Bug Summary

File:tools/polly/lib/External/isl/isl_map_simplify.c
Warning:line 671, column 41
Division by zero

Annotated Source Code

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clang -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 -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -mthread-model posix -mframe-pointer=none -fmath-errno -masm-verbose -mconstructor-aliases -munwind-tables -fuse-init-array -target-cpu x86-64 -dwarf-column-info -debugger-tuning=gdb -ffunction-sections -fdata-sections -resource-dir /usr/lib/llvm-10/lib/clang/10.0.0 -D _DEBUG -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I /build/llvm-toolchain-snapshot-10~svn374877/build-llvm/tools/polly/lib/External -I /build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External -I /build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/pet/include -I /build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/ppcg/include -I /build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/ppcg/imath -I /build/llvm-toolchain-snapshot-10~svn374877/build-llvm/tools/polly/lib/External/ppcg -I /build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl -I /build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/include -I /build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/imath -I /build/llvm-toolchain-snapshot-10~svn374877/build-llvm/tools/polly/lib/External/isl -I /build/llvm-toolchain-snapshot-10~svn374877/build-llvm/tools/polly/include -I /build/llvm-toolchain-snapshot-10~svn374877/build-llvm/tools/polly/lib/External/isl/include -I /build/llvm-toolchain-snapshot-10~svn374877/tools/polly/include -I /build/llvm-toolchain-snapshot-10~svn374877/build-llvm/include -I /build/llvm-toolchain-snapshot-10~svn374877/include -U NDEBUG -internal-isystem /usr/local/include -internal-isystem /usr/lib/llvm-10/lib/clang/10.0.0/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-10~svn374877/build-llvm/tools/polly/lib/External -fdebug-prefix-map=/build/llvm-toolchain-snapshot-10~svn374877=. -ferror-limit 19 -fmessage-length 0 -stack-protector 2 -fgnuc-version=4.2.1 -fobjc-runtime=gcc -fdiagnostics-show-option -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -o /tmp/scan-build-2019-10-15-233810-7101-1 -x c /build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c

/build/llvm-toolchain-snapshot-10~svn374877/tools/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(struct isl_basic_map *bmap, int a, int b)
32{
33 isl_int *t = bmap->eq[a];
34 bmap->eq[a] = bmap->eq[b];
35 bmap->eq[b] = t;
36}
37
38static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
39{
40 if (a != b) {
41 isl_int *t = bmap->ineq[a];
42 bmap->ineq[a] = bmap->ineq[b];
43 bmap->ineq[b] = t;
44 }
45}
46
47__isl_give isl_basic_map *isl_basic_map_normalize_constraints(
48 __isl_take isl_basic_map *bmap)
49{
50 int i;
51 isl_int gcd;
52 unsigned total = isl_basic_map_total_dim(bmap);
53
54 if (!bmap)
55 return NULL((void*)0);
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 isl_basic_map_drop_equality(bmap, i);
66 continue;
67 }
68 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4)))))
69 isl_int_gcd(gcd, gcd, bmap->eq[i][0])isl_sioimath_gcd((gcd), *(gcd), *(bmap->eq[i][0]));
70 if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0))
71 continue;
72 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)isl_sioimath_is_divisible_by(*(bmap->eq[i][0]), *(gcd))) {
73 bmap = isl_basic_map_set_to_empty(bmap);
74 break;
75 }
76 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
77 }
78
79 for (i = bmap->n_ineq - 1; i >= 0; --i) {
80 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
81 if (isl_int_is_zero(gcd)(isl_sioimath_sgn(*(gcd)) == 0)) {
82 if (isl_int_is_neg(bmap->ineq[i][0])(isl_sioimath_sgn(*(bmap->ineq[i][0])) < 0)) {
83 bmap = isl_basic_map_set_to_empty(bmap);
84 break;
85 }
86 isl_basic_map_drop_inequality(bmap, i);
87 continue;
88 }
89 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4)))))
90 isl_int_gcd(gcd, gcd, bmap->ineq[i][0])isl_sioimath_gcd((gcd), *(gcd), *(bmap->ineq[i][0]));
91 if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0))
92 continue;
93 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))
;
94 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
95 }
96 isl_int_clear(gcd)isl_sioimath_clear((gcd));
97
98 return bmap;
99}
100
101__isl_give isl_basic_setisl_basic_map *isl_basic_set_normalize_constraints(
102 __isl_take isl_basic_setisl_basic_map *bset)
103{
104 isl_basic_map *bmap = bset_to_bmap(bset);
105 return bset_from_bmap(isl_basic_map_normalize_constraints(bmap));
106}
107
108/* Reduce the coefficient of the variable at position "pos"
109 * in integer division "div", such that it lies in the half-open
110 * interval (1/2,1/2], extracting any excess value from this integer division.
111 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
112 * corresponds to the constant term.
113 *
114 * That is, the integer division is of the form
115 *
116 * floor((... + (c * d + r) * x_pos + ...)/d)
117 *
118 * with -d < 2 * r <= d.
119 * Replace it by
120 *
121 * floor((... + r * x_pos + ...)/d) + c * x_pos
122 *
123 * If 2 * ((c * d + r) % d) <= d, then c = floor((c * d + r)/d).
124 * Otherwise, c = floor((c * d + r)/d) + 1.
125 *
126 * This is the same normalization that is performed by isl_aff_floor.
127 */
128static __isl_give isl_basic_map *reduce_coefficient_in_div(
129 __isl_take isl_basic_map *bmap, int div, int pos)
130{
131 isl_int shift;
132 int add_one;
133
134 isl_int_init(shift)isl_sioimath_init((shift));
135 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]))
;
136 isl_int_mul_ui(shift, shift, 2)isl_sioimath_mul_ui((shift), *(shift), 2);
137 add_one = isl_int_gt(shift, bmap->div[div][0])(isl_sioimath_cmp(*(shift), *(bmap->div[div][0])) > 0);
138 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]))
;
139 if (add_one)
140 isl_int_add_ui(shift, shift, 1)isl_sioimath_add_ui((shift), *(shift), 1);
141 isl_int_neg(shift, shift)isl_sioimath_neg((shift), *(shift));
142 bmap = isl_basic_map_shift_div(bmap, div, pos, shift);
143 isl_int_clear(shift)isl_sioimath_clear((shift));
144
145 return bmap;
146}
147
148/* Does the coefficient of the variable at position "pos"
149 * in integer division "div" need to be reduced?
150 * That is, does it lie outside the half-open interval (1/2,1/2]?
151 * The coefficient c/d lies outside this interval if abs(2 * c) >= d and
152 * 2 * c != d.
153 */
154static isl_bool needs_reduction(__isl_keep isl_basic_map *bmap, int div,
155 int pos)
156{
157 isl_bool r;
158
159 if (isl_int_is_zero(bmap->div[div][1 + pos])(isl_sioimath_sgn(*(bmap->div[div][1 + pos])) == 0))
160 return isl_bool_false;
161
162 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)
;
163 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)
&&
164 !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)
;
165 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)
166 bmap->div[div][1 + pos], 2)isl_sioimath_tdiv_q_ui((bmap->div[div][1 + pos]), *(bmap->
div[div][1 + pos]), 2)
;
167
168 return r;
169}
170
171/* Reduce the coefficients (including the constant term) of
172 * integer division "div", if needed.
173 * In particular, make sure all coefficients lie in
174 * the half-open interval (1/2,1/2].
175 */
176static __isl_give isl_basic_map *reduce_div_coefficients_of_div(
177 __isl_take isl_basic_map *bmap, int div)
178{
179 int i;
180 unsigned total = 1 + isl_basic_map_total_dim(bmap);
181
182 for (i = 0; i < total; ++i) {
183 isl_bool reduce;
184
185 reduce = needs_reduction(bmap, div, i);
186 if (reduce < 0)
187 return isl_basic_map_free(bmap);
188 if (!reduce)
189 continue;
190 bmap = reduce_coefficient_in_div(bmap, div, i);
191 if (!bmap)
192 break;
193 }
194
195 return bmap;
196}
197
198/* Reduce the coefficients (including the constant term) of
199 * the known integer divisions, if needed
200 * In particular, make sure all coefficients lie in
201 * the half-open interval (1/2,1/2].
202 */
203static __isl_give isl_basic_map *reduce_div_coefficients(
204 __isl_take isl_basic_map *bmap)
205{
206 int i;
207
208 if (!bmap)
209 return NULL((void*)0);
210 if (bmap->n_div == 0)
211 return bmap;
212
213 for (i = 0; i < bmap->n_div; ++i) {
214 if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
215 continue;
216 bmap = reduce_div_coefficients_of_div(bmap, i);
217 if (!bmap)
218 break;
219 }
220
221 return bmap;
222}
223
224/* Remove any common factor in numerator and denominator of the div expression,
225 * not taking into account the constant term.
226 * That is, if the div is of the form
227 *
228 * floor((a + m f(x))/(m d))
229 *
230 * then replace it by
231 *
232 * floor((floor(a/m) + f(x))/d)
233 *
234 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
235 * and can therefore not influence the result of the floor.
236 */
237static void normalize_div_expression(__isl_keep isl_basic_map *bmap, int div)
238{
239 unsigned total = isl_basic_map_total_dim(bmap);
240 isl_ctx *ctx = bmap->ctx;
241
242 if (isl_int_is_zero(bmap->div[div][0])(isl_sioimath_sgn(*(bmap->div[div][0])) == 0))
243 return;
244 isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd);
245 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]))
;
246 if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0))
247 return;
248 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))
249 ctx->normalize_gcd)isl_sioimath_fdiv_q((bmap->div[div][1]), *(bmap->div[div
][1]), *(ctx->normalize_gcd))
;
250 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))
251 ctx->normalize_gcd)isl_sioimath_tdiv_q((bmap->div[div][0]), *(bmap->div[div
][0]), *(ctx->normalize_gcd))
;
252 isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2,
253 ctx->normalize_gcd, total);
254}
255
256/* Remove any common factor in numerator and denominator of a div expression,
257 * not taking into account the constant term.
258 * That is, look for any div of the form
259 *
260 * floor((a + m f(x))/(m d))
261 *
262 * and replace it by
263 *
264 * floor((floor(a/m) + f(x))/d)
265 *
266 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
267 * and can therefore not influence the result of the floor.
268 */
269static __isl_give isl_basic_map *normalize_div_expressions(
270 __isl_take isl_basic_map *bmap)
271{
272 int i;
273
274 if (!bmap)
275 return NULL((void*)0);
276 if (bmap->n_div == 0)
277 return bmap;
278
279 for (i = 0; i < bmap->n_div; ++i)
280 normalize_div_expression(bmap, i);
281
282 return bmap;
283}
284
285/* Assumes divs have been ordered if keep_divs is set.
286 */
287static void eliminate_var_using_equality(struct isl_basic_map *bmap,
288 unsigned pos, isl_int *eq, int keep_divs, int *progress)
289{
290 unsigned total;
291 unsigned space_total;
292 int k;
293 int last_div;
294
295 total = isl_basic_map_total_dim(bmap);
296 space_total = isl_space_dim(bmap->dim, isl_dim_all);
297 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
298 for (k = 0; k < bmap->n_eq; ++k) {
299 if (bmap->eq[k] == eq)
300 continue;
301 if (isl_int_is_zero(bmap->eq[k][1+pos])(isl_sioimath_sgn(*(bmap->eq[k][1+pos])) == 0))
302 continue;
303 if (progress)
304 *progress = 1;
305 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL((void*)0));
306 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
307 }
308
309 for (k = 0; k < bmap->n_ineq; ++k) {
310 if (isl_int_is_zero(bmap->ineq[k][1+pos])(isl_sioimath_sgn(*(bmap->ineq[k][1+pos])) == 0))
311 continue;
312 if (progress)
313 *progress = 1;
314 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL((void*)0));
315 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
316 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED)(((bmap)->flags) &= ~((1 << 5)));
317 }
318
319 for (k = 0; k < bmap->n_div; ++k) {
320 if (isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0))
321 continue;
322 if (isl_int_is_zero(bmap->div[k][1+1+pos])(isl_sioimath_sgn(*(bmap->div[k][1+1+pos])) == 0))
323 continue;
324 if (progress)
325 *progress = 1;
326 /* We need to be careful about circular definitions,
327 * so for now we just remove the definition of div k
328 * if the equality contains any divs.
329 * If keep_divs is set, then the divs have been ordered
330 * and we can keep the definition as long as the result
331 * is still ordered.
332 */
333 if (last_div == -1 || (keep_divs && last_div < k)) {
334 isl_seq_elim(bmap->div[k]+1, eq,
335 1+pos, 1+total, &bmap->div[k][0]);
336 normalize_div_expression(bmap, k);
337 } else
338 isl_seq_clr(bmap->div[k], 1 + total);
339 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED)(((bmap)->flags) &= ~((1 << 5)));
340 }
341}
342
343/* Assumes divs have been ordered if keep_divs is set.
344 */
345static __isl_give isl_basic_map *eliminate_div(__isl_take isl_basic_map *bmap,
346 isl_int *eq, unsigned div, int keep_divs)
347{
348 unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
349
350 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL((void*)0));
351
352 bmap = isl_basic_map_drop_div(bmap, div);
353
354 return bmap;
355}
356
357/* Check if elimination of div "div" using equality "eq" would not
358 * result in a div depending on a later div.
359 */
360static isl_bool ok_to_eliminate_div(__isl_keep isl_basic_map *bmap, isl_int *eq,
361 unsigned div)
362{
363 int k;
364 int last_div;
365 unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
366 unsigned pos = space_total + div;
367
368 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
369 if (last_div < 0 || last_div <= div)
370 return isl_bool_true;
371
372 for (k = 0; k <= last_div; ++k) {
373 if (isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0))
374 continue;
375 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos])(isl_sioimath_sgn(*(bmap->div[k][1 + 1 + pos])) == 0))
376 return isl_bool_false;
377 }
378
379 return isl_bool_true;
380}
381
382/* Eliminate divs based on equalities
383 */
384static __isl_give isl_basic_map *eliminate_divs_eq(
385 __isl_take isl_basic_map *bmap, int *progress)
386{
387 int d;
388 int i;
389 int modified = 0;
390 unsigned off;
391
392 bmap = isl_basic_map_order_divs(bmap);
393
394 if (!bmap)
395 return NULL((void*)0);
396
397 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
398
399 for (d = bmap->n_div - 1; d >= 0 ; --d) {
400 for (i = 0; i < bmap->n_eq; ++i) {
401 isl_bool ok;
402
403 if (!isl_int_is_one(bmap->eq[i][off + d])(isl_sioimath_cmp_si(*(bmap->eq[i][off + d]), 1) == 0) &&
404 !isl_int_is_negone(bmap->eq[i][off + d])(isl_sioimath_cmp_si(*(bmap->eq[i][off + d]), -1) == 0))
405 continue;
406 ok = ok_to_eliminate_div(bmap, bmap->eq[i], d);
407 if (ok < 0)
408 return isl_basic_map_free(bmap);
409 if (!ok)
410 continue;
411 modified = 1;
412 *progress = 1;
413 bmap = eliminate_div(bmap, bmap->eq[i], d, 1);
414 if (isl_basic_map_drop_equality(bmap, i) < 0)
415 return isl_basic_map_free(bmap);
416 break;
417 }
418 }
419 if (modified)
420 return eliminate_divs_eq(bmap, progress);
421 return bmap;
422}
423
424/* Eliminate divs based on inequalities
425 */
426static __isl_give isl_basic_map *eliminate_divs_ineq(
427 __isl_take isl_basic_map *bmap, int *progress)
428{
429 int d;
430 int i;
431 unsigned off;
432 struct isl_ctx *ctx;
433
434 if (!bmap)
435 return NULL((void*)0);
436
437 ctx = bmap->ctx;
438 off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
439
440 for (d = bmap->n_div - 1; d >= 0 ; --d) {
441 for (i = 0; i < bmap->n_eq; ++i)
442 if (!isl_int_is_zero(bmap->eq[i][off + d])(isl_sioimath_sgn(*(bmap->eq[i][off + d])) == 0))
443 break;
444 if (i < bmap->n_eq)
445 continue;
446 for (i = 0; i < bmap->n_ineq; ++i)
447 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one)(isl_sioimath_abs_cmp(*(bmap->ineq[i][off + d]), *(ctx->
one)) > 0)
)
448 break;
449 if (i < bmap->n_ineq)
450 continue;
451 *progress = 1;
452 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
453 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1)))))
454 break;
455 bmap = isl_basic_map_drop_div(bmap, d);
456 if (!bmap)
457 break;
458 }
459 return bmap;
460}
461
462/* Does the equality constraint at position "eq" in "bmap" involve
463 * any local variables in the range [first, first + n)
464 * that are not marked as having an explicit representation?
