File: | polly/lib/External/isl/isl_map_simplify.c |
Warning: | line 58, column 11 Access to field 'n_eq' results in a dereference of a null pointer (loaded from variable 'bmap') |
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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(__isl_keep 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(__isl_keep 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 | * results 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
| ||||
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(__isl_keep 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 | /* Given a known integer division "div" that is not integral | ||||
1326 | * (with denominator 1), eliminate it from the constraints in "bmap" | ||||
1327 | * where it appears with a (positive or negative) unit coefficient. | ||||
1328 | * If "progress" is not NULL, then it gets set if the elimination | ||||
1329 | * results in any changes. | ||||
1330 | * | ||||
1331 | * That is, replace | ||||
1332 | * | ||||
1333 | * floor(e/m) + f >= 0 | ||||
1334 | * | ||||
1335 | * by | ||||
1336 | * | ||||
1337 | * e + m f >= 0 | ||||
1338 | * | ||||
1339 | * and | ||||
1340 | * | ||||
1341 | * -floor(e/m) + f >= 0 | ||||
1342 | * | ||||
1343 | * by | ||||
1344 | * | ||||
1345 | * -e + m f + m - 1 >= 0 | ||||
1346 | * | ||||
1347 | * The first conversion is valid because floor(e/m) >= -f is equivalent | ||||
1348 | * to e/m >= -f because -f is an integral expression. | ||||
1349 | * The second conversion follows from the fact that | ||||
1350 | * | ||||
1351 | * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m) | ||||
1352 | * | ||||
1353 | * | ||||
1354 | * Note that one of the div constraints may have been eliminated | ||||
1355 | * due to being redundant with respect to the constraint that is | ||||
1356 | * being modified by this function. The modified constraint may | ||||
1357 | * no longer imply this div constraint, so we add it back to make | ||||
1358 | * sure we do not lose any information. | ||||
1359 | */ | ||||
1360 | static __isl_give isl_basic_map *eliminate_unit_div( | ||||
1361 | __isl_take isl_basic_map *bmap, int div, int *progress) | ||||
1362 | { | ||||
1363 | int j; | ||||
1364 | isl_size v_div, dim; | ||||
1365 | isl_ctx *ctx; | ||||
1366 | |||||
1367 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
1368 | dim = isl_basic_map_dim(bmap, isl_dim_all); | ||||
1369 | if (v_div < 0 || dim < 0) | ||||
1370 | return isl_basic_map_free(bmap); | ||||
1371 | |||||
1372 | ctx = isl_basic_map_get_ctx(bmap); | ||||
1373 | |||||
1374 | for (j = 0; j < bmap->n_ineq; ++j) { | ||||
1375 | int s; | ||||
1376 | |||||
1377 | if (!isl_int_is_one(bmap->ineq[j][1 + v_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[j][1 + v_div + div]), 1) == 0) && | ||||
1378 | !isl_int_is_negone(bmap->ineq[j][1 + v_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[j][1 + v_div + div]), -1 ) == 0)) | ||||
1379 | continue; | ||||
1380 | |||||
1381 | if (progress) | ||||
1382 | *progress = 1; | ||||
1383 | |||||
1384 | s = isl_int_sgn(bmap->ineq[j][1 + v_div + div])isl_sioimath_sgn(*(bmap->ineq[j][1 + v_div + div])); | ||||
1385 | isl_int_set_si(bmap->ineq[j][1 + v_div + div], 0)isl_sioimath_set_si((bmap->ineq[j][1 + v_div + div]), 0); | ||||
1386 | if (s < 0) | ||||
1387 | isl_seq_combine(bmap->ineq[j], | ||||
1388 | ctx->negone, bmap->div[div] + 1, | ||||
1389 | bmap->div[div][0], bmap->ineq[j], 1 + dim); | ||||
1390 | else | ||||
1391 | isl_seq_combine(bmap->ineq[j], | ||||
1392 | ctx->one, bmap->div[div] + 1, | ||||
1393 | bmap->div[div][0], bmap->ineq[j], 1 + dim); | ||||
1394 | if (s < 0) { | ||||
1395 | isl_int_add(bmap->ineq[j][0],isl_sioimath_add((bmap->ineq[j][0]), *(bmap->ineq[j][0] ), *(bmap->div[div][0])) | ||||
1396 | bmap->ineq[j][0], bmap->div[div][0])isl_sioimath_add((bmap->ineq[j][0]), *(bmap->ineq[j][0] ), *(bmap->div[div][0])); | ||||
1397 | isl_int_sub_ui(bmap->ineq[j][0],isl_sioimath_sub_ui((bmap->ineq[j][0]), *(bmap->ineq[j] [0]), 1) | ||||
1398 | bmap->ineq[j][0], 1)isl_sioimath_sub_ui((bmap->ineq[j][0]), *(bmap->ineq[j] [0]), 1); | ||||
1399 | } | ||||
1400 | |||||
1401 | bmap = isl_basic_map_extend_constraints(bmap, 0, 1); | ||||
1402 | bmap = isl_basic_map_add_div_constraint(bmap, div, s); | ||||
1403 | if (!bmap) | ||||
1404 | return NULL((void*)0); | ||||
1405 | } | ||||
1406 | |||||
1407 | return bmap; | ||||
1408 | } | ||||
1409 | |||||
1410 | /* Eliminate selected known divs from constraints where they appear with | ||||
1411 | * a (positive or negative) unit coefficient. | ||||
1412 | * In particular, only handle those for which "select" returns isl_bool_true. | ||||
1413 | * If "progress" is not NULL, then it gets set if the elimination | ||||
1414 | * results in any changes. | ||||
1415 | * | ||||
1416 | * We skip integral divs, i.e., those with denominator 1, as we would | ||||
1417 | * risk eliminating the div from the div constraints. We do not need | ||||
1418 | * to handle those divs here anyway since the div constraints will turn | ||||
1419 | * out to form an equality and this equality can then be used to eliminate | ||||
1420 | * the div from all constraints. | ||||
1421 | */ | ||||
1422 | static __isl_give isl_basic_map *eliminate_selected_unit_divs( | ||||
1423 | __isl_take isl_basic_map *bmap, | ||||
1424 | isl_bool (*select)(__isl_keep isl_basic_map *bmap, int div), | ||||
1425 | int *progress) | ||||
1426 | { | ||||
1427 | int i; | ||||
1428 | |||||
1429 | if (!bmap
| ||||
1430 | return NULL((void*)0); | ||||
1431 | |||||
1432 | for (i = 0; i < bmap->n_div; ++i) { | ||||
1433 | isl_bool selected; | ||||
1434 | |||||
1435 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
1436 | continue; | ||||
1437 | if (isl_int_is_one(bmap->div[i][0])(isl_sioimath_cmp_si(*(bmap->div[i][0]), 1) == 0)) | ||||
1438 | continue; | ||||
1439 | selected = select(bmap, i); | ||||
1440 | if (selected < 0) | ||||
1441 | return isl_basic_map_free(bmap); | ||||
1442 | if (!selected) | ||||
1443 | continue; | ||||
1444 | bmap = eliminate_unit_div(bmap, i, progress); | ||||
1445 | if (!bmap) | ||||
1446 | return NULL((void*)0); | ||||
1447 | } | ||||
1448 | |||||
1449 | return bmap; | ||||
1450 | } | ||||
1451 | |||||
1452 | /* eliminate_selected_unit_divs callback that selects every | ||||
1453 | * integer division. | ||||
1454 | */ | ||||
1455 | static isl_bool is_any_div(__isl_keep isl_basic_map *bmap, int div) | ||||
1456 | { | ||||
1457 | return isl_bool_true; | ||||
1458 | } | ||||
1459 | |||||
1460 | /* Eliminate known divs from constraints where they appear with | ||||
1461 | * a (positive or negative) unit coefficient. | ||||
1462 | * If "progress" is not NULL, then it gets set if the elimination | ||||
1463 | * results in any changes. | ||||
1464 | */ | ||||
1465 | static __isl_give isl_basic_map *eliminate_unit_divs( | ||||
1466 | __isl_take isl_basic_map *bmap, int *progress) | ||||
1467 | { | ||||
1468 | return eliminate_selected_unit_divs(bmap, &is_any_div, progress); | ||||
1469 | } | ||||
1470 | |||||
1471 | /* eliminate_selected_unit_divs callback that selects | ||||
1472 | * integer divisions that only appear with | ||||
1473 | * a (positive or negative) unit coefficient | ||||
1474 | * (outside their div constraints). | ||||
1475 | */ | ||||
1476 | static isl_bool is_pure_unit_div(__isl_keep isl_basic_map *bmap, int div) | ||||
1477 | { | ||||
1478 | int i; | ||||
1479 | isl_size v_div, n_ineq; | ||||
1480 | |||||
1481 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
1482 | n_ineq = isl_basic_map_n_inequality(bmap); | ||||
1483 | if (v_div < 0 || n_ineq < 0) | ||||
1484 | return isl_bool_error; | ||||
1485 | |||||
1486 | for (i = 0; i < n_ineq; ++i) { | ||||
1487 | isl_bool skip; | ||||
1488 | |||||
1489 | if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div])) == 0)) | ||||
1490 | continue; | ||||
1491 | skip = isl_basic_map_is_div_constraint(bmap, | ||||
1492 | bmap->ineq[i], div); | ||||
1493 | if (skip < 0) | ||||
1494 | return isl_bool_error; | ||||
1495 | if (skip) | ||||
1496 | continue; | ||||
1497 | if (!isl_int_is_one(bmap->ineq[i][1 + v_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[i][1 + v_div + div]), 1) == 0) && | ||||
1498 | !isl_int_is_negone(bmap->ineq[i][1 + v_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[i][1 + v_div + div]), -1 ) == 0)) | ||||
1499 | return isl_bool_false; | ||||
1500 | } | ||||
1501 | |||||
1502 | return isl_bool_true; | ||||
1503 | } | ||||
1504 | |||||
1505 | /* Eliminate known divs from constraints where they appear with | ||||
1506 | * a (positive or negative) unit coefficient, | ||||
1507 | * but only if they do not appear in any other constraints | ||||
1508 | * (other than the div constraints). | ||||
1509 | */ | ||||
1510 | __isl_give isl_basic_map *isl_basic_map_eliminate_pure_unit_divs( | ||||
1511 | __isl_take isl_basic_map *bmap) | ||||
1512 | { | ||||
1513 | return eliminate_selected_unit_divs(bmap, &is_pure_unit_div, NULL((void*)0)); | ||||
1514 | } | ||||
1515 | |||||
1516 | __isl_give isl_basic_map *isl_basic_map_simplify(__isl_take isl_basic_map *bmap) | ||||
1517 | { | ||||
1518 | int progress = 1; | ||||
1519 | if (!bmap) | ||||
1520 | return NULL((void*)0); | ||||
1521 | while (progress) { | ||||
1522 | isl_bool empty; | ||||
1523 | |||||
1524 | progress = 0; | ||||
1525 | empty = isl_basic_map_plain_is_empty(bmap); | ||||
1526 | if (empty < 0) | ||||
1527 | return isl_basic_map_free(bmap); | ||||
1528 | if (empty) | ||||
1529 | break; | ||||
1530 | bmap = isl_basic_map_normalize_constraints(bmap); | ||||
1531 | bmap = reduce_div_coefficients(bmap); | ||||
1532 | bmap = normalize_div_expressions(bmap); | ||||
1533 | bmap = remove_duplicate_divs(bmap, &progress); | ||||
1534 | bmap = eliminate_unit_divs(bmap, &progress); | ||||
1535 | bmap = eliminate_divs_eq(bmap, &progress); | ||||
1536 | bmap = eliminate_divs_ineq(bmap, &progress); | ||||
1537 | bmap = isl_basic_map_gauss(bmap, &progress); | ||||
1538 | /* requires equalities in normal form */ | ||||
1539 | bmap = normalize_divs(bmap, &progress); | ||||
1540 | bmap = isl_basic_map_remove_duplicate_constraints(bmap, | ||||
1541 | &progress, 1); | ||||
1542 | if (bmap && progress) | ||||
1543 | ISL_F_CLR(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(((bmap)->flags) &= ~((1 << 8))); | ||||
1544 | } | ||||
1545 | return bmap; | ||||
1546 | } | ||||
1547 | |||||
1548 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_simplify( | ||||
1549 | __isl_take isl_basic_setisl_basic_map *bset) | ||||
1550 | { | ||||
1551 | return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset))); | ||||
1552 | } | ||||
1553 | |||||
1554 | |||||
1555 | isl_bool isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap, | ||||
1556 | isl_int *constraint, unsigned div) | ||||
1557 | { | ||||
1558 | unsigned pos; | ||||
1559 | |||||
1560 | if (!bmap) | ||||
1561 | return isl_bool_error; | ||||
1562 | |||||
1563 | pos = isl_basic_map_offset(bmap, isl_dim_div) + div; | ||||
1564 | |||||
1565 | if (isl_int_eq(constraint[pos], bmap->div[div][0])(isl_sioimath_cmp(*(constraint[pos]), *(bmap->div[div][0]) ) == 0)) { | ||||
1566 | int neg; | ||||
1567 | isl_int_sub(bmap->div[div][1],isl_sioimath_sub((bmap->div[div][1]), *(bmap->div[div][ 1]), *(bmap->div[div][0])) | ||||
1568 | bmap->div[div][1], bmap->div[div][0])isl_sioimath_sub((bmap->div[div][1]), *(bmap->div[div][ 1]), *(bmap->div[div][0])); | ||||
1569 | 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); | ||||
1570 | neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos); | ||||
1571 | 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); | ||||
1572 | isl_int_add(bmap->div[div][1],isl_sioimath_add((bmap->div[div][1]), *(bmap->div[div][ 1]), *(bmap->div[div][0])) | ||||
1573 | bmap->div[div][1], bmap->div[div][0])isl_sioimath_add((bmap->div[div][1]), *(bmap->div[div][ 1]), *(bmap->div[div][0])); | ||||
1574 | if (!neg) | ||||
1575 | return isl_bool_false; | ||||
1576 | if (isl_seq_first_non_zero(constraint+pos+1, | ||||
1577 | bmap->n_div-div-1) != -1) | ||||
1578 | return isl_bool_false; | ||||
1579 | } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])(isl_sioimath_abs_cmp(*(constraint[pos]), *(bmap->div[div] [0])) == 0)) { | ||||
1580 | if (!isl_seq_eq(constraint, bmap->div[div]+1, pos)) | ||||
1581 | return isl_bool_false; | ||||
1582 | if (isl_seq_first_non_zero(constraint+pos+1, | ||||
1583 | bmap->n_div-div-1) != -1) | ||||
1584 | return isl_bool_false; | ||||
1585 | } else | ||||
1586 | return isl_bool_false; | ||||
1587 | |||||
1588 | return isl_bool_true; | ||||
1589 | } | ||||
1590 | |||||
1591 | /* If the only constraints a div d=floor(f/m) | ||||
1592 | * appears in are its two defining constraints | ||||
1593 | * | ||||
1594 | * f - m d >=0 | ||||
1595 | * -(f - (m - 1)) + m d >= 0 | ||||
1596 | * | ||||
1597 | * then it can safely be removed. | ||||
1598 | */ | ||||
1599 | static isl_bool div_is_redundant(__isl_keep isl_basic_map *bmap, int div) | ||||
1600 | { | ||||
1601 | int i; | ||||
1602 | isl_size v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
1603 | unsigned pos = 1 + v_div + div; | ||||
1604 | |||||
1605 | if (v_div < 0) | ||||
1606 | return isl_bool_error; | ||||
1607 | |||||
1608 | for (i = 0; i < bmap->n_eq; ++i) | ||||
1609 | if (!isl_int_is_zero(bmap->eq[i][pos])(isl_sioimath_sgn(*(bmap->eq[i][pos])) == 0)) | ||||
1610 | return isl_bool_false; | ||||
1611 | |||||
1612 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
1613 | isl_bool red; | ||||
1614 | |||||
1615 | if (isl_int_is_zero(bmap->ineq[i][pos])(isl_sioimath_sgn(*(bmap->ineq[i][pos])) == 0)) | ||||
1616 | continue; | ||||
1617 | red = isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div); | ||||
1618 | if (red < 0 || !red) | ||||
1619 | return red; | ||||
1620 | } | ||||
1621 | |||||
1622 | for (i = 0; i < bmap->n_div; ++i) { | ||||
1623 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
1624 | continue; | ||||
1625 | if (!isl_int_is_zero(bmap->div[i][1+pos])(isl_sioimath_sgn(*(bmap->div[i][1+pos])) == 0)) | ||||
1626 | return isl_bool_false; | ||||
1627 | } | ||||
1628 | |||||
1629 | return isl_bool_true; | ||||
1630 | } | ||||
1631 | |||||
1632 | /* | ||||
1633 | * Remove divs that don't occur in any of the constraints or other divs. | ||||
1634 | * These can arise when dropping constraints from a basic map or | ||||
1635 | * when the divs of a basic map have been temporarily aligned | ||||
1636 | * with the divs of another basic map. | ||||
1637 | */ | ||||
1638 | static __isl_give isl_basic_map *remove_redundant_divs( | ||||
1639 | __isl_take isl_basic_map *bmap) | ||||
1640 | { | ||||
1641 | int i; | ||||
1642 | isl_size v_div; | ||||
1643 | |||||
1644 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
1645 | if (v_div < 0) | ||||
1646 | return isl_basic_map_free(bmap); | ||||
1647 | |||||
1648 | for (i = bmap->n_div-1; i >= 0; --i) { | ||||
1649 | isl_bool redundant; | ||||
1650 | |||||
1651 | redundant = div_is_redundant(bmap, i); | ||||
1652 | if (redundant < 0) | ||||
1653 | return isl_basic_map_free(bmap); | ||||
1654 | if (!redundant) | ||||
1655 | continue; | ||||
1656 | bmap = isl_basic_map_drop_constraints_involving(bmap, | ||||
1657 | v_div + i, 1); | ||||
1658 | bmap = isl_basic_map_drop_div(bmap, i); | ||||
1659 | } | ||||
1660 | return bmap; | ||||
1661 | } | ||||
1662 | |||||
1663 | /* Mark "bmap" as final, without checking for obviously redundant | ||||
1664 | * integer divisions. This function should be used when "bmap" | ||||
1665 | * is known not to involve any such integer divisions. | ||||
1666 | */ | ||||
1667 | __isl_give isl_basic_map *isl_basic_map_mark_final( | ||||
1668 | __isl_take isl_basic_map *bmap) | ||||
1669 | { | ||||
1670 | if (!bmap) | ||||
1671 | return NULL((void*)0); | ||||
1672 | ISL_F_SET(bmap, ISL_BASIC_SET_FINAL)(((bmap)->flags) |= ((1 << 0))); | ||||
1673 | return bmap; | ||||
1674 | } | ||||
1675 | |||||
1676 | /* Mark "bmap" as final, after removing obviously redundant integer divisions. | ||||
1677 | */ | ||||
1678 | __isl_give isl_basic_map *isl_basic_map_finalize(__isl_take isl_basic_map *bmap) | ||||
1679 | { | ||||
1680 | bmap = remove_redundant_divs(bmap); | ||||
1681 | bmap = isl_basic_map_mark_final(bmap); | ||||
1682 | return bmap; | ||||
1683 | } | ||||
1684 | |||||
1685 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_finalize( | ||||
1686 | __isl_take isl_basic_setisl_basic_map *bset) | ||||
1687 | { | ||||
1688 | return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset))); | ||||
1689 | } | ||||
1690 | |||||
1691 | /* Remove definition of any div that is defined in terms of the given variable. | ||||
1692 | * The div itself is not removed. Functions such as | ||||
1693 | * eliminate_divs_ineq depend on the other divs remaining in place. | ||||
1694 | */ | ||||
1695 | static __isl_give isl_basic_map *remove_dependent_vars( | ||||
1696 | __isl_take isl_basic_map *bmap, int pos) | ||||
1697 | { | ||||
1698 | int i; | ||||
1699 | |||||
1700 | if (!bmap) | ||||
1701 | return NULL((void*)0); | ||||
1702 | |||||
1703 | for (i = 0; i < bmap->n_div; ++i) { | ||||
1704 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
1705 | continue; | ||||
1706 | if (isl_int_is_zero(bmap->div[i][1+1+pos])(isl_sioimath_sgn(*(bmap->div[i][1+1+pos])) == 0)) | ||||
1707 | continue; | ||||
1708 | bmap = isl_basic_map_mark_div_unknown(bmap, i); | ||||
1709 | if (!bmap) | ||||
1710 | return NULL((void*)0); | ||||
1711 | } | ||||
1712 | return bmap; | ||||
1713 | } | ||||
1714 | |||||
1715 | /* Eliminate the specified variables from the constraints using | ||||
1716 | * Fourier-Motzkin. The variables themselves are not removed. | ||||
1717 | */ | ||||
1718 | __isl_give isl_basic_map *isl_basic_map_eliminate_vars( | ||||
1719 | __isl_take isl_basic_map *bmap, unsigned pos, unsigned n) | ||||
1720 | { | ||||
1721 | int d; | ||||
1722 | int i, j, k; | ||||
1723 | isl_size total; | ||||
1724 | int need_gauss = 0; | ||||
1725 | |||||
1726 | if (n == 0) | ||||
1727 | return bmap; | ||||
1728 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
1729 | if (total < 0) | ||||
1730 | return isl_basic_map_free(bmap); | ||||
1731 | |||||
1732 | bmap = isl_basic_map_cow(bmap); | ||||
1733 | for (d = pos + n - 1; d >= 0 && d >= pos; --d) | ||||
1734 | bmap = remove_dependent_vars(bmap, d); | ||||
1735 | if (!bmap) | ||||
1736 | return NULL((void*)0); | ||||
1737 | |||||
1738 | for (d = pos + n - 1; | ||||
1739 | d >= 0 && d >= total - bmap->n_div && d >= pos; --d) | ||||
1740 | isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total); | ||||
1741 | for (d = pos + n - 1; d >= 0 && d >= pos; --d) { | ||||
1742 | int n_lower, n_upper; | ||||
1743 | if (!bmap) | ||||
1744 | return NULL((void*)0); | ||||
1745 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
1746 | if (isl_int_is_zero(bmap->eq[i][1+d])(isl_sioimath_sgn(*(bmap->eq[i][1+d])) == 0)) | ||||
1747 | continue; | ||||
1748 | bmap = eliminate_var_using_equality(bmap, d, | ||||
1749 | bmap->eq[i], 0, NULL((void*)0)); | ||||
1750 | if (isl_basic_map_drop_equality(bmap, i) < 0) | ||||
1751 | return isl_basic_map_free(bmap); | ||||
1752 | need_gauss = 1; | ||||
1753 | break; | ||||
1754 | } | ||||
1755 | if (i < bmap->n_eq) | ||||
1756 | continue; | ||||
1757 | n_lower = 0; | ||||
1758 | n_upper = 0; | ||||
1759 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
1760 | if (isl_int_is_pos(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) > 0)) | ||||
1761 | n_lower++; | ||||
1762 | else if (isl_int_is_neg(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) < 0)) | ||||
1763 | n_upper++; | ||||
1764 | } | ||||
1765 | bmap = isl_basic_map_extend_constraints(bmap, | ||||
1766 | 0, n_lower * n_upper); | ||||
1767 | if (!bmap) | ||||
1768 | goto error; | ||||
1769 | for (i = bmap->n_ineq - 1; i >= 0; --i) { | ||||
1770 | int last; | ||||
1771 | if (isl_int_is_zero(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) == 0)) | ||||
1772 | continue; | ||||
1773 | last = -1; | ||||
1774 | for (j = 0; j < i; ++j) { | ||||
1775 | if (isl_int_is_zero(bmap->ineq[j][1+d])(isl_sioimath_sgn(*(bmap->ineq[j][1+d])) == 0)) | ||||
1776 | continue; | ||||
1777 | last = j; | ||||
1778 | if (isl_int_sgn(bmap->ineq[i][1+d])isl_sioimath_sgn(*(bmap->ineq[i][1+d])) == | ||||
1779 | isl_int_sgn(bmap->ineq[j][1+d])isl_sioimath_sgn(*(bmap->ineq[j][1+d]))) | ||||
1780 | continue; | ||||
1781 | k = isl_basic_map_alloc_inequality(bmap); | ||||
1782 | if (k < 0) | ||||
1783 | goto error; | ||||
1784 | isl_seq_cpy(bmap->ineq[k], bmap->ineq[i], | ||||
1785 | 1+total); | ||||
1786 | isl_seq_elim(bmap->ineq[k], bmap->ineq[j], | ||||
1787 | 1+d, 1+total, NULL((void*)0)); | ||||
1788 | } | ||||
1789 | isl_basic_map_drop_inequality(bmap, i); | ||||
1790 | i = last + 1; | ||||
1791 | } | ||||
1792 | if (n_lower > 0 && n_upper > 0) { | ||||
1793 | bmap = isl_basic_map_normalize_constraints(bmap); | ||||
1794 | bmap = isl_basic_map_remove_duplicate_constraints(bmap, | ||||
1795 | NULL((void*)0), 0); | ||||
1796 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
1797 | bmap = isl_basic_map_remove_redundancies(bmap); | ||||
1798 | need_gauss = 0; | ||||
1799 | if (!bmap) | ||||
1800 | goto error; | ||||
1801 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1))))) | ||||
1802 | break; | ||||
1803 | } | ||||
1804 | } | ||||
1805 | if (need_gauss) | ||||
1806 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
1807 | return bmap; | ||||
1808 | error: | ||||
1809 | isl_basic_map_free(bmap); | ||||
1810 | return NULL((void*)0); | ||||
1811 | } | ||||
1812 | |||||
1813 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_eliminate_vars( | ||||
1814 | __isl_take isl_basic_setisl_basic_map *bset, unsigned pos, unsigned n) | ||||
1815 | { | ||||
1816 | return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset), | ||||
1817 | pos, n)); | ||||
1818 | } | ||||
1819 | |||||
1820 | /* Eliminate the specified n dimensions starting at first from the | ||||
1821 | * constraints, without removing the dimensions from the space. | ||||
1822 | * If the set is rational, the dimensions are eliminated using Fourier-Motzkin. | ||||
1823 | * Otherwise, they are projected out and the original space is restored. | ||||
1824 | */ | ||||
1825 | __isl_give isl_basic_map *isl_basic_map_eliminate( | ||||
1826 | __isl_take isl_basic_map *bmap, | ||||
1827 | enum isl_dim_type type, unsigned first, unsigned n) | ||||
1828 | { | ||||
1829 | isl_space *space; | ||||
1830 | |||||
1831 | if (!bmap) | ||||
1832 | return NULL((void*)0); | ||||
1833 | if (n == 0) | ||||
1834 | return bmap; | ||||
1835 | |||||
1836 | if (isl_basic_map_check_range(bmap, type, first, n) < 0) | ||||
1837 | return isl_basic_map_free(bmap); | ||||
1838 | |||||
1839 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4))))) { | ||||
1840 | first += isl_basic_map_offset(bmap, type) - 1; | ||||
1841 | bmap = isl_basic_map_eliminate_vars(bmap, first, n); | ||||
1842 | return isl_basic_map_finalize(bmap); | ||||
1843 | } | ||||
