Bug Summary

File:polly/lib/External/isl/isl_map_simplify.c
Warning:line 1253, column 6
3rd function call argument is an uninitialized value

Annotated Source Code

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clang -cc1 -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name isl_map_simplify.c -analyzer-store=region -analyzer-opt-analyze-nested-blocks -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -mframe-pointer=none -fmath-errno -fno-rounding-math -mconstructor-aliases -munwind-tables -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -ffunction-sections -fdata-sections -fcoverage-compilation-dir=/build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/tools/polly/lib/External -resource-dir /usr/lib/llvm-14/lib/clang/14.0.0 -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/tools/polly/lib/External -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/polly/lib/External -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/polly/lib/External/isl -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/polly/lib/External/isl/include -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/polly/lib/External/isl/imath -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/tools/polly/lib/External/isl -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/tools/polly/include -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/polly/lib/External/pet/include -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/tools/polly/lib/External/isl/include -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/polly/include -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/include -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/llvm/include -D NDEBUG -internal-isystem /usr/lib/llvm-14/lib/clang/14.0.0/include -internal-isystem /usr/local/include -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../x86_64-linux-gnu/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -O2 -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-comment -std=gnu99 -fconst-strings -fdebug-compilation-dir=/build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/tools/polly/lib/External -fdebug-prefix-map=/build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e=. -ferror-limit 19 -stack-protector 2 -fgnuc-version=4.2.1 -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /tmp/scan-build-2021-09-04-040900-46481-1 -x c /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/polly/lib/External/isl/isl_map_simplify.c
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
31static 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
38static 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;
101error:
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 */
134static __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 */
160static 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 */
182static __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 */
212static __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 */
246static __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 */
283static __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 */
301static __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 */
366static __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 */
386static 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 */
415static __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 */
457static __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 */
497static 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 */
545static __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 && !drop)
609 bmap = isl_basic_map_order_divs(bmap);
610
611 total = isl_basic_map_dim(bmap, isl_dim_all);
612 if (total < 0)
613 return isl_basic_map_free(bmap);
614
615 total_var = total - bmap->n_div;
616
617 last_var = total - 1;
618 for (done = 0; done < bmap->n_eq; ++done) {
619 for (; last_var >= 0; --last_var) {
620 for (k = done; k < bmap->n_eq; ++k)
621 if (!isl_int_is_zero(bmap->eq[k][1+last_var])(isl_sioimath_sgn(*(bmap->eq[k][1+last_var])) == 0))
622 break;
623 if (k < bmap->n_eq)
624 break;
625 }
626 if (last_var < 0)
627 break;
628 if (k != done) {
629 swap_equality(bmap, k, done);
630 if (swap && swap(k, done, user) < 0)
631 return isl_basic_map_free(bmap);
632 }
633 if (isl_int_is_neg(bmap->eq[done][1+last_var])(isl_sioimath_sgn(*(bmap->eq[done][1+last_var])) < 0))
634 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
635
636 bmap = eliminate_var_using_equality(bmap, last_var,
637 bmap->eq[done], 1, progress);
638
639 if (last_var >= total_var)
640 bmap = set_div_from_eq(bmap, last_var - total_var,
641 done, progress);
642 if (!bmap)
643 return NULL((void*)0);
644 }
645 if (done == bmap->n_eq)
646 return bmap;
647 for (k = done; k < bmap->n_eq; ++k) {
648 if (isl_int_is_zero(bmap->eq[k][0])(isl_sioimath_sgn(*(bmap->eq[k][0])) == 0))
649 continue;
650 if (drop && drop(bmap->n_eq, user) < 0)
651 return isl_basic_map_free(bmap);
652 return isl_basic_map_set_to_empty(bmap);
653 }
654 n_drop = bmap->n_eq - done;
655 bmap = isl_basic_map_free_equality(bmap, n_drop);
656 if (drop && drop(n_drop, user) < 0)
657 return isl_basic_map_free(bmap);
658 return bmap;
659}
660
661__isl_give isl_basic_map *isl_basic_map_gauss(__isl_take isl_basic_map *bmap,
662 int *progress)
663{
664 return isl_basic_map_gauss5(bmap, progress, NULL((void*)0), NULL((void*)0), NULL((void*)0));
665}
666
667__isl_give isl_basic_setisl_basic_map *isl_basic_set_gauss(
668 __isl_take isl_basic_setisl_basic_map *bset, int *progress)
669{
670 return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset),
671 progress));
672}
673
674
675static 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 */
694struct 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 */
703static 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
36.1
'bmap' is non-null
)
37
Taking false branch
710 return isl_stat_error;
711 ci->total = isl_basic_map_dim(bmap, isl_dim_all);
712 if (ci->total < 0)
38
Assuming field 'total' is >= 0
39
Taking false branch
713 return isl_stat_error;
714 if (bmap->n_ineq == 0)
40
Assuming field 'n_ineq' is equal to 0
41
Taking true branch
715 return isl_stat_ok;
42
Returning without writing to 'ci->bits'
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 */
728static 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 */
739static 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 */
757static 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
763static 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 */
771static 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 */
800static 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 */
816static __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);
891out:
892 free(index);
893 free(elim_for);
894 return bmap;
895}
896
897static 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 */
964static __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;
1104done:
1105 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS)(((bmap)->flags) |= ((1 << 6)));
1106
1107 return bmap;
1108error:
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
1117static __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 */
1137static 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 */
1174static 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 */
1207static __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)
33
Assuming 'total' is >= 0
34
Assuming field 'n_ineq' is > 1
35
Taking false branch
1248 return bmap;
1249
1250 if (create_constraint_index(&ci, bmap) < 0)
36
Calling 'create_constraint_index'
43
Returning from 'create_constraint_index'
44
Taking false branch
1251 return bmap;
1252
1253 h = isl_seq_get_hash_bits(bmap->ineq[0] + 1, total, ci.bits);
45
3rd function call argument is an uninitialized value
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 */
1360static __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 */
1422static __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 */
1455static 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 */
1465static __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 */
1476static 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
25.1
'bmap' is non-null
)
26
Taking false branch
1520 return NULL((void*)0);
1521 while (progress) {
27
Loop condition is true. Entering loop body
1522 isl_bool empty;
1523
1524 progress = 0;
1525 empty = isl_basic_map_plain_is_empty(bmap);
1526 if (empty < 0)
28
Assuming 'empty' is >= 0
29
Taking false branch
1527 return isl_basic_map_free(bmap);
1528 if (empty)
30
Assuming 'empty' is 0
31
Taking false branch
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,
32
Calling 'isl_basic_map_remove_duplicate_constraints'
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
1555isl_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 */
1599static 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 */
1638static __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 */
1695static __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;
1808error:
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 */
1958static 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