465 */
466static isl_bool bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map *bmap,
467 int eq, unsigned first, unsigned n)
468{
469 unsigned o_div;
470 int i;
471
472 if (!bmap)
473 return isl_bool_error;
474
475 o_div = isl_basic_map_offset(bmap, isl_dim_div);
476 for (i = 0; i < n; ++i) {
477 isl_bool unknown;
478
479 if (isl_int_is_zero(bmap->eq[eq][o_div + first + i])(isl_sioimath_sgn(*(bmap->eq[eq][o_div + first + i])) == 0
)
)
480 continue;
481 unknown = isl_basic_map_div_is_marked_unknown(bmap, first + i);
482 if (unknown < 0)
483 return isl_bool_error;
484 if (unknown)
485 return isl_bool_true;
486 }
487
488 return isl_bool_false;
489}
490
491/* The last local variable involved in the equality constraint
492 * at position "eq" in "bmap" is the local variable at position "div".
493 * It can therefore be used to extract an explicit representation
494 * for that variable.
495 * Do so unless the local variable already has an explicit representation or
496 * the explicit representation would involve any other local variables
497 * that in turn do not have an explicit representation.
498 * An equality constraint involving local variables without an explicit
499 * representation can be used in isl_basic_map_drop_redundant_divs
500 * to separate out an independent local variable. Introducing
501 * an explicit representation here would block this transformation,
502 * while the partial explicit representation in itself is not very useful.
503 * Set *progress if anything is changed.
504 *
505 * The equality constraint is of the form
506 *
507 * f(x) + n e >= 0
508 *
509 * with n a positive number. The explicit representation derived from
510 * this constraint is
511 *
512 * floor((-f(x))/n)
513 */
514static __isl_give isl_basic_map *set_div_from_eq(__isl_take isl_basic_map *bmap,
515 int div, int eq, int *progress)
516{
517 unsigned total, o_div;
518 isl_bool involves;
519
520 if (!bmap)
521 return NULL((void*)0);
522
523 if (!isl_int_is_zero(bmap->div[div][0])(isl_sioimath_sgn(*(bmap->div[div][0])) == 0))
524 return bmap;
525
526 involves = bmap_eq_involves_unknown_divs(bmap, eq, 0, div);
527 if (involves < 0)
528 return isl_basic_map_free(bmap);
529 if (involves)
530 return bmap;
531
532 total = isl_basic_map_dim(bmap, isl_dim_all);
533 o_div = isl_basic_map_offset(bmap, isl_dim_div);
534 isl_seq_neg(bmap->div[div] + 1, bmap->eq[eq], 1 + total);
535 isl_int_set_si(bmap->div[div][1 + o_div + div], 0)isl_sioimath_set_si((bmap->div[div][1 + o_div + div]), 0);
536 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]))
;
537 if (progress)
538 *progress = 1;
539 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED)(((bmap)->flags) &= ~((1 << 5)));
540
541 return bmap;
542}
543
544__isl_give isl_basic_map *isl_basic_map_gauss(__isl_take isl_basic_map *bmap,
545 int *progress)
546{
547 int k;
548 int done;
549 int last_var;
550 unsigned total_var;
551 unsigned total;
552
553 bmap = isl_basic_map_order_divs(bmap);
554
555 if (!bmap)
556 return NULL((void*)0);
557
558 total = isl_basic_map_total_dim(bmap);
559 total_var = total - bmap->n_div;
560
561 last_var = total - 1;
562 for (done = 0; done < bmap->n_eq; ++done) {
563 for (; last_var >= 0; --last_var) {
564 for (k = done; k < bmap->n_eq; ++k)
565 if (!isl_int_is_zero(bmap->eq[k][1+last_var])(isl_sioimath_sgn(*(bmap->eq[k][1+last_var])) == 0))
566 break;
567 if (k < bmap->n_eq)
568 break;
569 }
570 if (last_var < 0)
571 break;
572 if (k != done)
573 swap_equality(bmap, k, done);
574 if (isl_int_is_neg(bmap->eq[done][1+last_var])(isl_sioimath_sgn(*(bmap->eq[done][1+last_var])) < 0))
575 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
576
577 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
578 progress);
579
580 if (last_var >= total_var)
581 bmap = set_div_from_eq(bmap, last_var - total_var,
582 done, progress);
583 if (!bmap)
584 return NULL((void*)0);
585 }
586 if (done == bmap->n_eq)
587 return bmap;
588 for (k = done; k < bmap->n_eq; ++k) {
589 if (isl_int_is_zero(bmap->eq[k][0])(isl_sioimath_sgn(*(bmap->eq[k][0])) == 0))
590 continue;
591 return isl_basic_map_set_to_empty(bmap);
592 }
593 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
594 return bmap;
595}
596
597__isl_give isl_basic_setisl_basic_map *isl_basic_set_gauss(
598 __isl_take isl_basic_setisl_basic_map *bset, int *progress)
599{
600 return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset),
601 progress));
602}
603
604
605static unsigned int round_up(unsigned int v)
606{
607 int old_v = v;
608
609 while (v) {
88
Loop condition is false. Execution continues on line 613
610 old_v = v;
611 v ^= v & -v;
612 }
613 return old_v << 1;
89
Returning zero
614}
615
616/* Hash table of inequalities in a basic map.
617 * "index" is an array of addresses of inequalities in the basic map, some
618 * of which are NULL. The inequalities are hashed on the coefficients
619 * except the constant term.
620 * "size" is the number of elements in the array and is always a power of two
621 * "bits" is the number of bits need to represent an index into the array.
622 * "total" is the total dimension of the basic map.
623 */
624struct isl_constraint_index {
625 unsigned int size;
626 int bits;
627 isl_int ***index;
628 unsigned total;
629};
630
631/* Fill in the "ci" data structure for holding the inequalities of "bmap".
632 */
633static isl_stat create_constraint_index(struct isl_constraint_index *ci,
634 __isl_keep isl_basic_map *bmap)
635{
636 isl_ctx *ctx;
637
638 ci->index = NULL((void*)0);
639 if (!bmap
84.1
'bmap' is non-null
84.1
'bmap' is non-null
)
85
Taking false branch
640 return isl_stat_error;
641 ci->total = isl_basic_set_total_dim(bmap);
642 if (bmap->n_ineq
85.1
Field 'n_ineq' is not equal to 0
85.1
Field 'n_ineq' is not equal to 0
== 0)
86
Taking false branch
643 return isl_stat_ok;
644 ci->size = round_up(4 * (bmap->n_ineq + 1) / 3 - 1);
87
Calling 'round_up'
90
Returning from 'round_up'
91
The value 0 is assigned to 'ci.size'
645 ci->bits = ffs(ci->size) - 1;
646 ctx = isl_basic_map_get_ctx(bmap);
647 ci->index = isl_calloc_array(ctx, isl_int **, ci->size)((isl_int ** *)isl_calloc_or_die(ctx, ci->size, sizeof(isl_int
**)))
;
648 if (!ci->index)
92
Assuming field 'index' is non-null
93
Taking false branch
649 return isl_stat_error;
650
651 return isl_stat_ok;
652}
653
654/* Free the memory allocated by create_constraint_index.
655 */
656static void constraint_index_free(struct isl_constraint_index *ci)
657{
658 free(ci->index);
659}
660
661/* Return the position in ci->index that contains the address of
662 * an inequality that is equal to *ineq up to the constant term,
663 * provided this address is not identical to "ineq".
664 * If there is no such inequality, then return the position where
665 * such an inequality should be inserted.
666 */
667static int hash_index_ineq(struct isl_constraint_index *ci, isl_int **ineq)
668{
669 int h;
670 uint32_t hash = isl_seq_get_hash_bits((*ineq) + 1, ci->total, ci->bits);
671 for (h = hash; ci->index[h]; h = (h+1) % ci->size)
100
Loop condition is true. Entering loop body
102
Division by zero
672 if (ineq != ci->index[h] &&
101
Assuming the condition is false
673 isl_seq_eq((*ineq) + 1, ci->index[h][0]+1, ci->total))
674 break;
675 return h;
676}
677
678/* Return the position in ci->index that contains the address of
679 * an inequality that is equal to the k'th inequality of "bmap"
680 * up to the constant term, provided it does not point to the very
681 * same inequality.
682 * If there is no such inequality, then return the position where
683 * such an inequality should be inserted.
684 */
685static int hash_index(struct isl_constraint_index *ci,
686 __isl_keep isl_basic_map *bmap, int k)
687{
688 return hash_index_ineq(ci, &bmap->ineq[k]);
99
Calling 'hash_index_ineq'
689}
690
691static int set_hash_index(struct isl_constraint_index *ci,
692 __isl_keep isl_basic_setisl_basic_map *bset, int k)
693{
694 return hash_index(ci, bset, k);
695}
696
697/* Fill in the "ci" data structure with the inequalities of "bset".
698 */
699static isl_stat setup_constraint_index(struct isl_constraint_index *ci,
700 __isl_keep isl_basic_setisl_basic_map *bset)
701{
702 int k, h;
703
704 if (create_constraint_index(ci, bset) < 0)
705 return isl_stat_error;
706
707 for (k = 0; k < bset->n_ineq; ++k) {
708 h = set_hash_index(ci, bset, k);
709 ci->index[h] = &bset->ineq[k];
710 }
711
712 return isl_stat_ok;
713}
714
715/* Is the inequality ineq (obviously) redundant with respect
716 * to the constraints in "ci"?
717 *
718 * Look for an inequality in "ci" with the same coefficients and then
719 * check if the contant term of "ineq" is greater than or equal
720 * to the constant term of that inequality. If so, "ineq" is clearly
721 * redundant.
722 *
723 * Note that hash_index_ineq ignores a stored constraint if it has
724 * the same address as the passed inequality. It is ok to pass
725 * the address of a local variable here since it will never be
726 * the same as the address of a constraint in "ci".
727 */
728static isl_bool constraint_index_is_redundant(struct isl_constraint_index *ci,
729 isl_int *ineq)
730{
731 int h;
732
733 h = hash_index_ineq(ci, &ineq);
734 if (!ci->index[h])
735 return isl_bool_false;
736 return isl_int_ge(ineq[0], (*ci->index[h])[0])(isl_sioimath_cmp(*(ineq[0]), *((*ci->index[h])[0])) >=
0)
;
737}
738
739/* If we can eliminate more than one div, then we need to make
740 * sure we do it from last div to first div, in order not to
741 * change the position of the other divs that still need to
742 * be removed.
743 */
744static __isl_give isl_basic_map *remove_duplicate_divs(
745 __isl_take isl_basic_map *bmap, int *progress)
746{
747 unsigned int size;
748 int *index;
749 int *elim_for;
750 int k, l, h;
751 int bits;
752 struct isl_blk eq;
753 unsigned total_var;
754 unsigned total;
755 struct isl_ctx *ctx;
756
757 bmap = isl_basic_map_order_divs(bmap);
758 if (!bmap || bmap->n_div <= 1)
759 return bmap;
760
761 total_var = isl_space_dim(bmap->dim, isl_dim_all);
762 total = total_var + bmap->n_div;
763
764 ctx = bmap->ctx;
765 for (k = bmap->n_div - 1; k >= 0; --k)
766 if (!isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0))
767 break;
768 if (k <= 0)
769 return bmap;
770
771 size = round_up(4 * bmap->n_div / 3 - 1);
772 if (size == 0)
773 return bmap;
774 elim_for = isl_calloc_array(ctx, int, bmap->n_div)((int *)isl_calloc_or_die(ctx, bmap->n_div, sizeof(int)));
775 bits = ffs(size) - 1;
776 index = isl_calloc_array(ctx, int, size)((int *)isl_calloc_or_die(ctx, size, sizeof(int)));
777 if (!elim_for || !index)
778 goto out;
779 eq = isl_blk_alloc(ctx, 1+total);
780 if (isl_blk_is_error(eq))
781 goto out;
782
783 isl_seq_clr(eq.data, 1+total);
784 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
785 for (--k; k >= 0; --k) {
786 uint32_t hash;
787
788 if (isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0))
789 continue;
790
791 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
792 for (h = hash; index[h]; h = (h+1) % size)
793 if (isl_seq_eq(bmap->div[k],
794 bmap->div[index[h]-1], 2+total))
795 break;
796 if (index[h]) {
797 *progress = 1;
798 l = index[h] - 1;
799 elim_for[l] = k + 1;
800 }
801 index[h] = k+1;
802 }
803 for (l = bmap->n_div - 1; l >= 0; --l) {
804 if (!elim_for[l])
805 continue;
806 k = elim_for[l] - 1;
807 isl_int_set_si(eq.data[1+total_var+k], -1)isl_sioimath_set_si((eq.data[1+total_var+k]), -1);
808 isl_int_set_si(eq.data[1+total_var+l], 1)isl_sioimath_set_si((eq.data[1+total_var+l]), 1);
809 bmap = eliminate_div(bmap, eq.data, l, 1);
810 if (!bmap)
811 break;
812 isl_int_set_si(eq.data[1+total_var+k], 0)isl_sioimath_set_si((eq.data[1+total_var+k]), 0);
813 isl_int_set_si(eq.data[1+total_var+l], 0)isl_sioimath_set_si((eq.data[1+total_var+l]), 0);
814 }
815
816 isl_blk_free(ctx, eq);
817out:
818 free(index);
819 free(elim_for);
820 return bmap;
821}
822
823static int n_pure_div_eq(struct isl_basic_map *bmap)
824{
825 int i, j;
826 unsigned total;
827
828 total = isl_space_dim(bmap->dim, isl_dim_all);
829 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
830 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j])(isl_sioimath_sgn(*(bmap->eq[i][1 + total + j])) == 0))
831 --j;
832 if (j < 0)
833 break;
834 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
835 return 0;
836 }
837 return i;
838}
839
840/* Normalize divs that appear in equalities.
841 *
842 * In particular, we assume that bmap contains some equalities
843 * of the form
844 *
845 * a x = m * e_i
846 *
847 * and we want to replace the set of e_i by a minimal set and
848 * such that the new e_i have a canonical representation in terms
849 * of the vector x.
850 * If any of the equalities involves more than one divs, then
851 * we currently simply bail out.
852 *
853 * Let us first additionally assume that all equalities involve
854 * a div. The equalities then express modulo constraints on the
855 * remaining variables and we can use "parameter compression"
856 * to find a minimal set of constraints. The result is a transformation
857 *
858 * x = T(x') = x_0 + G x'
859 *
860 * with G a lower-triangular matrix with all elements below the diagonal
861 * non-negative and smaller than the diagonal element on the same row.
862 * We first normalize x_0 by making the same property hold in the affine
863 * T matrix.
864 * The rows i of G with a 1 on the diagonal do not impose any modulo
865 * constraint and simply express x_i = x'_i.
866 * For each of the remaining rows i, we introduce a div and a corresponding
867 * equality. In particular
868 *
869 * g_ii e_j = x_i - g_i(x')
870 *
871 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
872 * corresponding div (if g_kk != 1).
873 *
874 * If there are any equalities not involving any div, then we
875 * first apply a variable compression on the variables x:
876 *
877 * x = C x'' x'' = C_2 x
878 *
879 * and perform the above parameter compression on A C instead of on A.
880 * The resulting compression is then of the form
881 *
882 * x'' = T(x') = x_0 + G x'
883 *
884 * and in constructing the new divs and the corresponding equalities,
885 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
886 * by the corresponding row from C_2.