1844 | |||||
1845 | space = isl_basic_map_get_space(bmap); | ||||
1846 | bmap = isl_basic_map_project_out(bmap, type, first, n); | ||||
1847 | bmap = isl_basic_map_insert_dims(bmap, type, first, n); | ||||
1848 | bmap = isl_basic_map_reset_space(bmap, space); | ||||
1849 | return bmap; | ||||
1850 | } | ||||
1851 | |||||
1852 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_eliminate( | ||||
1853 | __isl_take isl_basic_setisl_basic_map *bset, | ||||
1854 | enum isl_dim_type type, unsigned first, unsigned n) | ||||
1855 | { | ||||
1856 | return isl_basic_map_eliminate(bset, type, first, n); | ||||
1857 | } | ||||
1858 | |||||
1859 | /* Remove all constraints from "bmap" that reference any unknown local | ||||
1860 | * variables (directly or indirectly). | ||||
1861 | * | ||||
1862 | * Dropping all constraints on a local variable will make it redundant, | ||||
1863 | * so it will get removed implicitly by | ||||
1864 | * isl_basic_map_drop_constraints_involving_dims. Some other local | ||||
1865 | * variables may also end up becoming redundant if they only appear | ||||
1866 | * in constraints together with the unknown local variable. | ||||
1867 | * Therefore, start over after calling | ||||
1868 | * isl_basic_map_drop_constraints_involving_dims. | ||||
1869 | */ | ||||
1870 | __isl_give isl_basic_map *isl_basic_map_drop_constraints_involving_unknown_divs( | ||||
1871 | __isl_take isl_basic_map *bmap) | ||||
1872 | { | ||||
1873 | isl_bool known; | ||||
1874 | isl_size n_div; | ||||
1875 | int i, o_div; | ||||
1876 | |||||
1877 | known = isl_basic_map_divs_known(bmap); | ||||
1878 | if (known < 0) | ||||
1879 | return isl_basic_map_free(bmap); | ||||
1880 | if (known) | ||||
1881 | return bmap; | ||||
1882 | |||||
1883 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
1884 | if (n_div < 0) | ||||
1885 | return isl_basic_map_free(bmap); | ||||
1886 | o_div = isl_basic_map_offset(bmap, isl_dim_div) - 1; | ||||
1887 | |||||
1888 | for (i = 0; i < n_div; ++i) { | ||||
1889 | known = isl_basic_map_div_is_known(bmap, i); | ||||
1890 | if (known < 0) | ||||
1891 | return isl_basic_map_free(bmap); | ||||
1892 | if (known) | ||||
1893 | continue; | ||||
1894 | bmap = remove_dependent_vars(bmap, o_div + i); | ||||
1895 | bmap = isl_basic_map_drop_constraints_involving_dims(bmap, | ||||
1896 | isl_dim_div, i, 1); | ||||
1897 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
1898 | if (n_div < 0) | ||||
1899 | return isl_basic_map_free(bmap); | ||||
1900 | i = -1; | ||||
1901 | } | ||||
1902 | |||||
1903 | return bmap; | ||||
1904 | } | ||||
1905 | |||||
1906 | /* Remove all constraints from "bset" that reference any unknown local | ||||
1907 | * variables (directly or indirectly). | ||||
1908 | */ | ||||
1909 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_drop_constraints_involving_unknown_divs( | ||||
1910 | __isl_take isl_basic_setisl_basic_map *bset) | ||||
1911 | { | ||||
1912 | isl_basic_map *bmap; | ||||
1913 | |||||
1914 | bmap = bset_to_bmap(bset); | ||||
1915 | bmap = isl_basic_map_drop_constraints_involving_unknown_divs(bmap); | ||||
1916 | return bset_from_bmap(bmap); | ||||
1917 | } | ||||
1918 | |||||
1919 | /* Remove all constraints from "map" that reference any unknown local | ||||
1920 | * variables (directly or indirectly). | ||||
1921 | * | ||||
1922 | * Since constraints may get dropped from the basic maps, | ||||
1923 | * they may no longer be disjoint from each other. | ||||
1924 | */ | ||||
1925 | __isl_give isl_map *isl_map_drop_constraints_involving_unknown_divs( | ||||
1926 | __isl_take isl_map *map) | ||||
1927 | { | ||||
1928 | int i; | ||||
1929 | isl_bool known; | ||||
1930 | |||||
1931 | known = isl_map_divs_known(map); | ||||
1932 | if (known < 0) | ||||
1933 | return isl_map_free(map); | ||||
1934 | if (known) | ||||
1935 | return map; | ||||
1936 | |||||
1937 | map = isl_map_cow(map); | ||||
1938 | if (!map) | ||||
1939 | return NULL((void*)0); | ||||
1940 | |||||
1941 | for (i = 0; i < map->n; ++i) { | ||||
1942 | map->p[i] = | ||||
1943 | isl_basic_map_drop_constraints_involving_unknown_divs( | ||||
1944 | map->p[i]); | ||||
1945 | if (!map->p[i]) | ||||
1946 | return isl_map_free(map); | ||||
1947 | } | ||||
1948 | |||||
1949 | if (map->n > 1) | ||||
1950 | ISL_F_CLR(map, ISL_MAP_DISJOINT)(((map)->flags) &= ~((1 << 0))); | ||||
1951 | |||||
1952 | return map; | ||||
1953 | } | ||||
1954 | |||||
1955 | /* Don't assume equalities are in order, because align_divs | ||||
1956 | * may have changed the order of the divs. | ||||
1957 | */ | ||||
1958 | static void compute_elimination_index(__isl_keep isl_basic_map *bmap, int *elim, | ||||
1959 | unsigned len) | ||||
1960 | { | ||||
1961 | int d, i; | ||||
1962 | |||||
1963 | for (d = 0; d < len; ++d) | ||||
1964 | elim[d] = -1; | ||||
1965 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
1966 | for (d = len - 1; d >= 0; --d) { | ||||
1967 | if (isl_int_is_zero(bmap->eq[i][1+d])(isl_sioimath_sgn(*(bmap->eq[i][1+d])) == 0)) | ||||
1968 | continue; | ||||
1969 | elim[d] = i; | ||||
1970 | break; | ||||
1971 | } | ||||
1972 | } | ||||
1973 | } | ||||
1974 | |||||
1975 | static void set_compute_elimination_index(__isl_keep isl_basic_setisl_basic_map *bset, | ||||
1976 | int *elim, unsigned len) | ||||
1977 | { | ||||
1978 | compute_elimination_index(bset_to_bmap(bset), elim, len); | ||||
1979 | } | ||||
1980 | |||||
1981 | static int reduced_using_equalities(isl_int *dst, isl_int *src, | ||||
1982 | __isl_keep isl_basic_map *bmap, int *elim, unsigned total) | ||||
1983 | { | ||||
1984 | int d; | ||||
1985 | int copied = 0; | ||||
1986 | |||||
1987 | for (d = total - 1; d >= 0; --d) { | ||||
1988 | if (isl_int_is_zero(src[1+d])(isl_sioimath_sgn(*(src[1+d])) == 0)) | ||||
1989 | continue; | ||||
1990 | if (elim[d] == -1) | ||||
1991 | continue; | ||||
1992 | if (!copied) { | ||||
1993 | isl_seq_cpy(dst, src, 1 + total); | ||||
1994 | copied = 1; | ||||
1995 | } | ||||
1996 | isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL((void*)0)); | ||||
1997 | } | ||||
1998 | return copied; | ||||
1999 | } | ||||
2000 | |||||
2001 | static int set_reduced_using_equalities(isl_int *dst, isl_int *src, | ||||
2002 | __isl_keep isl_basic_setisl_basic_map *bset, int *elim, unsigned total) | ||||
2003 | { | ||||
2004 | return reduced_using_equalities(dst, src, | ||||
2005 | bset_to_bmap(bset), elim, total); | ||||
2006 | } | ||||
2007 | |||||
2008 | static __isl_give isl_basic_setisl_basic_map *isl_basic_set_reduce_using_equalities( | ||||
2009 | __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context) | ||||
2010 | { | ||||
2011 | int i; | ||||
2012 | int *elim; | ||||
2013 | isl_size dim; | ||||
2014 | |||||
2015 | if (!bset || !context) | ||||
2016 | goto error; | ||||
2017 | |||||
2018 | if (context->n_eq == 0) { | ||||
2019 | isl_basic_set_free(context); | ||||
2020 | return bset; | ||||
2021 | } | ||||
2022 | |||||
2023 | bset = isl_basic_set_cow(bset); | ||||
2024 | dim = isl_basic_set_dim(bset, isl_dim_set); | ||||
2025 | if (dim < 0) | ||||
2026 | goto error; | ||||
2027 | |||||
2028 | elim = isl_alloc_array(bset->ctx, int, dim)((int *)isl_malloc_or_die(bset->ctx, (dim)*sizeof(int))); | ||||
2029 | if (!elim) | ||||
2030 | goto error; | ||||
2031 | set_compute_elimination_index(context, elim, dim); | ||||
2032 | for (i = 0; i < bset->n_eq; ++i) | ||||
2033 | set_reduced_using_equalities(bset->eq[i], bset->eq[i], | ||||
2034 | context, elim, dim); | ||||
2035 | for (i = 0; i < bset->n_ineq; ++i) | ||||
2036 | set_reduced_using_equalities(bset->ineq[i], bset->ineq[i], | ||||
2037 | context, elim, dim); | ||||
2038 | isl_basic_set_free(context); | ||||
2039 | free(elim); | ||||
2040 | bset = isl_basic_set_simplify(bset); | ||||
2041 | bset = isl_basic_set_finalize(bset); | ||||
2042 | return bset; | ||||
2043 | error: | ||||
2044 | isl_basic_set_free(bset); | ||||
2045 | isl_basic_set_free(context); | ||||
2046 | return NULL((void*)0); | ||||
2047 | } | ||||
2048 | |||||
2049 | /* For each inequality in "ineq" that is a shifted (more relaxed) | ||||
2050 | * copy of an inequality in "context", mark the corresponding entry | ||||
2051 | * in "row" with -1. | ||||
2052 | * If an inequality only has a non-negative constant term, then | ||||
2053 | * mark it as well. | ||||
2054 | */ | ||||
2055 | static isl_stat mark_shifted_constraints(__isl_keep isl_mat *ineq, | ||||
2056 | __isl_keep isl_basic_setisl_basic_map *context, int *row) | ||||
2057 | { | ||||
2058 | struct isl_constraint_index ci; | ||||
2059 | isl_size n_ineq, cols; | ||||
2060 | unsigned total; | ||||
2061 | int k; | ||||
2062 | |||||
2063 | if (!ineq || !context) | ||||
2064 | return isl_stat_error; | ||||
2065 | if (context->n_ineq == 0) | ||||
2066 | return isl_stat_ok; | ||||
2067 | if (setup_constraint_index(&ci, context) < 0) | ||||
2068 | return isl_stat_error; | ||||
2069 | |||||
2070 | n_ineq = isl_mat_rows(ineq); | ||||
2071 | cols = isl_mat_cols(ineq); | ||||
2072 | if (n_ineq < 0 || cols < 0) | ||||
2073 | return isl_stat_error; | ||||
2074 | total = cols - 1; | ||||
2075 | for (k = 0; k < n_ineq; ++k) { | ||||
2076 | int l; | ||||
2077 | isl_bool redundant; | ||||
2078 | |||||
2079 | l = isl_seq_first_non_zero(ineq->row[k] + 1, total); | ||||
2080 | if (l < 0 && isl_int_is_nonneg(ineq->row[k][0])(isl_sioimath_sgn(*(ineq->row[k][0])) >= 0)) { | ||||
2081 | row[k] = -1; | ||||
2082 | continue; | ||||
2083 | } | ||||
2084 | redundant = constraint_index_is_redundant(&ci, ineq->row[k]); | ||||
2085 | if (redundant < 0) | ||||
2086 | goto error; | ||||
2087 | if (!redundant) | ||||
2088 | continue; | ||||
2089 | row[k] = -1; | ||||
2090 | } | ||||
2091 | constraint_index_free(&ci); | ||||
2092 | return isl_stat_ok; | ||||
2093 | error: | ||||
2094 | constraint_index_free(&ci); | ||||
2095 | return isl_stat_error; | ||||
2096 | } | ||||
2097 | |||||
2098 | static __isl_give isl_basic_setisl_basic_map *remove_shifted_constraints( | ||||
2099 | __isl_take isl_basic_setisl_basic_map *bset, __isl_keep isl_basic_setisl_basic_map *context) | ||||
2100 | { | ||||
2101 | struct isl_constraint_index ci; | ||||
2102 | int k; | ||||
2103 | |||||
2104 | if (!bset || !context) | ||||
2105 | return bset; | ||||
2106 | |||||
2107 | if (context->n_ineq == 0) | ||||
2108 | return bset; | ||||
2109 | if (setup_constraint_index(&ci, context) < 0) | ||||
2110 | return bset; | ||||
2111 | |||||
2112 | for (k = 0; k < bset->n_ineq; ++k) { | ||||
2113 | isl_bool redundant; | ||||
2114 | |||||
2115 | redundant = constraint_index_is_redundant(&ci, bset->ineq[k]); | ||||
2116 | if (redundant < 0) | ||||
2117 | goto error; | ||||
2118 | if (!redundant) | ||||
2119 | continue; | ||||
2120 | bset = isl_basic_set_cow(bset); | ||||
2121 | if (!bset) | ||||
2122 | goto error; | ||||
2123 | isl_basic_set_drop_inequality(bset, k); | ||||
2124 | --k; | ||||
2125 | } | ||||
2126 | constraint_index_free(&ci); | ||||
2127 | return bset; | ||||
2128 | error: | ||||
2129 | constraint_index_free(&ci); | ||||
2130 | return bset; | ||||
2131 | } | ||||
2132 | |||||
2133 | /* Remove constraints from "bmap" that are identical to constraints | ||||
2134 | * in "context" or that are more relaxed (greater constant term). | ||||
2135 | * | ||||
2136 | * We perform the test for shifted copies on the pure constraints | ||||
2137 | * in remove_shifted_constraints. | ||||
2138 | */ | ||||
2139 | static __isl_give isl_basic_map *isl_basic_map_remove_shifted_constraints( | ||||
2140 | __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context) | ||||
2141 | { | ||||
2142 | isl_basic_setisl_basic_map *bset, *bset_context; | ||||
2143 | |||||
2144 | if (!bmap || !context) | ||||
2145 | goto error; | ||||
2146 | |||||
2147 | if (bmap->n_ineq == 0 || context->n_ineq == 0) { | ||||
2148 | isl_basic_map_free(context); | ||||
2149 | return bmap; | ||||
2150 | } | ||||
2151 | |||||
2152 | bmap = isl_basic_map_order_divs(bmap); | ||||
2153 | context = isl_basic_map_align_divs(context, bmap); | ||||
2154 | bmap = isl_basic_map_align_divs(bmap, context); | ||||
2155 | |||||
2156 | bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap)); | ||||
2157 | bset_context = isl_basic_map_underlying_set(context); | ||||
2158 | bset = remove_shifted_constraints(bset, bset_context); | ||||
2159 | isl_basic_set_free(bset_context); | ||||
2160 | |||||
2161 | bmap = isl_basic_map_overlying_set(bset, bmap); | ||||
2162 | |||||
2163 | return bmap; | ||||
2164 | error: | ||||
2165 | isl_basic_map_free(bmap); | ||||
2166 | isl_basic_map_free(context); | ||||
2167 | return NULL((void*)0); | ||||
2168 | } | ||||
2169 | |||||
2170 | /* Does the (linear part of a) constraint "c" involve any of the "len" | ||||
2171 | * "relevant" dimensions? | ||||
2172 | */ | ||||
2173 | static int is_related(isl_int *c, int len, int *relevant) | ||||
2174 | { | ||||
2175 | int i; | ||||
2176 | |||||
2177 | for (i = 0; i < len; ++i) { | ||||
2178 | if (!relevant[i]) | ||||
2179 | continue; | ||||
2180 | if (!isl_int_is_zero(c[i])(isl_sioimath_sgn(*(c[i])) == 0)) | ||||
2181 | return 1; | ||||
2182 | } | ||||
2183 | |||||
2184 | return 0; | ||||
2185 | } | ||||
2186 | |||||
2187 | /* Drop constraints from "bmap" that do not involve any of | ||||
2188 | * the dimensions marked "relevant". | ||||
2189 | */ | ||||
2190 | static __isl_give isl_basic_map *drop_unrelated_constraints( | ||||
2191 | __isl_take isl_basic_map *bmap, int *relevant) | ||||
2192 | { | ||||
2193 | int i; | ||||
2194 | isl_size dim; | ||||
2195 | |||||
2196 | dim = isl_basic_map_dim(bmap, isl_dim_all); | ||||
2197 | if (dim < 0) | ||||
2198 | return isl_basic_map_free(bmap); | ||||
2199 | for (i = 0; i < dim; ++i) | ||||
2200 | if (!relevant[i]) | ||||
2201 | break; | ||||
2202 | if (i >= dim) | ||||
2203 | return bmap; | ||||
2204 | |||||
2205 | for (i = bmap->n_eq - 1; i >= 0; --i) | ||||
2206 | if (!is_related(bmap->eq[i] + 1, dim, relevant)) { | ||||
2207 | bmap = isl_basic_map_cow(bmap); | ||||
2208 | if (isl_basic_map_drop_equality(bmap, i) < 0) | ||||
2209 | return isl_basic_map_free(bmap); | ||||
2210 | } | ||||
2211 | |||||
2212 | for (i = bmap->n_ineq - 1; i >= 0; --i) | ||||
2213 | if (!is_related(bmap->ineq[i] + 1, dim, relevant)) { | ||||
2214 | bmap = isl_basic_map_cow(bmap); | ||||
2215 | if (isl_basic_map_drop_inequality(bmap, i) < 0) | ||||
2216 | return isl_basic_map_free(bmap); | ||||
2217 | } | ||||
2218 | |||||
2219 | return bmap; | ||||
2220 | } | ||||
2221 | |||||
2222 | /* Update the groups in "group" based on the (linear part of a) constraint "c". | ||||
2223 | * | ||||
2224 | * In particular, for any variable involved in the constraint, | ||||
2225 | * find the actual group id from before and replace the group | ||||
2226 | * of the corresponding variable by the minimal group of all | ||||
2227 | * the variables involved in the constraint considered so far | ||||
2228 | * (if this minimum is smaller) or replace the minimum by this group | ||||
2229 | * (if the minimum is larger). | ||||
2230 | * | ||||
2231 | * At the end, all the variables in "c" will (indirectly) point | ||||
2232 | * to the minimal of the groups that they referred to originally. | ||||
2233 | */ | ||||
2234 | static void update_groups(int dim, int *group, isl_int *c) | ||||
2235 | { | ||||
2236 | int j; | ||||
2237 | int min = dim; | ||||
2238 | |||||
2239 | for (j = 0; j < dim; ++j) { | ||||
2240 | if (isl_int_is_zero(c[j])(isl_sioimath_sgn(*(c[j])) == 0)) | ||||
2241 | continue; | ||||
2242 | while (group[j] >= 0 && group[group[j]] != group[j]) | ||||
2243 | group[j] = group[group[j]]; | ||||
2244 | if (group[j] == min) | ||||
2245 | continue; | ||||
2246 | if (group[j] < min) { | ||||
2247 | if (min >= 0 && min < dim) | ||||
2248 | group[min] = group[j]; | ||||
2249 | min = group[j]; | ||||
2250 | } else | ||||
2251 | group[group[j]] = min; | ||||
2252 | } | ||||
2253 | } | ||||
2254 | |||||
2255 | /* Allocate an array of groups of variables, one for each variable | ||||
2256 | * in "context", initialized to zero. | ||||
2257 | */ | ||||
2258 | static int *alloc_groups(__isl_keep isl_basic_setisl_basic_map *context) | ||||
2259 | { | ||||
2260 | isl_ctx *ctx; | ||||
2261 | isl_size dim; | ||||
2262 | |||||
2263 | dim = isl_basic_set_dim(context, isl_dim_set); | ||||
2264 | if (dim < 0) | ||||
2265 | return NULL((void*)0); | ||||
2266 | ctx = isl_basic_set_get_ctx(context); | ||||
2267 | return isl_calloc_array(ctx, int, dim)((int *)isl_calloc_or_die(ctx, dim, sizeof(int))); | ||||
2268 | } | ||||
2269 | |||||
2270 | /* Drop constraints from "bmap" that only involve variables that are | ||||
2271 | * not related to any of the variables marked with a "-1" in "group". | ||||
2272 | * | ||||
2273 | * We construct groups of variables that collect variables that | ||||
2274 | * (indirectly) appear in some common constraint of "bmap". | ||||
2275 | * Each group is identified by the first variable in the group, | ||||
2276 | * except for the special group of variables that was already identified | ||||
2277 | * in the input as -1 (or are related to those variables). | ||||
2278 | * If group[i] is equal to i (or -1), then the group of i is i (or -1), | ||||
2279 | * otherwise the group of i is the group of group[i]. | ||||
2280 | * | ||||
2281 | * We first initialize groups for the remaining variables. | ||||
2282 | * Then we iterate over the constraints of "bmap" and update the | ||||
2283 | * group of the variables in the constraint by the smallest group. | ||||
2284 | * Finally, we resolve indirect references to groups by running over | ||||
2285 | * the variables. | ||||
2286 | * | ||||
2287 | * After computing the groups, we drop constraints that do not involve | ||||
2288 | * any variables in the -1 group. | ||||
2289 | */ | ||||
2290 | __isl_give isl_basic_map *isl_basic_map_drop_unrelated_constraints( | ||||
2291 | __isl_take isl_basic_map *bmap, __isl_take int *group) | ||||
2292 | { | ||||
2293 | isl_size dim; | ||||
2294 | int i; | ||||
2295 | int last; | ||||
2296 | |||||
2297 | dim = isl_basic_map_dim(bmap, isl_dim_all); | ||||
2298 | if (dim < 0) | ||||
2299 | return isl_basic_map_free(bmap); | ||||
2300 | |||||
2301 | last = -1; | ||||
2302 | for (i = 0; i < dim; ++i) | ||||
2303 | if (group[i] >= 0) | ||||
2304 | last = group[i] = i; | ||||
2305 | if (last < 0) { | ||||
2306 | free(group); | ||||
2307 | return bmap; | ||||
2308 | } | ||||
2309 | |||||
2310 | for (i = 0; i < bmap->n_eq; ++i) | ||||
2311 | update_groups(dim, group, bmap->eq[i] + 1); | ||||
2312 | for (i = 0; i < bmap->n_ineq; ++i) | ||||
2313 | update_groups(dim, group, bmap->ineq[i] + 1); | ||||
2314 | |||||
2315 | for (i = 0; i < dim; ++i) | ||||
2316 | if (group[i] >= 0) | ||||
2317 | group[i] = group[group[i]]; | ||||
2318 | |||||
2319 | for (i = 0; i < dim; ++i) | ||||
2320 | group[i] = group[i] == -1; | ||||
2321 | |||||
2322 | bmap = drop_unrelated_constraints(bmap, group); | ||||
2323 | |||||
2324 | free(group); | ||||
2325 | return bmap; | ||||
2326 | } | ||||
2327 | |||||
2328 | /* Drop constraints from "context" that are irrelevant for computing | ||||
2329 | * the gist of "bset". | ||||
2330 | * | ||||
2331 | * In particular, drop constraints in variables that are not related | ||||
2332 | * to any of the variables involved in the constraints of "bset" | ||||
2333 | * in the sense that there is no sequence of constraints that connects them. | ||||
2334 | * | ||||
2335 | * We first mark all variables that appear in "bset" as belonging | ||||
2336 | * to a "-1" group and then continue with group_and_drop_irrelevant_constraints. | ||||
2337 | */ | ||||
2338 | static __isl_give isl_basic_setisl_basic_map *drop_irrelevant_constraints( | ||||
2339 | __isl_take isl_basic_setisl_basic_map *context, __isl_keep isl_basic_setisl_basic_map *bset) | ||||
2340 | { | ||||
2341 | int *group; | ||||
2342 | isl_size dim; | ||||
2343 | int i, j; | ||||
2344 | |||||
2345 | dim = isl_basic_set_dim(bset, isl_dim_set); | ||||
2346 | if (!context || dim < 0) | ||||
2347 | return isl_basic_set_free(context); | ||||
2348 | |||||
2349 | group = alloc_groups(context); | ||||
2350 | |||||
2351 | if (!group) | ||||
2352 | return isl_basic_set_free(context); | ||||
2353 | |||||
2354 | for (i = 0; i < dim; ++i) { | ||||
2355 | for (j = 0; j < bset->n_eq; ++j) | ||||
2356 | if (!isl_int_is_zero(bset->eq[j][1 + i])(isl_sioimath_sgn(*(bset->eq[j][1 + i])) == 0)) | ||||
2357 | break; | ||||
2358 | if (j < bset->n_eq) { | ||||
2359 | group[i] = -1; | ||||
2360 | continue; | ||||
2361 | } | ||||
2362 | for (j = 0; j < bset->n_ineq; ++j) | ||||
2363 | if (!isl_int_is_zero(bset->ineq[j][1 + i])(isl_sioimath_sgn(*(bset->ineq[j][1 + i])) == 0)) | ||||
2364 | break; | ||||
2365 | if (j < bset->n_ineq) | ||||
2366 | group[i] = -1; | ||||
2367 | } | ||||
2368 | |||||
2369 | return isl_basic_map_drop_unrelated_constraints(context, group); | ||||
2370 | } | ||||
2371 | |||||
2372 | /* Drop constraints from "context" that are irrelevant for computing | ||||
2373 | * the gist of the inequalities "ineq". | ||||
2374 | * Inequalities in "ineq" for which the corresponding element of row | ||||
2375 | * is set to -1 have already been marked for removal and should be ignored. | ||||
2376 | * | ||||
2377 | * In particular, drop constraints in variables that are not related | ||||
2378 | * to any of the variables involved in "ineq" | ||||
2379 | * in the sense that there is no sequence of constraints that connects them. | ||||
2380 | * | ||||
2381 | * We first mark all variables that appear in "bset" as belonging | ||||
2382 | * to a "-1" group and then continue with group_and_drop_irrelevant_constraints. | ||||
2383 | */ | ||||
2384 | static __isl_give isl_basic_setisl_basic_map *drop_irrelevant_constraints_marked( | ||||
2385 | __isl_take isl_basic_setisl_basic_map *context, __isl_keep isl_mat *ineq, int *row) | ||||
2386 | { | ||||
2387 | int *group; | ||||
2388 | isl_size dim; | ||||
2389 | int i, j; | ||||
2390 | isl_size n; | ||||
2391 | |||||
2392 | dim = isl_basic_set_dim(context, isl_dim_set); | ||||
2393 | n = isl_mat_rows(ineq); | ||||
2394 | if (dim < 0 || n < 0) | ||||
2395 | return isl_basic_set_free(context); | ||||
2396 | |||||
2397 | group = alloc_groups(context); | ||||
2398 | |||||
2399 | if (!group) | ||||
2400 | return isl_basic_set_free(context); | ||||
2401 | |||||
2402 | for (i = 0; i < dim; ++i) { | ||||
2403 | for (j = 0; j < n; ++j) { | ||||
2404 | if (row[j] < 0) | ||||
2405 | continue; | ||||
2406 | if (!isl_int_is_zero(ineq->row[j][1 + i])(isl_sioimath_sgn(*(ineq->row[j][1 + i])) == 0)) | ||||
2407 | break; | ||||
2408 | } | ||||
2409 | if (j < n) | ||||
2410 | group[i] = -1; | ||||
2411 | } | ||||
2412 | |||||
2413 | return isl_basic_map_drop_unrelated_constraints(context, group); | ||||
2414 | } | ||||
2415 | |||||
2416 | /* Do all "n" entries of "row" contain a negative value? | ||||
2417 | */ | ||||
2418 | static int all_neg(int *row, int n) | ||||
2419 | { | ||||
2420 | int i; | ||||
2421 | |||||
2422 | for (i = 0; i < n; ++i) | ||||
2423 | if (row[i] >= 0) | ||||