1975static 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
1981static 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
2001static 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
2008static __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;
2043error:
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 */
2055static 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;
2093error:
2094 constraint_index_free(&ci);
2095 return isl_stat_error;
2096}
2097
2098static __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;
2128error:
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 */
2139static __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;
2164error:
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 */
2173static 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 */
2190static __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 */
2234static 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 */
2258static 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 */
2338static __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 */
2384static __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 */
2418static 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 */
2442static __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 */
2483static __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 */
2530static __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;
2615error:
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 */
2627static __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 */
2648static __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 */
2659static __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 */
2699static __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);
2748error:
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 */
2757static __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 */
2807static __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;
2863error:
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 */
2873static 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 */
2901static __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~++20210903100615+fd66b44ec19e/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~++20210903100615+fd66b44ec19e/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;
2928error:
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 */
2955static __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 */
3022static __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 */
3089static 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 */
3153static __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~++20210903100615+fd66b44ec19e/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~++20210903100615+fd66b44ec19e/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~++20210903100615+fd66b44ec19e/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;
3199error:
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 */
3214static __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;
3325error:
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;
3371error:
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 */
3390static __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 */
3447static __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~++20210903100615+fd66b44ec19e/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~++20210903100615+fd66b44ec19e/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;
3537error:
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 */
3545static __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~++20210903100615+fd66b44ec19e/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~++20210903100615+fd66b44ec19e/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;
3600error:
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 */
3636static __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);
3727error:
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 */
3810isl_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;
3865disjoint:
3866 isl_vec_free(v);
3867 free(elim);
3868 return isl_bool_true;
3869error:
3870 isl_vec_free(v);
3871 free(elim);
3872 return isl_bool_error;
3873}
3874
3875int 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 */
3884static 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 */
3910static 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 */
3952isl_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 */
3979static 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 */
3994isl_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 */
4034isl_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 */
4071isl_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
4077isl_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 */
4085isl_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 */
4092static 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 */
4100static 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 */
4109static 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 */
4150static 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 */
4247struct 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 */
4257static 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 */
4270static 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 */
4337static 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 */
4391static __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);
4471error:
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 */
4527static __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 */
4586static __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);
4627error:
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 */
4636static 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 */
4645static 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 */
4660static 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 */
4677static __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 */
4690static 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 */
4725static 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 */
4741static __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 */
4755static __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 */
4786static 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 */
4810static 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 */
4845static 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 */
4915static __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 */
4938static 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 */
5005static __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;
5131error:
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 */
5140static 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 */
5168static __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~++20210903100615+fd66b44ec19e/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~++20210903100615+fd66b44ec19e/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;
5202error:
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)
1
Assuming 'bmap' is non-null
2
Taking false branch
5261 return NULL((void*)0);
5262 if (isl_basic_map_divs_known(bmap))
3
Assuming the condition is false
4
Taking false branch
5263 return isl_basic_map_drop_redundant_divs_ineq(bmap);
5264 if (bmap->n_eq == 0)
5
Assuming field 'n_eq' is not equal to 0
6
Taking false branch
5265 return isl_basic_map_drop_redundant_divs_ineq(bmap);
5266 bmap = isl_basic_map_sort_divs(bmap);
5267 if (!bmap)
7
Assuming 'bmap' is non-null
8
Taking false branch
5268 return NULL((void*)0);
5269
5270 first = isl_basic_map_first_unknown_div(bmap);
5271 if (first < 0)
9
Assuming 'first' is >= 0
10
Taking false branch
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)
11
Assuming 'n_div' is >= 0
12
Taking false branch
5277 return isl_basic_map_free(bmap);
5278
5279 for (i = 0; i < bmap->n_eq; ++i) {
13
Assuming 'i' is < field 'n_eq'
14
Loop condition is true. Entering loop body
5280 l = isl_seq_first_non_zero(bmap->eq[i] + o_div + first,
5281 n_div - (first));
5282 if (l < 0)
15
Assuming 'l' is >= 0
16
Taking false branch
5283 continue;
5284 l += first;
5285 if (isl_seq_first_non_zero(bmap->eq[i] + o_div + l + 1,
17
Assuming the condition is false
18
Taking false branch
5286 n_div - (l + 1)) == -1)
5287 continue;
5288 break;
5289 }
5290 if (i
19.1
'i' is < field 'n_eq'
>= bmap->n_eq)
19
Execution continues on line 5290
20
Taking false branch
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)
21
Assuming 'T' is non-null
22
Taking false branch
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)
23
Assuming 'i' is >= 'n_div'
24
Loop condition is false. Execution continues on line 5304
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);
25
Calling 'isl_basic_map_simplify'
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 */
5313static 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 */
5355static __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;
5486error:
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}