * |
| 207 | * a v + b stride = 1 |
| 208 | * |
| 209 | * We have |
| 210 | * |
| 211 | * g v i = -h(p) + g stride f(alpha) |
| 212 | * |
| 213 | * a g v i = -a h(p) + g stride f(alpha) |
| 214 | * |
| 215 | * a g v i + b g stride i = -a h(p) + g stride * (...) |
| 216 | * |
| 217 | * g i = -a h(p) + g stride * (...) |
| 218 | * |
| 219 | * i = -a h(p)/g + stride * (...) |
| 220 | * |
| 221 | * The expression "-a h(p)/g" can therefore be used as offset. |
| 222 | */ |
| 223 | static isl_stat detect_stride(__isl_take isl_constraint *c, void *user) |
| 224 | { |
| 225 | struct isl_detect_stride_data *data = user; |
| 226 | int i; |
| 227 | isl_size n_div; |
| 228 | isl_ctx *ctx; |
| 229 | isl_stat r = isl_stat_ok; |
| 230 | isl_val *v, *stride, *m; |
| 231 | isl_bool is_eq, relevant, has_stride; |
| 232 | |
| 233 | is_eq = isl_constraint_is_equality(constraint: c); |
| 234 | relevant = isl_constraint_involves_dims(constraint: c, type: isl_dim_set, first: data->pos, n: 1); |
| 235 | if (is_eq < 0 || relevant < 0) |
| 236 | goto error; |
| 237 | if (!is_eq || !relevant) { |
| 238 | isl_constraint_free(c); |
| 239 | return isl_stat_ok; |
| 240 | } |
| 241 | |
| 242 | n_div = isl_constraint_dim(constraint: c, type: isl_dim_div); |
| 243 | if (n_div < 0) |
| 244 | goto error; |
| 245 | ctx = isl_constraint_get_ctx(c); |
| 246 | stride = isl_val_zero(ctx); |
| 247 | for (i = 0; i < n_div; ++i) { |
| 248 | v = isl_constraint_get_coefficient_val(constraint: c, type: isl_dim_div, pos: i); |
| 249 | stride = isl_val_gcd(v1: stride, v2: v); |
| 250 | } |
| 251 | |
| 252 | v = isl_constraint_get_coefficient_val(constraint: c, type: isl_dim_set, pos: data->pos); |
| 253 | m = isl_val_gcd(v1: isl_val_copy(v: stride), v2: isl_val_copy(v)); |
| 254 | stride = isl_val_div(v1: stride, v2: isl_val_copy(v: m)); |
| 255 | v = isl_val_div(v1: v, v2: isl_val_copy(v: m)); |
| 256 | |
| 257 | has_stride = isl_val_gt_si(v: stride, i: 1); |
| 258 | if (has_stride >= 0 && has_stride) { |
| 259 | isl_aff *aff; |
| 260 | isl_val *gcd, *a, *b; |
| 261 | |
| 262 | gcd = isl_val_gcdext(v1: v, v2: isl_val_copy(v: stride), x: &a, y: &b); |
| 263 | isl_val_free(v: gcd); |
| 264 | isl_val_free(v: b); |
| 265 | |
| 266 | aff = isl_constraint_get_aff(constraint: c); |
| 267 | for (i = 0; i < n_div; ++i) |
| 268 | aff = isl_aff_set_coefficient_si(aff, |
| 269 | type: isl_dim_div, pos: i, v: 0); |
| 270 | aff = isl_aff_set_coefficient_si(aff, type: isl_dim_in, pos: data->pos, v: 0); |
| 271 | aff = isl_aff_remove_unused_divs(aff); |
| 272 | a = isl_val_neg(v: a); |
| 273 | aff = isl_aff_scale_val(aff, v: a); |
| 274 | aff = isl_aff_scale_down_val(aff, v: m); |
| 275 | r = set_stride(data, stride, offset: aff); |
| 276 | } else { |
| 277 | isl_val_free(v: stride); |
| 278 | isl_val_free(v: m); |
| 279 | isl_val_free(v); |
| 280 | } |
| 281 | |
| 282 | isl_constraint_free(c); |
| 283 | if (has_stride < 0) |
| 284 | return isl_stat_error; |
| 285 | return r; |
| 286 | error: |
| 287 | isl_constraint_free(c); |
| 288 | return isl_stat_error; |
| 289 | } |
| 290 | |
| 291 | /* Check if the constraints in "set" imply any stride on set dimension "pos" and |
| 292 | * store the results in data->stride and data->offset. |
| 293 | * |
| 294 | * In particular, compute the affine hull and then check if |
| 295 | * any of the constraints in the hull impose any stride on the dimension. |
| 296 | * If no such constraint can be found, then the offset is taken |