2424 | return 0; | ||||
2425 | |||||
2426 | return 1; | ||||
2427 | } | ||||
2428 | |||||
2429 | /* Update the inequalities in "bset" based on the information in "row" | ||||
2430 | * and "tab". | ||||
2431 | * | ||||
2432 | * In particular, the array "row" contains either -1, meaning that | ||||
2433 | * the corresponding inequality of "bset" is redundant, or the index | ||||
2434 | * of an inequality in "tab". | ||||
2435 | * | ||||
2436 | * If the row entry is -1, then drop the inequality. | ||||
2437 | * Otherwise, if the constraint is marked redundant in the tableau, | ||||
2438 | * then drop the inequality. Similarly, if it is marked as an equality | ||||
2439 | * in the tableau, then turn the inequality into an equality and | ||||
2440 | * perform Gaussian elimination. | ||||
2441 | */ | ||||
2442 | static __isl_give isl_basic_setisl_basic_map *update_ineq(__isl_take isl_basic_setisl_basic_map *bset, | ||||
2443 | __isl_keep int *row, struct isl_tab *tab) | ||||
2444 | { | ||||
2445 | int i; | ||||
2446 | unsigned n_ineq; | ||||
2447 | unsigned n_eq; | ||||
2448 | int found_equality = 0; | ||||
2449 | |||||
2450 | if (!bset) | ||||
2451 | return NULL((void*)0); | ||||
2452 | if (tab && tab->empty) | ||||
2453 | return isl_basic_set_set_to_empty(bset); | ||||
2454 | |||||
2455 | n_ineq = bset->n_ineq; | ||||
2456 | for (i = n_ineq - 1; i >= 0; --i) { | ||||
2457 | if (row[i] < 0) { | ||||
2458 | if (isl_basic_set_drop_inequality(bset, i) < 0) | ||||
2459 | return isl_basic_set_free(bset); | ||||
2460 | continue; | ||||
2461 | } | ||||
2462 | if (!tab) | ||||
2463 | continue; | ||||
2464 | n_eq = tab->n_eq; | ||||
2465 | if (isl_tab_is_equality(tab, n_eq + row[i])) { | ||||
2466 | isl_basic_map_inequality_to_equality(bset, i); | ||||
2467 | found_equality = 1; | ||||
2468 | } else if (isl_tab_is_redundant(tab, n_eq + row[i])) { | ||||
2469 | if (isl_basic_set_drop_inequality(bset, i) < 0) | ||||
2470 | return isl_basic_set_free(bset); | ||||
2471 | } | ||||
2472 | } | ||||
2473 | |||||
2474 | if (found_equality) | ||||
2475 | bset = isl_basic_set_gauss(bset, NULL((void*)0)); | ||||
2476 | bset = isl_basic_set_finalize(bset); | ||||
2477 | return bset; | ||||
2478 | } | ||||
2479 | |||||
2480 | /* Update the inequalities in "bset" based on the information in "row" | ||||
2481 | * and "tab" and free all arguments (other than "bset"). | ||||
2482 | */ | ||||
2483 | static __isl_give isl_basic_setisl_basic_map *update_ineq_free( | ||||
2484 | __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_mat *ineq, | ||||
2485 | __isl_take isl_basic_setisl_basic_map *context, __isl_take int *row, | ||||
2486 | struct isl_tab *tab) | ||||
2487 | { | ||||
2488 | isl_mat_free(ineq); | ||||
2489 | isl_basic_set_free(context); | ||||
2490 | |||||
2491 | bset = update_ineq(bset, row, tab); | ||||
2492 | |||||
2493 | free(row); | ||||
2494 | isl_tab_free(tab); | ||||
2495 | return bset; | ||||
2496 | } | ||||
2497 | |||||
2498 | /* Remove all information from bset that is redundant in the context | ||||
2499 | * of context. | ||||
2500 | * "ineq" contains the (possibly transformed) inequalities of "bset", | ||||
2501 | * in the same order. | ||||
2502 | * The (explicit) equalities of "bset" are assumed to have been taken | ||||
2503 | * into account by the transformation such that only the inequalities | ||||
2504 | * are relevant. | ||||
2505 | * "context" is assumed not to be empty. | ||||
2506 | * | ||||
2507 | * "row" keeps track of the constraint index of a "bset" inequality in "tab". | ||||
2508 | * A value of -1 means that the inequality is obviously redundant and may | ||||
2509 | * not even appear in "tab". | ||||
2510 | * | ||||
2511 | * We first mark the inequalities of "bset" | ||||
2512 | * that are obviously redundant with respect to some inequality in "context". | ||||
2513 | * Then we remove those constraints from "context" that have become | ||||
2514 | * irrelevant for computing the gist of "bset". | ||||
2515 | * Note that this removal of constraints cannot be replaced by | ||||
2516 | * a factorization because factors in "bset" may still be connected | ||||
2517 | * to each other through constraints in "context". | ||||
2518 | * | ||||
2519 | * If there are any inequalities left, we construct a tableau for | ||||
2520 | * the context and then add the inequalities of "bset". | ||||
2521 | * Before adding these inequalities, we freeze all constraints such that | ||||
2522 | * they won't be considered redundant in terms of the constraints of "bset". | ||||
2523 | * Then we detect all redundant constraints (among the | ||||
2524 | * constraints that weren't frozen), first by checking for redundancy in the | ||||
2525 | * the tableau and then by checking if replacing a constraint by its negation | ||||
2526 | * would lead to an empty set. This last step is fairly expensive | ||||
2527 | * and could be optimized by more reuse of the tableau. | ||||
2528 | * Finally, we update bset according to the results. | ||||
2529 | */ | ||||
2530 | static __isl_give isl_basic_setisl_basic_map *uset_gist_full(__isl_take isl_basic_setisl_basic_map *bset, | ||||
2531 | __isl_take isl_mat *ineq, __isl_take isl_basic_setisl_basic_map *context) | ||||
2532 | { | ||||
2533 | int i, r; | ||||
2534 | int *row = NULL((void*)0); | ||||
2535 | isl_ctx *ctx; | ||||
2536 | isl_basic_setisl_basic_map *combined = NULL((void*)0); | ||||
2537 | struct isl_tab *tab = NULL((void*)0); | ||||
2538 | unsigned n_eq, context_ineq; | ||||
2539 | |||||
2540 | if (!bset || !ineq || !context) | ||||
2541 | goto error; | ||||
2542 | |||||
2543 | if (bset->n_ineq == 0 || isl_basic_set_plain_is_universe(context)) { | ||||
2544 | isl_basic_set_free(context); | ||||
2545 | isl_mat_free(ineq); | ||||
2546 | return bset; | ||||
2547 | } | ||||
2548 | |||||
2549 | ctx = isl_basic_set_get_ctx(context); | ||||
2550 | row = isl_calloc_array(ctx, int, bset->n_ineq)((int *)isl_calloc_or_die(ctx, bset->n_ineq, sizeof(int))); | ||||
2551 | if (!row) | ||||
2552 | goto error; | ||||
2553 | |||||
2554 | if (mark_shifted_constraints(ineq, context, row) < 0) | ||||
2555 | goto error; | ||||
2556 | if (all_neg(row, bset->n_ineq)) | ||||
2557 | return update_ineq_free(bset, ineq, context, row, NULL((void*)0)); | ||||
2558 | |||||
2559 | context = drop_irrelevant_constraints_marked(context, ineq, row); | ||||
2560 | if (!context) | ||||
2561 | goto error; | ||||
2562 | if (isl_basic_set_plain_is_universe(context)) | ||||
2563 | return update_ineq_free(bset, ineq, context, row, NULL((void*)0)); | ||||
2564 | |||||
2565 | n_eq = context->n_eq; | ||||
2566 | context_ineq = context->n_ineq; | ||||
2567 | combined = isl_basic_set_cow(isl_basic_set_copy(context)); | ||||
2568 | combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq); | ||||
2569 | tab = isl_tab_from_basic_set(combined, 0); | ||||
2570 | for (i = 0; i < context_ineq; ++i) | ||||
2571 | if (isl_tab_freeze_constraint(tab, n_eq + i) < 0) | ||||
2572 | goto error; | ||||
2573 | if (isl_tab_extend_cons(tab, bset->n_ineq) < 0) | ||||
2574 | goto error; | ||||
2575 | r = context_ineq; | ||||
2576 | for (i = 0; i < bset->n_ineq; ++i) { | ||||
2577 | if (row[i] < 0) | ||||
2578 | continue; | ||||
2579 | combined = isl_basic_set_add_ineq(combined, ineq->row[i]); | ||||
2580 | if (isl_tab_add_ineq(tab, ineq->row[i]) < 0) | ||||
2581 | goto error; | ||||
2582 | row[i] = r++; | ||||
2583 | } | ||||
2584 | if (isl_tab_detect_implicit_equalities(tab) < 0) | ||||
2585 | goto error; | ||||
2586 | if (isl_tab_detect_redundant(tab) < 0) | ||||
2587 | goto error; | ||||
2588 | for (i = bset->n_ineq - 1; i >= 0; --i) { | ||||
2589 | isl_basic_setisl_basic_map *test; | ||||
2590 | int is_empty; | ||||
2591 | |||||
2592 | if (row[i] < 0) | ||||
2593 | continue; | ||||
2594 | r = row[i]; | ||||
2595 | if (tab->con[n_eq + r].is_redundant) | ||||
2596 | continue; | ||||
2597 | test = isl_basic_set_dup(combined); | ||||
2598 | test = isl_inequality_negate(test, r); | ||||
2599 | test = isl_basic_set_update_from_tab(test, tab); | ||||
2600 | is_empty = isl_basic_set_is_empty(test); | ||||
2601 | isl_basic_set_free(test); | ||||
2602 | if (is_empty < 0) | ||||
2603 | goto error; | ||||
2604 | if (is_empty) | ||||
2605 | tab->con[n_eq + r].is_redundant = 1; | ||||
2606 | } | ||||
2607 | bset = update_ineq_free(bset, ineq, context, row, tab); | ||||
2608 | if (bset) { | ||||
2609 | ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) |= ((1 << 2))); | ||||
2610 | ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT)(((bset)->flags) |= ((1 << 3))); | ||||
2611 | } | ||||
2612 | |||||
2613 | isl_basic_set_free(combined); | ||||
2614 | return bset; | ||||
2615 | error: | ||||
2616 | free(row); | ||||
2617 | isl_mat_free(ineq); | ||||
2618 | isl_tab_free(tab); | ||||
2619 | isl_basic_set_free(combined); | ||||
2620 | isl_basic_set_free(context); | ||||
2621 | isl_basic_set_free(bset); | ||||
2622 | return NULL((void*)0); | ||||
2623 | } | ||||
2624 | |||||
2625 | /* Extract the inequalities of "bset" as an isl_mat. | ||||
2626 | */ | ||||
2627 | static __isl_give isl_mat *extract_ineq(__isl_keep isl_basic_setisl_basic_map *bset) | ||||
2628 | { | ||||
2629 | isl_size total; | ||||
2630 | isl_ctx *ctx; | ||||
2631 | isl_mat *ineq; | ||||
2632 | |||||
2633 | total = isl_basic_set_dim(bset, isl_dim_all); | ||||
2634 | if (total < 0) | ||||
2635 | return NULL((void*)0); | ||||
2636 | |||||
2637 | ctx = isl_basic_set_get_ctx(bset); | ||||
2638 | ineq = isl_mat_sub_alloc6(ctx, bset->ineq, 0, bset->n_ineq, | ||||
2639 | 0, 1 + total); | ||||
2640 | |||||
2641 | return ineq; | ||||
2642 | } | ||||
2643 | |||||
2644 | /* Remove all information from "bset" that is redundant in the context | ||||
2645 | * of "context", for the case where both "bset" and "context" are | ||||
2646 | * full-dimensional. | ||||
2647 | */ | ||||
2648 | static __isl_give isl_basic_setisl_basic_map *uset_gist_uncompressed( | ||||
2649 | __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context) | ||||
2650 | { | ||||
2651 | isl_mat *ineq; | ||||
2652 | |||||
2653 | ineq = extract_ineq(bset); | ||||
2654 | return uset_gist_full(bset, ineq, context); | ||||
2655 | } | ||||
2656 | |||||
2657 | /* Replace "bset" by an empty basic set in the same space. | ||||
2658 | */ | ||||
2659 | static __isl_give isl_basic_setisl_basic_map *replace_by_empty( | ||||
2660 | __isl_take isl_basic_setisl_basic_map *bset) | ||||
2661 | { | ||||
2662 | isl_space *space; | ||||
2663 | |||||
2664 | space = isl_basic_set_get_space(bset); | ||||
2665 | isl_basic_set_free(bset); | ||||
2666 | return isl_basic_set_empty(space); | ||||
2667 | } | ||||
2668 | |||||
2669 | /* Remove all information from "bset" that is redundant in the context | ||||
2670 | * of "context", for the case where the combined equalities of | ||||
2671 | * "bset" and "context" allow for a compression that can be obtained | ||||
2672 | * by preapplication of "T". | ||||
2673 | * If the compression of "context" is empty, meaning that "bset" and | ||||
2674 | * "context" do not intersect, then return the empty set. | ||||
2675 | * | ||||
2676 | * "bset" itself is not transformed by "T". Instead, the inequalities | ||||
2677 | * are extracted from "bset" and those are transformed by "T". | ||||
2678 | * uset_gist_full then determines which of the transformed inequalities | ||||
2679 | * are redundant with respect to the transformed "context" and removes | ||||
2680 | * the corresponding inequalities from "bset". | ||||
2681 | * | ||||
2682 | * After preapplying "T" to the inequalities, any common factor is | ||||
2683 | * removed from the coefficients. If this results in a tightening | ||||
2684 | * of the constant term, then the same tightening is applied to | ||||
2685 | * the corresponding untransformed inequality in "bset". | ||||
2686 | * That is, if after plugging in T, a constraint f(x) >= 0 is of the form | ||||
2687 | * | ||||
2688 | * g f'(x) + r >= 0 | ||||
2689 | * | ||||
2690 | * with 0 <= r < g, then it is equivalent to | ||||
2691 | * | ||||
2692 | * f'(x) >= 0 | ||||
2693 | * | ||||
2694 | * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine | ||||
2695 | * subspace compressed by T since the latter would be transformed to | ||||
2696 | * | ||||
2697 | * g f'(x) >= 0 | ||||
2698 | */ | ||||
2699 | static __isl_give isl_basic_setisl_basic_map *uset_gist_compressed( | ||||
2700 | __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context, | ||||
2701 | __isl_take isl_mat *T) | ||||
2702 | { | ||||
2703 | isl_ctx *ctx; | ||||
2704 | isl_mat *ineq; | ||||
2705 | int i; | ||||
2706 | isl_size n_row, n_col; | ||||
2707 | isl_int rem; | ||||
2708 | |||||
2709 | ineq = extract_ineq(bset); | ||||
2710 | ineq = isl_mat_product(ineq, isl_mat_copy(T)); | ||||
2711 | context = isl_basic_set_preimage(context, T); | ||||
2712 | |||||
2713 | if (!ineq || !context) | ||||
2714 | goto error; | ||||
2715 | if (isl_basic_set_plain_is_empty(context)) { | ||||
2716 | isl_mat_free(ineq); | ||||
2717 | isl_basic_set_free(context); | ||||
2718 | return replace_by_empty(bset); | ||||
2719 | } | ||||
2720 | |||||
2721 | ctx = isl_mat_get_ctx(ineq); | ||||
2722 | n_row = isl_mat_rows(ineq); | ||||
2723 | n_col = isl_mat_cols(ineq); | ||||
2724 | if (n_row < 0 || n_col < 0) | ||||
2725 | goto error; | ||||
2726 | isl_int_init(rem)isl_sioimath_init((rem)); | ||||
2727 | for (i = 0; i < n_row; ++i) { | ||||
2728 | isl_seq_gcd(ineq->row[i] + 1, n_col - 1, &ctx->normalize_gcd); | ||||
2729 | if (isl_int_is_zero(ctx->normalize_gcd)(isl_sioimath_sgn(*(ctx->normalize_gcd)) == 0)) | ||||
2730 | continue; | ||||
2731 | if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0)) | ||||
2732 | continue; | ||||
2733 | isl_seq_scale_down(ineq->row[i] + 1, ineq->row[i] + 1, | ||||
2734 | ctx->normalize_gcd, n_col - 1); | ||||
2735 | isl_int_fdiv_r(rem, ineq->row[i][0], ctx->normalize_gcd)isl_sioimath_fdiv_r((rem), *(ineq->row[i][0]), *(ctx->normalize_gcd )); | ||||
2736 | isl_int_fdiv_q(ineq->row[i][0],isl_sioimath_fdiv_q((ineq->row[i][0]), *(ineq->row[i][0 ]), *(ctx->normalize_gcd)) | ||||
2737 | ineq->row[i][0], ctx->normalize_gcd)isl_sioimath_fdiv_q((ineq->row[i][0]), *(ineq->row[i][0 ]), *(ctx->normalize_gcd)); | ||||
2738 | if (isl_int_is_zero(rem)(isl_sioimath_sgn(*(rem)) == 0)) | ||||
2739 | continue; | ||||
2740 | bset = isl_basic_set_cow(bset); | ||||
2741 | if (!bset) | ||||
2742 | break; | ||||
2743 | isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], rem)isl_sioimath_sub((bset->ineq[i][0]), *(bset->ineq[i][0] ), *(rem)); | ||||
2744 | } | ||||
2745 | isl_int_clear(rem)isl_sioimath_clear((rem)); | ||||
2746 | |||||
2747 | return uset_gist_full(bset, ineq, context); | ||||
2748 | error: | ||||
2749 | isl_mat_free(ineq); | ||||
2750 | isl_basic_set_free(context); | ||||
2751 | isl_basic_set_free(bset); | ||||
2752 | return NULL((void*)0); | ||||
2753 | } | ||||
2754 | |||||
2755 | /* Project "bset" onto the variables that are involved in "template". | ||||
2756 | */ | ||||
2757 | static __isl_give isl_basic_setisl_basic_map *project_onto_involved( | ||||
2758 | __isl_take isl_basic_setisl_basic_map *bset, __isl_keep isl_basic_setisl_basic_map *template) | ||||
2759 | { | ||||
2760 | int i; | ||||
2761 | isl_size n; | ||||
2762 | |||||
2763 | n = isl_basic_set_dim(template, isl_dim_set); | ||||
2764 | if (n < 0 || !template) | ||||
2765 | return isl_basic_set_free(bset); | ||||
2766 | |||||
2767 | for (i = 0; i < n; ++i) { | ||||
2768 | isl_bool involved; | ||||
2769 | |||||
2770 | involved = isl_basic_set_involves_dims(template, | ||||
2771 | isl_dim_set, i, 1); | ||||
2772 | if (involved < 0) | ||||
2773 | return isl_basic_set_free(bset); | ||||
2774 | if (involved) | ||||
2775 | continue; | ||||
2776 | bset = isl_basic_set_eliminate_vars(bset, i, 1); | ||||
2777 | } | ||||
2778 | |||||
2779 | return bset; | ||||
2780 | } | ||||
2781 | |||||
2782 | /* Remove all information from bset that is redundant in the context | ||||
2783 | * of context. In particular, equalities that are linear combinations | ||||
2784 | * of those in context are removed. Then the inequalities that are | ||||
2785 | * redundant in the context of the equalities and inequalities of | ||||
2786 | * context are removed. | ||||
2787 | * | ||||
2788 | * First of all, we drop those constraints from "context" | ||||
2789 | * that are irrelevant for computing the gist of "bset". | ||||
2790 | * Alternatively, we could factorize the intersection of "context" and "bset". | ||||
2791 | * | ||||
2792 | * We first compute the intersection of the integer affine hulls | ||||
2793 | * of "bset" and "context", | ||||
2794 | * compute the gist inside this intersection and then reduce | ||||
2795 | * the constraints with respect to the equalities of the context | ||||
2796 | * that only involve variables already involved in the input. | ||||
2797 | * If the intersection of the affine hulls turns out to be empty, | ||||
2798 | * then return the empty set. | ||||
2799 | * | ||||
2800 | * If two constraints are mutually redundant, then uset_gist_full | ||||
2801 | * will remove the second of those constraints. We therefore first | ||||
2802 | * sort the constraints so that constraints not involving existentially | ||||
2803 | * quantified variables are given precedence over those that do. | ||||
2804 | * We have to perform this sorting before the variable compression, | ||||
2805 | * because that may effect the order of the variables. | ||||
2806 | */ | ||||
2807 | static __isl_give isl_basic_setisl_basic_map *uset_gist(__isl_take isl_basic_setisl_basic_map *bset, | ||||
2808 | __isl_take isl_basic_setisl_basic_map *context) | ||||
2809 | { | ||||
2810 | isl_mat *eq; | ||||
2811 | isl_mat *T; | ||||
2812 | isl_basic_setisl_basic_map *aff; | ||||
2813 | isl_basic_setisl_basic_map *aff_context; | ||||
2814 | isl_size total; | ||||
2815 | |||||
2816 | total = isl_basic_set_dim(bset, isl_dim_all); | ||||
2817 | if (total < 0 || !context) | ||||
2818 | goto error; | ||||
2819 | |||||
2820 | context = drop_irrelevant_constraints(context, bset); | ||||
2821 | |||||
2822 | bset = isl_basic_set_detect_equalities(bset); | ||||
2823 | aff = isl_basic_set_copy(bset); | ||||
2824 | aff = isl_basic_set_plain_affine_hull(aff); | ||||
2825 | context = isl_basic_set_detect_equalities(context); | ||||
2826 | aff_context = isl_basic_set_copy(context); | ||||
2827 | aff_context = isl_basic_set_plain_affine_hull(aff_context); | ||||
2828 | aff = isl_basic_set_intersect(aff, aff_context); | ||||
2829 | if (!aff) | ||||
2830 | goto error; | ||||
2831 | if (isl_basic_set_plain_is_empty(aff)) { | ||||
2832 | isl_basic_set_free(bset); | ||||
2833 | isl_basic_set_free(context); | ||||
2834 | return aff; | ||||
2835 | } | ||||
2836 | bset = isl_basic_set_sort_constraints(bset); | ||||
2837 | if (aff->n_eq == 0) { | ||||
2838 | isl_basic_set_free(aff); | ||||
2839 | return uset_gist_uncompressed(bset, context); | ||||
2840 | } | ||||
2841 | eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total); | ||||
2842 | eq = isl_mat_cow(eq); | ||||
2843 | T = isl_mat_variable_compression(eq, NULL((void*)0)); | ||||
2844 | isl_basic_set_free(aff); | ||||
2845 | if (T && T->n_col == 0) { | ||||
2846 | isl_mat_free(T); | ||||
2847 | isl_basic_set_free(context); | ||||
2848 | return replace_by_empty(bset); | ||||
2849 | } | ||||
2850 | |||||
2851 | aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context)); | ||||
2852 | aff_context = project_onto_involved(aff_context, bset); | ||||
2853 | |||||
2854 | bset = uset_gist_compressed(bset, context, T); | ||||
2855 | bset = isl_basic_set_reduce_using_equalities(bset, aff_context); | ||||
2856 | |||||
2857 | if (bset) { | ||||
2858 | ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) |= ((1 << 2))); | ||||
2859 | ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT)(((bset)->flags) |= ((1 << 3))); | ||||
2860 | } | ||||
2861 | |||||
2862 | return bset; | ||||
2863 | error: | ||||
2864 | isl_basic_set_free(bset); | ||||
2865 | isl_basic_set_free(context); | ||||
2866 | return NULL((void*)0); | ||||
2867 | } | ||||
2868 | |||||
2869 | /* Return the number of equality constraints in "bmap" that involve | ||||
2870 | * local variables. This function assumes that Gaussian elimination | ||||
2871 | * has been applied to the equality constraints. | ||||
2872 | */ | ||||
2873 | static int n_div_eq(__isl_keep isl_basic_map *bmap) | ||||
2874 | { | ||||
2875 | int i; | ||||
2876 | isl_size total, n_div; | ||||
2877 | |||||
2878 | if (!bmap) | ||||
2879 | return -1; | ||||
2880 | |||||
2881 | if (bmap->n_eq == 0) | ||||
2882 | return 0; | ||||
2883 | |||||
2884 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
2885 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
2886 | if (total < 0 || n_div < 0) | ||||
2887 | return -1; | ||||
2888 | total -= n_div; | ||||
2889 | |||||
2890 | for (i = 0; i < bmap->n_eq; ++i) | ||||
2891 | if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, | ||||
2892 | n_div) == -1) | ||||
2893 | return i; | ||||
2894 | |||||
2895 | return bmap->n_eq; | ||||
2896 | } | ||||
2897 | |||||
2898 | /* Construct a basic map in "space" defined by the equality constraints in "eq". | ||||
2899 | * The constraints are assumed not to involve any local variables. | ||||
2900 | */ | ||||
2901 | static __isl_give isl_basic_map *basic_map_from_equalities( | ||||
2902 | __isl_take isl_space *space, __isl_take isl_mat *eq) | ||||
2903 | { | ||||
2904 | int i, k; | ||||
2905 | isl_size total; | ||||
2906 | isl_basic_map *bmap = NULL((void*)0); | ||||
2907 | |||||
2908 | total = isl_space_dim(space, isl_dim_all); | ||||
2909 | if (total < 0 || !eq) | ||||
2910 | goto error; | ||||
2911 | |||||
2912 | if (1 + total != eq->n_col) | ||||
2913 | 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-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 2914); goto error; } while (0) | ||||
2914 | "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-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 2914); goto error; } while (0); | ||||
2915 | |||||
2916 | bmap = isl_basic_map_alloc_space(isl_space_copy(space), | ||||
2917 | 0, eq->n_row, 0); | ||||
2918 | for (i = 0; i < eq->n_row; ++i) { | ||||
2919 | k = isl_basic_map_alloc_equality(bmap); | ||||
2920 | if (k < 0) | ||||
2921 | goto error; | ||||
2922 | isl_seq_cpy(bmap->eq[k], eq->row[i], eq->n_col); | ||||
2923 | } | ||||
2924 | |||||
2925 | isl_space_free(space); | ||||
2926 | isl_mat_free(eq); | ||||
2927 | return bmap; | ||||
2928 | error: | ||||
2929 | isl_space_free(space); | ||||
2930 | isl_mat_free(eq); | ||||
2931 | isl_basic_map_free(bmap); | ||||
2932 | return NULL((void*)0); | ||||
2933 | } | ||||
2934 | |||||
2935 | /* Construct and return a variable compression based on the equality | ||||
2936 | * constraints in "bmap1" and "bmap2" that do not involve the local variables. | ||||
2937 | * "n1" is the number of (initial) equality constraints in "bmap1" | ||||
2938 | * that do involve local variables. | ||||