887 */
888static __isl_give isl_basic_map *normalize_divs(__isl_take isl_basic_map *bmap,
889 int *progress)
890{
891 int i, j, k;
892 int total;
893 int div_eq;
894 struct isl_mat *B;
895 struct isl_vec *d;
896 struct isl_mat *T = NULL((void*)0);
897 struct isl_mat *C = NULL((void*)0);
898 struct isl_mat *C2 = NULL((void*)0);
899 isl_int v;
900 int *pos = NULL((void*)0);
901 int dropped, needed;
902
903 if (!bmap)
904 return NULL((void*)0);
905
906 if (bmap->n_div == 0)
907 return bmap;
908
909 if (bmap->n_eq == 0)
910 return bmap;
911
912 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS)(!!(((bmap)->flags) & ((1 << 6)))))
913 return bmap;
914
915 total = isl_space_dim(bmap->dim, isl_dim_all);
916 div_eq = n_pure_div_eq(bmap);
917 if (div_eq == 0)
918 return bmap;
919
920 if (div_eq < bmap->n_eq) {
921 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
922 bmap->n_eq - div_eq, 0, 1 + total);
923 C = isl_mat_variable_compression(B, &C2);
924 if (!C || !C2)
925 goto error;
926 if (C->n_col == 0) {
927 bmap = isl_basic_map_set_to_empty(bmap);
928 isl_mat_free(C);
929 isl_mat_free(C2);
930 goto done;
931 }
932 }
933
934 d = isl_vec_alloc(bmap->ctx, div_eq);
935 if (!d)
936 goto error;
937 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
938 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j])(isl_sioimath_sgn(*(bmap->eq[i][1 + total + j])) == 0))
939 --j;
940 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j])isl_sioimath_set((d->block.data[i]), *(bmap->eq[i][1 + total
+ j]))
;
941 }
942 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
943
944 if (C) {
945 B = isl_mat_product(B, C);
946 C = NULL((void*)0);
947 }
948
949 T = isl_mat_parameter_compression(B, d);
950 if (!T)
951 goto error;
952 if (T->n_col == 0) {
953 bmap = isl_basic_map_set_to_empty(bmap);
954 isl_mat_free(C2);
955 isl_mat_free(T);
956 goto done;
957 }
958 isl_int_init(v)isl_sioimath_init((v));
959 for (i = 0; i < T->n_row - 1; ++i) {
960 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]))
;
961 if (isl_int_is_zero(v)(isl_sioimath_sgn(*(v)) == 0))
962 continue;
963 isl_mat_col_submul(T, 0, v, 1 + i);
964 }
965 isl_int_clear(v)isl_sioimath_clear((v));
966 pos = isl_alloc_array(bmap->ctx, int, T->n_row)((int *)isl_malloc_or_die(bmap->ctx, (T->n_row)*sizeof(
int)))
;
967 if (!pos)
968 goto error;
969 /* We have to be careful because dropping equalities may reorder them */
970 dropped = 0;
971 for (j = bmap->n_div - 1; j >= 0; --j) {
972 for (i = 0; i < bmap->n_eq; ++i)
973 if (!isl_int_is_zero(bmap->eq[i][1 + total + j])(isl_sioimath_sgn(*(bmap->eq[i][1 + total + j])) == 0))
974 break;
975 if (i < bmap->n_eq) {
976 bmap = isl_basic_map_drop_div(bmap, j);
977 isl_basic_map_drop_equality(bmap, i);
978 ++dropped;
979 }
980 }
981 pos[0] = 0;
982 needed = 0;
983 for (i = 1; i < T->n_row; ++i) {
984 if (isl_int_is_one(T->row[i][i])(isl_sioimath_cmp_si(*(T->row[i][i]), 1) == 0))
985 pos[i] = i;
986 else
987 needed++;
988 }
989 if (needed > dropped) {
990 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
991 needed, needed, 0);
992 if (!bmap)
993 goto error;
994 }
995 for (i = 1; i < T->n_row; ++i) {
996 if (isl_int_is_one(T->row[i][i])(isl_sioimath_cmp_si(*(T->row[i][i]), 1) == 0))
997 continue;
998 k = isl_basic_map_alloc_div(bmap);
999 pos[i] = 1 + total + k;
1000 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
1001 isl_int_set(bmap->div[k][0], T->row[i][i])isl_sioimath_set((bmap->div[k][0]), *(T->row[i][i]));
1002 if (C2)
1003 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
1004 else
1005 isl_int_set_si(bmap->div[k][1 + i], 1)isl_sioimath_set_si((bmap->div[k][1 + i]), 1);
1006 for (j = 0; j < i; ++j) {
1007 if (isl_int_is_zero(T->row[i][j])(isl_sioimath_sgn(*(T->row[i][j])) == 0))
1008 continue;
1009 if (pos[j] < T->n_row && C2)
1010 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
1011 C2->row[pos[j]], 1 + total);
1012 else
1013 isl_int_neg(bmap->div[k][1 + pos[j]],isl_sioimath_neg((bmap->div[k][1 + pos[j]]), *(T->row[i
][j]))
1014 T->row[i][j])isl_sioimath_neg((bmap->div[k][1 + pos[j]]), *(T->row[i
][j]))
;
1015 }
1016 j = isl_basic_map_alloc_equality(bmap);
1017 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
1018 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0])isl_sioimath_set((bmap->eq[j][pos[i]]), *(bmap->div[k][
0]))
;
1019 }
1020 free(pos);
1021 isl_mat_free(C2);
1022 isl_mat_free(T);
1023
1024 if (progress)
1025 *progress = 1;
1026done:
1027 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS)(((bmap)->flags) |= ((1 << 6)));
1028
1029 return bmap;
1030error:
1031 free(pos);
1032 isl_mat_free(C);
1033 isl_mat_free(C2);
1034 isl_mat_free(T);
1035 return bmap;
1036}
1037
1038static __isl_give isl_basic_map *set_div_from_lower_bound(
1039 __isl_take isl_basic_map *bmap, int div, int ineq)
1040{
1041 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1042
1043 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
1044 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div])isl_sioimath_set((bmap->div[div][0]), *(bmap->ineq[ineq
][total + div]))
;
1045 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]))
;
1046 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)
;
1047 isl_int_set_si(bmap->div[div][1 + total + div], 0)isl_sioimath_set_si((bmap->div[div][1 + total + div]), 0);
1048
1049 return bmap;
1050}
1051
1052/* Check whether it is ok to define a div based on an inequality.
1053 * To avoid the introduction of circular definitions of divs, we
1054 * do not allow such a definition if the resulting expression would refer to
1055 * any other undefined divs or if any known div is defined in
1056 * terms of the unknown div.
1057 */
1058static isl_bool ok_to_set_div_from_bound(__isl_keep isl_basic_map *bmap,
1059 int div, int ineq)
1060{
1061 int j;
1062 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1063
1064 /* Not defined in terms of unknown divs */
1065 for (j = 0; j < bmap->n_div; ++j) {
1066 if (div == j)
1067 continue;
1068 if (isl_int_is_zero(bmap->ineq[ineq][total + j])(isl_sioimath_sgn(*(bmap->ineq[ineq][total + j])) == 0))
1069 continue;
1070 if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0))
1071 return isl_bool_false;
1072 }
1073
1074 /* No other div defined in terms of this one => avoid loops */
1075 for (j = 0; j < bmap->n_div; ++j) {
1076 if (div == j)
1077 continue;
1078 if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0))
1079 continue;
1080 if (!isl_int_is_zero(bmap->div[j][1 + total + div])(isl_sioimath_sgn(*(bmap->div[j][1 + total + div])) == 0))
1081 return isl_bool_false;
1082 }
1083
1084 return isl_bool_true;
1085}
1086
1087/* Would an expression for div "div" based on inequality "ineq" of "bmap"
1088 * be a better expression than the current one?
1089 *
1090 * If we do not have any expression yet, then any expression would be better.
1091 * Otherwise we check if the last variable involved in the inequality
1092 * (disregarding the div that it would define) is in an earlier position
1093 * than the last variable involved in the current div expression.
1094 */
1095static isl_bool better_div_constraint(__isl_keep isl_basic_map *bmap,
1096 int div, int ineq)
1097{
1098 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1099 int last_div;
1100 int last_ineq;
1101
1102 if (isl_int_is_zero(bmap->div[div][0])(isl_sioimath_sgn(*(bmap->div[div][0])) == 0))
1103 return isl_bool_true;
1104
1105 if (isl_seq_last_non_zero(bmap->ineq[ineq] + total + div + 1,
1106 bmap->n_div - (div + 1)) >= 0)
1107 return isl_bool_false;
1108
1109 last_ineq = isl_seq_last_non_zero(bmap->ineq[ineq], total + div);
1110 last_div = isl_seq_last_non_zero(bmap->div[div] + 1,
1111 total + bmap->n_div);
1112
1113 return last_ineq < last_div;
1114}
1115
1116/* Given two constraints "k" and "l" that are opposite to each other,
1117 * except for the constant term, check if we can use them
1118 * to obtain an expression for one of the hitherto unknown divs or
1119 * a "better" expression for a div for which we already have an expression.
1120 * "sum" is the sum of the constant terms of the constraints.
1121 * If this sum is strictly smaller than the coefficient of one
1122 * of the divs, then this pair can be used define the div.
1123 * To avoid the introduction of circular definitions of divs, we
1124 * do not use the pair if the resulting expression would refer to
1125 * any other undefined divs or if any known div is defined in
1126 * terms of the unknown div.
1127 */
1128static __isl_give isl_basic_map *check_for_div_constraints(
1129 __isl_take isl_basic_map *bmap, int k, int l, isl_int sum,
1130 int *progress)
1131{
1132 int i;
1133 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1134
1135 for (i = 0; i < bmap->n_div; ++i) {
1136 isl_bool set_div;
1137
1138 if (isl_int_is_zero(bmap->ineq[k][total + i])(isl_sioimath_sgn(*(bmap->ineq[k][total + i])) == 0))
1139 continue;
1140 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i])(isl_sioimath_abs_cmp(*(sum), *(bmap->ineq[k][total + i]))
>= 0)
)
1141 continue;
1142 set_div = better_div_constraint(bmap, i, k);
1143 if (set_div >= 0 && set_div)
1144 set_div = ok_to_set_div_from_bound(bmap, i, k);
1145 if (set_div < 0)
1146 return isl_basic_map_free(bmap);
1147 if (!set_div)
1148 break;
1149 if (isl_int_is_pos(bmap->ineq[k][total + i])(isl_sioimath_sgn(*(bmap->ineq[k][total + i])) > 0))
1150 bmap = set_div_from_lower_bound(bmap, i, k);
1151 else
1152 bmap = set_div_from_lower_bound(bmap, i, l);
1153 if (progress)
1154 *progress = 1;
1155 break;
1156 }
1157 return bmap;
1158}
1159
1160__isl_give isl_basic_map *isl_basic_map_remove_duplicate_constraints(
1161 __isl_take isl_basic_map *bmap, int *progress, int detect_divs)
1162{
1163 struct isl_constraint_index ci;
1164 int k, l, h;
1165 unsigned total = isl_basic_map_total_dim(bmap);
1166 isl_int sum;
1167
1168 if (!bmap
62.1
'bmap' is non-null
81.1
'bmap' is non-null
62.1
'bmap' is non-null
81.1
'bmap' is non-null
|| bmap->n_ineq
62.2
Field 'n_ineq' is > 1
62.2
Field 'n_ineq' is > 1
<= 1
)
63
Taking false branch
82
Assuming field 'n_ineq' is > 1
83
Taking false branch
1169 return bmap;
1170
1171 if (create_constraint_index(&ci, bmap) < 0)
64
Taking false branch
84
Calling 'create_constraint_index'
94
Returning from 'create_constraint_index'
95
Taking false branch
1172 return bmap;
1173
1174 h = isl_seq_get_hash_bits(bmap->ineq[0] + 1, total, ci.bits);
1175 ci.index[h] = &bmap->ineq[0];
1176 for (k = 1; k < bmap->n_ineq; ++k) {
65
Assuming 'k' is >= field 'n_ineq'
66
Loop condition is false. Execution continues on line 1190
96
Assuming 'k' is < field 'n_ineq'
97
Loop condition is true. Entering loop body
1177 h = hash_index(&ci, bmap, k);
98
Calling 'hash_index'
1178 if (!ci.index[h]) {
1179 ci.index[h] = &bmap->ineq[k];
1180 continue;
1181 }
1182 if (progress)
1183 *progress = 1;
1184 l = ci.index[h] - &bmap->ineq[0];
1185 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0])(isl_sioimath_cmp(*(bmap->ineq[k][0]), *(bmap->ineq[l][
0])) < 0)
)
1186 swap_inequality(bmap, k, l);
1187 isl_basic_map_drop_inequality(bmap, k);
1188 --k;
1189 }
1190 isl_int_init(sum)isl_sioimath_init((sum));
1191 for (k = 0; k < bmap->n_ineq-1; ++k) {
67
Assuming the condition is true
68
Loop condition is true. Entering loop body
1192 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1193 h = hash_index(&ci, bmap, k);
1194 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1195 if (!ci.index[h])
69
Assuming the condition is false
70
Taking false branch
1196 continue;
1197 l = ci.index[h] - &bmap->ineq[0];
1198 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0])isl_sioimath_add((sum), *(bmap->ineq[k][0]), *(bmap->ineq
[l][0]))
;
1199 if (isl_int_is_pos(sum)(isl_sioimath_sgn(*(sum)) > 0)) {
71
Assuming the condition is false
72
Taking false branch
1200 if (detect_divs)
1201 bmap = check_for_div_constraints(bmap, k, l,
1202 sum, progress);
1203 continue;
1204 }
1205 if (isl_int_is_zero(sum)(isl_sioimath_sgn(*(sum)) == 0)) {
73
Taking true branch
1206 /* We need to break out of the loop after these
1207 * changes since the contents of the hash
1208 * will no longer be valid.
1209 * Plus, we probably we want to regauss first.
1210 */
1211 if (progress
73.1
'progress' is non-null
73.1
'progress' is non-null
)
74
Taking true branch
1212 *progress = 1;
75
The value 1 is assigned to 'duplicate', which participates in a condition later
1213 isl_basic_map_drop_inequality(bmap, l);
1214 isl_basic_map_inequality_to_equality(bmap, k);
1215 } else
1216 bmap = isl_basic_map_set_to_empty(bmap);
1217 break;
76
Execution continues on line 1219
1218 }
1219 isl_int_clear(sum)isl_sioimath_clear((sum));
1220
1221 constraint_index_free(&ci);
1222 return bmap;
77
Returning pointer (loaded from 'bmap'), which participates in a condition later
1223}
1224
1225/* Detect all pairs of inequalities that form an equality.
1226 *
1227 * isl_basic_map_remove_duplicate_constraints detects at most one such pair.
1228 * Call it repeatedly while it is making progress.
1229 */
1230__isl_give isl_basic_map *isl_basic_map_detect_inequality_pairs(
1231 __isl_take isl_basic_map *bmap, int *progress)
1232{
1233 int duplicate;
1234
1235 do {
80
Loop condition is true. Execution continues on line 1236
1236 duplicate = 0;
1237 bmap = isl_basic_map_remove_duplicate_constraints(bmap,
62
Calling 'isl_basic_map_remove_duplicate_constraints'
78
Returning from 'isl_basic_map_remove_duplicate_constraints'
81
Calling 'isl_basic_map_remove_duplicate_constraints'
1238 &duplicate, 0);
1239 if (progress
78.1
'progress' is non-null
78.1
'progress' is non-null
&& duplicate
78.2
'duplicate' is 1
78.2
'duplicate' is 1
)
79
Taking true branch
1240 *progress = 1;
1241 } while (duplicate);
1242
1243 return bmap;
1244}
1245
1246/* Eliminate knowns divs from constraints where they appear with
1247 * a (positive or negative) unit coefficient.
1248 *
1249 * That is, replace
1250 *
1251 * floor(e/m) + f >= 0
1252 *
1253 * by
1254 *
1255 * e + m f >= 0
1256 *
1257 * and
1258 *
1259 * -floor(e/m) + f >= 0
1260 *
1261 * by
1262 *
1263 * -e + m f + m - 1 >= 0
1264 *
1265 * The first conversion is valid because floor(e/m) >= -f is equivalent
1266 * to e/m >= -f because -f is an integral expression.
1267 * The second conversion follows from the fact that
1268 *
1269 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1270 *
1271 *
1272 * Note that one of the div constraints may have been eliminated
1273 * due to being redundant with respect to the constraint that is
1274 * being modified by this function. The modified constraint may
1275 * no longer imply this div constraint, so we add it back to make
1276 * sure we do not lose any information.
1277 *
1278 * We skip integral divs, i.e., those with denominator 1, as we would
1279 * risk eliminating the div from the div constraints. We do not need
1280 * to handle those divs here anyway since the div constraints will turn
1281 * out to form an equality and this equality can then be used to eliminate
1282 * the div from all constraints.