| 297 | * to be the zero expression and the stride is taken to be one. |
| 298 | */ |
| 299 | static void set_detect_stride(__isl_keep isl_set *set, int pos, |
| 300 | struct isl_detect_stride_data *data) |
| 301 | { |
| 302 | isl_basic_set *hull; |
| 303 | |
| 304 | hull = isl_set_affine_hull(set: isl_set_copy(set)); |
| 305 | |
| 306 | data->pos = pos; |
| 307 | data->found = 0; |
| 308 | data->stride = NULL; |
| 309 | data->offset = NULL; |
| 310 | if (isl_basic_set_foreach_constraint(bset: hull, fn: &detect_stride, user: data) < 0) |
| 311 | goto error; |
| 312 | |
| 313 | if (!data->found) { |
| 314 | data->stride = isl_val_one(ctx: isl_set_get_ctx(set)); |
| 315 | if (data->want_offset) { |
| 316 | isl_space *space; |
| 317 | isl_local_space *ls; |
| 318 | |
| 319 | space = isl_set_get_space(set); |
| 320 | ls = isl_local_space_from_space(space); |
| 321 | data->offset = isl_aff_zero_on_domain(ls); |
| 322 | } |
| 323 | } |
| 324 | isl_basic_set_free(bset: hull); |
| 325 | return; |
| 326 | error: |
| 327 | isl_basic_set_free(bset: hull); |
| 328 | data->stride = isl_val_free(v: data->stride); |
| 329 | data->offset = isl_aff_free(aff: data->offset); |
| 330 | } |
| 331 | |
| 332 | /* Check if the constraints in "set" imply any stride on set dimension "pos" and |
| 333 | * return the results in the form of an offset and a stride. |
| 334 | */ |
| 335 | __isl_give isl_stride_info *isl_set_get_stride_info(__isl_keep isl_set *set, |
| 336 | int pos) |
| 337 | { |
| 338 | struct isl_detect_stride_data data; |
| 339 | |
| 340 | data.want_offset = 1; |
| 341 | set_detect_stride(set, pos, data: &data); |
| 342 | |
| 343 | return isl_stride_info_alloc(stride: data.stride, offset: data.offset); |
| 344 | } |
| 345 | |
| 346 | /* Check if the constraints in "set" imply any stride on set dimension "pos" and |
| 347 | * return this stride. |
| 348 | */ |
| 349 | __isl_give isl_val *isl_set_get_stride(__isl_keep isl_set *set, int pos) |
| 350 | { |
| 351 | struct isl_detect_stride_data data; |
| 352 | |
| 353 | data.want_offset = 0; |
| 354 | set_detect_stride(set, pos, data: &data); |
| 355 | |
| 356 | return data.stride; |
| 357 | } |
| 358 | |
| 359 | /* Check if the constraints in "map" imply any stride on output dimension "pos", |
| 360 | * independently of any other output dimensions, and |
| 361 | * return the results in the form of an offset and a stride. |
| 362 | * |
| 363 | * Convert the input to a set with only the input dimensions and |
| 364 | * the single output dimension such that it be passed to |
| 365 | * isl_set_get_stride_info and convert the result back to |
| 366 | * an expression defined over the domain of "map". |
| 367 | */ |
| 368 | __isl_give isl_stride_info *isl_map_get_range_stride_info( |
| 369 | __isl_keep isl_map *map, int pos) |
| 370 | { |
| 371 | isl_stride_info *si; |
| 372 | isl_set *set; |
| 373 | isl_size n_in; |
| 374 | |
| 375 | n_in = isl_map_dim(map, type: isl_dim_in); |
| 376 | if (n_in < 0) |
| 377 | return NULL; |
| 378 | map = isl_map_copy(map); |
| 379 | map = isl_map_project_onto(map, type: isl_dim_out, first: pos, n: 1); |
| 380 | set = isl_map_wrap(map); |
| 381 | si = isl_set_get_stride_info(set, pos: n_in); |
| 382 | isl_set_free(set); |
| 383 | if (!si) |
| 384 | return NULL; |
| 385 | si->offset = isl_aff_domain_factor_domain(aff: si->offset); |
| 386 | if (!si->offset) |
| 387 | return isl_stride_info_free(si); |
| 388 | return si; |
| 389 | } |
| 390 | |