2939 | * "n2" is the number of (initial) equality constraints in "bmap2" | ||||
2940 | * that do involve local variables. | ||||
2941 | * "total" is the total number of other variables. | ||||
2942 | * This function assumes that Gaussian elimination | ||||
2943 | * has been applied to the equality constraints in both "bmap1" and "bmap2" | ||||
2944 | * such that the equality constraints not involving local variables | ||||
2945 | * are those that start at "n1" or "n2". | ||||
2946 | * | ||||
2947 | * If either of "bmap1" and "bmap2" does not have such equality constraints, | ||||
2948 | * then simply compute the compression based on the equality constraints | ||||
2949 | * in the other basic map. | ||||
2950 | * Otherwise, combine the equality constraints from both into a new | ||||
2951 | * basic map such that Gaussian elimination can be applied to this combination | ||||
2952 | * and then construct a variable compression from the resulting | ||||
2953 | * equality constraints. | ||||
2954 | */ | ||||
2955 | static __isl_give isl_mat *combined_variable_compression( | ||||
2956 | __isl_keep isl_basic_map *bmap1, int n1, | ||||
2957 | __isl_keep isl_basic_map *bmap2, int n2, int total) | ||||
2958 | { | ||||
2959 | isl_ctx *ctx; | ||||
2960 | isl_mat *E1, *E2, *V; | ||||
2961 | isl_basic_map *bmap; | ||||
2962 | |||||
2963 | ctx = isl_basic_map_get_ctx(bmap1); | ||||
2964 | if (bmap1->n_eq == n1) { | ||||
2965 | E2 = isl_mat_sub_alloc6(ctx, bmap2->eq, | ||||
2966 | n2, bmap2->n_eq - n2, 0, 1 + total); | ||||
2967 | return isl_mat_variable_compression(E2, NULL((void*)0)); | ||||
2968 | } | ||||
2969 | if (bmap2->n_eq == n2) { | ||||
2970 | E1 = isl_mat_sub_alloc6(ctx, bmap1->eq, | ||||
2971 | n1, bmap1->n_eq - n1, 0, 1 + total); | ||||
2972 | return isl_mat_variable_compression(E1, NULL((void*)0)); | ||||
2973 | } | ||||
2974 | E1 = isl_mat_sub_alloc6(ctx, bmap1->eq, | ||||
2975 | n1, bmap1->n_eq - n1, 0, 1 + total); | ||||
2976 | E2 = isl_mat_sub_alloc6(ctx, bmap2->eq, | ||||
2977 | n2, bmap2->n_eq - n2, 0, 1 + total); | ||||
2978 | E1 = isl_mat_concat(E1, E2); | ||||
2979 | bmap = basic_map_from_equalities(isl_basic_map_get_space(bmap1), E1); | ||||
2980 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
2981 | if (!bmap) | ||||
2982 | return NULL((void*)0); | ||||
2983 | E1 = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total); | ||||
2984 | V = isl_mat_variable_compression(E1, NULL((void*)0)); | ||||
2985 | isl_basic_map_free(bmap); | ||||
2986 | |||||
2987 | return V; | ||||
2988 | } | ||||
2989 | |||||
2990 | /* Extract the stride constraints from "bmap", compressed | ||||
2991 | * with respect to both the stride constraints in "context" and | ||||
2992 | * the remaining equality constraints in both "bmap" and "context". | ||||
2993 | * "bmap_n_eq" is the number of (initial) stride constraints in "bmap". | ||||
2994 | * "context_n_eq" is the number of (initial) stride constraints in "context". | ||||
2995 | * | ||||
2996 | * Let x be all variables in "bmap" (and "context") other than the local | ||||
2997 | * variables. First compute a variable compression | ||||
2998 | * | ||||
2999 | * x = V x' | ||||
3000 | * | ||||
3001 | * based on the non-stride equality constraints in "bmap" and "context". | ||||
3002 | * Consider the stride constraints of "context", | ||||
3003 | * | ||||
3004 | * A(x) + B(y) = 0 | ||||
3005 | * | ||||
3006 | * with y the local variables and plug in the variable compression, | ||||
3007 | * resulting in | ||||
3008 | * | ||||
3009 | * A(V x') + B(y) = 0 | ||||
3010 | * | ||||
3011 | * Use these constraints to compute a parameter compression on x' | ||||
3012 | * | ||||
3013 | * x' = T x'' | ||||
3014 | * | ||||
3015 | * Now consider the stride constraints of "bmap" | ||||
3016 | * | ||||
3017 | * C(x) + D(y) = 0 | ||||
3018 | * | ||||
3019 | * and plug in x = V*T x''. | ||||
3020 | * That is, return A = [C*V*T D]. | ||||
3021 | */ | ||||
3022 | static __isl_give isl_mat *extract_compressed_stride_constraints( | ||||
3023 | __isl_keep isl_basic_map *bmap, int bmap_n_eq, | ||||
3024 | __isl_keep isl_basic_map *context, int context_n_eq) | ||||
3025 | { | ||||
3026 | isl_size total, n_div; | ||||
3027 | isl_ctx *ctx; | ||||
3028 | isl_mat *A, *B, *T, *V; | ||||
3029 | |||||
3030 | total = isl_basic_map_dim(context, isl_dim_all); | ||||
3031 | n_div = isl_basic_map_dim(context, isl_dim_div); | ||||
3032 | if (total < 0 || n_div < 0) | ||||
3033 | return NULL((void*)0); | ||||
3034 | total -= n_div; | ||||
3035 | |||||
3036 | ctx = isl_basic_map_get_ctx(bmap); | ||||
3037 | |||||
3038 | V = combined_variable_compression(bmap, bmap_n_eq, | ||||
3039 | context, context_n_eq, total); | ||||
3040 | |||||
3041 | A = isl_mat_sub_alloc6(ctx, context->eq, 0, context_n_eq, 0, 1 + total); | ||||
3042 | B = isl_mat_sub_alloc6(ctx, context->eq, | ||||
3043 | 0, context_n_eq, 1 + total, n_div); | ||||
3044 | A = isl_mat_product(A, isl_mat_copy(V)); | ||||
3045 | T = isl_mat_parameter_compression_ext(A, B); | ||||
3046 | T = isl_mat_product(V, T); | ||||
3047 | |||||
3048 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
3049 | if (n_div < 0) | ||||
3050 | T = isl_mat_free(T); | ||||
3051 | else | ||||
3052 | T = isl_mat_diagonal(T, isl_mat_identity(ctx, n_div)); | ||||
3053 | |||||
3054 | A = isl_mat_sub_alloc6(ctx, bmap->eq, | ||||
3055 | 0, bmap_n_eq, 0, 1 + total + n_div); | ||||
3056 | A = isl_mat_product(A, T); | ||||
3057 | |||||
3058 | return A; | ||||
3059 | } | ||||
3060 | |||||
3061 | /* Remove the prime factors from *g that have an exponent that | ||||
3062 | * is strictly smaller than the exponent in "c". | ||||
3063 | * All exponents in *g are known to be smaller than or equal | ||||
3064 | * to those in "c". | ||||
3065 | * | ||||
3066 | * That is, if *g is equal to | ||||
3067 | * | ||||
3068 | * p_1^{e_1} p_2^{e_2} ... p_n^{e_n} | ||||
3069 | * | ||||
3070 | * and "c" is equal to | ||||
3071 | * | ||||
3072 | * p_1^{f_1} p_2^{f_2} ... p_n^{f_n} | ||||
3073 | * | ||||
3074 | * then update *g to | ||||
3075 | * | ||||
3076 | * p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ... | ||||
3077 | * p_n^{e_n * (e_n = f_n)} | ||||
3078 | * | ||||
3079 | * If e_i = f_i, then c / *g does not have any p_i factors and therefore | ||||
3080 | * neither does the gcd of *g and c / *g. | ||||
3081 | * If e_i < f_i, then the gcd of *g and c / *g has a positive | ||||
3082 | * power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors. | ||||
3083 | * Dividing *g by this gcd therefore strictly reduces the exponent | ||||
3084 | * of the prime factors that need to be removed, while leaving the | ||||
3085 | * other prime factors untouched. | ||||
3086 | * Repeating this process until gcd(*g, c / *g) = 1 therefore | ||||
3087 | * removes all undesired factors, without removing any others. | ||||
3088 | */ | ||||
3089 | static void remove_incomplete_powers(isl_int *g, isl_int c) | ||||
3090 | { | ||||
3091 | isl_int t; | ||||
3092 | |||||
3093 | isl_int_init(t)isl_sioimath_init((t)); | ||||
3094 | for (;;) { | ||||
3095 | isl_int_divexact(t, c, *g)isl_sioimath_tdiv_q((t), *(c), *(*g)); | ||||
3096 | isl_int_gcd(t, t, *g)isl_sioimath_gcd((t), *(t), *(*g)); | ||||
3097 | if (isl_int_is_one(t)(isl_sioimath_cmp_si(*(t), 1) == 0)) | ||||
3098 | break; | ||||
3099 | isl_int_divexact(*g, *g, t)isl_sioimath_tdiv_q((*g), *(*g), *(t)); | ||||
3100 | } | ||||
3101 | isl_int_clear(t)isl_sioimath_clear((t)); | ||||
3102 | } | ||||
3103 | |||||
3104 | /* Reduce the "n" stride constraints in "bmap" based on a copy "A" | ||||
3105 | * of the same stride constraints in a compressed space that exploits | ||||
3106 | * all equalities in the context and the other equalities in "bmap". | ||||
3107 | * | ||||
3108 | * If the stride constraints of "bmap" are of the form | ||||
3109 | * | ||||
3110 | * C(x) + D(y) = 0 | ||||
3111 | * | ||||
3112 | * then A is of the form | ||||
3113 | * | ||||
3114 | * B(x') + D(y) = 0 | ||||
3115 | * | ||||
3116 | * If any of these constraints involves only a single local variable y, | ||||
3117 | * then the constraint appears as | ||||
3118 | * | ||||
3119 | * f(x) + m y_i = 0 | ||||
3120 | * | ||||
3121 | * in "bmap" and as | ||||
3122 | * | ||||
3123 | * h(x') + m y_i = 0 | ||||
3124 | * | ||||
3125 | * in "A". | ||||
3126 | * | ||||
3127 | * Let g be the gcd of m and the coefficients of h. | ||||
3128 | * Then, in particular, g is a divisor of the coefficients of h and | ||||
3129 | * | ||||
3130 | * f(x) = h(x') | ||||
3131 | * | ||||
3132 | * is known to be a multiple of g. | ||||
3133 | * If some prime factor in m appears with the same exponent in g, | ||||
3134 | * then it can be removed from m because f(x) is already known | ||||
3135 | * to be a multiple of g and therefore in particular of this power | ||||
3136 | * of the prime factors. | ||||
3137 | * Prime factors that appear with a smaller exponent in g cannot | ||||
3138 | * be removed from m. | ||||
3139 | * Let g' be the divisor of g containing all prime factors that | ||||
3140 | * appear with the same exponent in m and g, then | ||||
3141 | * | ||||
3142 | * f(x) + m y_i = 0 | ||||
3143 | * | ||||
3144 | * can be replaced by | ||||
3145 | * | ||||
3146 | * f(x) + m/g' y_i' = 0 | ||||
3147 | * | ||||
3148 | * Note that (if g' != 1) this changes the explicit representation | ||||
3149 | * of y_i to that of y_i', so the integer division at position i | ||||
3150 | * is marked unknown and later recomputed by a call to | ||||
3151 | * isl_basic_map_gauss. | ||||
3152 | */ | ||||
3153 | static __isl_give isl_basic_map *reduce_stride_constraints( | ||||
3154 | __isl_take isl_basic_map *bmap, int n, __isl_keep isl_mat *A) | ||||
3155 | { | ||||
3156 | int i; | ||||
3157 | isl_size total, n_div; | ||||
3158 | int any = 0; | ||||
3159 | isl_int gcd; | ||||
3160 | |||||
3161 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
3162 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
3163 | if (total < 0 || n_div < 0 || !A) | ||||
3164 | return isl_basic_map_free(bmap); | ||||
3165 | total -= n_div; | ||||
3166 | |||||
3167 | isl_int_init(gcd)isl_sioimath_init((gcd)); | ||||
3168 | for (i = 0; i < n; ++i) { | ||||
3169 | int div; | ||||
3170 | |||||
3171 | div = isl_seq_first_non_zero(bmap->eq[i] + 1 + total, n_div); | ||||
3172 | if (div < 0) | ||||
3173 | 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-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 3175); goto error; } while (0) | ||||
3174 | "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-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 3175); goto error; } while (0) | ||||
3175 | goto error)do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_internal , "equality constraints modified unexpectedly", "/build/llvm-toolchain-snapshot-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 3175); goto error; } while (0); | ||||
3176 | if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total + div + 1, | ||||
3177 | n_div - div - 1) != -1) | ||||
3178 | continue; | ||||
3179 | if (isl_mat_row_gcd(A, i, &gcd) < 0) | ||||
3180 | goto error; | ||||
3181 | if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0)) | ||||
3182 | continue; | ||||
3183 | remove_incomplete_powers(&gcd, bmap->eq[i][1 + total + div]); | ||||
3184 | if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0)) | ||||
3185 | continue; | ||||
3186 | 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)) | ||||
3187 | bmap->eq[i][1 + total + div], gcd)isl_sioimath_tdiv_q((bmap->eq[i][1 + total + div]), *(bmap ->eq[i][1 + total + div]), *(gcd)); | ||||
3188 | bmap = isl_basic_map_mark_div_unknown(bmap, div); | ||||
3189 | if (!bmap) | ||||
3190 | goto error; | ||||
3191 | any = 1; | ||||
3192 | } | ||||
3193 | isl_int_clear(gcd)isl_sioimath_clear((gcd)); | ||||
3194 | |||||
3195 | if (any) | ||||
3196 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
3197 | |||||
3198 | return bmap; | ||||
3199 | error: | ||||
3200 | isl_int_clear(gcd)isl_sioimath_clear((gcd)); | ||||
3201 | isl_basic_map_free(bmap); | ||||
3202 | return NULL((void*)0); | ||||
3203 | } | ||||
3204 | |||||
3205 | /* Simplify the stride constraints in "bmap" based on | ||||
3206 | * the remaining equality constraints in "bmap" and all equality | ||||
3207 | * constraints in "context". | ||||
3208 | * Only do this if both "bmap" and "context" have stride constraints. | ||||
3209 | * | ||||
3210 | * First extract a copy of the stride constraints in "bmap" in a compressed | ||||
3211 | * space exploiting all the other equality constraints and then | ||||
3212 | * use this compressed copy to simplify the original stride constraints. | ||||
3213 | */ | ||||
3214 | static __isl_give isl_basic_map *gist_strides(__isl_take isl_basic_map *bmap, | ||||
3215 | __isl_keep isl_basic_map *context) | ||||
3216 | { | ||||
3217 | int bmap_n_eq, context_n_eq; | ||||
3218 | isl_mat *A; | ||||
3219 | |||||
3220 | if (!bmap || !context) | ||||
3221 | return isl_basic_map_free(bmap); | ||||
3222 | |||||
3223 | bmap_n_eq = n_div_eq(bmap); | ||||
3224 | context_n_eq = n_div_eq(context); | ||||
3225 | |||||
3226 | if (bmap_n_eq < 0 || context_n_eq < 0) | ||||
3227 | return isl_basic_map_free(bmap); | ||||
3228 | if (bmap_n_eq == 0 || context_n_eq == 0) | ||||
3229 | return bmap; | ||||
3230 | |||||
3231 | A = extract_compressed_stride_constraints(bmap, bmap_n_eq, | ||||
3232 | context, context_n_eq); | ||||
3233 | bmap = reduce_stride_constraints(bmap, bmap_n_eq, A); | ||||
3234 | |||||
3235 | isl_mat_free(A); | ||||
3236 | |||||
3237 | return bmap; | ||||
3238 | } | ||||
3239 | |||||
3240 | /* Return a basic map that has the same intersection with "context" as "bmap" | ||||
3241 | * and that is as "simple" as possible. | ||||
3242 | * | ||||
3243 | * The core computation is performed on the pure constraints. | ||||
3244 | * When we add back the meaning of the integer divisions, we need | ||||
3245 | * to (re)introduce the div constraints. If we happen to have | ||||
3246 | * discovered that some of these integer divisions are equal to | ||||
3247 | * some affine combination of other variables, then these div | ||||
3248 | * constraints may end up getting simplified in terms of the equalities, | ||||
3249 | * resulting in extra inequalities on the other variables that | ||||
3250 | * may have been removed already or that may not even have been | ||||
3251 | * part of the input. We try and remove those constraints of | ||||
3252 | * this form that are most obviously redundant with respect to | ||||
3253 | * the context. We also remove those div constraints that are | ||||
3254 | * redundant with respect to the other constraints in the result. | ||||
3255 | * | ||||
3256 | * The stride constraints among the equality constraints in "bmap" are | ||||
3257 | * also simplified with respecting to the other equality constraints | ||||
3258 | * in "bmap" and with respect to all equality constraints in "context". | ||||
3259 | */ | ||||
3260 | __isl_give isl_basic_map *isl_basic_map_gist(__isl_take isl_basic_map *bmap, | ||||
3261 | __isl_take isl_basic_map *context) | ||||
3262 | { | ||||
3263 | isl_basic_setisl_basic_map *bset, *eq; | ||||
3264 | isl_basic_map *eq_bmap; | ||||
3265 | isl_size total, n_div, n_div_bmap; | ||||
3266 | unsigned extra, n_eq, n_ineq; | ||||
3267 | |||||
3268 | if (!bmap || !context) | ||||
3269 | goto error; | ||||
3270 | |||||
3271 | if (isl_basic_map_plain_is_universe(bmap)) { | ||||
3272 | isl_basic_map_free(context); | ||||
3273 | return bmap; | ||||
3274 | } | ||||
3275 | if (isl_basic_map_plain_is_empty(context)) { | ||||
3276 | isl_space *space = isl_basic_map_get_space(bmap); | ||||
3277 | isl_basic_map_free(bmap); | ||||
3278 | isl_basic_map_free(context); | ||||
3279 | return isl_basic_map_universe(space); | ||||
3280 | } | ||||
3281 | if (isl_basic_map_plain_is_empty(bmap)) { | ||||
3282 | isl_basic_map_free(context); | ||||
3283 | return bmap; | ||||
3284 | } | ||||
3285 | |||||
3286 | bmap = isl_basic_map_remove_redundancies(bmap); | ||||
3287 | context = isl_basic_map_remove_redundancies(context); | ||||
3288 | bmap = isl_basic_map_order_divs(bmap); | ||||
3289 | context = isl_basic_map_align_divs(context, bmap); | ||||
3290 | |||||
3291 | n_div = isl_basic_map_dim(context, isl_dim_div); | ||||
3292 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
3293 | n_div_bmap = isl_basic_map_dim(bmap, isl_dim_div); | ||||
3294 | if (n_div < 0 || total < 0 || n_div_bmap < 0) | ||||
3295 | goto error; | ||||
3296 | extra = n_div - n_div_bmap; | ||||
3297 | |||||
3298 | bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap)); | ||||
3299 | bset = isl_basic_set_add_dims(bset, isl_dim_set, extra); | ||||
3300 | bset = uset_gist(bset, | ||||
3301 | isl_basic_map_underlying_set(isl_basic_map_copy(context))); | ||||
3302 | bset = isl_basic_set_project_out(bset, isl_dim_set, total, extra); | ||||
3303 | |||||
3304 | if (!bset || bset->n_eq == 0 || n_div == 0 || | ||||
3305 | isl_basic_set_plain_is_empty(bset)) { | ||||
3306 | isl_basic_map_free(context); | ||||
3307 | return isl_basic_map_overlying_set(bset, bmap); | ||||
3308 | } | ||||
3309 | |||||
3310 | n_eq = bset->n_eq; | ||||
3311 | n_ineq = bset->n_ineq; | ||||
3312 | eq = isl_basic_set_copy(bset); | ||||
3313 | eq = isl_basic_set_cow(eq); | ||||
3314 | eq = isl_basic_set_free_inequality(eq, n_ineq); | ||||
3315 | bset = isl_basic_set_free_equality(bset, n_eq); | ||||
3316 | |||||
3317 | eq_bmap = isl_basic_map_overlying_set(eq, isl_basic_map_copy(bmap)); | ||||
3318 | eq_bmap = gist_strides(eq_bmap, context); | ||||
3319 | eq_bmap = isl_basic_map_remove_shifted_constraints(eq_bmap, context); | ||||
3320 | bmap = isl_basic_map_overlying_set(bset, bmap); | ||||
3321 | bmap = isl_basic_map_intersect(bmap, eq_bmap); | ||||
3322 | bmap = isl_basic_map_remove_redundancies(bmap); | ||||
3323 | |||||
3324 | return bmap; | ||||
3325 | error: | ||||
3326 | isl_basic_map_free(bmap); | ||||
3327 | isl_basic_map_free(context); | ||||
3328 | return NULL((void*)0); | ||||
3329 | } | ||||
3330 | |||||
3331 | /* | ||||
3332 | * Assumes context has no implicit divs. | ||||
3333 | */ | ||||
3334 | __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map, | ||||
3335 | __isl_take isl_basic_map *context) | ||||
3336 | { | ||||
3337 | int i; | ||||
3338 | |||||
3339 | if (!map || !context) | ||||
3340 | goto error; | ||||
3341 | |||||
3342 | if (isl_basic_map_plain_is_empty(context)) { | ||||
3343 | isl_space *space = isl_map_get_space(map); | ||||
3344 | isl_map_free(map); | ||||
3345 | isl_basic_map_free(context); | ||||
3346 | return isl_map_universe(space); | ||||
3347 | } | ||||
3348 | |||||
3349 | context = isl_basic_map_remove_redundancies(context); | ||||
3350 | map = isl_map_cow(map); | ||||
3351 | if (isl_map_basic_map_check_equal_space(map, context) < 0) | ||||
3352 | goto error; | ||||
3353 | map = isl_map_compute_divs(map); | ||||
3354 | if (!map) | ||||
3355 | goto error; | ||||
3356 | for (i = map->n - 1; i >= 0; --i) { | ||||
3357 | map->p[i] = isl_basic_map_gist(map->p[i], | ||||
3358 | isl_basic_map_copy(context)); | ||||
3359 | if (!map->p[i]) | ||||
3360 | goto error; | ||||
3361 | if (isl_basic_map_plain_is_empty(map->p[i])) { | ||||
3362 | isl_basic_map_free(map->p[i]); | ||||
3363 | if (i != map->n - 1) | ||||
3364 | map->p[i] = map->p[map->n - 1]; | ||||
3365 | map->n--; | ||||
3366 | } | ||||
3367 | } | ||||
3368 | isl_basic_map_free(context); | ||||
3369 | ISL_F_CLR(map, ISL_MAP_NORMALIZED)(((map)->flags) &= ~((1 << 1))); | ||||
3370 | return map; | ||||
3371 | error: | ||||
3372 | isl_map_free(map); | ||||
3373 | isl_basic_map_free(context); | ||||
3374 | return NULL((void*)0); | ||||
3375 | } | ||||
3376 | |||||
3377 | /* Drop all inequalities from "bmap" that also appear in "context". | ||||
3378 | * "context" is assumed to have only known local variables and | ||||
3379 | * the initial local variables of "bmap" are assumed to be the same | ||||
3380 | * as those of "context". | ||||
3381 | * The constraints of both "bmap" and "context" are assumed | ||||
3382 | * to have been sorted using isl_basic_map_sort_constraints. | ||||
3383 | * | ||||
3384 | * Run through the inequality constraints of "bmap" and "context" | ||||
3385 | * in sorted order. | ||||
3386 | * If a constraint of "bmap" involves variables not in "context", | ||||
3387 | * then it cannot appear in "context". | ||||
3388 | * If a matching constraint is found, it is removed from "bmap". | ||||
3389 | */ | ||||
3390 | static __isl_give isl_basic_map *drop_inequalities( | ||||
3391 | __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context) | ||||
3392 | { | ||||
3393 | int i1, i2; | ||||
3394 | isl_size total, bmap_total; | ||||
3395 | unsigned extra; | ||||
3396 | |||||
3397 | total = isl_basic_map_dim(context, isl_dim_all); | ||||
3398 | bmap_total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
3399 | if (total < 0 || bmap_total < 0) | ||||
3400 | return isl_basic_map_free(bmap); | ||||
3401 | |||||
3402 | extra = bmap_total - total; | ||||
3403 | |||||
3404 | i1 = bmap->n_ineq - 1; | ||||
3405 | i2 = context->n_ineq - 1; | ||||
3406 | while (bmap && i1 >= 0 && i2 >= 0) { | ||||
3407 | int cmp; | ||||
3408 | |||||
3409 | if (isl_seq_first_non_zero(bmap->ineq[i1] + 1 + total, | ||||
3410 | extra) != -1) { | ||||
3411 | --i1; | ||||
3412 | continue; | ||||
3413 | } | ||||
3414 | cmp = isl_basic_map_constraint_cmp(context, bmap->ineq[i1], | ||||
3415 | context->ineq[i2]); | ||||
3416 | if (cmp < 0) { | ||||
3417 | --i2; | ||||
3418 | continue; | ||||
3419 | } | ||||
3420 | if (cmp > 0) { | ||||
3421 | --i1; | ||||
3422 | continue; | ||||
3423 | } | ||||
3424 | if (isl_int_eq(bmap->ineq[i1][0], context->ineq[i2][0])(isl_sioimath_cmp(*(bmap->ineq[i1][0]), *(context->ineq [i2][0])) == 0)) { | ||||
3425 | bmap = isl_basic_map_cow(bmap); | ||||
3426 | if (isl_basic_map_drop_inequality(bmap, i1) < 0) | ||||
3427 | bmap = isl_basic_map_free(bmap); | ||||
3428 | } | ||||
3429 | --i1; | ||||
3430 | --i2; | ||||
3431 | } | ||||
3432 | |||||
3433 | return bmap; | ||||
3434 | } | ||||
3435 | |||||
3436 | /* Drop all equalities from "bmap" that also appear in "context". | ||||
3437 | * "context" is assumed to have only known local variables and | ||||
3438 | * the initial local variables of "bmap" are assumed to be the same | ||||
3439 | * as those of "context". | ||||
3440 | * | ||||
3441 | * Run through the equality constraints of "bmap" and "context" | ||||
3442 | * in sorted order. | ||||
3443 | * If a constraint of "bmap" involves variables not in "context", | ||||
3444 | * then it cannot appear in "context". | ||||
3445 | * If a matching constraint is found, it is removed from "bmap". | ||||
3446 | */ | ||||
3447 | static __isl_give isl_basic_map *drop_equalities( | ||||
3448 | __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context) | ||||
3449 | { | ||||
3450 | int i1, i2; | ||||
3451 | isl_size total, bmap_total; | ||||
3452 | unsigned extra; | ||||
3453 | |||||
3454 | total = isl_basic_map_dim(context, isl_dim_all); | ||||