1283 */
1284static __isl_give isl_basic_map *eliminate_unit_divs(
1285 __isl_take isl_basic_map *bmap, int *progress)
1286{
1287 int i, j;
1288 isl_ctx *ctx;
1289 unsigned total;
1290
1291 if (!bmap)
1292 return NULL((void*)0);
1293
1294 ctx = isl_basic_map_get_ctx(bmap);
1295 total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1296
1297 for (i = 0; i < bmap->n_div; ++i) {
1298 if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
1299 continue;
1300 if (isl_int_is_one(bmap->div[i][0])(isl_sioimath_cmp_si(*(bmap->div[i][0]), 1) == 0))
1301 continue;
1302 for (j = 0; j < bmap->n_ineq; ++j) {
1303 int s;
1304
1305 if (!isl_int_is_one(bmap->ineq[j][total + i])(isl_sioimath_cmp_si(*(bmap->ineq[j][total + i]), 1) == 0) &&
1306 !isl_int_is_negone(bmap->ineq[j][total + i])(isl_sioimath_cmp_si(*(bmap->ineq[j][total + i]), -1) == 0
)
)
1307 continue;
1308
1309 *progress = 1;
1310
1311 s = isl_int_sgn(bmap->ineq[j][total + i])isl_sioimath_sgn(*(bmap->ineq[j][total + i]));
1312 isl_int_set_si(bmap->ineq[j][total + i], 0)isl_sioimath_set_si((bmap->ineq[j][total + i]), 0);
1313 if (s < 0)
1314 isl_seq_combine(bmap->ineq[j],
1315 ctx->negone, bmap->div[i] + 1,
1316 bmap->div[i][0], bmap->ineq[j],
1317 total + bmap->n_div);
1318 else
1319 isl_seq_combine(bmap->ineq[j],
1320 ctx->one, bmap->div[i] + 1,
1321 bmap->div[i][0], bmap->ineq[j],
1322 total + bmap->n_div);
1323 if (s < 0) {
1324 isl_int_add(bmap->ineq[j][0],isl_sioimath_add((bmap->ineq[j][0]), *(bmap->ineq[j][0]
), *(bmap->div[i][0]))
1325 bmap->ineq[j][0], bmap->div[i][0])isl_sioimath_add((bmap->ineq[j][0]), *(bmap->ineq[j][0]
), *(bmap->div[i][0]))
;
1326 isl_int_sub_ui(bmap->ineq[j][0],isl_sioimath_sub_ui((bmap->ineq[j][0]), *(bmap->ineq[j]
[0]), 1)
1327 bmap->ineq[j][0], 1)isl_sioimath_sub_ui((bmap->ineq[j][0]), *(bmap->ineq[j]
[0]), 1)
;
1328 }
1329
1330 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
1331 if (isl_basic_map_add_div_constraint(bmap, i, s) < 0)
1332 return isl_basic_map_free(bmap);
1333 }
1334 }
1335
1336 return bmap;
1337}
1338
1339__isl_give isl_basic_map *isl_basic_map_simplify(__isl_take isl_basic_map *bmap)
1340{
1341 int progress = 1;
1342 if (!bmap)
1343 return NULL((void*)0);
1344 while (progress) {
1345 isl_bool empty;
1346
1347 progress = 0;
1348 empty = isl_basic_map_plain_is_empty(bmap);
1349 if (empty < 0)
1350 return isl_basic_map_free(bmap);
1351 if (empty)
1352 break;
1353 bmap = isl_basic_map_normalize_constraints(bmap);
1354 bmap = reduce_div_coefficients(bmap);
1355 bmap = normalize_div_expressions(bmap);
1356 bmap = remove_duplicate_divs(bmap, &progress);
1357 bmap = eliminate_unit_divs(bmap, &progress);
1358 bmap = eliminate_divs_eq(bmap, &progress);
1359 bmap = eliminate_divs_ineq(bmap, &progress);
1360 bmap = isl_basic_map_gauss(bmap, &progress);
1361 /* requires equalities in normal form */
1362 bmap = normalize_divs(bmap, &progress);
1363 bmap = isl_basic_map_remove_duplicate_constraints(bmap,
1364 &progress, 1);
1365 if (bmap && progress)
1366 ISL_F_CLR(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(((bmap)->flags) &= ~((1 << 8)));
1367 }
1368 return bmap;
1369}
1370
1371struct isl_basic_setisl_basic_map *isl_basic_set_simplify(struct isl_basic_setisl_basic_map *bset)
1372{
1373 return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset)));
1374}
1375
1376
1377isl_bool isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1378 isl_int *constraint, unsigned div)
1379{
1380 unsigned pos;
1381
1382 if (!bmap)
1383 return isl_bool_error;
1384
1385 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1386
1387 if (isl_int_eq(constraint[pos], bmap->div[div][0])(isl_sioimath_cmp(*(constraint[pos]), *(bmap->div[div][0])
) == 0)
) {
1388 int neg;
1389 isl_int_sub(bmap->div[div][1],isl_sioimath_sub((bmap->div[div][1]), *(bmap->div[div][
1]), *(bmap->div[div][0]))
1390 bmap->div[div][1], bmap->div[div][0])isl_sioimath_sub((bmap->div[div][1]), *(bmap->div[div][
1]), *(bmap->div[div][0]))
;
1391 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)
;
1392 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1393 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)
;
1394 isl_int_add(bmap->div[div][1],isl_sioimath_add((bmap->div[div][1]), *(bmap->div[div][
1]), *(bmap->div[div][0]))
1395 bmap->div[div][1], bmap->div[div][0])isl_sioimath_add((bmap->div[div][1]), *(bmap->div[div][
1]), *(bmap->div[div][0]))
;
1396 if (!neg)
1397 return isl_bool_false;
1398 if (isl_seq_first_non_zero(constraint+pos+1,
1399 bmap->n_div-div-1) != -1)
1400 return isl_bool_false;
1401 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])(isl_sioimath_abs_cmp(*(constraint[pos]), *(bmap->div[div]
[0])) == 0)
) {
1402 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1403 return isl_bool_false;
1404 if (isl_seq_first_non_zero(constraint+pos+1,
1405 bmap->n_div-div-1) != -1)
1406 return isl_bool_false;
1407 } else
1408 return isl_bool_false;
1409
1410 return isl_bool_true;
1411}
1412
1413isl_bool isl_basic_set_is_div_constraint(__isl_keep isl_basic_setisl_basic_map *bset,
1414 isl_int *constraint, unsigned div)
1415{
1416 return isl_basic_map_is_div_constraint(bset, constraint, div);
1417}
1418
1419
1420/* If the only constraints a div d=floor(f/m)
1421 * appears in are its two defining constraints
1422 *
1423 * f - m d >=0
1424 * -(f - (m - 1)) + m d >= 0
1425 *
1426 * then it can safely be removed.
1427 */
1428static isl_bool div_is_redundant(__isl_keep isl_basic_map *bmap, int div)
1429{
1430 int i;
1431 unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1432
1433 for (i = 0; i < bmap->n_eq; ++i)
1434 if (!isl_int_is_zero(bmap->eq[i][pos])(isl_sioimath_sgn(*(bmap->eq[i][pos])) == 0))
1435 return isl_bool_false;
1436
1437 for (i = 0; i < bmap->n_ineq; ++i) {
1438 isl_bool red;
1439
1440 if (isl_int_is_zero(bmap->ineq[i][pos])(isl_sioimath_sgn(*(bmap->ineq[i][pos])) == 0))
1441 continue;
1442 red = isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div);
1443 if (red < 0 || !red)
1444 return red;
1445 }
1446
1447 for (i = 0; i < bmap->n_div; ++i) {
1448 if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
1449 continue;
1450 if (!isl_int_is_zero(bmap->div[i][1+pos])(isl_sioimath_sgn(*(bmap->div[i][1+pos])) == 0))
1451 return isl_bool_false;
1452 }
1453
1454 return isl_bool_true;
1455}
1456
1457/*
1458 * Remove divs that don't occur in any of the constraints or other divs.
1459 * These can arise when dropping constraints from a basic map or
1460 * when the divs of a basic map have been temporarily aligned
1461 * with the divs of another basic map.
1462 */
1463static __isl_give isl_basic_map *remove_redundant_divs(
1464 __isl_take isl_basic_map *bmap)
1465{
1466 int i;
1467
1468 if (!bmap)
1469 return NULL((void*)0);
1470
1471 for (i = bmap->n_div-1; i >= 0; --i) {
1472 isl_bool redundant;
1473
1474 redundant = div_is_redundant(bmap, i);
1475 if (redundant < 0)
1476 return isl_basic_map_free(bmap);
1477 if (!redundant)
1478 continue;
1479 bmap = isl_basic_map_drop_div(bmap, i);
1480 }
1481 return bmap;
1482}
1483
1484/* Mark "bmap" as final, without checking for obviously redundant
1485 * integer divisions. This function should be used when "bmap"
1486 * is known not to involve any such integer divisions.
1487 */
1488__isl_give isl_basic_map *isl_basic_map_mark_final(
1489 __isl_take isl_basic_map *bmap)
1490{
1491 if (!bmap)
1492 return NULL((void*)0);
1493 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL)(((bmap)->flags) |= ((1 << 0)));
1494 return bmap;
1495}
1496
1497/* Mark "bmap" as final, after removing obviously redundant integer divisions.
1498 */
1499__isl_give isl_basic_map *isl_basic_map_finalize(__isl_take isl_basic_map *bmap)
1500{
1501 bmap = remove_redundant_divs(bmap);
1502 bmap = isl_basic_map_mark_final(bmap);
1503 return bmap;
1504}
1505
1506struct isl_basic_setisl_basic_map *isl_basic_set_finalize(struct isl_basic_setisl_basic_map *bset)
1507{
1508 return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset)));
1509}
1510
1511/* Remove definition of any div that is defined in terms of the given variable.
1512 * The div itself is not removed. Functions such as
1513 * eliminate_divs_ineq depend on the other divs remaining in place.
1514 */
1515static __isl_give isl_basic_map *remove_dependent_vars(
1516 __isl_take isl_basic_map *bmap, int pos)
1517{
1518 int i;
1519
1520 if (!bmap)
1521 return NULL((void*)0);
1522
1523 for (i = 0; i < bmap->n_div; ++i) {
1524 if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
1525 continue;
1526 if (isl_int_is_zero(bmap->div[i][1+1+pos])(isl_sioimath_sgn(*(bmap->div[i][1+1+pos])) == 0))
1527 continue;
1528 bmap = isl_basic_map_mark_div_unknown(bmap, i);
1529 if (!bmap)
1530 return NULL((void*)0);
1531 }
1532 return bmap;
1533}
1534
1535/* Eliminate the specified variables from the constraints using
1536 * Fourier-Motzkin. The variables themselves are not removed.
1537 */
1538__isl_give isl_basic_map *isl_basic_map_eliminate_vars(
1539 __isl_take isl_basic_map *bmap, unsigned pos, unsigned n)
1540{
1541 int d;
1542 int i, j, k;
1543 unsigned total;
1544 int need_gauss = 0;
1545
1546 if (n == 0)
1547 return bmap;
1548 if (!bmap)
1549 return NULL((void*)0);
1550 total = isl_basic_map_total_dim(bmap);
1551
1552 bmap = isl_basic_map_cow(bmap);
1553 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1554 bmap = remove_dependent_vars(bmap, d);
1555 if (!bmap)
1556 return NULL((void*)0);
1557
1558 for (d = pos + n - 1;
1559 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1560 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1561 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1562 int n_lower, n_upper;
1563 if (!bmap)
1564 return NULL((void*)0);
1565 for (i = 0; i < bmap->n_eq; ++i) {
1566 if (isl_int_is_zero(bmap->eq[i][1+d])(isl_sioimath_sgn(*(bmap->eq[i][1+d])) == 0))
1567 continue;
1568 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL((void*)0));
1569 isl_basic_map_drop_equality(bmap, i);
1570 need_gauss = 1;
1571 break;
1572 }
1573 if (i < bmap->n_eq)
1574 continue;
1575 n_lower = 0;
1576 n_upper = 0;
1577 for (i = 0; i < bmap->n_ineq; ++i) {
1578 if (isl_int_is_pos(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) > 0))
1579 n_lower++;
1580 else if (isl_int_is_neg(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) < 0))
1581 n_upper++;
1582 }
1583 bmap = isl_basic_map_extend_constraints(bmap,
1584 0, n_lower * n_upper);
1585 if (!bmap)
1586 goto error;
1587 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1588 int last;
1589 if (isl_int_is_zero(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) == 0))
1590 continue;
1591 last = -1;
1592 for (j = 0; j < i; ++j) {
1593 if (isl_int_is_zero(bmap->ineq[j][1+d])(isl_sioimath_sgn(*(bmap->ineq[j][1+d])) == 0))
1594 continue;
1595 last = j;
1596 if (isl_int_sgn(bmap->ineq[i][1+d])isl_sioimath_sgn(*(bmap->ineq[i][1+d])) ==
1597 isl_int_sgn(bmap->ineq[j][1+d])isl_sioimath_sgn(*(bmap->ineq[j][1+d])))
1598 continue;
1599 k = isl_basic_map_alloc_inequality(bmap);
1600 if (k < 0)
1601 goto error;
1602 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1603 1+total);
1604 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1605 1+d, 1+total, NULL((void*)0));
1606 }
1607 isl_basic_map_drop_inequality(bmap, i);
1608 i = last + 1;
1609 }
1610 if (n_lower > 0 && n_upper > 0) {
1611 bmap = isl_basic_map_normalize_constraints(bmap);
1612 bmap = isl_basic_map_remove_duplicate_constraints(bmap,
1613 NULL((void*)0), 0);
1614 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
1615 bmap = isl_basic_map_remove_redundancies(bmap);
1616 need_gauss = 0;
1617 if (!bmap)
1618 goto error;
1619 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1)))))
1620 break;
1621 }
1622 }
1623 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED)(((bmap)->flags) &= ~((1 << 5)));
1624 if (need_gauss)
1625 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
1626 return bmap;
1627error:
1628 isl_basic_map_free(bmap);
1629 return NULL((void*)0);
1630}
1631
1632struct isl_basic_setisl_basic_map *isl_basic_set_eliminate_vars(
1633 struct isl_basic_setisl_basic_map *bset, unsigned pos, unsigned n)
1634{
1635 return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset),
1636 pos, n));
1637}
1638
1639/* Eliminate the specified n dimensions starting at first from the
1640 * constraints, without removing the dimensions from the space.
1641 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1642 * Otherwise, they are projected out and the original space is restored.
1643 */
1644__isl_give isl_basic_map *isl_basic_map_eliminate(
1645 __isl_take isl_basic_map *bmap,
1646 enum isl_dim_type type, unsigned first, unsigned n)
1647{
1648 isl_space *space;
1649
1650 if (!bmap)
1651 return NULL((void*)0);
1652 if (n == 0)
1653 return bmap;
1654
1655 if (first + n > isl_basic_map_dim(bmap, type) || first + n < first)
1656 isl_die(bmap->ctx, isl_error_invalid,do { isl_handle_error(bmap->ctx, isl_error_invalid, "index out of bounds"
, "/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 1657); goto error; } while (0)
1657 "index out of bounds", goto error)do { isl_handle_error(bmap->ctx, isl_error_invalid, "index out of bounds"
, "/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 1657); goto error; } while (0)
;
1658
1659 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4))))) {
1660 first += isl_basic_map_offset(bmap, type) - 1;
1661 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1662 return isl_basic_map_finalize(bmap);
1663 }
1664
1665 space = isl_basic_map_get_space(bmap);
1666 bmap = isl_basic_map_project_out(bmap, type, first, n);
1667 bmap = isl_basic_map_insert_dims(bmap, type, first, n);
1668 bmap = isl_basic_map_reset_space(bmap, space);
1669 return bmap;
1670error:
1671 isl_basic_map_free(bmap);
1672 return NULL((void*)0);
1673}
1674
1675__isl_give isl_basic_setisl_basic_map *isl_basic_set_eliminate(
1676 __isl_take isl_basic_setisl_basic_map *bset,
1677 enum isl_dim_type type, unsigned first, unsigned n)
1678{
1679 return isl_basic_map_eliminate(bset, type, first, n);
1680}
1681
1682/* Remove all constraints from "bmap" that reference any unknown local
1683 * variables (directly or indirectly).
1684 *
1685 * Dropping all constraints on a local variable will make it redundant,
1686 * so it will get removed implicitly by
1687 * isl_basic_map_drop_constraints_involving_dims. Some other local
1688 * variables may also end up becoming redundant if they only appear
1689 * in constraints together with the unknown local variable.
1690 * Therefore, start over after calling
1691 * isl_basic_map_drop_constraints_involving_dims.
1692 */
1693__isl_give isl_basic_map *isl_basic_map_drop_constraint_involving_unknown_divs(
1694 __isl_take isl_basic_map *bmap)
1695{
1696 isl_bool known;
1697 int i, n_div, o_div;
1698
1699 known = isl_basic_map_divs_known(bmap);
1700 if (known < 0)
1701 return isl_basic_map_free(bmap);
1702 if (known)
1703 return bmap;
1704
1705 n_div = isl_basic_map_dim(bmap, isl_dim_div);
1706 o_div = isl_basic_map_offset(bmap, isl_dim_div) - 1;
1707
1708 for (i = 0; i < n_div; ++i) {
1709 known = isl_basic_map_div_is_known(bmap, i);
1710 if (known < 0)
1711 return isl_basic_map_free(bmap);
1712 if (known)
1713 continue;
1714 bmap = remove_dependent_vars(bmap, o_div + i);
1715 bmap = isl_basic_map_drop_constraints_involving_dims(bmap,
1716 isl_dim_div, i, 1);
1717 if (!bmap)
1718 return NULL((void*)0);
1719 n_div = isl_basic_map_dim(bmap, isl_dim_div);
1720 i = -1;
1721 }
1722
1723 return bmap;
1724}
1725
1726/* Remove all constraints from "map" that reference any unknown local
1727 * variables (directly or indirectly).
1728 *
1729 * Since constraints may get dropped from the basic maps,
1730 * they may no longer be disjoint from each other.
1731 */
1732__isl_give isl_map *isl_map_drop_constraint_involving_unknown_divs(
1733 __isl_take isl_map *map)
1734{
1735 int i;
1736 isl_bool known;
1737
1738 known = isl_map_divs_known(map);
1739 if (known < 0)
1740 return isl_map_free(map);
1741 if (known)
1742 return map;
1743
1744 map = isl_map_cow(map);
1745 if (!map)
1746 return NULL((void*)0);
1747
1748 for (i = 0; i < map->n; ++i) {
1749 map->p[i] =
1750 isl_basic_map_drop_constraint_involving_unknown_divs(
1751 map->p[i]);
1752 if (!map->p[i])
1753 return isl_map_free(map);
1754 }
1755
1756 if (map->n > 1)
1757 ISL_F_CLR(map, ISL_MAP_DISJOINT)(((map)->flags) &= ~((1 << 0)));
1758
1759 return map;
1760}
1761
1762/* Don't assume equalities are in order, because align_divs
1763 * may have changed the order of the divs.