3455 | bmap_total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
3456 | if (total < 0 || bmap_total < 0) | ||||
3457 | return isl_basic_map_free(bmap); | ||||
3458 | |||||
3459 | extra = bmap_total - total; | ||||
3460 | |||||
3461 | i1 = bmap->n_eq - 1; | ||||
3462 | i2 = context->n_eq - 1; | ||||
3463 | |||||
3464 | while (bmap && i1 >= 0 && i2 >= 0) { | ||||
3465 | int last1, last2; | ||||
3466 | |||||
3467 | if (isl_seq_first_non_zero(bmap->eq[i1] + 1 + total, | ||||
3468 | extra) != -1) | ||||
3469 | break; | ||||
3470 | last1 = isl_seq_last_non_zero(bmap->eq[i1] + 1, total); | ||||
3471 | last2 = isl_seq_last_non_zero(context->eq[i2] + 1, total); | ||||
3472 | if (last1 > last2) { | ||||
3473 | --i2; | ||||
3474 | continue; | ||||
3475 | } | ||||
3476 | if (last1 < last2) { | ||||
3477 | --i1; | ||||
3478 | continue; | ||||
3479 | } | ||||
3480 | if (isl_seq_eq(bmap->eq[i1], context->eq[i2], 1 + total)) { | ||||
3481 | bmap = isl_basic_map_cow(bmap); | ||||
3482 | if (isl_basic_map_drop_equality(bmap, i1) < 0) | ||||
3483 | bmap = isl_basic_map_free(bmap); | ||||
3484 | } | ||||
3485 | --i1; | ||||
3486 | --i2; | ||||
3487 | } | ||||
3488 | |||||
3489 | return bmap; | ||||
3490 | } | ||||
3491 | |||||
3492 | /* Remove the constraints in "context" from "bmap". | ||||
3493 | * "context" is assumed to have explicit representations | ||||
3494 | * for all local variables. | ||||
3495 | * | ||||
3496 | * First align the divs of "bmap" to those of "context" and | ||||
3497 | * sort the constraints. Then drop all constraints from "bmap" | ||||
3498 | * that appear in "context". | ||||
3499 | */ | ||||
3500 | __isl_give isl_basic_map *isl_basic_map_plain_gist( | ||||
3501 | __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context) | ||||
3502 | { | ||||
3503 | isl_bool done, known; | ||||
3504 | |||||
3505 | done = isl_basic_map_plain_is_universe(context); | ||||
3506 | if (done == isl_bool_false) | ||||
3507 | done = isl_basic_map_plain_is_universe(bmap); | ||||
3508 | if (done == isl_bool_false) | ||||
3509 | done = isl_basic_map_plain_is_empty(context); | ||||
3510 | if (done == isl_bool_false) | ||||
3511 | done = isl_basic_map_plain_is_empty(bmap); | ||||
3512 | if (done < 0) | ||||
3513 | goto error; | ||||
3514 | if (done) { | ||||
3515 | isl_basic_map_free(context); | ||||
3516 | return bmap; | ||||
3517 | } | ||||
3518 | known = isl_basic_map_divs_known(context); | ||||
3519 | if (known < 0) | ||||
3520 | goto error; | ||||
3521 | if (!known) | ||||
3522 | 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-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 3523); goto error; } while (0) | ||||
3523 | "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-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 3523); goto error; } while (0); | ||||
3524 | |||||
3525 | context = isl_basic_map_order_divs(context); | ||||
3526 | bmap = isl_basic_map_align_divs(bmap, context); | ||||
3527 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
3528 | bmap = isl_basic_map_sort_constraints(bmap); | ||||
3529 | context = isl_basic_map_sort_constraints(context); | ||||
3530 | |||||
3531 | bmap = drop_inequalities(bmap, context); | ||||
3532 | bmap = drop_equalities(bmap, context); | ||||
3533 | |||||
3534 | isl_basic_map_free(context); | ||||
3535 | bmap = isl_basic_map_finalize(bmap); | ||||
3536 | return bmap; | ||||
3537 | error: | ||||
3538 | isl_basic_map_free(bmap); | ||||
3539 | isl_basic_map_free(context); | ||||
3540 | return NULL((void*)0); | ||||
3541 | } | ||||
3542 | |||||
3543 | /* Replace "map" by the disjunct at position "pos" and free "context". | ||||
3544 | */ | ||||
3545 | static __isl_give isl_map *replace_by_disjunct(__isl_take isl_map *map, | ||||
3546 | int pos, __isl_take isl_basic_map *context) | ||||
3547 | { | ||||
3548 | isl_basic_map *bmap; | ||||
3549 | |||||
3550 | bmap = isl_basic_map_copy(map->p[pos]); | ||||
3551 | isl_map_free(map); | ||||
3552 | isl_basic_map_free(context); | ||||
3553 | return isl_map_from_basic_map(bmap); | ||||
3554 | } | ||||
3555 | |||||
3556 | /* Remove the constraints in "context" from "map". | ||||
3557 | * If any of the disjuncts in the result turns out to be the universe, | ||||
3558 | * then return this universe. | ||||
3559 | * "context" is assumed to have explicit representations | ||||
3560 | * for all local variables. | ||||
3561 | */ | ||||
3562 | __isl_give isl_map *isl_map_plain_gist_basic_map(__isl_take isl_map *map, | ||||
3563 | __isl_take isl_basic_map *context) | ||||
3564 | { | ||||
3565 | int i; | ||||
3566 | isl_bool univ, known; | ||||
3567 | |||||
3568 | univ = isl_basic_map_plain_is_universe(context); | ||||
3569 | if (univ < 0) | ||||
3570 | goto error; | ||||
3571 | if (univ) { | ||||
3572 | isl_basic_map_free(context); | ||||
3573 | return map; | ||||
3574 | } | ||||
3575 | known = isl_basic_map_divs_known(context); | ||||
3576 | if (known < 0) | ||||
3577 | goto error; | ||||
3578 | if (!known) | ||||
3579 | 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-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 3580); goto error; } while (0) | ||||
3580 | "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-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 3580); goto error; } while (0); | ||||
3581 | |||||
3582 | map = isl_map_cow(map); | ||||
3583 | if (!map) | ||||
3584 | goto error; | ||||
3585 | for (i = 0; i < map->n; ++i) { | ||||
3586 | map->p[i] = isl_basic_map_plain_gist(map->p[i], | ||||
3587 | isl_basic_map_copy(context)); | ||||
3588 | univ = isl_basic_map_plain_is_universe(map->p[i]); | ||||
3589 | if (univ < 0) | ||||
3590 | goto error; | ||||
3591 | if (univ && map->n > 1) | ||||
3592 | return replace_by_disjunct(map, i, context); | ||||
3593 | } | ||||
3594 | |||||
3595 | isl_basic_map_free(context); | ||||
3596 | ISL_F_CLR(map, ISL_MAP_NORMALIZED)(((map)->flags) &= ~((1 << 1))); | ||||
3597 | if (map->n > 1) | ||||
3598 | ISL_F_CLR(map, ISL_MAP_DISJOINT)(((map)->flags) &= ~((1 << 0))); | ||||
3599 | return map; | ||||
3600 | error: | ||||
3601 | isl_map_free(map); | ||||
3602 | isl_basic_map_free(context); | ||||
3603 | return NULL((void*)0); | ||||
3604 | } | ||||
3605 | |||||
3606 | /* Remove the constraints in "context" from "set". | ||||
3607 | * If any of the disjuncts in the result turns out to be the universe, | ||||
3608 | * then return this universe. | ||||
3609 | * "context" is assumed to have explicit representations | ||||
3610 | * for all local variables. | ||||
3611 | */ | ||||
3612 | __isl_give isl_setisl_map *isl_set_plain_gist_basic_set(__isl_take isl_setisl_map *set, | ||||
3613 | __isl_take isl_basic_setisl_basic_map *context) | ||||
3614 | { | ||||
3615 | return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set), | ||||
3616 | bset_to_bmap(context))); | ||||
3617 | } | ||||
3618 | |||||
3619 | /* Remove the constraints in "context" from "map". | ||||
3620 | * If any of the disjuncts in the result turns out to be the universe, | ||||
3621 | * then return this universe. | ||||
3622 | * "context" is assumed to consist of a single disjunct and | ||||
3623 | * to have explicit representations for all local variables. | ||||
3624 | */ | ||||
3625 | __isl_give isl_map *isl_map_plain_gist(__isl_take isl_map *map, | ||||
3626 | __isl_take isl_map *context) | ||||
3627 | { | ||||
3628 | isl_basic_map *hull; | ||||
3629 | |||||
3630 | hull = isl_map_unshifted_simple_hull(context); | ||||
3631 | return isl_map_plain_gist_basic_map(map, hull); | ||||
3632 | } | ||||
3633 | |||||
3634 | /* Replace "map" by a universe map in the same space and free "drop". | ||||
3635 | */ | ||||
3636 | static __isl_give isl_map *replace_by_universe(__isl_take isl_map *map, | ||||
3637 | __isl_take isl_map *drop) | ||||
3638 | { | ||||
3639 | isl_map *res; | ||||
3640 | |||||
3641 | res = isl_map_universe(isl_map_get_space(map)); | ||||
3642 | isl_map_free(map); | ||||
3643 | isl_map_free(drop); | ||||
3644 | return res; | ||||
3645 | } | ||||
3646 | |||||
3647 | /* Return a map that has the same intersection with "context" as "map" | ||||
3648 | * and that is as "simple" as possible. | ||||
3649 | * | ||||
3650 | * If "map" is already the universe, then we cannot make it any simpler. | ||||
3651 | * Similarly, if "context" is the universe, then we cannot exploit it | ||||
3652 | * to simplify "map" | ||||
3653 | * If "map" and "context" are identical to each other, then we can | ||||
3654 | * return the corresponding universe. | ||||
3655 | * | ||||
3656 | * If either "map" or "context" consists of multiple disjuncts, | ||||
3657 | * then check if "context" happens to be a subset of "map", | ||||
3658 | * in which case all constraints can be removed. | ||||
3659 | * In case of multiple disjuncts, the standard procedure | ||||
3660 | * may not be able to detect that all constraints can be removed. | ||||
3661 | * | ||||
3662 | * If none of these cases apply, we have to work a bit harder. | ||||
3663 | * During this computation, we make use of a single disjunct context, | ||||
3664 | * so if the original context consists of more than one disjunct | ||||
3665 | * then we need to approximate the context by a single disjunct set. | ||||
3666 | * Simply taking the simple hull may drop constraints that are | ||||
3667 | * only implicitly available in each disjunct. We therefore also | ||||
3668 | * look for constraints among those defining "map" that are valid | ||||
3669 | * for the context. These can then be used to simplify away | ||||
3670 | * the corresponding constraints in "map". | ||||
3671 | */ | ||||
3672 | __isl_give isl_map *isl_map_gist(__isl_take isl_map *map, | ||||
3673 | __isl_take isl_map *context) | ||||
3674 | { | ||||
3675 | int equal; | ||||
3676 | int is_universe; | ||||
3677 | isl_size n_disjunct_map, n_disjunct_context; | ||||
3678 | isl_bool subset; | ||||
3679 | isl_basic_map *hull; | ||||
3680 | |||||
3681 | is_universe = isl_map_plain_is_universe(map); | ||||
3682 | if (is_universe >= 0 && !is_universe) | ||||
3683 | is_universe = isl_map_plain_is_universe(context); | ||||
3684 | if (is_universe < 0) | ||||
3685 | goto error; | ||||
3686 | if (is_universe) { | ||||
3687 | isl_map_free(context); | ||||
3688 | return map; | ||||
3689 | } | ||||
3690 | |||||
3691 | isl_map_align_params_bin(&map, &context); | ||||
3692 | equal = isl_map_plain_is_equal(map, context); | ||||
3693 | if (equal < 0) | ||||
3694 | goto error; | ||||
3695 | if (equal) | ||||
3696 | return replace_by_universe(map, context); | ||||
3697 | |||||
3698 | n_disjunct_map = isl_map_n_basic_map(map); | ||||
3699 | n_disjunct_context = isl_map_n_basic_map(context); | ||||
3700 | if (n_disjunct_map < 0 || n_disjunct_context < 0) | ||||
3701 | goto error; | ||||
3702 | if (n_disjunct_map != 1 || n_disjunct_context != 1) { | ||||
3703 | subset = isl_map_is_subset(context, map); | ||||
3704 | if (subset < 0) | ||||
3705 | goto error; | ||||
3706 | if (subset) | ||||
3707 | return replace_by_universe(map, context); | ||||
3708 | } | ||||
3709 | |||||
3710 | context = isl_map_compute_divs(context); | ||||
3711 | if (!context) | ||||
3712 | goto error; | ||||
3713 | if (n_disjunct_context == 1) { | ||||
3714 | hull = isl_map_simple_hull(context); | ||||
3715 | } else { | ||||
3716 | isl_ctx *ctx; | ||||
3717 | isl_map_list *list; | ||||
3718 | |||||
3719 | ctx = isl_map_get_ctx(map); | ||||
3720 | list = isl_map_list_alloc(ctx, 2); | ||||
3721 | list = isl_map_list_add(list, isl_map_copy(context)); | ||||
3722 | list = isl_map_list_add(list, isl_map_copy(map)); | ||||
3723 | hull = isl_map_unshifted_simple_hull_from_map_list(context, | ||||
3724 | list); | ||||
3725 | } | ||||
3726 | return isl_map_gist_basic_map(map, hull); | ||||
3727 | error: | ||||
3728 | isl_map_free(map); | ||||
3729 | isl_map_free(context); | ||||
3730 | return NULL((void*)0); | ||||
3731 | } | ||||
3732 | |||||
3733 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_gist(__isl_take isl_basic_setisl_basic_map *bset, | ||||
3734 | __isl_take isl_basic_setisl_basic_map *context) | ||||
3735 | { | ||||
3736 | return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset), | ||||
3737 | bset_to_bmap(context))); | ||||
3738 | } | ||||
3739 | |||||
3740 | __isl_give isl_setisl_map *isl_set_gist_basic_set(__isl_take isl_setisl_map *set, | ||||
3741 | __isl_take isl_basic_setisl_basic_map *context) | ||||
3742 | { | ||||
3743 | return set_from_map(isl_map_gist_basic_map(set_to_map(set), | ||||
3744 | bset_to_bmap(context))); | ||||
3745 | } | ||||
3746 | |||||
3747 | __isl_give isl_setisl_map *isl_set_gist_params_basic_set(__isl_take isl_setisl_map *set, | ||||
3748 | __isl_take isl_basic_setisl_basic_map *context) | ||||
3749 | { | ||||
3750 | isl_space *space = isl_set_get_space(set); | ||||
3751 | isl_basic_setisl_basic_map *dom_context = isl_basic_set_universe(space); | ||||
3752 | dom_context = isl_basic_set_intersect_params(dom_context, context); | ||||
3753 | return isl_set_gist_basic_set(set, dom_context); | ||||
3754 | } | ||||
3755 | |||||
3756 | __isl_give isl_setisl_map *isl_set_gist(__isl_take isl_setisl_map *set, | ||||
3757 | __isl_take isl_setisl_map *context) | ||||
3758 | { | ||||
3759 | return set_from_map(isl_map_gist(set_to_map(set), set_to_map(context))); | ||||
3760 | } | ||||
3761 | |||||
3762 | /* Compute the gist of "bmap" with respect to the constraints "context" | ||||
3763 | * on the domain. | ||||
3764 | */ | ||||
3765 | __isl_give isl_basic_map *isl_basic_map_gist_domain( | ||||
3766 | __isl_take isl_basic_map *bmap, __isl_take isl_basic_setisl_basic_map *context) | ||||
3767 | { | ||||
3768 | isl_space *space = isl_basic_map_get_space(bmap); | ||||
3769 | isl_basic_map *bmap_context = isl_basic_map_universe(space); | ||||
3770 | |||||
3771 | bmap_context = isl_basic_map_intersect_domain(bmap_context, context); | ||||
3772 | return isl_basic_map_gist(bmap, bmap_context); | ||||
3773 | } | ||||
3774 | |||||
3775 | __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map, | ||||
3776 | __isl_take isl_setisl_map *context) | ||||
3777 | { | ||||
3778 | isl_map *map_context = isl_map_universe(isl_map_get_space(map)); | ||||
3779 | map_context = isl_map_intersect_domain(map_context, context); | ||||
3780 | return isl_map_gist(map, map_context); | ||||
3781 | } | ||||
3782 | |||||
3783 | __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map, | ||||
3784 | __isl_take isl_setisl_map *context) | ||||
3785 | { | ||||
3786 | isl_map *map_context = isl_map_universe(isl_map_get_space(map)); | ||||
3787 | map_context = isl_map_intersect_range(map_context, context); | ||||
3788 | return isl_map_gist(map, map_context); | ||||
3789 | } | ||||
3790 | |||||
3791 | __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map, | ||||
3792 | __isl_take isl_setisl_map *context) | ||||
3793 | { | ||||
3794 | isl_map *map_context = isl_map_universe(isl_map_get_space(map)); | ||||
3795 | map_context = isl_map_intersect_params(map_context, context); | ||||
3796 | return isl_map_gist(map, map_context); | ||||
3797 | } | ||||
3798 | |||||
3799 | __isl_give isl_setisl_map *isl_set_gist_params(__isl_take isl_setisl_map *set, | ||||
3800 | __isl_take isl_setisl_map *context) | ||||
3801 | { | ||||
3802 | return isl_map_gist_params(set, context); | ||||
3803 | } | ||||
3804 | |||||
3805 | /* Quick check to see if two basic maps are disjoint. | ||||
3806 | * In particular, we reduce the equalities and inequalities of | ||||
3807 | * one basic map in the context of the equalities of the other | ||||
3808 | * basic map and check if we get a contradiction. | ||||
3809 | */ | ||||
3810 | isl_bool isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1, | ||||
3811 | __isl_keep isl_basic_map *bmap2) | ||||
3812 | { | ||||
3813 | struct isl_vec *v = NULL((void*)0); | ||||
3814 | int *elim = NULL((void*)0); | ||||
3815 | isl_size total; | ||||
3816 | int i; | ||||
3817 | |||||
3818 | if (isl_basic_map_check_equal_space(bmap1, bmap2) < 0) | ||||
3819 | return isl_bool_error; | ||||
3820 | if (bmap1->n_div || bmap2->n_div) | ||||
3821 | return isl_bool_false; | ||||
3822 | if (!bmap1->n_eq && !bmap2->n_eq) | ||||
3823 | return isl_bool_false; | ||||
3824 | |||||
3825 | total = isl_space_dim(bmap1->dim, isl_dim_all); | ||||
3826 | if (total < 0) | ||||
3827 | return isl_bool_error; | ||||
3828 | if (total == 0) | ||||
3829 | return isl_bool_false; | ||||
3830 | v = isl_vec_alloc(bmap1->ctx, 1 + total); | ||||
3831 | if (!v) | ||||
3832 | goto error; | ||||
3833 | elim = isl_alloc_array(bmap1->ctx, int, total)((int *)isl_malloc_or_die(bmap1->ctx, (total)*sizeof(int)) ); | ||||
3834 | if (!elim) | ||||
3835 | goto error; | ||||
3836 | compute_elimination_index(bmap1, elim, total); | ||||
3837 | for (i = 0; i < bmap2->n_eq; ++i) { | ||||
3838 | int reduced; | ||||
3839 | reduced = reduced_using_equalities(v->block.data, bmap2->eq[i], | ||||
3840 | bmap1, elim, total); | ||||
3841 | if (reduced && !isl_int_is_zero(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) == 0) && | ||||
3842 | isl_seq_first_non_zero(v->block.data + 1, total) == -1) | ||||
3843 | goto disjoint; | ||||
3844 | } | ||||
3845 | for (i = 0; i < bmap2->n_ineq; ++i) { | ||||
3846 | int reduced; | ||||
3847 | reduced = reduced_using_equalities(v->block.data, | ||||
3848 | bmap2->ineq[i], bmap1, elim, total); | ||||
3849 | if (reduced && isl_int_is_neg(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) < 0) && | ||||
3850 | isl_seq_first_non_zero(v->block.data + 1, total) == -1) | ||||
3851 | goto disjoint; | ||||
3852 | } | ||||
3853 | compute_elimination_index(bmap2, elim, total); | ||||
3854 | for (i = 0; i < bmap1->n_ineq; ++i) { | ||||
3855 | int reduced; | ||||
3856 | reduced = reduced_using_equalities(v->block.data, | ||||
3857 | bmap1->ineq[i], bmap2, elim, total); | ||||
3858 | if (reduced && isl_int_is_neg(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) < 0) && | ||||
3859 | isl_seq_first_non_zero(v->block.data + 1, total) == -1) | ||||
3860 | goto disjoint; | ||||
3861 | } | ||||
3862 | isl_vec_free(v); | ||||
3863 | free(elim); | ||||
3864 | return isl_bool_false; | ||||
3865 | disjoint: | ||||
3866 | isl_vec_free(v); | ||||
3867 | free(elim); | ||||
3868 | return isl_bool_true; | ||||
3869 | error: | ||||
3870 | isl_vec_free(v); | ||||
3871 | free(elim); | ||||
3872 | return isl_bool_error; | ||||
3873 | } | ||||
3874 | |||||
3875 | int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_setisl_basic_map *bset1, | ||||
3876 | __isl_keep isl_basic_setisl_basic_map *bset2) | ||||
3877 | { | ||||
3878 | return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1), | ||||
3879 | bset_to_bmap(bset2)); | ||||
3880 | } | ||||
3881 | |||||
3882 | /* Does "test" hold for all pairs of basic maps in "map1" and "map2"? | ||||
3883 | */ | ||||
3884 | static isl_bool all_pairs(__isl_keep isl_map *map1, __isl_keep isl_map *map2, | ||||
3885 | isl_bool (*test)(__isl_keep isl_basic_map *bmap1, | ||||
3886 | __isl_keep isl_basic_map *bmap2)) | ||||
3887 | { | ||||
3888 | int i, j; | ||||
3889 | |||||
3890 | if (!map1 || !map2) | ||||
3891 | return isl_bool_error; | ||||
3892 | |||||
3893 | for (i = 0; i < map1->n; ++i) { | ||||
3894 | for (j = 0; j < map2->n; ++j) { | ||||
3895 | isl_bool d = test(map1->p[i], map2->p[j]); | ||||
3896 | if (d != isl_bool_true) | ||||
3897 | return d; | ||||
3898 | } | ||||
3899 | } | ||||
3900 | |||||
3901 | return isl_bool_true; | ||||
3902 | } | ||||
3903 | |||||
3904 | /* Are "map1" and "map2" obviously disjoint, based on information | ||||
3905 | * that can be derived without looking at the individual basic maps? | ||||
3906 | * | ||||
3907 | * In particular, if one of them is empty or if they live in different spaces | ||||
3908 | * (ignoring parameters), then they are clearly disjoint. | ||||
3909 | */ | ||||
3910 | static isl_bool isl_map_plain_is_disjoint_global(__isl_keep isl_map *map1, | ||||
3911 | __isl_keep isl_map *map2) | ||||
3912 | { | ||||
3913 | isl_bool disjoint; | ||||
3914 | isl_bool match; | ||||
3915 | |||||
3916 | if (!map1 || !map2) | ||||
3917 | return isl_bool_error; | ||||
3918 | |||||
3919 | disjoint = isl_map_plain_is_empty(map1); | ||||
3920 | if (disjoint < 0 || disjoint) | ||||
3921 | return disjoint; | ||||
3922 | |||||
3923 | disjoint = isl_map_plain_is_empty(map2); | ||||
3924 | if (disjoint < 0 || disjoint) | ||||
3925 | return disjoint; | ||||
3926 | |||||
3927 | match = isl_map_tuple_is_equal(map1, isl_dim_in, map2, isl_dim_in); | ||||
3928 | if (match < 0 || !match) | ||||
3929 | return match < 0 ? isl_bool_error : isl_bool_true; | ||||
3930 | |||||
3931 | match = isl_map_tuple_is_equal(map1, isl_dim_out, map2, isl_dim_out); | ||||
3932 | if (match < 0 || !match) | ||||
3933 | return match < 0 ? isl_bool_error : isl_bool_true; | ||||
3934 | |||||
3935 | return isl_bool_false; | ||||
3936 | } | ||||
3937 | |||||
3938 | /* Are "map1" and "map2" obviously disjoint? | ||||
3939 | * | ||||
3940 | * If one of them is empty or if they live in different spaces (ignoring | ||||
3941 | * parameters), then they are clearly disjoint. | ||||
3942 | * This is checked by isl_map_plain_is_disjoint_global. | ||||
3943 | * | ||||
3944 | * If they have different parameters, then we skip any further tests. | ||||
3945 | * | ||||
3946 | * If they are obviously equal, but not obviously empty, then we will | ||||
3947 | * not be able to detect if they are disjoint. | ||||
3948 | * | ||||
3949 | * Otherwise we check if each basic map in "map1" is obviously disjoint | ||||
3950 | * from each basic map in "map2". | ||||
3951 | */ | ||||
3952 | isl_bool isl_map_plain_is_disjoint(__isl_keep isl_map *map1, | ||||
3953 | __isl_keep isl_map *map2) | ||||
3954 | { | ||||
3955 | isl_bool disjoint; | ||||
3956 | isl_bool intersect; | ||||
3957 | isl_bool match; | ||||
3958 | |||||
3959 | disjoint = isl_map_plain_is_disjoint_global(map1, map2); | ||||
3960 | if (disjoint < 0 || disjoint) | ||||
3961 | return disjoint; | ||||
3962 | |||||
3963 | match = isl_map_has_equal_params(map1, map2); | ||||
3964 | if (match < 0 || !match) | ||||
3965 | return match < 0 ? isl_bool_error : isl_bool_false; | ||||
3966 | |||||
3967 | intersect = isl_map_plain_is_equal(map1, map2); | ||||
3968 | if (intersect < 0 || intersect) | ||||
3969 | return intersect < 0 ? isl_bool_error : isl_bool_false; | ||||
3970 | |||||
3971 | return all_pairs(map1, map2, &isl_basic_map_plain_is_disjoint); | ||||
3972 | } | ||||
3973 | |||||
3974 | /* Are "map1" and "map2" disjoint? | ||||
3975 | * The parameters are assumed to have been aligned. | ||||
3976 | * | ||||
3977 | * In particular, check whether all pairs of basic maps are disjoint. | ||||
3978 | */ | ||||
3979 | static isl_bool isl_map_is_disjoint_aligned(__isl_keep isl_map *map1, | ||||
3980 | __isl_keep isl_map *map2) | ||||
3981 | { | ||||
3982 | return all_pairs(map1, map2, &isl_basic_map_is_disjoint); | ||||
3983 | } | ||||
3984 | |||||
3985 | /* Are "map1" and "map2" disjoint? | ||||
3986 | * | ||||
3987 | * They are disjoint if they are "obviously disjoint" or if one of them | ||||
3988 | * is empty. Otherwise, they are not disjoint if one of them is universal. | ||||
3989 | * If the two inputs are (obviously) equal and not empty, then they are | ||||
3990 | * not disjoint. | ||||
3991 | * If none of these cases apply, then check if all pairs of basic maps | ||||
3992 | * are disjoint after aligning the parameters. | ||||
3993 | */ | ||||
3994 | isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2) | ||||
3995 | { | ||||
3996 | isl_bool disjoint; | ||||
3997 | isl_bool intersect; | ||||
3998 | |||||
3999 | disjoint = isl_map_plain_is_disjoint_global(map1, map2); | ||||
4000 | if (disjoint < 0 || disjoint) | ||||
4001 | return disjoint; | ||||
4002 | |||||
4003 | disjoint = isl_map_is_empty(map1); | ||||
4004 | if (disjoint < 0 || disjoint) | ||||
4005 | return disjoint; | ||||
4006 | |||||
4007 | disjoint = isl_map_is_empty(map2); | ||||
4008 | if (disjoint < 0 || disjoint) | ||||
4009 | return disjoint; | ||||
4010 | |||||
4011 | intersect = isl_map_plain_is_universe(map1); | ||||
4012 | if (intersect < 0 || intersect) | ||||
4013 | return isl_bool_not(intersect); | ||||
4014 | |||||
4015 | intersect = isl_map_plain_is_universe(map2); | ||||
4016 | if (intersect < 0 || intersect) | ||||
4017 | return isl_bool_not(intersect); | ||||
4018 | |||||
4019 | intersect = isl_map_plain_is_equal(map1, map2); | ||||
4020 | if (intersect < 0 || intersect) | ||||
4021 | return isl_bool_not(intersect); | ||||
4022 | |||||
4023 | return isl_map_align_params_map_map_and_test(map1, map2, | ||||
4024 | &isl_map_is_disjoint_aligned); | ||||
4025 | } | ||||
4026 | |||||
4027 | /* Are "bmap1" and "bmap2" disjoint? | ||||
4028 | * | ||||
4029 | * They are disjoint if they are "obviously disjoint" or if one of them | ||||
4030 | * is empty. Otherwise, they are not disjoint if one of them is universal. | ||||
4031 | * If none of these cases apply, we compute the intersection and see if | ||||
4032 | * the result is empty. | ||||
4033 | */ | ||||
4034 | isl_bool isl_basic_map_is_disjoint(__isl_keep isl_basic_map *bmap1, | ||||
4035 | __isl_keep isl_basic_map *bmap2) | ||||
4036 | { | ||||
4037 | isl_bool disjoint; | ||||
4038 | isl_bool intersect; | ||||
4039 | isl_basic_map *test; | ||||
4040 | |||||
4041 | disjoint = isl_basic_map_plain_is_disjoint(bmap1, bmap2); | ||||
4042 | if (disjoint < 0 || disjoint) | ||||
4043 | return disjoint; | ||||
4044 | |||||
4045 | disjoint = isl_basic_map_is_empty(bmap1); | ||||
4046 | if (disjoint < 0 || disjoint) | ||||
4047 | return disjoint; | ||||
4048 | |||||
4049 | disjoint = isl_basic_map_is_empty(bmap2); | ||||
4050 | if (disjoint < 0 || disjoint) | ||||
4051 | return disjoint; | ||||
4052 | |||||
4053 | intersect = isl_basic_map_plain_is_universe(bmap1); | ||||
4054 | if (intersect < 0 || intersect) | ||||
4055 | return isl_bool_not(intersect); | ||||
4056 | |||||
4057 | intersect = isl_basic_map_plain_is_universe(bmap2); | ||||
4058 | if (intersect < 0 || intersect) | ||||
4059 | return isl_bool_not(intersect); | ||||
4060 | |||||
4061 | test = isl_basic_map_intersect(isl_basic_map_copy(bmap1), | ||||
4062 | isl_basic_map_copy(bmap2)); | ||||
4063 | disjoint = isl_basic_map_is_empty(test); | ||||
4064 | isl_basic_map_free(test); | ||||
4065 | |||||
4066 | return disjoint; | ||||
4067 | } | ||||
4068 | |||||
4069 | /* Are "bset1" and "bset2" disjoint? | ||||
4070 | */ | ||||
4071 | isl_bool isl_basic_set_is_disjoint(__isl_keep isl_basic_setisl_basic_map *bset1, | ||||
4072 | __isl_keep isl_basic_setisl_basic_map *bset2) | ||||
4073 | { | ||||
4074 | return isl_basic_map_is_disjoint(bset1, bset2); | ||||
4075 | } | ||||
4076 | |||||
4077 | isl_bool isl_set_plain_is_disjoint(__isl_keep isl_setisl_map *set1, | ||||
4078 | __isl_keep isl_setisl_map *set2) | ||||
4079 | { | ||||
4080 | return isl_map_plain_is_disjoint(set_to_map(set1), set_to_map(set2)); | ||||
4081 | } | ||||
4082 | |||||
4083 | /* Are "set1" and "set2" disjoint? | ||||
4084 | */ | ||||
4085 | isl_bool isl_set_is_disjoint(__isl_keep isl_setisl_map *set1, __isl_keep isl_setisl_map *set2) | ||||
4086 | { | ||||
4087 | return isl_map_is_disjoint(set1, set2); | ||||
4088 | } | ||||
4089 | |||||
4090 | /* Is "v" equal to 0, 1 or -1? | ||||
4091 | */ | ||||
4092 | static int is_zero_or_one(isl_int v) | ||||
4093 | { | ||||
4094 | 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); | ||||
4095 | } | ||||
4096 | |||||
4097 | /* Are the "n" coefficients starting at "first" of inequality constraints | ||||
4098 | * "i" and "j" of "bmap" opposite to each other? | ||||
4099 | */ | ||||
4100 | static int is_opposite_part(__isl_keep isl_basic_map *bmap, int i, int j, | ||||
4101 | int first, int n) | ||||
4102 | { | ||||
4103 | return isl_seq_is_neg(bmap->ineq[i] + first, bmap->ineq[j] + first, n); | ||||
4104 | } | ||||
4105 | |||||
4106 | /* Are inequality constraints "i" and "j" of "bmap" opposite to each other, | ||||
4107 | * apart from the constant term? | ||||
4108 | */ | ||||
4109 | static isl_bool is_opposite(__isl_keep isl_basic_map *bmap, int i, int j) | ||||
4110 | { | ||||
4111 | isl_size total; | ||||
4112 | |||||
4113 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
4114 | if (total < 0) | ||||
4115 | return isl_bool_error; | ||||
4116 | return is_opposite_part(bmap, i, j, 1, total); | ||||
4117 | } | ||||
4118 | |||||
4119 | /* Check if we can combine a given div with lower bound l and upper | ||||
4120 | * bound u with some other div and if so return that other div. | ||||
4121 | * Otherwise, return a position beyond the integer divisions. | ||||
4122 | * Return -1 on error. | ||||
4123 | * | ||||
4124 | * We first check that | ||||
4125 | * - the bounds are opposites of each other (except for the constant | ||||
4126 | * term) | ||||
4127 | * - the bounds do not reference any other div | ||||
4128 | * - no div is defined in terms of this div | ||||
4129 | * | ||||
4130 | * Let m be the size of the range allowed on the div by the bounds. | ||||
4131 | * That is, the bounds are of the form | ||||
4132 | * | ||||
4133 | * e <= a <= e + m - 1 | ||||
4134 | * | ||||
4135 | * with e some expression in the other variables. | ||||
4136 | * We look for another div b such that no third div is defined in terms | ||||
4137 | * of this second div b and such that in any constraint that contains | ||||
4138 | * a (except for the given lower and upper bound), also contains b | ||||
4139 | * with a coefficient that is m times that of b. | ||||
4140 | * That is, all constraints (except for the lower and upper bound) | ||||
4141 | * are of the form | ||||
4142 | * | ||||
4143 | * e + f (a + m b) >= 0 | ||||
4144 | * | ||||
4145 | * Furthermore, in the constraints that only contain b, the coefficient | ||||
4146 | * of b should be equal to 1 or -1. | ||||
4147 | * If so, we return b so that "a + m b" can be replaced by | ||||
4148 | * a single div "c = a + m b". | ||||
4149 | */ | ||||
4150 | static int div_find_coalesce(__isl_keep isl_basic_map *bmap, int *pairs, | ||||
4151 | unsigned div, unsigned l, unsigned u) | ||||
4152 | { | ||||
4153 | int i, j; | ||||
4154 | unsigned n_div; | ||||
4155 | isl_size v_div; | ||||
4156 | int coalesce; | ||||
4157 | isl_bool opp; | ||||
4158 | |||||
4159 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
4160 | if (n_div <= 1) | ||||
4161 | return n_div; | ||||
4162 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
4163 | if (v_div < 0) | ||||
4164 | return -1; | ||||
4165 | if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + v_div, div) != -1) | ||||
4166 | return n_div; | ||||
4167 | if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + v_div + div + 1, | ||||
4168 | n_div - div - 1) != -1) | ||||
4169 | return n_div; | ||||
4170 | opp = is_opposite(bmap, l, u); | ||||
4171 | if (opp < 0 || !opp) | ||||
4172 | return opp < 0 ? -1 : n_div; | ||||
4173 | |||||
4174 | for (i = 0; i < n_div; ++i) { | ||||
4175 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
4176 | continue; | ||||
4177 | 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)) | ||||
4178 | return n_div; | ||||
4179 | } | ||||
4180 | |||||
4181 | 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])); | ||||
4182 | if (isl_int_is_neg(bmap->ineq[l][0])(isl_sioimath_sgn(*(bmap->ineq[l][0])) < 0)) { | ||||
4183 | isl_int_sub(bmap->ineq[l][0],isl_sioimath_sub((bmap->ineq[l][0]), *(bmap->ineq[l][0] ), *(bmap->ineq[u][0])) | ||||
4184 | bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_sub((bmap->ineq[l][0]), *(bmap->ineq[l][0] ), *(bmap->ineq[u][0])); | ||||
4185 | bmap = isl_basic_map_copy(bmap); | ||||
4186 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
4187 | isl_basic_map_free(bmap); | ||||
4188 | return n_div; | ||||
4189 | } | ||||
4190 | 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); | ||||
4191 | coalesce = n_div; | ||||
4192 | for (i = 0; i < n_div; ++i) { | ||||
4193 | if (i == div) | ||||
4194 | continue; | ||||
4195 | if (!pairs[i]) | ||||
4196 | continue; | ||||
4197 | for (j = 0; j < n_div; ++j) { | ||||
4198 | if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0)) | ||||
4199 | continue; | ||||
4200 | 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 )) | ||||
4201 | break; | ||||
4202 | } | ||||
4203 | if (j < n_div) | ||||
4204 | continue; | ||||
4205 | for (j = 0; j < bmap->n_ineq; ++j) { | ||||
4206 | int valid; | ||||
4207 | if (j == l || j == u) | ||||
4208 | continue; | ||||
4209 | if (isl_int_is_zero(bmap->ineq[j][1 + v_div + div])(isl_sioimath_sgn(*(bmap->ineq[j][1 + v_div + div])) == 0)) { | ||||
4210 | if (is_zero_or_one(bmap->ineq[j][1 + v_div + i])) | ||||
4211 | continue; | ||||
4212 | break; | ||||
4213 | } | ||||
4214 | if (isl_int_is_zero(bmap->ineq[j][1 + v_div + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + v_div + i])) == 0)) | ||||
4215 | break; | ||||
4216 | 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])) | ||||
4217 | 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])) | ||||
4218 | 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])); | ||||
4219 | 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) | ||||
4220 | 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); | ||||
4221 | 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])) | ||||
4222 | 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])) | ||||
4223 | 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])); | ||||
4224 | if (!valid) | ||||
4225 | break; | ||||
4226 | } | ||||
4227 | if (j < bmap->n_ineq) | ||||
4228 | continue; | ||||
4229 | coalesce = i; | ||||
4230 | break; | ||||
4231 | } | ||||
4232 | 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); | ||||
4233 | 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])); | ||||
4234 | return coalesce; | ||||
4235 | } | ||||
4236 | |||||
4237 | /* Internal data structure used during the construction and/or evaluation of | ||||
4238 | * an inequality that ensures that a pair of bounds always allows | ||||
4239 | * for an integer value. | ||||
4240 | * | ||||
4241 | * "tab" is the tableau in which the inequality is evaluated. It may | ||||
4242 | * be NULL until it is actually needed. | ||||
4243 | * "v" contains the inequality coefficients. | ||||
4244 | * "g", "fl" and "fu" are temporary scalars used during the construction and | ||||
4245 | * evaluation. | ||||
4246 | */ | ||||
4247 | struct test_ineq_data { | ||||
4248 | struct isl_tab *tab; | ||||
4249 | isl_vec *v; | ||||
4250 | isl_int g; | ||||
4251 | isl_int fl; | ||||
4252 | isl_int fu; | ||||
4253 | }; | ||||
4254 | |||||
4255 | /* Free all the memory allocated by the fields of "data". | ||||
4256 | */ | ||||
4257 | static void test_ineq_data_clear(struct test_ineq_data *data) | ||||
4258 | { | ||||
4259 | isl_tab_free(data->tab); | ||||
4260 | isl_vec_free(data->v); | ||||
4261 | isl_int_clear(data->g)isl_sioimath_clear((data->g)); | ||||
4262 | isl_int_clear(data->fl)isl_sioimath_clear((data->fl)); | ||||
4263 | isl_int_clear(data->fu)isl_sioimath_clear((data->fu)); | ||||
4264 | } | ||||
4265 | |||||
4266 | /* Is the inequality stored in data->v satisfied by "bmap"? | ||||
4267 | * That is, does it only attain non-negative values? | ||||
4268 | * data->tab is a tableau corresponding to "bmap". | ||||
4269 | */ | ||||
4270 | static isl_bool test_ineq_is_satisfied(__isl_keep isl_basic_map *bmap, | ||||
4271 | struct test_ineq_data *data) | ||||
4272 | { | ||||
4273 | isl_ctx *ctx; | ||||
4274 | enum isl_lp_result res; | ||||
4275 | |||||
4276 | ctx = isl_basic_map_get_ctx(bmap); | ||||
4277 | if (!data->tab) | ||||
4278 | data->tab = isl_tab_from_basic_map(bmap, 0); | ||||
4279 | res = isl_tab_min(data->tab, data->v->el, ctx->one, &data->g, NULL((void*)0), 0); | ||||
4280 | if (res == isl_lp_error) | ||||
4281 | return isl_bool_error; | ||||
4282 | return res == isl_lp_ok && isl_int_is_nonneg(data->g)(isl_sioimath_sgn(*(data->g)) >= 0); | ||||
4283 | } | ||||
4284 | |||||
4285 | /* Given a lower and an upper bound on div i, do they always allow | ||||
4286 | * for an integer value of the given div? | ||||
4287 | * Determine this property by constructing an inequality | ||||
4288 | * such that the property is guaranteed when the inequality is nonnegative. | ||||
4289 | * The lower bound is inequality l, while the upper bound is inequality u. | ||||
4290 | * The constructed inequality is stored in data->v. | ||||
4291 | * | ||||
4292 | * Let the upper bound be | ||||
4293 | * | ||||
4294 | * -n_u a + e_u >= 0 | ||||
4295 | * | ||||
4296 | * and the lower bound | ||||
4297 | * | ||||
4298 | * n_l a + e_l >= 0 | ||||
4299 | * | ||||
4300 | * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l). | ||||
4301 | * We have | ||||
4302 | * | ||||
4303 | * - f_u e_l <= f_u f_l g a <= f_l e_u | ||||
4304 | * | ||||
4305 | * Since all variables are integer valued, this is equivalent to | ||||
4306 | * | ||||
4307 | * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1) | ||||
4308 | * | ||||
4309 | * If this interval is at least f_u f_l g, then it contains at least | ||||
4310 | * one integer value for a. | ||||
4311 | * That is, the test constraint is | ||||
4312 | * | ||||
4313 | * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g | ||||
4314 | * | ||||
4315 | * or | ||||
4316 | * | ||||
4317 | * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0 | ||||
4318 | * | ||||
4319 | * If the coefficients of f_l e_u + f_u e_l have a common divisor g', | ||||
4320 | * then the constraint can be scaled down by a factor g', | ||||
4321 | * with the constant term replaced by | ||||
4322 | * floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g'). | ||||
4323 | * Note that the result of applying Fourier-Motzkin to this pair | ||||
4324 | * of constraints is | ||||
4325 | * | ||||
4326 | * f_l e_u + f_u e_l >= 0 | ||||
4327 | * | ||||
4328 | * If the constant term of the scaled down version of this constraint, | ||||
4329 | * i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant | ||||
4330 | * term of the scaled down test constraint, then the test constraint | ||||
4331 | * is known to hold and no explicit evaluation is required. | ||||
4332 | * This is essentially the Omega test. | ||||
4333 | * | ||||
4334 | * If the test constraint consists of only a constant term, then | ||||
4335 | * it is sufficient to look at the sign of this constant term. | ||||
4336 | */ | ||||
4337 | static isl_bool int_between_bounds(__isl_keep isl_basic_map *bmap, int i, | ||||
4338 | int l, int u, struct test_ineq_data *data) | ||||
4339 | { | ||||
4340 | unsigned offset; | ||||
4341 | isl_size n_div; | ||||
4342 | |||||
4343 | offset = isl_basic_map_offset(bmap, isl_dim_div); | ||||
4344 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
4345 | if (n_div < 0) | ||||
4346 | return isl_bool_error; | ||||
4347 | |||||
4348 | isl_int_gcd(data->g,isl_sioimath_gcd((data->g), *(bmap->ineq[l][offset + i] ), *(bmap->ineq[u][offset + i])) | ||||
4349 | 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])); | ||||
4350 | 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)); | ||||
4351 | 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)); | ||||
4352 | isl_int_neg(data->fu, data->fu)isl_sioimath_neg((data->fu), *(data->fu)); | ||||
4353 | isl_seq_combine(data->v->el, data->fl, bmap->ineq[u], | ||||
4354 | data->fu, bmap->ineq[l], offset + n_div); | ||||
4355 | isl_int_mul(data->g, data->g, data->fl)isl_sioimath_mul((data->g), *(data->g), *(data->fl)); | ||||
4356 | isl_int_mul(data->g, data->g, data->fu)isl_sioimath_mul((data->g), *(data->g), *(data->fu)); | ||||
4357 | isl_int_sub(data->g, data->g, data->fl)isl_sioimath_sub((data->g), *(data->g), *(data->fl)); | ||||
4358 | isl_int_sub(data->g, data->g, data->fu)isl_sioimath_sub((data->g), *(data->g), *(data->fu)); | ||||
4359 | isl_int_add_ui(data->g, data->g, 1)isl_sioimath_add_ui((data->g), *(data->g), 1); | ||||
4360 | isl_int_sub(data->fl, data->v->el[0], data->g)isl_sioimath_sub((data->fl), *(data->v->el[0]), *(data ->g)); | ||||
4361 | |||||
4362 | isl_seq_gcd(data->v->el + 1, offset - 1 + n_div, &data->g); | ||||
4363 | if (isl_int_is_zero(data->g)(isl_sioimath_sgn(*(data->g)) == 0)) | ||||
4364 | return isl_int_is_nonneg(data->fl)(isl_sioimath_sgn(*(data->fl)) >= 0); | ||||
4365 | if (isl_int_is_one(data->g)(isl_sioimath_cmp_si(*(data->g), 1) == 0)) { | ||||
4366 | isl_int_set(data->v->el[0], data->fl)isl_sioimath_set((data->v->el[0]), *(data->fl)); | ||||
4367 | return test_ineq_is_satisfied(bmap, data); | ||||
4368 | } | ||||
4369 | isl_int_fdiv_q(data->fl, data->fl, data->g)isl_sioimath_fdiv_q((data->fl), *(data->fl), *(data-> g)); | ||||
4370 | 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)); | ||||
4371 | if (isl_int_eq(data->fl, data->v->el[0])(isl_sioimath_cmp(*(data->fl), *(data->v->el[0])) == 0)) | ||||
4372 | return isl_bool_true; | ||||
4373 | isl_int_set(data->v->el[0], data->fl)isl_sioimath_set((data->v->el[0]), *(data->fl)); | ||||
4374 | isl_seq_scale_down(data->v->el + 1, data->v->el + 1, data->g, | ||||
4375 | offset - 1 + n_div); | ||||
4376 | |||||
4377 | return test_ineq_is_satisfied(bmap, data); | ||||
4378 | } | ||||
4379 | |||||
4380 | /* Remove more kinds of divs that are not strictly needed. | ||||
4381 | * In particular, if all pairs of lower and upper bounds on a div | ||||
4382 | * are such that they allow at least one integer value of the div, | ||||
4383 | * then we can eliminate the div using Fourier-Motzkin without | ||||
4384 | * introducing any spurious solutions. | ||||
4385 | * | ||||
4386 | * If at least one of the two constraints has a unit coefficient for the div, | ||||
4387 | * then the presence of such a value is guaranteed so there is no need to check. | ||||
4388 | * In particular, the value attained by the bound with unit coefficient | ||||
4389 | * can serve as this intermediate value. | ||||
4390 | */ | ||||
4391 | static __isl_give isl_basic_map *drop_more_redundant_divs( | ||||
4392 | __isl_take isl_basic_map *bmap, __isl_take int *pairs, int n) | ||||
4393 | { | ||||
4394 | isl_ctx *ctx; | ||||
4395 | struct test_ineq_data data = { NULL((void*)0), NULL((void*)0) }; | ||||
4396 | unsigned off; | ||||
4397 | isl_size n_div; | ||||
4398 | int remove = -1; | ||||
4399 | |||||
4400 | isl_int_init(data.g)isl_sioimath_init((data.g)); | ||||
4401 | isl_int_init(data.fl)isl_sioimath_init((data.fl)); | ||||
4402 | isl_int_init(data.fu)isl_sioimath_init((data.fu)); | ||||
4403 | |||||
4404 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
4405 | if (n_div < 0) | ||||
4406 | goto error; | ||||
4407 | |||||
4408 | ctx = isl_basic_map_get_ctx(bmap); | ||||
4409 | off = isl_basic_map_offset(bmap, isl_dim_div); | ||||
4410 | data.v = isl_vec_alloc(ctx, off + n_div); | ||||
4411 | if (!data.v) | ||||
4412 | goto error; | ||||
4413 | |||||
4414 | while (n > 0) { | ||||
4415 | int i, l, u; | ||||
4416 | int best = -1; | ||||
4417 | isl_bool has_int; | ||||
4418 | |||||
4419 | for (i = 0; i < n_div; ++i) { | ||||
4420 | if (!pairs[i]) | ||||
4421 | continue; | ||||
4422 | if (best >= 0 && pairs[best] <= pairs[i]) | ||||
4423 | continue; | ||||
4424 | best = i; | ||||
4425 | } | ||||
4426 | |||||
4427 | i = best; | ||||
4428 | for (l = 0; l < bmap->n_ineq; ++l) { | ||||
4429 | if (!isl_int_is_pos(bmap->ineq[l][off + i])(isl_sioimath_sgn(*(bmap->ineq[l][off + i])) > 0)) | ||||
4430 | continue; | ||||
4431 | if (isl_int_is_one(bmap->ineq[l][off + i])(isl_sioimath_cmp_si(*(bmap->ineq[l][off + i]), 1) == 0)) | ||||
4432 | continue; | ||||
4433 | for (u = 0; u < bmap->n_ineq; ++u) { | ||||
4434 | if (!isl_int_is_neg(bmap->ineq[u][off + i])(isl_sioimath_sgn(*(bmap->ineq[u][off + i])) < 0)) | ||||
4435 | continue; | ||||
4436 | if (isl_int_is_negone(bmap->ineq[u][off + i])(isl_sioimath_cmp_si(*(bmap->ineq[u][off + i]), -1) == 0)) | ||||
4437 | continue; | ||||
4438 | has_int = int_between_bounds(bmap, i, l, u, | ||||
4439 | &data); | ||||
4440 | if (has_int < 0) | ||||
4441 | goto error; | ||||
4442 | if (data.tab && data.tab->empty) | ||||
4443 | break; | ||||
4444 | if (!has_int) | ||||
4445 | break; | ||||
4446 | } | ||||
4447 | if (u < bmap->n_ineq) | ||||
4448 | break; | ||||
4449 | } | ||||
4450 | if (data.tab && data.tab->empty) { | ||||
4451 | bmap = isl_basic_map_set_to_empty(bmap); | ||||
4452 | break; | ||||
4453 | } | ||||
4454 | if (l == bmap->n_ineq) { | ||||
4455 | remove = i; | ||||
4456 | break; | ||||
4457 | } | ||||
4458 | pairs[i] = 0; | ||||
4459 | --n; | ||||
4460 | } | ||||
4461 | |||||
4462 | test_ineq_data_clear(&data); | ||||
4463 | |||||
4464 | free(pairs); | ||||
4465 | |||||
4466 | if (remove < 0) | ||||
4467 | return bmap; | ||||
4468 | |||||
4469 | bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1); | ||||
4470 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
4471 | error: | ||||
4472 | free(pairs); | ||||
4473 | isl_basic_map_free(bmap); | ||||
4474 | test_ineq_data_clear(&data); | ||||
4475 | return NULL((void*)0); | ||||
4476 | } | ||||
4477 | |||||
4478 | /* Given a pair of divs div1 and div2 such that, except for the lower bound l | ||||
4479 | * and the upper bound u, div1 always occurs together with div2 in the form | ||||
4480 | * (div1 + m div2), where m is the constant range on the variable div1 | ||||
4481 | * allowed by l and u, replace the pair div1 and div2 by a single | ||||
4482 | * div that is equal to div1 + m div2. | ||||
4483 | * | ||||
4484 | * The new div will appear in the location that contains div2. | ||||
4485 | * We need to modify all constraints that contain | ||||
4486 | * div2 = (div - div1) / m | ||||
4487 | * The coefficient of div2 is known to be equal to 1 or -1. | ||||
4488 | * (If a constraint does not contain div2, it will also not contain div1.) | ||||
4489 | * If the constraint also contains div1, then we know they appear | ||||
4490 | * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div, | ||||
4491 | * i.e., the coefficient of div is f. | ||||
4492 | * | ||||
4493 | * Otherwise, we first need to introduce div1 into the constraint. | ||||