1764 */
1765static void compute_elimination_index(__isl_keep isl_basic_map *bmap, int *elim)
1766{
1767 int d, i;
1768 unsigned total;
1769
1770 total = isl_space_dim(bmap->dim, isl_dim_all);
1771 for (d = 0; d < total; ++d)
1772 elim[d] = -1;
1773 for (i = 0; i < bmap->n_eq; ++i) {
1774 for (d = total - 1; d >= 0; --d) {
1775 if (isl_int_is_zero(bmap->eq[i][1+d])(isl_sioimath_sgn(*(bmap->eq[i][1+d])) == 0))
1776 continue;
1777 elim[d] = i;
1778 break;
1779 }
1780 }
1781}
1782
1783static void set_compute_elimination_index(__isl_keep isl_basic_setisl_basic_map *bset,
1784 int *elim)
1785{
1786 compute_elimination_index(bset_to_bmap(bset), elim);
1787}
1788
1789static int reduced_using_equalities(isl_int *dst, isl_int *src,
1790 __isl_keep isl_basic_map *bmap, int *elim)
1791{
1792 int d;
1793 int copied = 0;
1794 unsigned total;
1795
1796 total = isl_space_dim(bmap->dim, isl_dim_all);
1797 for (d = total - 1; d >= 0; --d) {
1798 if (isl_int_is_zero(src[1+d])(isl_sioimath_sgn(*(src[1+d])) == 0))
1799 continue;
1800 if (elim[d] == -1)
1801 continue;
1802 if (!copied) {
1803 isl_seq_cpy(dst, src, 1 + total);
1804 copied = 1;
1805 }
1806 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL((void*)0));
1807 }
1808 return copied;
1809}
1810
1811static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1812 __isl_keep isl_basic_setisl_basic_map *bset, int *elim)
1813{
1814 return reduced_using_equalities(dst, src,
1815 bset_to_bmap(bset), elim);
1816}
1817
1818static __isl_give isl_basic_setisl_basic_map *isl_basic_set_reduce_using_equalities(
1819 __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context)
1820{
1821 int i;
1822 int *elim;
1823
1824 if (!bset || !context)
1825 goto error;
1826
1827 if (context->n_eq == 0) {
1828 isl_basic_set_free(context);
1829 return bset;
1830 }
1831
1832 bset = isl_basic_set_cow(bset);
1833 if (!bset)
1834 goto error;
1835
1836 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset))((int *)isl_malloc_or_die(bset->ctx, (isl_basic_set_n_dim(
bset))*sizeof(int)))
;
1837 if (!elim)
1838 goto error;
1839 set_compute_elimination_index(context, elim);
1840 for (i = 0; i < bset->n_eq; ++i)
1841 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1842 context, elim);
1843 for (i = 0; i < bset->n_ineq; ++i)
1844 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1845 context, elim);
1846 isl_basic_set_free(context);
1847 free(elim);
1848 bset = isl_basic_set_simplify(bset);
1849 bset = isl_basic_set_finalize(bset);
1850 return bset;
1851error:
1852 isl_basic_set_free(bset);
1853 isl_basic_set_free(context);
1854 return NULL((void*)0);
1855}
1856
1857/* For each inequality in "ineq" that is a shifted (more relaxed)
1858 * copy of an inequality in "context", mark the corresponding entry
1859 * in "row" with -1.
1860 * If an inequality only has a non-negative constant term, then
1861 * mark it as well.
1862 */
1863static isl_stat mark_shifted_constraints(__isl_keep isl_mat *ineq,
1864 __isl_keep isl_basic_setisl_basic_map *context, int *row)
1865{
1866 struct isl_constraint_index ci;
1867 int n_ineq;
1868 unsigned total;
1869 int k;
1870
1871 if (!ineq || !context)
1872 return isl_stat_error;
1873 if (context->n_ineq == 0)
1874 return isl_stat_ok;
1875 if (setup_constraint_index(&ci, context) < 0)
1876 return isl_stat_error;
1877
1878 n_ineq = isl_mat_rows(ineq);
1879 total = isl_mat_cols(ineq) - 1;
1880 for (k = 0; k < n_ineq; ++k) {
1881 int l;
1882 isl_bool redundant;
1883
1884 l = isl_seq_first_non_zero(ineq->row[k] + 1, total);
1885 if (l < 0 && isl_int_is_nonneg(ineq->row[k][0])(isl_sioimath_sgn(*(ineq->row[k][0])) >= 0)) {
1886 row[k] = -1;
1887 continue;
1888 }
1889 redundant = constraint_index_is_redundant(&ci, ineq->row[k]);
1890 if (redundant < 0)
1891 goto error;
1892 if (!redundant)
1893 continue;
1894 row[k] = -1;
1895 }
1896 constraint_index_free(&ci);
1897 return isl_stat_ok;
1898error:
1899 constraint_index_free(&ci);
1900 return isl_stat_error;
1901}
1902
1903static __isl_give isl_basic_setisl_basic_map *remove_shifted_constraints(
1904 __isl_take isl_basic_setisl_basic_map *bset, __isl_keep isl_basic_setisl_basic_map *context)
1905{
1906 struct isl_constraint_index ci;
1907 int k;
1908
1909 if (!bset || !context)
1910 return bset;
1911
1912 if (context->n_ineq == 0)
1913 return bset;
1914 if (setup_constraint_index(&ci, context) < 0)
1915 return bset;
1916
1917 for (k = 0; k < bset->n_ineq; ++k) {
1918 isl_bool redundant;
1919
1920 redundant = constraint_index_is_redundant(&ci, bset->ineq[k]);
1921 if (redundant < 0)
1922 goto error;
1923 if (!redundant)
1924 continue;
1925 bset = isl_basic_set_cow(bset);
1926 if (!bset)
1927 goto error;
1928 isl_basic_set_drop_inequality(bset, k);
1929 --k;
1930 }
1931 constraint_index_free(&ci);
1932 return bset;
1933error:
1934 constraint_index_free(&ci);
1935 return bset;
1936}
1937
1938/* Remove constraints from "bmap" that are identical to constraints
1939 * in "context" or that are more relaxed (greater constant term).
1940 *
1941 * We perform the test for shifted copies on the pure constraints
1942 * in remove_shifted_constraints.
1943 */
1944static __isl_give isl_basic_map *isl_basic_map_remove_shifted_constraints(
1945 __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context)
1946{
1947 isl_basic_setisl_basic_map *bset, *bset_context;
1948
1949 if (!bmap || !context)
1950 goto error;
1951
1952 if (bmap->n_ineq == 0 || context->n_ineq == 0) {
1953 isl_basic_map_free(context);
1954 return bmap;
1955 }
1956
1957 context = isl_basic_map_align_divs(context, bmap);
1958 bmap = isl_basic_map_align_divs(bmap, context);
1959
1960 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1961 bset_context = isl_basic_map_underlying_set(context);
1962 bset = remove_shifted_constraints(bset, bset_context);
1963 isl_basic_set_free(bset_context);
1964
1965 bmap = isl_basic_map_overlying_set(bset, bmap);
1966
1967 return bmap;
1968error:
1969 isl_basic_map_free(bmap);
1970 isl_basic_map_free(context);
1971 return NULL((void*)0);
1972}
1973
1974/* Does the (linear part of a) constraint "c" involve any of the "len"
1975 * "relevant" dimensions?
1976 */
1977static int is_related(isl_int *c, int len, int *relevant)
1978{
1979 int i;
1980
1981 for (i = 0; i < len; ++i) {
1982 if (!relevant[i])
1983 continue;
1984 if (!isl_int_is_zero(c[i])(isl_sioimath_sgn(*(c[i])) == 0))
1985 return 1;
1986 }
1987
1988 return 0;
1989}
1990
1991/* Drop constraints from "bmap" that do not involve any of
1992 * the dimensions marked "relevant".
1993 */
1994static __isl_give isl_basic_map *drop_unrelated_constraints(
1995 __isl_take isl_basic_map *bmap, int *relevant)
1996{
1997 int i, dim;
1998
1999 dim = isl_basic_map_dim(bmap, isl_dim_all);
2000 for (i = 0; i < dim; ++i)
2001 if (!relevant[i])
2002 break;
2003 if (i >= dim)
2004 return bmap;
2005
2006 for (i = bmap->n_eq - 1; i >= 0; --i)
2007 if (!is_related(bmap->eq[i] + 1, dim, relevant)) {
2008 bmap = isl_basic_map_cow(bmap);
2009 if (isl_basic_map_drop_equality(bmap, i) < 0)
2010 return isl_basic_map_free(bmap);
2011 }
2012
2013 for (i = bmap->n_ineq - 1; i >= 0; --i)
2014 if (!is_related(bmap->ineq[i] + 1, dim, relevant)) {
2015 bmap = isl_basic_map_cow(bmap);
2016 if (isl_basic_map_drop_inequality(bmap, i) < 0)
2017 return isl_basic_map_free(bmap);
2018 }
2019
2020 return bmap;
2021}
2022
2023/* Update the groups in "group" based on the (linear part of a) constraint "c".
2024 *
2025 * In particular, for any variable involved in the constraint,
2026 * find the actual group id from before and replace the group
2027 * of the corresponding variable by the minimal group of all
2028 * the variables involved in the constraint considered so far
2029 * (if this minimum is smaller) or replace the minimum by this group
2030 * (if the minimum is larger).
2031 *
2032 * At the end, all the variables in "c" will (indirectly) point
2033 * to the minimal of the groups that they referred to originally.
2034 */
2035static void update_groups(int dim, int *group, isl_int *c)
2036{
2037 int j;
2038 int min = dim;
2039
2040 for (j = 0; j < dim; ++j) {
2041 if (isl_int_is_zero(c[j])(isl_sioimath_sgn(*(c[j])) == 0))
2042 continue;
2043 while (group[j] >= 0 && group[group[j]] != group[j])
2044 group[j] = group[group[j]];
2045 if (group[j] == min)
2046 continue;
2047 if (group[j] < min) {
2048 if (min >= 0 && min < dim)
2049 group[min] = group[j];
2050 min = group[j];
2051 } else
2052 group[group[j]] = min;
2053 }
2054}
2055
2056/* Allocate an array of groups of variables, one for each variable
2057 * in "context", initialized to zero.
2058 */
2059static int *alloc_groups(__isl_keep isl_basic_setisl_basic_map *context)
2060{
2061 isl_ctx *ctx;
2062 int dim;
2063
2064 dim = isl_basic_set_dim(context, isl_dim_set);
2065 ctx = isl_basic_set_get_ctx(context);
2066 return isl_calloc_array(ctx, int, dim)((int *)isl_calloc_or_die(ctx, dim, sizeof(int)));
2067}
2068
2069/* Drop constraints from "bmap" that only involve variables that are
2070 * not related to any of the variables marked with a "-1" in "group".
2071 *
2072 * We construct groups of variables that collect variables that
2073 * (indirectly) appear in some common constraint of "bmap".
2074 * Each group is identified by the first variable in the group,
2075 * except for the special group of variables that was already identified
2076 * in the input as -1 (or are related to those variables).
2077 * If group[i] is equal to i (or -1), then the group of i is i (or -1),
2078 * otherwise the group of i is the group of group[i].
2079 *
2080 * We first initialize groups for the remaining variables.
2081 * Then we iterate over the constraints of "bmap" and update the
2082 * group of the variables in the constraint by the smallest group.
2083 * Finally, we resolve indirect references to groups by running over
2084 * the variables.
2085 *
2086 * After computing the groups, we drop constraints that do not involve
2087 * any variables in the -1 group.
2088 */
2089__isl_give isl_basic_map *isl_basic_map_drop_unrelated_constraints(
2090 __isl_take isl_basic_map *bmap, __isl_take int *group)
2091{
2092 int dim;
2093 int i;
2094 int last;
2095
2096 if (!bmap)
2097 return NULL((void*)0);
2098
2099 dim = isl_basic_map_dim(bmap, isl_dim_all);
2100
2101 last = -1;
2102 for (i = 0; i < dim; ++i)
2103 if (group[i] >= 0)
2104 last = group[i] = i;
2105 if (last < 0) {
2106 free(group);
2107 return bmap;
2108 }
2109
2110 for (i = 0; i < bmap->n_eq; ++i)
2111 update_groups(dim, group, bmap->eq[i] + 1);
2112 for (i = 0; i < bmap->n_ineq; ++i)
2113 update_groups(dim, group, bmap->ineq[i] + 1);
2114
2115 for (i = 0; i < dim; ++i)
2116 if (group[i] >= 0)
2117 group[i] = group[group[i]];
2118
2119 for (i = 0; i < dim; ++i)
2120 group[i] = group[i] == -1;
2121
2122 bmap = drop_unrelated_constraints(bmap, group);
2123
2124 free(group);
2125 return bmap;
2126}
2127
2128/* Drop constraints from "context" that are irrelevant for computing
2129 * the gist of "bset".
2130 *
2131 * In particular, drop constraints in variables that are not related
2132 * to any of the variables involved in the constraints of "bset"
2133 * in the sense that there is no sequence of constraints that connects them.
2134 *
2135 * We first mark all variables that appear in "bset" as belonging
2136 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2137 */
2138static __isl_give isl_basic_setisl_basic_map *drop_irrelevant_constraints(
2139 __isl_take isl_basic_setisl_basic_map *context, __isl_keep isl_basic_setisl_basic_map *bset)
2140{
2141 int *group;
2142 int dim;
2143 int i, j;
2144
2145 if (!context || !bset)
2146 return isl_basic_set_free(context);
2147
2148 group = alloc_groups(context);
2149
2150 if (!group)
2151 return isl_basic_set_free(context);
2152
2153 dim = isl_basic_set_dim(bset, isl_dim_set);
2154 for (i = 0; i < dim; ++i) {
2155 for (j = 0; j < bset->n_eq; ++j)
2156 if (!isl_int_is_zero(bset->eq[j][1 + i])(isl_sioimath_sgn(*(bset->eq[j][1 + i])) == 0))
2157 break;
2158 if (j < bset->n_eq) {
2159 group[i] = -1;
2160 continue;
2161 }
2162 for (j = 0; j < bset->n_ineq; ++j)
2163 if (!isl_int_is_zero(bset->ineq[j][1 + i])(isl_sioimath_sgn(*(bset->ineq[j][1 + i])) == 0))
2164 break;
2165 if (j < bset->n_ineq)
2166 group[i] = -1;
2167 }
2168
2169 return isl_basic_map_drop_unrelated_constraints(context, group);
2170}
2171
2172/* Drop constraints from "context" that are irrelevant for computing
2173 * the gist of the inequalities "ineq".
2174 * Inequalities in "ineq" for which the corresponding element of row
2175 * is set to -1 have already been marked for removal and should be ignored.
2176 *
2177 * In particular, drop constraints in variables that are not related
2178 * to any of the variables involved in "ineq"
2179 * in the sense that there is no sequence of constraints that connects them.
2180 *
2181 * We first mark all variables that appear in "bset" as belonging
2182 * to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
2183 */
2184static __isl_give isl_basic_setisl_basic_map *drop_irrelevant_constraints_marked(
2185 __isl_take isl_basic_setisl_basic_map *context, __isl_keep isl_mat *ineq, int *row)
2186{
2187 int *group;
2188 int dim;
2189 int i, j, n;
2190
2191 if (!context || !ineq)
2192 return isl_basic_set_free(context);
2193
2194 group = alloc_groups(context);
2195
2196 if (!group)
2197 return isl_basic_set_free(context);
2198
2199 dim = isl_basic_set_dim(context, isl_dim_set);
2200 n = isl_mat_rows(ineq);
2201 for (i = 0; i < dim; ++i) {
2202 for (j = 0; j < n; ++j) {
2203 if (row[j] < 0)
2204 continue;
2205 if (!isl_int_is_zero(ineq->row[j][1 + i])(isl_sioimath_sgn(*(ineq->row[j][1 + i])) == 0))
2206 break;
2207 }
2208 if (j < n)
2209 group[i] = -1;
2210 }
2211
2212 return isl_basic_map_drop_unrelated_constraints(context, group);
2213}
2214
2215/* Do all "n" entries of "row" contain a negative value?
2216 */
2217static int all_neg(int *row, int n)
2218{
2219 int i;
2220
2221 for (i = 0; i < n; ++i)
2222 if (row[i] >= 0)
2223 return 0;
2224
2225 return 1;
2226}
2227
2228/* Update the inequalities in "bset" based on the information in "row"
2229 * and "tab".
2230 *
2231 * In particular, the array "row" contains either -1, meaning that
2232 * the corresponding inequality of "bset" is redundant, or the index
2233 * of an inequality in "tab".
2234 *
2235 * If the row entry is -1, then drop the inequality.
2236 * Otherwise, if the constraint is marked redundant in the tableau,
2237 * then drop the inequality. Similarly, if it is marked as an equality
2238 * in the tableau, then turn the inequality into an equality and
2239 * perform Gaussian elimination.