4494 | * Let l be | ||||
4495 | * | ||||
4496 | * div1 + f >=0 | ||||
4497 | * | ||||
4498 | * and u | ||||
4499 | * | ||||
4500 | * -div1 + f' >= 0 | ||||
4501 | * | ||||
4502 | * A lower bound on div2 | ||||
4503 | * | ||||
4504 | * div2 + t >= 0 | ||||
4505 | * | ||||
4506 | * can be replaced by | ||||
4507 | * | ||||
4508 | * m div2 + div1 + m t + f >= 0 | ||||
4509 | * | ||||
4510 | * An upper bound | ||||
4511 | * | ||||
4512 | * -div2 + t >= 0 | ||||
4513 | * | ||||
4514 | * can be replaced by | ||||
4515 | * | ||||
4516 | * -(m div2 + div1) + m t + f' >= 0 | ||||
4517 | * | ||||
4518 | * These constraint are those that we would obtain from eliminating | ||||
4519 | * div1 using Fourier-Motzkin. | ||||
4520 | * | ||||
4521 | * After all constraints have been modified, we drop the lower and upper | ||||
4522 | * bound and then drop div1. | ||||
4523 | * Since the new div is only placed in the same location that used | ||||
4524 | * to store div2, but otherwise has a different meaning, any possible | ||||
4525 | * explicit representation of the original div2 is removed. | ||||
4526 | */ | ||||
4527 | static __isl_give isl_basic_map *coalesce_divs(__isl_take isl_basic_map *bmap, | ||||
4528 | unsigned div1, unsigned div2, unsigned l, unsigned u) | ||||
4529 | { | ||||
4530 | isl_ctx *ctx; | ||||
4531 | isl_int m; | ||||
4532 | isl_size v_div; | ||||
4533 | unsigned total; | ||||
4534 | int i; | ||||
4535 | |||||
4536 | ctx = isl_basic_map_get_ctx(bmap); | ||||
4537 | |||||
4538 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
4539 | if (v_div < 0) | ||||
4540 | return isl_basic_map_free(bmap); | ||||
4541 | total = 1 + v_div + bmap->n_div; | ||||
4542 | |||||
4543 | isl_int_init(m)isl_sioimath_init((m)); | ||||
4544 | isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_add((m), *(bmap->ineq[l][0]), *(bmap->ineq [u][0])); | ||||
4545 | isl_int_add_ui(m, m, 1)isl_sioimath_add_ui((m), *(m), 1); | ||||
4546 | |||||
4547 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
4548 | if (i == l || i == u) | ||||
4549 | continue; | ||||
4550 | if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div2])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div2])) == 0 )) | ||||
4551 | continue; | ||||
4552 | if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div1])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div1])) == 0 )) { | ||||
4553 | if (isl_int_is_pos(bmap->ineq[i][1 + v_div + div2])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div2])) > 0)) | ||||
4554 | isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i], | ||||
4555 | ctx->one, bmap->ineq[l], total); | ||||
4556 | else | ||||
4557 | isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i], | ||||
4558 | ctx->one, bmap->ineq[u], total); | ||||
4559 | } | ||||
4560 | 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])) | ||||
4561 | bmap->ineq[i][1 + v_div + div1])isl_sioimath_set((bmap->ineq[i][1 + v_div + div2]), *(bmap ->ineq[i][1 + v_div + div1])); | ||||
4562 | isl_int_set_si(bmap->ineq[i][1 + v_div + div1], 0)isl_sioimath_set_si((bmap->ineq[i][1 + v_div + div1]), 0); | ||||
4563 | } | ||||
4564 | |||||
4565 | isl_int_clear(m)isl_sioimath_clear((m)); | ||||
4566 | if (l > u) { | ||||
4567 | isl_basic_map_drop_inequality(bmap, l); | ||||
4568 | isl_basic_map_drop_inequality(bmap, u); | ||||
4569 | } else { | ||||
4570 | isl_basic_map_drop_inequality(bmap, u); | ||||
4571 | isl_basic_map_drop_inequality(bmap, l); | ||||
4572 | } | ||||
4573 | bmap = isl_basic_map_mark_div_unknown(bmap, div2); | ||||
4574 | bmap = isl_basic_map_drop_div(bmap, div1); | ||||
4575 | return bmap; | ||||
4576 | } | ||||
4577 | |||||
4578 | /* First check if we can coalesce any pair of divs and | ||||
4579 | * then continue with dropping more redundant divs. | ||||
4580 | * | ||||
4581 | * We loop over all pairs of lower and upper bounds on a div | ||||
4582 | * with coefficient 1 and -1, respectively, check if there | ||||
4583 | * is any other div "c" with which we can coalesce the div | ||||
4584 | * and if so, perform the coalescing. | ||||
4585 | */ | ||||
4586 | static __isl_give isl_basic_map *coalesce_or_drop_more_redundant_divs( | ||||
4587 | __isl_take isl_basic_map *bmap, int *pairs, int n) | ||||
4588 | { | ||||
4589 | int i, l, u; | ||||
4590 | isl_size v_div; | ||||
4591 | isl_size n_div; | ||||
4592 | |||||
4593 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
4594 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
4595 | if (v_div < 0 || n_div < 0) | ||||
4596 | return isl_basic_map_free(bmap); | ||||
4597 | |||||
4598 | for (i = 0; i < n_div; ++i) { | ||||
4599 | if (!pairs[i]) | ||||
4600 | continue; | ||||
4601 | for (l = 0; l < bmap->n_ineq; ++l) { | ||||
4602 | 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)) | ||||
4603 | continue; | ||||
4604 | for (u = 0; u < bmap->n_ineq; ++u) { | ||||
4605 | int c; | ||||
4606 | |||||
4607 | 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 )) | ||||
4608 | continue; | ||||
4609 | c = div_find_coalesce(bmap, pairs, i, l, u); | ||||
4610 | if (c < 0) | ||||
4611 | goto error; | ||||
4612 | if (c >= n_div) | ||||
4613 | continue; | ||||
4614 | free(pairs); | ||||
4615 | bmap = coalesce_divs(bmap, i, c, l, u); | ||||
4616 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
4617 | } | ||||
4618 | } | ||||
4619 | } | ||||
4620 | |||||
4621 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1))))) { | ||||
4622 | free(pairs); | ||||
4623 | return bmap; | ||||
4624 | } | ||||
4625 | |||||
4626 | return drop_more_redundant_divs(bmap, pairs, n); | ||||
4627 | error: | ||||
4628 | free(pairs); | ||||
4629 | isl_basic_map_free(bmap); | ||||
4630 | return NULL((void*)0); | ||||
4631 | } | ||||
4632 | |||||
4633 | /* Are the "n" coefficients starting at "first" of inequality constraints | ||||
4634 | * "i" and "j" of "bmap" equal to each other? | ||||
4635 | */ | ||||
4636 | static int is_parallel_part(__isl_keep isl_basic_map *bmap, int i, int j, | ||||
4637 | int first, int n) | ||||
4638 | { | ||||
4639 | return isl_seq_eq(bmap->ineq[i] + first, bmap->ineq[j] + first, n); | ||||
4640 | } | ||||
4641 | |||||
4642 | /* Are inequality constraints "i" and "j" of "bmap" equal to each other, | ||||
4643 | * apart from the constant term and the coefficient at position "pos"? | ||||
4644 | */ | ||||
4645 | static isl_bool is_parallel_except(__isl_keep isl_basic_map *bmap, int i, int j, | ||||
4646 | int pos) | ||||
4647 | { | ||||
4648 | isl_size total; | ||||
4649 | |||||
4650 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
4651 | if (total < 0) | ||||
4652 | return isl_bool_error; | ||||
4653 | return is_parallel_part(bmap, i, j, 1, pos - 1) && | ||||
4654 | is_parallel_part(bmap, i, j, pos + 1, total - pos); | ||||
4655 | } | ||||
4656 | |||||
4657 | /* Are inequality constraints "i" and "j" of "bmap" opposite to each other, | ||||
4658 | * apart from the constant term and the coefficient at position "pos"? | ||||
4659 | */ | ||||
4660 | static isl_bool is_opposite_except(__isl_keep isl_basic_map *bmap, int i, int j, | ||||
4661 | int pos) | ||||
4662 | { | ||||
4663 | isl_size total; | ||||
4664 | |||||
4665 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
4666 | if (total < 0) | ||||
4667 | return isl_bool_error; | ||||
4668 | return is_opposite_part(bmap, i, j, 1, pos - 1) && | ||||
4669 | is_opposite_part(bmap, i, j, pos + 1, total - pos); | ||||
4670 | } | ||||
4671 | |||||
4672 | /* Restart isl_basic_map_drop_redundant_divs after "bmap" has | ||||
4673 | * been modified, simplying it if "simplify" is set. | ||||
4674 | * Free the temporary data structure "pairs" that was associated | ||||
4675 | * to the old version of "bmap". | ||||
4676 | */ | ||||
4677 | static __isl_give isl_basic_map *drop_redundant_divs_again( | ||||
4678 | __isl_take isl_basic_map *bmap, __isl_take int *pairs, int simplify) | ||||
4679 | { | ||||
4680 | if (simplify
| ||||
4681 | bmap = isl_basic_map_simplify(bmap); | ||||
4682 | free(pairs); | ||||
4683 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
4684 | } | ||||
4685 | |||||
4686 | /* Is "div" the single unknown existentially quantified variable | ||||
4687 | * in inequality constraint "ineq" of "bmap"? | ||||
4688 | * "div" is known to have a non-zero coefficient in "ineq". | ||||
4689 | */ | ||||
4690 | static isl_bool single_unknown(__isl_keep isl_basic_map *bmap, int ineq, | ||||
4691 | int div) | ||||
4692 | { | ||||
4693 | int i; | ||||
4694 | isl_size n_div; | ||||
4695 | unsigned o_div; | ||||
4696 | isl_bool known; | ||||
4697 | |||||
4698 | known = isl_basic_map_div_is_known(bmap, div); | ||||
4699 | if (known < 0 || known) | ||||
4700 | return isl_bool_not(known); | ||||
4701 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
4702 | if (n_div < 0) | ||||
4703 | return isl_bool_error; | ||||
4704 | if (n_div == 1) | ||||
4705 | return isl_bool_true; | ||||
4706 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
4707 | for (i = 0; i < n_div; ++i) { | ||||
4708 | isl_bool known; | ||||
4709 | |||||
4710 | if (i == div) | ||||
4711 | continue; | ||||
4712 | if (isl_int_is_zero(bmap->ineq[ineq][o_div + i])(isl_sioimath_sgn(*(bmap->ineq[ineq][o_div + i])) == 0)) | ||||
4713 | continue; | ||||
4714 | known = isl_basic_map_div_is_known(bmap, i); | ||||
4715 | if (known < 0 || !known) | ||||
4716 | return known; | ||||
4717 | } | ||||
4718 | |||||
4719 | return isl_bool_true; | ||||
4720 | } | ||||
4721 | |||||
4722 | /* Does integer division "div" have coefficient 1 in inequality constraint | ||||
4723 | * "ineq" of "map"? | ||||
4724 | */ | ||||
4725 | static isl_bool has_coef_one(__isl_keep isl_basic_map *bmap, int div, int ineq) | ||||
4726 | { | ||||
4727 | unsigned o_div; | ||||
4728 | |||||
4729 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
4730 | if (isl_int_is_one(bmap->ineq[ineq][o_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[ineq][o_div + div]), 1) == 0)) | ||||
4731 | return isl_bool_true; | ||||
4732 | |||||
4733 | return isl_bool_false; | ||||
4734 | } | ||||
4735 | |||||
4736 | /* Turn inequality constraint "ineq" of "bmap" into an equality and | ||||
4737 | * then try and drop redundant divs again, | ||||
4738 | * freeing the temporary data structure "pairs" that was associated | ||||
4739 | * to the old version of "bmap". | ||||
4740 | */ | ||||
4741 | static __isl_give isl_basic_map *set_eq_and_try_again( | ||||
4742 | __isl_take isl_basic_map *bmap, int ineq, __isl_take int *pairs) | ||||
4743 | { | ||||
4744 | bmap = isl_basic_map_cow(bmap); | ||||
4745 | isl_basic_map_inequality_to_equality(bmap, ineq); | ||||
4746 | return drop_redundant_divs_again(bmap, pairs, 1); | ||||
| |||||
4747 | } | ||||
4748 | |||||
4749 | /* Drop the integer division at position "div", along with the two | ||||
4750 | * inequality constraints "ineq1" and "ineq2" in which it appears | ||||
4751 | * from "bmap" and then try and drop redundant divs again, | ||||
4752 | * freeing the temporary data structure "pairs" that was associated | ||||
4753 | * to the old version of "bmap". | ||||
4754 | */ | ||||
4755 | static __isl_give isl_basic_map *drop_div_and_try_again( | ||||
4756 | __isl_take isl_basic_map *bmap, int div, int ineq1, int ineq2, | ||||
4757 | __isl_take int *pairs) | ||||
4758 | { | ||||
4759 | if (ineq1 > ineq2) { | ||||
4760 | isl_basic_map_drop_inequality(bmap, ineq1); | ||||
4761 | isl_basic_map_drop_inequality(bmap, ineq2); | ||||
4762 | } else { | ||||
4763 | isl_basic_map_drop_inequality(bmap, ineq2); | ||||
4764 | isl_basic_map_drop_inequality(bmap, ineq1); | ||||
4765 | } | ||||
4766 | bmap = isl_basic_map_drop_div(bmap, div); | ||||
4767 | return drop_redundant_divs_again(bmap, pairs, 0); | ||||
4768 | } | ||||
4769 | |||||
4770 | /* Given two inequality constraints | ||||
4771 | * | ||||
4772 | * f(x) + n d + c >= 0, (ineq) | ||||
4773 | * | ||||
4774 | * with d the variable at position "pos", and | ||||
4775 | * | ||||
4776 | * f(x) + c0 >= 0, (lower) | ||||
4777 | * | ||||
4778 | * compute the maximal value of the lower bound ceil((-f(x) - c)/n) | ||||
4779 | * determined by the first constraint. | ||||
4780 | * That is, store | ||||
4781 | * | ||||
4782 | * ceil((c0 - c)/n) | ||||
4783 | * | ||||
4784 | * in *l. | ||||
4785 | */ | ||||
4786 | static void lower_bound_from_parallel(__isl_keep isl_basic_map *bmap, | ||||
4787 | int ineq, int lower, int pos, isl_int *l) | ||||
4788 | { | ||||
4789 | isl_int_neg(*l, bmap->ineq[ineq][0])isl_sioimath_neg((*l), *(bmap->ineq[ineq][0])); | ||||
4790 | isl_int_add(*l, *l, bmap->ineq[lower][0])isl_sioimath_add((*l), *(*l), *(bmap->ineq[lower][0])); | ||||
4791 | isl_int_cdiv_q(*l, *l, bmap->ineq[ineq][pos])isl_sioimath_cdiv_q((*l), *(*l), *(bmap->ineq[ineq][pos])); | ||||
4792 | } | ||||
4793 | |||||
4794 | /* Given two inequality constraints | ||||
4795 | * | ||||
4796 | * f(x) + n d + c >= 0, (ineq) | ||||
4797 | * | ||||
4798 | * with d the variable at position "pos", and | ||||
4799 | * | ||||
4800 | * -f(x) - c0 >= 0, (upper) | ||||
4801 | * | ||||
4802 | * compute the minimal value of the lower bound ceil((-f(x) - c)/n) | ||||
4803 | * determined by the first constraint. | ||||
4804 | * That is, store | ||||
4805 | * | ||||
4806 | * ceil((-c1 - c)/n) | ||||
4807 | * | ||||
4808 | * in *u. | ||||
4809 | */ | ||||
4810 | static void lower_bound_from_opposite(__isl_keep isl_basic_map *bmap, | ||||
4811 | int ineq, int upper, int pos, isl_int *u) | ||||
4812 | { | ||||
4813 | isl_int_neg(*u, bmap->ineq[ineq][0])isl_sioimath_neg((*u), *(bmap->ineq[ineq][0])); | ||||
4814 | isl_int_sub(*u, *u, bmap->ineq[upper][0])isl_sioimath_sub((*u), *(*u), *(bmap->ineq[upper][0])); | ||||
4815 | isl_int_cdiv_q(*u, *u, bmap->ineq[ineq][pos])isl_sioimath_cdiv_q((*u), *(*u), *(bmap->ineq[ineq][pos])); | ||||
4816 | } | ||||
4817 | |||||
4818 | /* Given a lower bound constraint "ineq" on "div" in "bmap", | ||||
4819 | * does the corresponding lower bound have a fixed value in "bmap"? | ||||
4820 | * | ||||
4821 | * In particular, "ineq" is of the form | ||||
4822 | * | ||||
4823 | * f(x) + n d + c >= 0 | ||||
4824 | * | ||||
4825 | * with n > 0, c the constant term and | ||||
4826 | * d the existentially quantified variable "div". | ||||
4827 | * That is, the lower bound is | ||||
4828 | * | ||||
4829 | * ceil((-f(x) - c)/n) | ||||
4830 | * | ||||
4831 | * Look for a pair of constraints | ||||
4832 | * | ||||
4833 | * f(x) + c0 >= 0 | ||||
4834 | * -f(x) + c1 >= 0 | ||||
4835 | * | ||||
4836 | * i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value. | ||||
4837 | * That is, check that | ||||
4838 | * | ||||
4839 | * ceil((-c1 - c)/n) = ceil((c0 - c)/n) | ||||
4840 | * | ||||
4841 | * If so, return the index of inequality f(x) + c0 >= 0. | ||||
4842 | * Otherwise, return bmap->n_ineq. | ||||
4843 | * Return -1 on error. | ||||
4844 | */ | ||||
4845 | static int lower_bound_is_cst(__isl_keep isl_basic_map *bmap, int div, int ineq) | ||||
4846 | { | ||||
4847 | int i; | ||||
4848 | int lower = -1, upper = -1; | ||||
4849 | unsigned o_div; | ||||
4850 | isl_int l, u; | ||||
4851 | int equal; | ||||
4852 | |||||
4853 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
4854 | for (i = 0; i < bmap->n_ineq && (lower < 0 || upper < 0); ++i) { | ||||
4855 | isl_bool par, opp; | ||||
4856 | |||||
4857 | if (i == ineq) | ||||
4858 | continue; | ||||
4859 | if (!isl_int_is_zero(bmap->ineq[i][o_div + div])(isl_sioimath_sgn(*(bmap->ineq[i][o_div + div])) == 0)) | ||||
4860 | continue; | ||||
4861 | par = isl_bool_false; | ||||
4862 | if (lower < 0) | ||||
4863 | par = is_parallel_except(bmap, ineq, i, o_div + div); | ||||
4864 | if (par < 0) | ||||
4865 | return -1; | ||||
4866 | if (par) { | ||||
4867 | lower = i; | ||||
4868 | continue; | ||||
4869 | } | ||||
4870 | opp = isl_bool_false; | ||||
4871 | if (upper < 0) | ||||
4872 | opp = is_opposite_except(bmap, ineq, i, o_div + div); | ||||
4873 | if (opp < 0) | ||||
4874 | return -1; | ||||
4875 | if (opp) | ||||
4876 | upper = i; | ||||
4877 | } | ||||
4878 | |||||
4879 | if (lower < 0 || upper < 0) | ||||
4880 | return bmap->n_ineq; | ||||
4881 | |||||
4882 | isl_int_init(l)isl_sioimath_init((l)); | ||||
4883 | isl_int_init(u)isl_sioimath_init((u)); | ||||
4884 | |||||
4885 | lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &l); | ||||
4886 | lower_bound_from_opposite(bmap, ineq, upper, o_div + div, &u); | ||||
4887 | |||||
4888 | equal = isl_int_eq(l, u)(isl_sioimath_cmp(*(l), *(u)) == 0); | ||||
4889 | |||||
4890 | isl_int_clear(l)isl_sioimath_clear((l)); | ||||
4891 | isl_int_clear(u)isl_sioimath_clear((u)); | ||||
4892 | |||||
4893 | return equal ? lower : bmap->n_ineq; | ||||
4894 | } | ||||
4895 | |||||
4896 | /* Given a lower bound constraint "ineq" on the existentially quantified | ||||
4897 | * variable "div", such that the corresponding lower bound has | ||||
4898 | * a fixed value in "bmap", assign this fixed value to the variable and | ||||
4899 | * then try and drop redundant divs again, | ||||
4900 | * freeing the temporary data structure "pairs" that was associated | ||||
4901 | * to the old version of "bmap". | ||||
4902 | * "lower" determines the constant value for the lower bound. | ||||
4903 | * | ||||
4904 | * In particular, "ineq" is of the form | ||||
4905 | * | ||||
4906 | * f(x) + n d + c >= 0, | ||||
4907 | * | ||||
4908 | * while "lower" is of the form | ||||
4909 | * | ||||
4910 | * f(x) + c0 >= 0 | ||||
4911 | * | ||||
4912 | * The lower bound is ceil((-f(x) - c)/n) and its constant value | ||||
4913 | * is ceil((c0 - c)/n). | ||||
4914 | */ | ||||
4915 | static __isl_give isl_basic_map *fix_cst_lower(__isl_take isl_basic_map *bmap, | ||||
4916 | int div, int ineq, int lower, int *pairs) | ||||
4917 | { | ||||
4918 | isl_int c; | ||||
4919 | unsigned o_div; | ||||
4920 | |||||
4921 | isl_int_init(c)isl_sioimath_init((c)); | ||||
4922 | |||||
4923 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
4924 | lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &c); | ||||
4925 | bmap = isl_basic_map_fix(bmap, isl_dim_div, div, c); | ||||
4926 | free(pairs); | ||||
4927 | |||||
4928 | isl_int_clear(c)isl_sioimath_clear((c)); | ||||
4929 | |||||
4930 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
4931 | } | ||||
4932 | |||||
4933 | /* Do any of the integer divisions of "bmap" involve integer division "div"? | ||||
4934 | * | ||||
4935 | * The integer division "div" could only ever appear in any later | ||||
4936 | * integer division (with an explicit representation). | ||||
4937 | */ | ||||
4938 | static isl_bool any_div_involves_div(__isl_keep isl_basic_map *bmap, int div) | ||||
4939 | { | ||||
4940 | int i; | ||||
4941 | isl_size v_div, n_div; | ||||
4942 | |||||
4943 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
4944 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
4945 | if (v_div < 0 || n_div < 0) | ||||
4946 | return isl_bool_error; | ||||
4947 | |||||
4948 | for (i = div + 1; i < n_div; ++i) { | ||||
4949 | isl_bool unknown; | ||||
4950 | |||||
4951 | unknown = isl_basic_map_div_is_marked_unknown(bmap, i); | ||||
4952 | if (unknown < 0) | ||||
4953 | return isl_bool_error; | ||||
4954 | if (unknown) | ||||
4955 | continue; | ||||
4956 | 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)) | ||||
4957 | return isl_bool_true; | ||||
4958 | } | ||||
4959 | |||||
4960 | return isl_bool_false; | ||||
4961 | } | ||||
4962 | |||||
4963 | /* Remove divs that are not strictly needed based on the inequality | ||||
4964 | * constraints. | ||||
4965 | * In particular, if a div only occurs positively (or negatively) | ||||
4966 | * in constraints, then it can simply be dropped. | ||||
4967 | * Also, if a div occurs in only two constraints and if moreover | ||||
4968 | * those two constraints are opposite to each other, except for the constant | ||||
4969 | * term and if the sum of the constant terms is such that for any value | ||||
4970 | * of the other values, there is always at least one integer value of the | ||||
4971 | * div, i.e., if one plus this sum is greater than or equal to | ||||
4972 | * the (absolute value) of the coefficient of the div in the constraints, | ||||
4973 | * then we can also simply drop the div. | ||||
4974 | * | ||||
4975 | * If an existentially quantified variable does not have an explicit | ||||
4976 | * representation, appears in only a single lower bound that does not | ||||
4977 | * involve any other such existentially quantified variables and appears | ||||
4978 | * in this lower bound with coefficient 1, | ||||
4979 | * then fix the variable to the value of the lower bound. That is, | ||||
4980 | * turn the inequality into an equality. | ||||
4981 | * If for any value of the other variables, there is any value | ||||
4982 | * for the existentially quantified variable satisfying the constraints, | ||||
4983 | * then this lower bound also satisfies the constraints. | ||||
4984 | * It is therefore safe to pick this lower bound. | ||||
4985 | * | ||||
4986 | * The same reasoning holds even if the coefficient is not one. | ||||
4987 | * However, fixing the variable to the value of the lower bound may | ||||
4988 | * in general introduce an extra integer division, in which case | ||||
4989 | * it may be better to pick another value. | ||||
4990 | * If this integer division has a known constant value, then plugging | ||||
4991 | * in this constant value removes the existentially quantified variable | ||||
4992 | * completely. In particular, if the lower bound is of the form | ||||
4993 | * ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and | ||||
4994 | * -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n), | ||||
4995 | * then the existentially quantified variable can be assigned this | ||||
4996 | * shared value. | ||||
4997 | * | ||||
4998 | * We skip divs that appear in equalities or in the definition of other divs. | ||||
4999 | * Divs that appear in the definition of other divs usually occur in at least | ||||
5000 | * 4 constraints, but the constraints may have been simplified. | ||||
5001 | * | ||||
5002 | * If any divs are left after these simple checks then we move on | ||||
5003 | * to more complicated cases in drop_more_redundant_divs. | ||||
5004 | */ | ||||
5005 | static __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs_ineq( | ||||
5006 | __isl_take isl_basic_map *bmap) | ||||
5007 | { | ||||
5008 | int i, j; | ||||
5009 | isl_size off; | ||||
5010 | int *pairs = NULL((void*)0); | ||||
5011 | int n = 0; | ||||
5012 | isl_size n_ineq; | ||||
5013 | |||||
5014 | if (!bmap) | ||||
5015 | goto error; | ||||
5016 | if (bmap->n_div == 0) | ||||
5017 | return bmap; | ||||
5018 | |||||
5019 | off = isl_basic_map_var_offset(bmap, isl_dim_div); | ||||
5020 | if (off < 0) | ||||
5021 | return isl_basic_map_free(bmap); | ||||
5022 | pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div)((int *)isl_calloc_or_die(bmap->ctx, bmap->n_div, sizeof (int))); | ||||
5023 | if (!pairs) | ||||
5024 | goto error; | ||||
5025 | |||||
5026 | n_ineq = isl_basic_map_n_inequality(bmap); | ||||
5027 | if (n_ineq < 0) | ||||
5028 | goto error; | ||||
5029 | for (i = 0; i < bmap->n_div; ++i) { | ||||
5030 | int pos, neg; | ||||
5031 | int last_pos, last_neg; | ||||
5032 | int redundant; | ||||
5033 | int defined; | ||||
5034 | isl_bool involves, opp, set_div; | ||||
5035 | |||||
5036 | defined = !isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0); | ||||
5037 | involves = any_div_involves_div(bmap, i); | ||||
5038 | if (involves < 0) | ||||
5039 | goto error; | ||||
5040 | if (involves) | ||||
5041 | continue; | ||||
5042 | for (j = 0; j < bmap->n_eq; ++j) | ||||
5043 | if (!isl_int_is_zero(bmap->eq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->eq[j][1 + off + i])) == 0)) | ||||
5044 | break; | ||||
5045 | if (j < bmap->n_eq) | ||||
5046 | continue; | ||||
5047 | ++n; | ||||
5048 | pos = neg = 0; | ||||
5049 | for (j = 0; j < bmap->n_ineq; ++j) { | ||||
5050 | if (isl_int_is_pos(bmap->ineq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + off + i])) > 0)) { | ||||
5051 | last_pos = j; | ||||
5052 | ++pos; | ||||
5053 | } | ||||
5054 | if (isl_int_is_neg(bmap->ineq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + off + i])) < 0)) { | ||||
5055 | last_neg = j; | ||||
5056 | ++neg; | ||||
5057 | } | ||||
5058 | } | ||||
5059 | pairs[i] = pos * neg; | ||||
5060 | if (pairs[i] == 0) { | ||||
5061 | for (j = bmap->n_ineq - 1; j >= 0; --j) | ||||
5062 | if (!isl_int_is_zero(bmap->ineq[j][1+off+i])(isl_sioimath_sgn(*(bmap->ineq[j][1+off+i])) == 0)) | ||||
5063 | isl_basic_map_drop_inequality(bmap, j); | ||||
5064 | bmap = isl_basic_map_drop_div(bmap, i); | ||||
5065 | return drop_redundant_divs_again(bmap, pairs, 0); | ||||
5066 | } | ||||
5067 | if (pairs[i] != 1) | ||||
5068 | opp = isl_bool_false; | ||||
5069 | else | ||||
5070 | opp = is_opposite(bmap, last_pos, last_neg); | ||||
5071 | if (opp < 0) | ||||
5072 | goto error; | ||||
5073 | if (!opp) { | ||||
5074 | int lower; | ||||
5075 | isl_bool single, one; | ||||
5076 | |||||
5077 | if (pos != 1) | ||||
5078 | continue; | ||||
5079 | single = single_unknown(bmap, last_pos, i); | ||||
5080 | if (single < 0) | ||||
5081 | goto error; | ||||
5082 | if (!single) | ||||
5083 | continue; | ||||
5084 | one = has_coef_one(bmap, i, last_pos); | ||||
5085 | if (one < 0) | ||||
5086 | goto error; | ||||
5087 | if (one) | ||||
5088 | return set_eq_and_try_again(bmap, last_pos, | ||||
5089 | pairs); | ||||
5090 | lower = lower_bound_is_cst(bmap, i, last_pos); | ||||
5091 | if (lower < 0) | ||||
5092 | goto error; | ||||
5093 | if (lower < n_ineq) | ||||
5094 | return fix_cst_lower(bmap, i, last_pos, lower, | ||||
5095 | pairs); | ||||
5096 | continue; | ||||
5097 | } | ||||
5098 | |||||
5099 | 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])) | ||||
5100 | 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])); | ||||
5101 | isl_int_add_ui(bmap->ineq[last_pos][0],isl_sioimath_add_ui((bmap->ineq[last_pos][0]), *(bmap-> ineq[last_pos][0]), 1) | ||||
5102 | bmap->ineq[last_pos][0], 1)isl_sioimath_add_ui((bmap->ineq[last_pos][0]), *(bmap-> ineq[last_pos][0]), 1); | ||||
5103 | 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) | ||||
5104 | bmap->ineq[last_pos][1+off+i])(isl_sioimath_cmp(*(bmap->ineq[last_pos][0]), *(bmap->ineq [last_pos][1+off+i])) >= 0); | ||||
5105 | isl_int_sub_ui(bmap->ineq[last_pos][0],isl_sioimath_sub_ui((bmap->ineq[last_pos][0]), *(bmap-> ineq[last_pos][0]), 1) | ||||
5106 | bmap->ineq[last_pos][0], 1)isl_sioimath_sub_ui((bmap->ineq[last_pos][0]), *(bmap-> ineq[last_pos][0]), 1); | ||||
5107 | 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])) | ||||
5108 | 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])); | ||||
5109 | if (redundant) | ||||
5110 | return drop_div_and_try_again(bmap, i, | ||||
5111 | last_pos, last_neg, pairs); | ||||
5112 | if (defined) | ||||
5113 | set_div = isl_bool_false; | ||||
5114 | else | ||||
5115 | set_div = ok_to_set_div_from_bound(bmap, i, last_pos); | ||||
5116 | if (set_div < 0) | ||||
5117 | return isl_basic_map_free(bmap); | ||||
5118 | if (set_div) { | ||||
5119 | bmap = set_div_from_lower_bound(bmap, i, last_pos); | ||||
5120 | return drop_redundant_divs_again(bmap, pairs, 1); | ||||
5121 | } | ||||
5122 | pairs[i] = 0; | ||||
5123 | --n; | ||||
5124 | } | ||||
5125 | |||||
5126 | if (n > 0) | ||||
5127 | return coalesce_or_drop_more_redundant_divs(bmap, pairs, n); | ||||
5128 | |||||
5129 | free(pairs); | ||||
5130 | return bmap; | ||||
5131 | error: | ||||
5132 | free(pairs); | ||||
5133 | isl_basic_map_free(bmap); | ||||
5134 | return NULL((void*)0); | ||||
5135 | } | ||||
5136 | |||||
5137 | /* Consider the coefficients at "c" as a row vector and replace | ||||
5138 | * them with their product with "T". "T" is assumed to be a square matrix. | ||||
5139 | */ | ||||
5140 | static isl_stat preimage(isl_int *c, __isl_keep isl_mat *T) | ||||
5141 | { | ||||
5142 | isl_size n; | ||||
5143 | isl_ctx *ctx; | ||||
5144 | isl_vec *v; | ||||
5145 | |||||
5146 | n = isl_mat_rows(T); | ||||
5147 | if (n < 0) | ||||
5148 | return isl_stat_error; | ||||
5149 | if (isl_seq_first_non_zero(c, n) == -1) | ||||
5150 | return isl_stat_ok; | ||||
5151 | ctx = isl_mat_get_ctx(T); | ||||
5152 | v = isl_vec_alloc(ctx, n); | ||||
5153 | if (!v) | ||||
5154 | return isl_stat_error; | ||||
5155 | isl_seq_swp_or_cpy(v->el, c, n); | ||||
5156 | v = isl_vec_mat_product(v, isl_mat_copy(T)); | ||||
5157 | if (!v) | ||||
5158 | return isl_stat_error; | ||||
5159 | isl_seq_swp_or_cpy(c, v->el, n); | ||||
5160 | isl_vec_free(v); | ||||
5161 | |||||
5162 | return isl_stat_ok; | ||||
5163 | } | ||||
5164 | |||||
5165 | /* Plug in T for the variables in "bmap" starting at "pos". | ||||
5166 | * T is a linear unimodular matrix, i.e., without constant term. | ||||
5167 | */ | ||||
5168 | static __isl_give isl_basic_map *isl_basic_map_preimage_vars( | ||||
5169 | __isl_take isl_basic_map *bmap, unsigned pos, __isl_take isl_mat *T) | ||||
5170 | { | ||||
5171 | int i; | ||||
5172 | isl_size n_row, n_col; | ||||
5173 | |||||
5174 | bmap = isl_basic_map_cow(bmap); | ||||
5175 | n_row = isl_mat_rows(T); | ||||
5176 | n_col = isl_mat_cols(T); | ||||
5177 | if (!bmap || n_row < 0 || n_col < 0) | ||||
5178 | goto error; | ||||
5179 | |||||
5180 | if (n_col != n_row) | ||||
5181 | 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-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 5182); goto error; } while (0) | ||||
5182 | "expecting square matrix", goto error)do { isl_handle_error(isl_mat_get_ctx(T), isl_error_invalid, "expecting square matrix" , "/build/llvm-toolchain-snapshot-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_map_simplify.c" , 5182); goto error; } while (0); | ||||
5183 | |||||
5184 | if (isl_basic_map_check_range(bmap, isl_dim_all, pos, n_col) < 0) | ||||
5185 | goto error; | ||||
5186 | |||||
5187 | for (i = 0; i < bmap->n_eq; ++i) | ||||
5188 | if (preimage(bmap->eq[i] + 1 + pos, T) < 0) | ||||
5189 | goto error; | ||||
5190 | for (i = 0; i < bmap->n_ineq; ++i) | ||||
5191 | if (preimage(bmap->ineq[i] + 1 + pos, T) < 0) | ||||
5192 | goto error; | ||||
5193 | for (i = 0; i < bmap->n_div; ++i) { | ||||
5194 | if (isl_basic_map_div_is_marked_unknown(bmap, i)) | ||||
5195 | continue; | ||||
5196 | if (preimage(bmap->div[i] + 1 + 1 + pos, T) < 0) | ||||
5197 | goto error; | ||||
5198 | } | ||||
5199 | |||||
5200 | isl_mat_free(T); | ||||
5201 | return bmap; | ||||
5202 | error: | ||||
5203 | isl_basic_map_free(bmap); | ||||
5204 | isl_mat_free(T); | ||||
5205 | return NULL((void*)0); | ||||
5206 | } | ||||
5207 | |||||
5208 | /* Remove divs that are not strictly needed. | ||||
5209 | * | ||||
5210 | * First look for an equality constraint involving two or more | ||||
5211 | * existentially quantified variables without an explicit | ||||
5212 | * representation. Replace the combination that appears | ||||
5213 | * in the equality constraint by a single existentially quantified | ||||
5214 | * variable such that the equality can be used to derive | ||||
5215 | * an explicit representation for the variable. | ||||
5216 | * If there are no more such equality constraints, then continue | ||||
5217 | * with isl_basic_map_drop_redundant_divs_ineq. | ||||
5218 | * | ||||
5219 | * In particular, if the equality constraint is of the form | ||||
5220 | * | ||||
5221 | * f(x) + \sum_i c_i a_i = 0 | ||||
5222 | * | ||||
5223 | * with a_i existentially quantified variable without explicit | ||||
5224 | * representation, then apply a transformation on the existentially | ||||
5225 | * quantified variables to turn the constraint into | ||||
5226 | * | ||||
5227 | * f(x) + g a_1' = 0 | ||||
5228 | * | ||||
5229 | * with g the gcd of the c_i. | ||||
5230 | * In order to easily identify which existentially quantified variables | ||||
5231 | * have a complete explicit representation, i.e., without being defined | ||||
5232 | * in terms of other existentially quantified variables without | ||||
5233 | * an explicit representation, the existentially quantified variables | ||||
5234 | * are first sorted. | ||||
5235 | * | ||||
5236 | * The variable transformation is computed by extending the row | ||||
5237 | * [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation | ||||
5238 | * | ||||
5239 | * [a_1'] [c_1/g ... c_n/g] [ a_1 ] | ||||
5240 | * [a_2'] [ a_2 ] | ||||
5241 | * ... = U .... | ||||
5242 | * [a_n'] [ a_n ] | ||||
5243 | * | ||||
5244 | * with [c_1/g ... c_n/g] representing the first row of U. | ||||
5245 | * The inverse of U is then plugged into the original constraints. | ||||
5246 | * The call to isl_basic_map_simplify makes sure the explicit | ||||
5247 | * representation for a_1' is extracted from the equality constraint. | ||||
5248 | */ | ||||
5249 | __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs( | ||||
5250 | __isl_take isl_basic_map *bmap) | ||||
5251 | { | ||||
5252 | int first; | ||||
5253 | int i; | ||||
5254 | unsigned o_div; | ||||
5255 | isl_size n_div; | ||||
5256 | int l; | ||||
5257 | isl_ctx *ctx; | ||||
5258 | isl_mat *T; | ||||
5259 | |||||
5260 | if (!bmap) | ||||
5261 | return NULL((void*)0); | ||||
5262 | if (isl_basic_map_divs_known(bmap)) | ||||
5263 | return isl_basic_map_drop_redundant_divs_ineq(bmap); | ||||
5264 | if (bmap->n_eq == 0) | ||||
5265 | return isl_basic_map_drop_redundant_divs_ineq(bmap); | ||||
5266 | bmap = isl_basic_map_sort_divs(bmap); | ||||
5267 | if (!bmap) | ||||
5268 | return NULL((void*)0); | ||||
5269 | |||||
5270 | first = isl_basic_map_first_unknown_div(bmap); | ||||
5271 | if (first < 0) | ||||
5272 | return isl_basic_map_free(bmap); | ||||
5273 | |||||
5274 | o_div = isl_basic_map_offset(bmap, isl_dim_div); | ||||
5275 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
5276 | if (n_div < 0) | ||||
5277 | return isl_basic_map_free(bmap); | ||||
5278 | |||||
5279 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
5280 | l = isl_seq_first_non_zero(bmap->eq[i] + o_div + first, | ||||
5281 | n_div - (first)); | ||||
5282 | if (l < 0) | ||||
5283 | continue; | ||||
5284 | l += first; | ||||
5285 | if (isl_seq_first_non_zero(bmap->eq[i] + o_div + l + 1, | ||||
5286 | n_div - (l + 1)) == -1) | ||||
5287 | continue; | ||||
5288 | break; | ||||
5289 | } | ||||
5290 | if (i >= bmap->n_eq) | ||||
5291 | return isl_basic_map_drop_redundant_divs_ineq(bmap); | ||||
5292 | |||||
5293 | ctx = isl_basic_map_get_ctx(bmap); | ||||
5294 | T = isl_mat_alloc(ctx, n_div - l, n_div - l); | ||||
5295 | if (!T) | ||||
5296 | return isl_basic_map_free(bmap); | ||||
5297 | isl_seq_cpy(T->row[0], bmap->eq[i] + o_div + l, n_div - l); | ||||
5298 | T = isl_mat_normalize_row(T, 0); | ||||
5299 | T = isl_mat_unimodular_complete(T, 1); | ||||
5300 | T = isl_mat_right_inverse(T); | ||||
5301 | |||||
5302 | for (i = l; i < n_div; ++i) | ||||
5303 | bmap = isl_basic_map_mark_div_unknown(bmap, i); | ||||
5304 | bmap = isl_basic_map_preimage_vars(bmap, o_div - 1 + l, T); | ||||
5305 | bmap = isl_basic_map_simplify(bmap); | ||||
5306 | |||||
5307 | return isl_basic_map_drop_redundant_divs(bmap); | ||||
5308 | } | ||||
5309 | |||||
5310 | /* Does "bmap" satisfy any equality that involves more than 2 variables | ||||
5311 | * and/or has coefficients different from -1 and 1? | ||||
5312 | */ | ||||
5313 | static isl_bool has_multiple_var_equality(__isl_keep isl_basic_map *bmap) | ||||
5314 | { | ||||
5315 | int i; | ||||
5316 | isl_size total; | ||||
5317 | |||||
5318 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
5319 | if (total < 0) | ||||
5320 | return isl_bool_error; | ||||
5321 | |||||
5322 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
5323 | int j, k; | ||||
5324 | |||||
5325 | j = isl_seq_first_non_zero(bmap->eq[i] + 1, total); | ||||
5326 | if (j < 0) | ||||
5327 | continue; | ||||
5328 | if (!isl_int_is_one(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), 1) == 0) && | ||||
5329 | !isl_int_is_negone(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), -1) == 0)) | ||||
5330 | return isl_bool_true; | ||||
5331 | |||||
5332 | j += 1; | ||||
5333 | k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j); | ||||
5334 | if (k < 0) | ||||
5335 | continue; | ||||
5336 | j += k; | ||||
5337 | if (!isl_int_is_one(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), 1) == 0) && | ||||
5338 | !isl_int_is_negone(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), -1) == 0)) | ||||
5339 | return isl_bool_true; | ||||
5340 | |||||
5341 | j += 1; | ||||
5342 | k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j); | ||||
5343 | if (k >= 0) | ||||
5344 | return isl_bool_true; | ||||
5345 | } | ||||
5346 | |||||
5347 | return isl_bool_false; | ||||
5348 | } | ||||
5349 | |||||
5350 | /* Remove any common factor g from the constraint coefficients in "v". | ||||
5351 | * The constant term is stored in the first position and is replaced | ||||
5352 | * by floor(c/g). If any common factor is removed and if this results | ||||
5353 | * in a tightening of the constraint, then set *tightened. | ||||
5354 | */ | ||||
5355 | static __isl_give isl_vec *normalize_constraint(__isl_take isl_vec *v, | ||||
5356 | int *tightened) | ||||
5357 | { | ||||
5358 | isl_ctx *ctx; | ||||
5359 | |||||
5360 | if (!v) | ||||
5361 | return NULL((void*)0); | ||||
5362 | ctx = isl_vec_get_ctx(v); | ||||
5363 | isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd); | ||||
5364 | if (isl_int_is_zero(ctx->normalize_gcd)(isl_sioimath_sgn(*(ctx->normalize_gcd)) == 0)) | ||||
5365 | return v; | ||||
5366 | if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0)) | ||||
5367 | return v; | ||||
5368 | v = isl_vec_cow(v); | ||||
5369 | if (!v) | ||||
5370 | return NULL((void*)0); | ||||
5371 | if (tightened && !isl_int_is_divisible_by(v->el[0], ctx->normalize_gcd)isl_sioimath_is_divisible_by(*(v->el[0]), *(ctx->normalize_gcd ))) | ||||
5372 | *tightened = 1; | ||||
5373 | 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)); | ||||
5374 | isl_seq_scale_down(v->el + 1, v->el + 1, ctx->normalize_gcd, | ||||
5375 | v->size - 1); | ||||
5376 | return v; | ||||
5377 | } | ||||
5378 | |||||
5379 | /* If "bmap" is an integer set that satisfies any equality involving | ||||
5380 | * more than 2 variables and/or has coefficients different from -1 and 1, | ||||
5381 | * then use variable compression to reduce the coefficients by removing | ||||
5382 | * any (hidden) common factor. | ||||
5383 | * In particular, apply the variable compression to each constraint, | ||||
5384 | * factor out any common factor in the non-constant coefficients and | ||||
5385 | * then apply the inverse of the compression. | ||||
5386 | * At the end, we mark the basic map as having reduced constants. | ||||
5387 | * If this flag is still set on the next invocation of this function, | ||||
5388 | * then we skip the computation. | ||||
5389 | * | ||||
5390 | * Removing a common factor may result in a tightening of some of | ||||
5391 | * the constraints. If this happens, then we may end up with two | ||||
5392 | * opposite inequalities that can be replaced by an equality. | ||||
5393 | * We therefore call isl_basic_map_detect_inequality_pairs, | ||||
5394 | * which checks for such pairs of inequalities as well as eliminate_divs_eq | ||||
5395 | * and isl_basic_map_gauss if such a pair was found. | ||||
5396 | * | ||||
5397 | * Tightening may also result in some other constraints becoming | ||||
5398 | * (rationally) redundant with respect to the tightened constraint | ||||
5399 | * (in combination with other constraints). The basic map may | ||||
5400 | * therefore no longer be assumed to have no redundant constraints. | ||||
5401 | * | ||||
5402 | * Note that this function may leave the result in an inconsistent state. | ||||
5403 | * In particular, the constraints may not be gaussed. | ||||
5404 | * Unfortunately, isl_map_coalesce actually depends on this inconsistent state | ||||
5405 | * for some of the test cases to pass successfully. | ||||
5406 | * Any potential modification of the representation is therefore only | ||||
5407 | * performed on a single copy of the basic map. | ||||
5408 | */ | ||||
5409 | __isl_give isl_basic_map *isl_basic_map_reduce_coefficients( | ||||
5410 | __isl_take isl_basic_map *bmap) | ||||
5411 | { | ||||
5412 | isl_size total; | ||||
5413 | isl_bool multi; | ||||
5414 | isl_ctx *ctx; | ||||
5415 | isl_vec *v; | ||||
5416 | isl_mat *eq, *T, *T2; | ||||
5417 | int i; | ||||
5418 | int tightened; | ||||
5419 | |||||
5420 | if (!bmap) | ||||
5421 | return NULL((void*)0); | ||||
5422 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(!!(((bmap)->flags) & ((1 << 8))))) | ||||
5423 | return bmap; | ||||
5424 | if (isl_basic_map_is_rational(bmap)) | ||||
5425 | return bmap; | ||||
5426 | if (bmap->n_eq == 0) | ||||
5427 | return bmap; | ||||
5428 | multi = has_multiple_var_equality(bmap); | ||||
5429 | if (multi < 0) | ||||
5430 | return isl_basic_map_free(bmap); | ||||
5431 | if (!multi) | ||||
5432 | return bmap; | ||||
5433 | |||||
5434 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
5435 | if (total < 0) | ||||
5436 | return isl_basic_map_free(bmap); | ||||
5437 | ctx = isl_basic_map_get_ctx(bmap); | ||||
5438 | v = isl_vec_alloc(ctx, 1 + total); | ||||
5439 | if (!v) | ||||
5440 | return isl_basic_map_free(bmap); | ||||
5441 | |||||
5442 | eq = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total); | ||||
5443 | T = isl_mat_variable_compression(eq, &T2); | ||||
5444 | if (!T || !T2) | ||||
5445 | goto error; | ||||
5446 | if (T->n_col == 0) { | ||||
5447 | isl_mat_free(T); | ||||
5448 | isl_mat_free(T2); | ||||
5449 | isl_vec_free(v); | ||||
5450 | return isl_basic_map_set_to_empty(bmap); | ||||
5451 | } | ||||
5452 | |||||
5453 | bmap = isl_basic_map_cow(bmap); | ||||
5454 | if (!bmap) | ||||
5455 | goto error; | ||||
5456 | |||||
5457 | tightened = 0; | ||||
5458 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
5459 | isl_seq_cpy(v->el, bmap->ineq[i], 1 + total); | ||||
5460 | v = isl_vec_mat_product(v, isl_mat_copy(T)); | ||||
5461 | v = normalize_constraint(v, &tightened); | ||||
5462 | v = isl_vec_mat_product(v, isl_mat_copy(T2)); | ||||
5463 | if (!v) | ||||
5464 | goto error; | ||||
5465 | isl_seq_cpy(bmap->ineq[i], v->el, 1 + total); | ||||
5466 | } | ||||
5467 | |||||
5468 | isl_mat_free(T); | ||||
5469 | isl_mat_free(T2); | ||||
5470 | isl_vec_free(v); | ||||
5471 | |||||
5472 | ISL_F_SET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(((bmap)->flags) |= ((1 << 8))); | ||||
5473 | |||||
5474 | if (tightened) { | ||||
5475 | int progress = 0; | ||||
5476 | |||||
5477 | ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT)(((bmap)->flags) &= ~((1 << 3))); | ||||
5478 | bmap = isl_basic_map_detect_inequality_pairs(bmap, &progress); | ||||
5479 | if (progress) { | ||||
5480 | bmap = eliminate_divs_eq(bmap, &progress); | ||||
5481 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | ||||
5482 | } | ||||
5483 | } | ||||
5484 | |||||
5485 | return bmap; | ||||
5486 | error: | ||||
5487 | isl_mat_free(T); | ||||
5488 | isl_mat_free(T2); | ||||
5489 | isl_vec_free(v); | ||||
5490 | return isl_basic_map_free(bmap); | ||||
5491 | } | ||||
5492 | |||||
5493 | /* Shift the integer division at position "div" of "bmap" | ||||
5494 | * by "shift" times the variable at position "pos". | ||||
5495 | * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0 | ||||
5496 | * corresponds to the constant term. | ||||
5497 | * | ||||
5498 | * That is, if the integer division has the form | ||||
5499 | * | ||||
5500 | * floor(f(x)/d) | ||||
5501 | * | ||||
5502 | * then replace it by | ||||
5503 | * | ||||
5504 | * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos | ||||
5505 | */ | ||||
5506 | __isl_give isl_basic_map *isl_basic_map_shift_div( | ||||
5507 | __isl_take isl_basic_map *bmap, int div, int pos, isl_int shift) | ||||
5508 | { | ||||
5509 | int i; | ||||
5510 | isl_size total, n_div; | ||||
5511 | |||||
5512 | if (isl_int_is_zero(shift)(isl_sioimath_sgn(*(shift)) == 0)) | ||||
5513 | return bmap; | ||||
5514 | total = isl_basic_map_dim(bmap, isl_dim_all); | ||||
5515 | n_div = isl_basic_map_dim(bmap, isl_dim_div); | ||||
5516 | total -= n_div; | ||||
5517 | if (total < 0 || n_div < 0) | ||||
5518 | return isl_basic_map_free(bmap); | ||||
5519 | |||||
5520 | 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])); | ||||
5521 | |||||
5522 | for (i = 0; i < bmap->n_eq; ++i) { | ||||
5523 | if (isl_int_is_zero(bmap->eq[i][1 + total + div])(isl_sioimath_sgn(*(bmap->eq[i][1 + total + div])) == 0)) | ||||
5524 | continue; | ||||
5525 | isl_int_submul(bmap->eq[i][pos],isl_sioimath_submul((bmap->eq[i][pos]), *(shift), *(bmap-> eq[i][1 + total + div])) | ||||
5526 | shift, bmap->eq[i][1 + total + div])isl_sioimath_submul((bmap->eq[i][pos]), *(shift), *(bmap-> eq[i][1 + total + div])); | ||||
5527 | } | ||||
5528 | for (i = 0; i < bmap->n_ineq; ++i) { | ||||
5529 | if (isl_int_is_zero(bmap->ineq[i][1 + total + div])(isl_sioimath_sgn(*(bmap->ineq[i][1 + total + div])) == 0)) | ||||
5530 | continue; | ||||
5531 | isl_int_submul(bmap->ineq[i][pos],isl_sioimath_submul((bmap->ineq[i][pos]), *(shift), *(bmap ->ineq[i][1 + total + div])) | ||||
5532 | shift, bmap->ineq[i][1 + total + div])isl_sioimath_submul((bmap->ineq[i][pos]), *(shift), *(bmap ->ineq[i][1 + total + div])); | ||||
5533 | } | ||||
5534 | for (i = 0; i < bmap->n_div; ++i) { | ||||
5535 | if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0)) | ||||
5536 | continue; | ||||
5537 | if (isl_int_is_zero(bmap->div[i][1 + 1 + total + div])(isl_sioimath_sgn(*(bmap->div[i][1 + 1 + total + div])) == 0)) | ||||
5538 | continue; | ||||
5539 | isl_int_submul(bmap->div[i][1 + pos],isl_sioimath_submul((bmap->div[i][1 + pos]), *(shift), *(bmap ->div[i][1 + 1 + total + div])) | ||||
5540 | shift, bmap->div[i][1 + 1 + total + div])isl_sioimath_submul((bmap->div[i][1 + pos]), *(shift), *(bmap ->div[i][1 + 1 + total + div])); | ||||
5541 | } | ||||
5542 | |||||
5543 | return bmap; | ||||
5544 | } |