2240 */
2241static __isl_give isl_basic_setisl_basic_map *update_ineq(__isl_take isl_basic_setisl_basic_map *bset,
2242 __isl_keep int *row, struct isl_tab *tab)
2243{
2244 int i;
2245 unsigned n_ineq;
2246 unsigned n_eq;
2247 int found_equality = 0;
2248
2249 if (!bset)
2250 return NULL((void*)0);
2251 if (tab && tab->empty)
2252 return isl_basic_set_set_to_empty(bset);
2253
2254 n_ineq = bset->n_ineq;
2255 for (i = n_ineq - 1; i >= 0; --i) {
2256 if (row[i] < 0) {
2257 if (isl_basic_set_drop_inequality(bset, i) < 0)
2258 return isl_basic_set_free(bset);
2259 continue;
2260 }
2261 if (!tab)
2262 continue;
2263 n_eq = tab->n_eq;
2264 if (isl_tab_is_equality(tab, n_eq + row[i])) {
2265 isl_basic_map_inequality_to_equality(bset, i);
2266 found_equality = 1;
2267 } else if (isl_tab_is_redundant(tab, n_eq + row[i])) {
2268 if (isl_basic_set_drop_inequality(bset, i) < 0)
2269 return isl_basic_set_free(bset);
2270 }
2271 }
2272
2273 if (found_equality)
2274 bset = isl_basic_set_gauss(bset, NULL((void*)0));
2275 bset = isl_basic_set_finalize(bset);
2276 return bset;
2277}
2278
2279/* Update the inequalities in "bset" based on the information in "row"
2280 * and "tab" and free all arguments (other than "bset").
2281 */
2282static __isl_give isl_basic_setisl_basic_map *update_ineq_free(
2283 __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_mat *ineq,
2284 __isl_take isl_basic_setisl_basic_map *context, __isl_take int *row,
2285 struct isl_tab *tab)
2286{
2287 isl_mat_free(ineq);
2288 isl_basic_set_free(context);
2289
2290 bset = update_ineq(bset, row, tab);
2291
2292 free(row);
2293 isl_tab_free(tab);
2294 return bset;
2295}
2296
2297/* Remove all information from bset that is redundant in the context
2298 * of context.
2299 * "ineq" contains the (possibly transformed) inequalities of "bset",
2300 * in the same order.
2301 * The (explicit) equalities of "bset" are assumed to have been taken
2302 * into account by the transformation such that only the inequalities
2303 * are relevant.
2304 * "context" is assumed not to be empty.
2305 *
2306 * "row" keeps track of the constraint index of a "bset" inequality in "tab".
2307 * A value of -1 means that the inequality is obviously redundant and may
2308 * not even appear in "tab".
2309 *
2310 * We first mark the inequalities of "bset"
2311 * that are obviously redundant with respect to some inequality in "context".
2312 * Then we remove those constraints from "context" that have become
2313 * irrelevant for computing the gist of "bset".
2314 * Note that this removal of constraints cannot be replaced by
2315 * a factorization because factors in "bset" may still be connected
2316 * to each other through constraints in "context".
2317 *
2318 * If there are any inequalities left, we construct a tableau for
2319 * the context and then add the inequalities of "bset".
2320 * Before adding these inequalities, we freeze all constraints such that
2321 * they won't be considered redundant in terms of the constraints of "bset".
2322 * Then we detect all redundant constraints (among the
2323 * constraints that weren't frozen), first by checking for redundancy in the
2324 * the tableau and then by checking if replacing a constraint by its negation
2325 * would lead to an empty set. This last step is fairly expensive
2326 * and could be optimized by more reuse of the tableau.
2327 * Finally, we update bset according to the results.
2328 */
2329static __isl_give isl_basic_setisl_basic_map *uset_gist_full(__isl_take isl_basic_setisl_basic_map *bset,
2330 __isl_take isl_mat *ineq, __isl_take isl_basic_setisl_basic_map *context)
2331{
2332 int i, r;
2333 int *row = NULL((void*)0);
2334 isl_ctx *ctx;
2335 isl_basic_setisl_basic_map *combined = NULL((void*)0);
2336 struct isl_tab *tab = NULL((void*)0);
2337 unsigned n_eq, context_ineq;
2338
2339 if (!bset || !ineq || !context)
2340 goto error;
2341
2342 if (bset->n_ineq == 0 || isl_basic_set_plain_is_universe(context)) {
2343 isl_basic_set_free(context);
2344 isl_mat_free(ineq);
2345 return bset;
2346 }
2347
2348 ctx = isl_basic_set_get_ctx(context);
2349 row = isl_calloc_array(ctx, int, bset->n_ineq)((int *)isl_calloc_or_die(ctx, bset->n_ineq, sizeof(int)));
2350 if (!row)
2351 goto error;
2352
2353 if (mark_shifted_constraints(ineq, context, row) < 0)
2354 goto error;
2355 if (all_neg(row, bset->n_ineq))
2356 return update_ineq_free(bset, ineq, context, row, NULL((void*)0));
2357
2358 context = drop_irrelevant_constraints_marked(context, ineq, row);
2359 if (!context)
2360 goto error;
2361 if (isl_basic_set_plain_is_universe(context))
2362 return update_ineq_free(bset, ineq, context, row, NULL((void*)0));
2363
2364 n_eq = context->n_eq;
2365 context_ineq = context->n_ineq;
2366 combined = isl_basic_set_cow(isl_basic_set_copy(context));
2367 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
2368 tab = isl_tab_from_basic_set(combined, 0);
2369 for (i = 0; i < context_ineq; ++i)
2370 if (isl_tab_freeze_constraint(tab, n_eq + i) < 0)
2371 goto error;
2372 if (isl_tab_extend_cons(tab, bset->n_ineq) < 0)
2373 goto error;
2374 r = context_ineq;
2375 for (i = 0; i < bset->n_ineq; ++i) {
2376 if (row[i] < 0)
2377 continue;
2378 combined = isl_basic_set_add_ineq(combined, ineq->row[i]);
2379 if (isl_tab_add_ineq(tab, ineq->row[i]) < 0)
2380 goto error;
2381 row[i] = r++;
2382 }
2383 if (isl_tab_detect_implicit_equalities(tab) < 0)
2384 goto error;
2385 if (isl_tab_detect_redundant(tab) < 0)
2386 goto error;
2387 for (i = bset->n_ineq - 1; i >= 0; --i) {
2388 isl_basic_setisl_basic_map *test;
2389 int is_empty;
2390
2391 if (row[i] < 0)
2392 continue;
2393 r = row[i];
2394 if (tab->con[n_eq + r].is_redundant)
2395 continue;
2396 test = isl_basic_set_dup(combined);
2397 if (isl_inequality_negate(test, r) < 0)
2398 test = isl_basic_set_free(test);
2399 test = isl_basic_set_update_from_tab(test, tab);
2400 is_empty = isl_basic_set_is_empty(test);
2401 isl_basic_set_free(test);
2402 if (is_empty < 0)
2403 goto error;
2404 if (is_empty)
2405 tab->con[n_eq + r].is_redundant = 1;
2406 }
2407 bset = update_ineq_free(bset, ineq, context, row, tab);
2408 if (bset) {
2409 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) |= ((1 << 2)));
2410 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT)(((bset)->flags) |= ((1 << 3)));
2411 }
2412
2413 isl_basic_set_free(combined);
2414 return bset;
2415error:
2416 free(row);
2417 isl_mat_free(ineq);
2418 isl_tab_free(tab);
2419 isl_basic_set_free(combined);
2420 isl_basic_set_free(context);
2421 isl_basic_set_free(bset);
2422 return NULL((void*)0);
2423}
2424
2425/* Extract the inequalities of "bset" as an isl_mat.
2426 */
2427static __isl_give isl_mat *extract_ineq(__isl_keep isl_basic_setisl_basic_map *bset)
2428{
2429 unsigned total;
2430 isl_ctx *ctx;
2431 isl_mat *ineq;
2432
2433 if (!bset)
2434 return NULL((void*)0);
2435
2436 ctx = isl_basic_set_get_ctx(bset);
2437 total = isl_basic_set_total_dim(bset);
2438 ineq = isl_mat_sub_alloc6(ctx, bset->ineq, 0, bset->n_ineq,
2439 0, 1 + total);
2440
2441 return ineq;
2442}
2443
2444/* Remove all information from "bset" that is redundant in the context
2445 * of "context", for the case where both "bset" and "context" are
2446 * full-dimensional.
2447 */
2448static __isl_give isl_basic_setisl_basic_map *uset_gist_uncompressed(
2449 __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context)
2450{
2451 isl_mat *ineq;
2452
2453 ineq = extract_ineq(bset);
2454 return uset_gist_full(bset, ineq, context);
2455}
2456
2457/* Remove all information from "bset" that is redundant in the context
2458 * of "context", for the case where the combined equalities of
2459 * "bset" and "context" allow for a compression that can be obtained
2460 * by preapplication of "T".
2461 *
2462 * "bset" itself is not transformed by "T". Instead, the inequalities
2463 * are extracted from "bset" and those are transformed by "T".
2464 * uset_gist_full then determines which of the transformed inequalities
2465 * are redundant with respect to the transformed "context" and removes
2466 * the corresponding inequalities from "bset".
2467 *
2468 * After preapplying "T" to the inequalities, any common factor is
2469 * removed from the coefficients. If this results in a tightening
2470 * of the constant term, then the same tightening is applied to
2471 * the corresponding untransformed inequality in "bset".
2472 * That is, if after plugging in T, a constraint f(x) >= 0 is of the form
2473 *
2474 * g f'(x) + r >= 0
2475 *
2476 * with 0 <= r < g, then it is equivalent to
2477 *
2478 * f'(x) >= 0
2479 *
2480 * This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine
2481 * subspace compressed by T since the latter would be transformed to
2482 *
2483 * g f'(x) >= 0
2484 */
2485static __isl_give isl_basic_setisl_basic_map *uset_gist_compressed(
2486 __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context,
2487 __isl_take isl_mat *T)
2488{
2489 isl_ctx *ctx;
2490 isl_mat *ineq;
2491 int i, n_row, n_col;
2492 isl_int rem;
2493
2494 ineq = extract_ineq(bset);
2495 ineq = isl_mat_product(ineq, isl_mat_copy(T));
2496 context = isl_basic_set_preimage(context, T);
2497
2498 if (!ineq || !context)
2499 goto error;
2500 if (isl_basic_set_plain_is_empty(context)) {
2501 isl_mat_free(ineq);
2502 isl_basic_set_free(context);
2503 return isl_basic_set_set_to_empty(bset);
2504 }
2505
2506 ctx = isl_mat_get_ctx(ineq);
2507 n_row = isl_mat_rows(ineq);
2508 n_col = isl_mat_cols(ineq);
2509 isl_int_init(rem)isl_sioimath_init((rem));
2510 for (i = 0; i < n_row; ++i) {
2511 isl_seq_gcd(ineq->row[i] + 1, n_col - 1, &ctx->normalize_gcd);
2512 if (isl_int_is_zero(ctx->normalize_gcd)(isl_sioimath_sgn(*(ctx->normalize_gcd)) == 0))
2513 continue;
2514 if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0))
2515 continue;
2516 isl_seq_scale_down(ineq->row[i] + 1, ineq->row[i] + 1,
2517 ctx->normalize_gcd, n_col - 1);
2518 isl_int_fdiv_r(rem, ineq->row[i][0], ctx->normalize_gcd)isl_sioimath_fdiv_r((rem), *(ineq->row[i][0]), *(ctx->normalize_gcd
))
;
2519 isl_int_fdiv_q(ineq->row[i][0],isl_sioimath_fdiv_q((ineq->row[i][0]), *(ineq->row[i][0
]), *(ctx->normalize_gcd))
2520 ineq->row[i][0], ctx->normalize_gcd)isl_sioimath_fdiv_q((ineq->row[i][0]), *(ineq->row[i][0
]), *(ctx->normalize_gcd))
;
2521 if (isl_int_is_zero(rem)(isl_sioimath_sgn(*(rem)) == 0))
2522 continue;
2523 bset = isl_basic_set_cow(bset);
2524 if (!bset)
2525 break;
2526 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], rem)isl_sioimath_sub((bset->ineq[i][0]), *(bset->ineq[i][0]
), *(rem))
;
2527 }
2528 isl_int_clear(rem)isl_sioimath_clear((rem));
2529
2530 return uset_gist_full(bset, ineq, context);
2531error:
2532 isl_mat_free(ineq);
2533 isl_basic_set_free(context);
2534 isl_basic_set_free(bset);
2535 return NULL((void*)0);
2536}
2537
2538/* Project "bset" onto the variables that are involved in "template".
2539 */
2540static __isl_give isl_basic_setisl_basic_map *project_onto_involved(
2541 __isl_take isl_basic_setisl_basic_map *bset, __isl_keep isl_basic_setisl_basic_map *template)
2542{
2543 int i, n;
2544
2545 if (!bset || !template)
2546 return isl_basic_set_free(bset);
2547
2548 n = isl_basic_set_dim(template, isl_dim_set);
2549
2550 for (i = 0; i < n; ++i) {
2551 isl_bool involved;
2552
2553 involved = isl_basic_set_involves_dims(template,
2554 isl_dim_set, i, 1);
2555 if (involved < 0)
2556 return isl_basic_set_free(bset);
2557 if (involved)
2558 continue;
2559 bset = isl_basic_set_eliminate_vars(bset, i, 1);
2560 }
2561
2562 return bset;
2563}
2564
2565/* Remove all information from bset that is redundant in the context
2566 * of context. In particular, equalities that are linear combinations
2567 * of those in context are removed. Then the inequalities that are
2568 * redundant in the context of the equalities and inequalities of
2569 * context are removed.
2570 *
2571 * First of all, we drop those constraints from "context"
2572 * that are irrelevant for computing the gist of "bset".
2573 * Alternatively, we could factorize the intersection of "context" and "bset".
2574 *
2575 * We first compute the intersection of the integer affine hulls
2576 * of "bset" and "context",
2577 * compute the gist inside this intersection and then reduce
2578 * the constraints with respect to the equalities of the context
2579 * that only involve variables already involved in the input.
2580 *
2581 * If two constraints are mutually redundant, then uset_gist_full
2582 * will remove the second of those constraints. We therefore first
2583 * sort the constraints so that constraints not involving existentially
2584 * quantified variables are given precedence over those that do.
2585 * We have to perform this sorting before the variable compression,
2586 * because that may effect the order of the variables.
2587 */
2588static __isl_give isl_basic_setisl_basic_map *uset_gist(__isl_take isl_basic_setisl_basic_map *bset,
2589 __isl_take isl_basic_setisl_basic_map *context)
2590{
2591 isl_mat *eq;
2592 isl_mat *T;
2593 isl_basic_setisl_basic_map *aff;
2594 isl_basic_setisl_basic_map *aff_context;
2595 unsigned total;
2596
2597 if (!bset || !context)
2598 goto error;
2599
2600 context = drop_irrelevant_constraints(context, bset);
2601
2602 bset = isl_basic_set_detect_equalities(bset);
2603 aff = isl_basic_set_copy(bset);
2604 aff = isl_basic_set_plain_affine_hull(aff);
2605 context = isl_basic_set_detect_equalities(context);
2606 aff_context = isl_basic_set_copy(context);
2607 aff_context = isl_basic_set_plain_affine_hull(aff_context);
2608 aff = isl_basic_set_intersect(aff, aff_context);
2609 if (!aff)
2610 goto error;
2611 if (isl_basic_set_plain_is_empty(aff)) {
2612 isl_basic_set_free(bset);
2613 isl_basic_set_free(context);
2614 return aff;
2615 }
2616 bset = isl_basic_set_sort_constraints(bset);
2617 if (aff->n_eq == 0) {
2618 isl_basic_set_free(aff);
2619 return uset_gist_uncompressed(bset, context);
2620 }
2621 total = isl_basic_set_total_dim(bset);
2622 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
2623 eq = isl_mat_cow(eq);
2624 T = isl_mat_variable_compression(eq, NULL((void*)0));
2625 isl_basic_set_free(aff);
2626 if (T && T->n_col == 0) {
2627 isl_mat_free(T);
2628 isl_basic_set_free(context);
2629 return isl_basic_set_set_to_empty(bset);
2630 }
2631
2632 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
2633 aff_context = project_onto_involved(aff_context, bset);
2634
2635 bset = uset_gist_compressed(bset, context, T);
2636 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
2637
2638 if (bset) {
2639 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) |= ((1 << 2)));
2640 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT)(((bset)->flags) |= ((1 << 3)));
2641 }
2642
2643 return bset;
2644error:
2645 isl_basic_set_free(bset);
2646 isl_basic_set_free(context);
2647 return NULL((void*)0);
2648}
2649
2650/* Return the number of equality constraints in "bmap" that involve
2651 * local variables. This function assumes that Gaussian elimination
2652 * has been applied to the equality constraints.
2653 */
2654static int n_div_eq(__isl_keep isl_basic_map *bmap)
2655{
2656 int i;
2657 int total, n_div;
2658
2659 if (!bmap)
2660 return -1;
2661
2662 if (bmap->n_eq == 0)
2663 return 0;
2664
2665 total = isl_basic_map_dim(bmap, isl_dim_all);
2666 n_div = isl_basic_map_dim(bmap, isl_dim_div);
2667 total -= n_div;
2668
2669 for (i = 0; i < bmap->n_eq; ++i)
2670 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total,
2671 n_div) == -1)
2672 return i;
2673
2674 return bmap->n_eq;
2675}
2676
2677/* Construct a basic map in "space" defined by the equality constraints in "eq".
2678 * The constraints are assumed not to involve any local variables.
2679 */
2680static __isl_give isl_basic_map *basic_map_from_equalities(
2681 __isl_take isl_space *space, __isl_take isl_mat *eq)
2682{
2683 int i, k;
2684 isl_basic_map *bmap = NULL((void*)0);
2685
2686 if (!space || !eq)
2687 goto error;
2688
2689 if (1 + isl_space_dim(space, isl_dim_all) != eq->n_col)
2690 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-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 2691); goto error; } while (0)
2691 "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-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 2691); goto error; } while (0)
;
2692
2693 bmap = isl_basic_map_alloc_space(isl_space_copy(space),
2694 0, eq->n_row, 0);
2695 for (i = 0; i < eq->n_row; ++i) {
2696 k = isl_basic_map_alloc_equality(bmap);
2697 if (k < 0)
2698 goto error;
2699 isl_seq_cpy(bmap->eq[k], eq->row[i], eq->n_col);
2700 }
2701
2702 isl_space_free(space);
2703 isl_mat_free(eq);
2704 return bmap;
2705error:
2706 isl_space_free(space);
2707 isl_mat_free(eq);
2708 isl_basic_map_free(bmap);
2709 return NULL((void*)0);
2710}
2711
2712/* Construct and return a variable compression based on the equality
2713 * constraints in "bmap1" and "bmap2" that do not involve the local variables.
2714 * "n1" is the number of (initial) equality constraints in "bmap1"
2715 * that do involve local variables.
2716 * "n2" is the number of (initial) equality constraints in "bmap2"
2717 * that do involve local variables.
2718 * "total" is the total number of other variables.
2719 * This function assumes that Gaussian elimination
2720 * has been applied to the equality constraints in both "bmap1" and "bmap2"
2721 * such that the equality constraints not involving local variables
2722 * are those that start at "n1" or "n2".
2723 *
2724 * If either of "bmap1" and "bmap2" does not have such equality constraints,
2725 * then simply compute the compression based on the equality constraints
2726 * in the other basic map.
2727 * Otherwise, combine the equality constraints from both into a new
2728 * basic map such that Gaussian elimination can be applied to this combination
2729 * and then construct a variable compression from the resulting
2730 * equality constraints.
2731 */
2732static __isl_give isl_mat *combined_variable_compression(
2733 __isl_keep isl_basic_map *bmap1, int n1,
2734 __isl_keep isl_basic_map *bmap2, int n2, int total)
2735{
2736 isl_ctx *ctx;
2737 isl_mat *E1, *E2, *V;
2738 isl_basic_map *bmap;
2739
2740 ctx = isl_basic_map_get_ctx(bmap1);
2741 if (bmap1->n_eq == n1) {
2742 E2 = isl_mat_sub_alloc6(ctx, bmap2->eq,
2743 n2, bmap2->n_eq - n2, 0, 1 + total);
2744 return isl_mat_variable_compression(E2, NULL((void*)0));
2745 }
2746 if (bmap2->n_eq == n2) {
2747 E1 = isl_mat_sub_alloc6(ctx, bmap1->eq,
2748 n1, bmap1->n_eq - n1, 0, 1 + total);
2749 return isl_mat_variable_compression(E1, NULL((void*)0));
2750 }
2751 E1 = isl_mat_sub_alloc6(ctx, bmap1->eq,
2752 n1, bmap1->n_eq - n1, 0, 1 + total);
2753 E2 = isl_mat_sub_alloc6(ctx, bmap2->eq,
2754 n2, bmap2->n_eq - n2, 0, 1 + total);
2755 E1 = isl_mat_concat(E1, E2);
2756 bmap = basic_map_from_equalities(isl_basic_map_get_space(bmap1), E1);
2757 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
2758 if (!bmap)
2759 return NULL((void*)0);
2760 E1 = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total);
2761 V = isl_mat_variable_compression(E1, NULL((void*)0));
2762 isl_basic_map_free(bmap);
2763
2764 return V;
2765}
2766
2767/* Extract the stride constraints from "bmap", compressed
2768 * with respect to both the stride constraints in "context" and
2769 * the remaining equality constraints in both "bmap" and "context".
2770 * "bmap_n_eq" is the number of (initial) stride constraints in "bmap".
2771 * "context_n_eq" is the number of (initial) stride constraints in "context".
2772 *
2773 * Let x be all variables in "bmap" (and "context") other than the local
2774 * variables. First compute a variable compression
2775 *
2776 * x = V x'
2777 *
2778 * based on the non-stride equality constraints in "bmap" and "context".
2779 * Consider the stride constraints of "context",
2780 *
2781 * A(x) + B(y) = 0
2782 *
2783 * with y the local variables and plug in the variable compression,
2784 * resulting in
2785 *
2786 * A(V x') + B(y) = 0
2787 *
2788 * Use these constraints to compute a parameter compression on x'
2789 *
2790 * x' = T x''
2791 *
2792 * Now consider the stride constraints of "bmap"
2793 *
2794 * C(x) + D(y) = 0
2795 *
2796 * and plug in x = V*T x''.
2797 * That is, return A = [C*V*T D].
2798 */
2799static __isl_give isl_mat *extract_compressed_stride_constraints(
2800 __isl_keep isl_basic_map *bmap, int bmap_n_eq,
2801 __isl_keep isl_basic_map *context, int context_n_eq)
2802{
2803 int total, n_div;
2804 isl_ctx *ctx;
2805 isl_mat *A, *B, *T, *V;
2806
2807 total = isl_basic_map_dim(context, isl_dim_all);
2808 n_div = isl_basic_map_dim(context, isl_dim_div);
2809 total -= n_div;
2810
2811 ctx = isl_basic_map_get_ctx(bmap);
2812
2813 V = combined_variable_compression(bmap, bmap_n_eq,
2814 context, context_n_eq, total);
2815
2816 A = isl_mat_sub_alloc6(ctx, context->eq, 0, context_n_eq, 0, 1 + total);
2817 B = isl_mat_sub_alloc6(ctx, context->eq,
2818 0, context_n_eq, 1 + total, n_div);
2819 A = isl_mat_product(A, isl_mat_copy(V));
2820 T = isl_mat_parameter_compression_ext(A, B);
2821 T = isl_mat_product(V, T);
2822
2823 n_div = isl_basic_map_dim(bmap, isl_dim_div);
2824 T = isl_mat_diagonal(T, isl_mat_identity(ctx, n_div));
2825
2826 A = isl_mat_sub_alloc6(ctx, bmap->eq,
2827 0, bmap_n_eq, 0, 1 + total + n_div);
2828 A = isl_mat_product(A, T);
2829
2830 return A;
2831}
2832
2833/* Remove the prime factors from *g that have an exponent that
2834 * is strictly smaller than the exponent in "c".
2835 * All exponents in *g are known to be smaller than or equal
2836 * to those in "c".
2837 *
2838 * That is, if *g is equal to
2839 *
2840 * p_1^{e_1} p_2^{e_2} ... p_n^{e_n}
2841 *
2842 * and "c" is equal to
2843 *
2844 * p_1^{f_1} p_2^{f_2} ... p_n^{f_n}
2845 *
2846 * then update *g to
2847 *
2848 * p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ...
2849 * p_n^{e_n * (e_n = f_n)}
2850 *
2851 * If e_i = f_i, then c / *g does not have any p_i factors and therefore
2852 * neither does the gcd of *g and c / *g.
2853 * If e_i < f_i, then the gcd of *g and c / *g has a positive
2854 * power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors.
2855 * Dividing *g by this gcd therefore strictly reduces the exponent
2856 * of the prime factors that need to be removed, while leaving the
2857 * other prime factors untouched.
2858 * Repeating this process until gcd(*g, c / *g) = 1 therefore
2859 * removes all undesired factors, without removing any others.
2860 */
2861static void remove_incomplete_powers(isl_int *g, isl_int c)
2862{
2863 isl_int t;
2864
2865 isl_int_init(t)isl_sioimath_init((t));
2866 for (;;) {
2867 isl_int_divexact(t, c, *g)isl_sioimath_tdiv_q((t), *(c), *(*g));
2868 isl_int_gcd(t, t, *g)isl_sioimath_gcd((t), *(t), *(*g));
2869 if (isl_int_is_one(t)(isl_sioimath_cmp_si(*(t), 1) == 0))
2870 break;
2871 isl_int_divexact(*g, *g, t)isl_sioimath_tdiv_q((*g), *(*g), *(t));
2872 }
2873 isl_int_clear(t)isl_sioimath_clear((t));
2874}
2875
2876/* Reduce the "n" stride constraints in "bmap" based on a copy "A"
2877 * of the same stride constraints in a compressed space that exploits
2878 * all equalities in the context and the other equalities in "bmap".
2879 *
2880 * If the stride constraints of "bmap" are of the form
2881 *
2882 * C(x) + D(y) = 0
2883 *
2884 * then A is of the form
2885 *
2886 * B(x') + D(y) = 0
2887 *
2888 * If any of these constraints involves only a single local variable y,
2889 * then the constraint appears as
2890 *
2891 * f(x) + m y_i = 0
2892 *
2893 * in "bmap" and as
2894 *
2895 * h(x') + m y_i = 0
2896 *
2897 * in "A".
2898 *
2899 * Let g be the gcd of m and the coefficients of h.
2900 * Then, in particular, g is a divisor of the coefficients of h and
2901 *
2902 * f(x) = h(x')
2903 *
2904 * is known to be a multiple of g.
2905 * If some prime factor in m appears with the same exponent in g,
2906 * then it can be removed from m because f(x) is already known
2907 * to be a multiple of g and therefore in particular of this power
2908 * of the prime factors.
2909 * Prime factors that appear with a smaller exponent in g cannot
2910 * be removed from m.
2911 * Let g' be the divisor of g containing all prime factors that
2912 * appear with the same exponent in m and g, then
2913 *
2914 * f(x) + m y_i = 0
2915 *
2916 * can be replaced by
2917 *
2918 * f(x) + m/g' y_i' = 0
2919 *
2920 * Note that (if g' != 1) this changes the explicit representation
2921 * of y_i to that of y_i', so the integer division at position i
2922 * is marked unknown and later recomputed by a call to
2923 * isl_basic_map_gauss.
2924 */
2925static __isl_give isl_basic_map *reduce_stride_constraints(
2926 __isl_take isl_basic_map *bmap, int n, __isl_keep isl_mat *A)
2927{
2928 int i;
2929 int total, n_div;
2930 int any = 0;
2931 isl_int gcd;
2932
2933 if (!bmap || !A)
2934 return isl_basic_map_free(bmap);
2935
2936 total = isl_basic_map_dim(bmap, isl_dim_all);
2937 n_div = isl_basic_map_dim(bmap, isl_dim_div);
2938 total -= n_div;
2939
2940 isl_int_init(gcd)isl_sioimath_init((gcd));
2941 for (i = 0; i < n; ++i) {
2942 int div;
2943
2944 div = isl_seq_first_non_zero(bmap->eq[i] + 1 + total, n_div);
2945 if (div < 0)
2946 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-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 2948); goto error; } while (0)
2947 "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-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 2948); goto error; } while (0)
2948 goto error)do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_internal
, "equality constraints modified unexpectedly", "/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 2948); goto error; } while (0)
;
2949 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total + div + 1,
2950 n_div - div - 1) != -1)
2951 continue;
2952 if (isl_mat_row_gcd(A, i, &gcd) < 0)
2953 goto error;
2954 if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0))
2955 continue;
2956 remove_incomplete_powers(&gcd, bmap->eq[i][1 + total + div]);
2957 if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0))
2958 continue;
2959 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))
2960 bmap->eq[i][1 + total + div], gcd)isl_sioimath_tdiv_q((bmap->eq[i][1 + total + div]), *(bmap
->eq[i][1 + total + div]), *(gcd))
;
2961 bmap = isl_basic_map_mark_div_unknown(bmap, div);
2962 if (!bmap)
2963 goto error;
2964 any = 1;
2965 }
2966 isl_int_clear(gcd)isl_sioimath_clear((gcd));
2967
2968 if (any)
2969 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
2970
2971 return bmap;
2972error:
2973 isl_int_clear(gcd)isl_sioimath_clear((gcd));
2974 isl_basic_map_free(bmap);
2975 return NULL((void*)0);
2976}
2977
2978/* Simplify the stride constraints in "bmap" based on
2979 * the remaining equality constraints in "bmap" and all equality
2980 * constraints in "context".
2981 * Only do this if both "bmap" and "context" have stride constraints.
2982 *
2983 * First extract a copy of the stride constraints in "bmap" in a compressed
2984 * space exploiting all the other equality constraints and then
2985 * use this compressed copy to simplify the original stride constraints.
2986 */
2987static __isl_give isl_basic_map *gist_strides(__isl_take isl_basic_map *bmap,
2988 __isl_keep isl_basic_map *context)
2989{
2990 int bmap_n_eq, context_n_eq;
2991 isl_mat *A;
2992
2993 if (!bmap || !context)
2994 return isl_basic_map_free(bmap);
2995
2996 bmap_n_eq = n_div_eq(bmap);
2997 context_n_eq = n_div_eq(context);
2998
2999 if (bmap_n_eq < 0 || context_n_eq < 0)
3000 return isl_basic_map_free(bmap);
3001 if (bmap_n_eq == 0 || context_n_eq == 0)
3002 return bmap;
3003
3004 A = extract_compressed_stride_constraints(bmap, bmap_n_eq,
3005 context, context_n_eq);
3006 bmap = reduce_stride_constraints(bmap, bmap_n_eq, A);
3007
3008 isl_mat_free(A);
3009
3010 return bmap;
3011}
3012
3013/* Return a basic map that has the same intersection with "context" as "bmap"
3014 * and that is as "simple" as possible.
3015 *
3016 * The core computation is performed on the pure constraints.
3017 * When we add back the meaning of the integer divisions, we need
3018 * to (re)introduce the div constraints. If we happen to have
3019 * discovered that some of these integer divisions are equal to
3020 * some affine combination of other variables, then these div
3021 * constraints may end up getting simplified in terms of the equalities,
3022 * resulting in extra inequalities on the other variables that
3023 * may have been removed already or that may not even have been
3024 * part of the input. We try and remove those constraints of
3025 * this form that are most obviously redundant with respect to
3026 * the context. We also remove those div constraints that are
3027 * redundant with respect to the other constraints in the result.
3028 *
3029 * The stride constraints among the equality constraints in "bmap" are
3030 * also simplified with respecting to the other equality constraints
3031 * in "bmap" and with respect to all equality constraints in "context".
3032 */
3033__isl_give isl_basic_map *isl_basic_map_gist(__isl_take isl_basic_map *bmap,
3034 __isl_take isl_basic_map *context)
3035{
3036 isl_basic_setisl_basic_map *bset, *eq;
3037 isl_basic_map *eq_bmap;
3038 unsigned total, n_div, extra, n_eq, n_ineq;
3039
3040 if (!bmap || !context)
3041 goto error;
3042
3043 if (isl_basic_map_plain_is_universe(bmap)) {
3044 isl_basic_map_free(context);
3045 return bmap;
3046 }
3047 if (isl_basic_map_plain_is_empty(context)) {
3048 isl_space *space = isl_basic_map_get_space(bmap);
3049 isl_basic_map_free(bmap);
3050 isl_basic_map_free(context);
3051 return isl_basic_map_universe(space);
3052 }
3053 if (isl_basic_map_plain_is_empty(bmap)) {
3054 isl_basic_map_free(context);
3055 return bmap;
3056 }
3057
3058 bmap = isl_basic_map_remove_redundancies(bmap);
3059 context = isl_basic_map_remove_redundancies(context);
3060 context = isl_basic_map_align_divs(context, bmap);
3061 if (!context)
3062 goto error;
3063
3064 n_div = isl_basic_map_dim(context, isl_dim_div);
3065 total = isl_basic_map_dim(bmap, isl_dim_all);
3066 extra = n_div - isl_basic_map_dim(bmap, isl_dim_div);
3067
3068 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3069 bset = isl_basic_set_add_dims(bset, isl_dim_set, extra);
3070 bset = uset_gist(bset,
3071 isl_basic_map_underlying_set(isl_basic_map_copy(context)));
3072 bset = isl_basic_set_project_out(bset, isl_dim_set, total, extra);
3073
3074 if (!bset || bset->n_eq == 0 || n_div == 0 ||
3075 isl_basic_set_plain_is_empty(bset)) {
3076 isl_basic_map_free(context);
3077 return isl_basic_map_overlying_set(bset, bmap);
3078 }
3079
3080 n_eq = bset->n_eq;
3081 n_ineq = bset->n_ineq;
3082 eq = isl_basic_set_copy(bset);
3083 eq = isl_basic_set_cow(eq);
3084 if (isl_basic_set_free_inequality(eq, n_ineq) < 0)
3085 eq = isl_basic_set_free(eq);
3086 if (isl_basic_set_free_equality(bset, n_eq) < 0)
3087 bset = isl_basic_set_free(bset);
3088
3089 eq_bmap = isl_basic_map_overlying_set(eq, isl_basic_map_copy(bmap));
3090 eq_bmap = gist_strides(eq_bmap, context);
3091 eq_bmap = isl_basic_map_remove_shifted_constraints(eq_bmap, context);
3092 bmap = isl_basic_map_overlying_set(bset, bmap);
3093 bmap = isl_basic_map_intersect(bmap, eq_bmap);
3094 bmap = isl_basic_map_remove_redundancies(bmap);
3095
3096 return bmap;
3097error:
3098 isl_basic_map_free(bmap);
3099 isl_basic_map_free(context);
3100 return NULL((void*)0);
3101}
3102
3103/*
3104 * Assumes context has no implicit divs.
3105 */
3106__isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
3107 __isl_take isl_basic_map *context)
3108{
3109 int i;
3110
3111 if (!map || !context)
3112 goto error;
3113
3114 if (isl_basic_map_plain_is_empty(context)) {
3115 isl_space *space = isl_map_get_space(map);
3116 isl_map_free(map);
3117 isl_basic_map_free(context);
3118 return isl_map_universe(space);
3119 }
3120
3121 context = isl_basic_map_remove_redundancies(context);
3122 map = isl_map_cow(map);
3123 if (!map || !context)
3124 goto error;
3125 isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error)do { if (isl_space_is_equal(map->dim, context->dim)) break
; do { isl_handle_error(map->ctx, isl_error_unknown, "Assertion \""
"isl_space_is_equal(map->dim, context->dim)" "\" failed"
, "/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 3125); goto error; } while (0); } while (0)
;
3126 map = isl_map_compute_divs(map);
3127 if (!map)
3128 goto error;
3129 for (i = map->n - 1; i >= 0; --i) {
3130 map->p[i] = isl_basic_map_gist(map->p[i],
3131 isl_basic_map_copy(context));
3132 if (!map->p[i])
3133 goto error;
3134 if (isl_basic_map_plain_is_empty(map->p[i])) {
3135 isl_basic_map_free(map->p[i]);
3136 if (i != map->n - 1)
3137 map->p[i] = map->p[map->n - 1];
3138 map->n--;
3139 }
3140 }
3141 isl_basic_map_free(context);
3142 ISL_F_CLR(map, ISL_MAP_NORMALIZED)(((map)->flags) &= ~((1 << 1)));
3143 return map;
3144error:
3145 isl_map_free(map);
3146 isl_basic_map_free(context);
3147 return NULL((void*)0);
3148}
3149
3150/* Drop all inequalities from "bmap" that also appear in "context".
3151 * "context" is assumed to have only known local variables and
3152 * the initial local variables of "bmap" are assumed to be the same
3153 * as those of "context".
3154 * The constraints of both "bmap" and "context" are assumed
3155 * to have been sorted using isl_basic_map_sort_constraints.
3156 *
3157 * Run through the inequality constraints of "bmap" and "context"
3158 * in sorted order.
3159 * If a constraint of "bmap" involves variables not in "context",
3160 * then it cannot appear in "context".
3161 * If a matching constraint is found, it is removed from "bmap".
3162 */
3163static __isl_give isl_basic_map *drop_inequalities(
3164 __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context)
3165{
3166 int i1, i2;
3167 unsigned total, extra;
3168
3169 if (!bmap || !context)
3170 return isl_basic_map_free(bmap);
3171
3172 total = isl_basic_map_total_dim(context);
3173 extra = isl_basic_map_total_dim(bmap) - total;
3174
3175 i1 = bmap->n_ineq - 1;
3176 i2 = context->n_ineq - 1;
3177 while (bmap && i1 >= 0 && i2 >= 0) {
3178 int cmp;
3179
3180 if (isl_seq_first_non_zero(bmap->ineq[i1] + 1 + total,
3181 extra) != -1) {
3182 --i1;
3183 continue;
3184 }
3185 cmp = isl_basic_map_constraint_cmp(context, bmap->ineq[i1],
3186 context->ineq[i2]);
3187 if (cmp < 0) {
3188 --i2;
3189 continue;
3190 }
3191 if (cmp > 0) {
3192 --i1;
3193 continue;
3194 }
3195 if (isl_int_eq(bmap->ineq[i1][0], context->ineq[i2][0])(isl_sioimath_cmp(*(bmap->ineq[i1][0]), *(context->ineq
[i2][0])) == 0)
) {
3196 bmap = isl_basic_map_cow(bmap);
3197 if (isl_basic_map_drop_inequality(bmap, i1) < 0)
3198 bmap = isl_basic_map_free(bmap);
3199 }
3200 --i1;
3201 --i2;
3202 }
3203
3204 return bmap;
3205}
3206
3207/* Drop all equalities from "bmap" that also appear in "context".
3208 * "context" is assumed to have only known local variables and
3209 * the initial local variables of "bmap" are assumed to be the same
3210 * as those of "context".
3211 *
3212 * Run through the equality constraints of "bmap" and "context"
3213 * in sorted order.
3214 * If a constraint of "bmap" involves variables not in "context",
3215 * then it cannot appear in "context".
3216 * If a matching constraint is found, it is removed from "bmap".
3217 */
3218static __isl_give isl_basic_map *drop_equalities(
3219 __isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context)
3220{
3221 int i1, i2;
3222 unsigned total, extra;
3223
3224 if (!bmap || !context)
3225 return isl_basic_map_free(bmap);
3226
3227 total = isl_basic_map_total_dim(context);
3228 extra = isl_basic_map_total_dim(bmap) - total;
3229
3230 i1 = bmap->n_eq - 1;
3231 i2 = context->n_eq - 1;
3232
3233 while (bmap && i1 >= 0 && i2 >= 0) {
3234 int last1, last2;
3235
3236 if (isl_seq_first_non_zero(bmap->eq[i1] + 1 + total,
3237 extra) != -1)
3238 break;
3239 last1 = isl_seq_last_non_zero(bmap->eq[i1] + 1, total);
3240 last2 = isl_seq_last_non_zero(context->eq[i2] + 1, total);
3241 if (last1 > last2) {
3242 --i2;
3243 continue;
3244 }
3245 if (last1 < last2) {
3246 --i1;
3247 continue;
3248 }
3249 if (isl_seq_eq(bmap->eq[i1], context->eq[i2], 1 + total)) {
3250 bmap = isl_basic_map_cow(bmap);
3251 if (isl_basic_map_drop_equality(bmap, i1) < 0)
3252 bmap = isl_basic_map_free(bmap);
3253 }
3254 --i1;
3255 --i2;
3256 }
3257
3258 return bmap;
3259}
3260
3261/* Remove the constraints in "context" from "bmap".
3262 * "context" is assumed to have explicit representations
3263 * for all local variables.
3264 *
3265 * First align the divs of "bmap" to those of "context" and
3266 * sort the constraints. Then drop all constraints from "bmap"
3267 * that appear in "context".
3268 */
3269__isl_give isl_basic_map *isl_basic_map_plain_gist(
3270 __isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context)
3271{
3272 isl_bool done, known;
3273
3274 done = isl_basic_map_plain_is_universe(context);
3275 if (done == isl_bool_false)
3276 done = isl_basic_map_plain_is_universe(bmap);
3277 if (done == isl_bool_false)
3278 done = isl_basic_map_plain_is_empty(context);
3279 if (done == isl_bool_false)
3280 done = isl_basic_map_plain_is_empty(bmap);
3281 if (done < 0)
3282 goto error;
3283 if (done) {
3284 isl_basic_map_free(context);
3285 return bmap;
3286 }
3287 known = isl_basic_map_divs_known(context);
3288 if (known < 0)
3289 goto error;
3290 if (!known)
3291 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-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 3292); goto error; } while (0)
3292 "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-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 3292); goto error; } while (0)
;
3293
3294 bmap = isl_basic_map_align_divs(bmap, context);
3295 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
3296 bmap = isl_basic_map_sort_constraints(bmap);
3297 context = isl_basic_map_sort_constraints(context);
3298
3299 bmap = drop_inequalities(bmap, context);
3300 bmap = drop_equalities(bmap, context);
3301
3302 isl_basic_map_free(context);
3303 bmap = isl_basic_map_finalize(bmap);
3304 return bmap;
3305error:
3306 isl_basic_map_free(bmap);
3307 isl_basic_map_free(context);
3308 return NULL((void*)0);
3309}
3310
3311/* Replace "map" by the disjunct at position "pos" and free "context".
3312 */
3313static __isl_give isl_map *replace_by_disjunct(__isl_take isl_map *map,
3314 int pos, __isl_take isl_basic_map *context)
3315{
3316 isl_basic_map *bmap;
3317
3318 bmap = isl_basic_map_copy(map->p[pos]);
3319 isl_map_free(map);
3320 isl_basic_map_free(context);
3321 return isl_map_from_basic_map(bmap);
3322}
3323
3324/* Remove the constraints in "context" from "map".
3325 * If any of the disjuncts in the result turns out to be the universe,
3326 * then return this universe.
3327 * "context" is assumed to have explicit representations
3328 * for all local variables.
3329 */
3330__isl_give isl_map *isl_map_plain_gist_basic_map(__isl_take isl_map *map,
3331 __isl_take isl_basic_map *context)
3332{
3333 int i;
3334 isl_bool univ, known;
3335
3336 univ = isl_basic_map_plain_is_universe(context);
3337 if (univ < 0)
3338 goto error;
3339 if (univ) {
3340 isl_basic_map_free(context);
3341 return map;
3342 }
3343 known = isl_basic_map_divs_known(context);
3344 if (known < 0)
3345 goto error;
3346 if (!known)
3347 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-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 3348); goto error; } while (0)
3348 "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-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 3348); goto error; } while (0)
;
3349
3350 map = isl_map_cow(map);
3351 if (!map)
3352 goto error;
3353 for (i = 0; i < map->n; ++i) {
3354 map->p[i] = isl_basic_map_plain_gist(map->p[i],
3355 isl_basic_map_copy(context));
3356 univ = isl_basic_map_plain_is_universe(map->p[i]);
3357 if (univ < 0)
3358 goto error;
3359 if (univ && map->n > 1)
3360 return replace_by_disjunct(map, i, context);
3361 }
3362
3363 isl_basic_map_free(context);
3364 ISL_F_CLR(map, ISL_MAP_NORMALIZED)(((map)->flags) &= ~((1 << 1)));
3365 if (map->n > 1)
3366 ISL_F_CLR(map, ISL_MAP_DISJOINT)(((map)->flags) &= ~((1 << 0)));
3367 return map;
3368error:
3369 isl_map_free(map);
3370 isl_basic_map_free(context);
3371 return NULL((void*)0);
3372}
3373
3374/* Remove the constraints in "context" from "set".
3375 * If any of the disjuncts in the result turns out to be the universe,
3376 * then return this universe.
3377 * "context" is assumed to have explicit representations
3378 * for all local variables.
3379 */
3380__isl_give isl_setisl_map *isl_set_plain_gist_basic_set(__isl_take isl_setisl_map *set,
3381 __isl_take isl_basic_setisl_basic_map *context)
3382{
3383 return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set),
3384 bset_to_bmap(context)));
3385}
3386
3387/* Remove the constraints in "context" from "map".
3388 * If any of the disjuncts in the result turns out to be the universe,
3389 * then return this universe.
3390 * "context" is assumed to consist of a single disjunct and
3391 * to have explicit representations for all local variables.
3392 */
3393__isl_give isl_map *isl_map_plain_gist(__isl_take isl_map *map,
3394 __isl_take isl_map *context)
3395{
3396 isl_basic_map *hull;
3397
3398 hull = isl_map_unshifted_simple_hull(context);
3399 return isl_map_plain_gist_basic_map(map, hull);
3400}
3401
3402/* Replace "map" by a universe map in the same space and free "drop".
3403 */
3404static __isl_give isl_map *replace_by_universe(__isl_take isl_map *map,
3405 __isl_take isl_map *drop)
3406{
3407 isl_map *res;
3408
3409 res = isl_map_universe(isl_map_get_space(map));
3410 isl_map_free(map);
3411 isl_map_free(drop);
3412 return res;
3413}
3414
3415/* Return a map that has the same intersection with "context" as "map"
3416 * and that is as "simple" as possible.
3417 *
3418 * If "map" is already the universe, then we cannot make it any simpler.
3419 * Similarly, if "context" is the universe, then we cannot exploit it
3420 * to simplify "map"
3421 * If "map" and "context" are identical to each other, then we can
3422 * return the corresponding universe.
3423 *
3424 * If either "map" or "context" consists of multiple disjuncts,
3425 * then check if "context" happens to be a subset of "map",
3426 * in which case all constraints can be removed.
3427 * In case of multiple disjuncts, the standard procedure
3428 * may not be able to detect that all constraints can be removed.
3429 *
3430 * If none of these cases apply, we have to work a bit harder.
3431 * During this computation, we make use of a single disjunct context,
3432 * so if the original context consists of more than one disjunct
3433 * then we need to approximate the context by a single disjunct set.
3434 * Simply taking the simple hull may drop constraints that are
3435 * only implicitly available in each disjunct. We therefore also
3436 * look for constraints among those defining "map" that are valid
3437 * for the context. These can then be used to simplify away
3438 * the corresponding constraints in "map".
3439 */
3440static __isl_give isl_map *map_gist(__isl_take isl_map *map,
3441 __isl_take isl_map *context)
3442{
3443 int equal;
3444 int is_universe;
3445 int single_disjunct_map, single_disjunct_context;
3446 isl_bool subset;
3447 isl_basic_map *hull;
3448
3449 is_universe = isl_map_plain_is_universe(map);
3450 if (is_universe >= 0 && !is_universe)
3451 is_universe = isl_map_plain_is_universe(context);
3452 if (is_universe < 0)
3453 goto error;
3454 if (is_universe) {
3455 isl_map_free(context);
3456 return map;
3457 }
3458
3459 equal = isl_map_plain_is_equal(map, context);
3460 if (equal < 0)
3461 goto error;
3462 if (equal)
3463 return replace_by_universe(map, context);
3464
3465 single_disjunct_map = isl_map_n_basic_map(map) == 1;
3466 single_disjunct_context = isl_map_n_basic_map(context) == 1;
3467 if (!single_disjunct_map || !single_disjunct_context) {
3468 subset = isl_map_is_subset(context, map);
3469 if (subset < 0)
3470 goto error;
3471 if (subset)
3472 return replace_by_universe(map, context);
3473 }
3474
3475 context = isl_map_compute_divs(context);
3476 if (!context)
3477 goto error;
3478 if (single_disjunct_context) {
3479 hull = isl_map_simple_hull(context);
3480 } else {
3481 isl_ctx *ctx;
3482 isl_map_list *list;
3483
3484 ctx = isl_map_get_ctx(map);
3485 list = isl_map_list_alloc(ctx, 2);
3486 list = isl_map_list_add(list, isl_map_copy(context));
3487 list = isl_map_list_add(list, isl_map_copy(map));
3488 hull = isl_map_unshifted_simple_hull_from_map_list(context,
3489 list);
3490 }
3491 return isl_map_gist_basic_map(map, hull);
3492error:
3493 isl_map_free(map);
3494 isl_map_free(context);
3495 return NULL((void*)0);
3496}
3497
3498__isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3499 __isl_take isl_map *context)
3500{
3501 return isl_map_align_params_map_map_and(map, context, &map_gist);
3502}
3503
3504struct isl_basic_setisl_basic_map *isl_basic_set_gist(struct isl_basic_setisl_basic_map *bset,
3505 struct isl_basic_setisl_basic_map *context)
3506{
3507 return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset),
3508 bset_to_bmap(context)));
3509}
3510
3511__isl_give isl_setisl_map *isl_set_gist_basic_set(__isl_take isl_setisl_map *set,
3512 __isl_take isl_basic_setisl_basic_map *context)
3513{
3514 return set_from_map(isl_map_gist_basic_map(set_to_map(set),
3515 bset_to_bmap(context)));
3516}
3517
3518__isl_give isl_setisl_map *isl_set_gist_params_basic_set(__isl_take isl_setisl_map *set,
3519 __isl_take isl_basic_setisl_basic_map *context)
3520{
3521 isl_space *space = isl_set_get_space(set);
3522 isl_basic_setisl_basic_map *dom_context = isl_basic_set_universe(space);
3523 dom_context = isl_basic_set_intersect_params(dom_context, context);
3524 return isl_set_gist_basic_set(set, dom_context);
3525}
3526
3527__isl_give isl_setisl_map *isl_set_gist(__isl_take isl_setisl_map *set,
3528 __isl_take isl_setisl_map *context)
3529{
3530 return set_from_map(isl_map_gist(set_to_map(set), set_to_map(context)));
3531}
3532
3533/* Compute the gist of "bmap" with respect to the constraints "context"
3534 * on the domain.
3535 */
3536__isl_give isl_basic_map *isl_basic_map_gist_domain(
3537 __isl_take isl_basic_map *bmap, __isl_take isl_basic_setisl_basic_map *context)
3538{
3539 isl_space *space = isl_basic_map_get_space(bmap);
3540 isl_basic_map *bmap_context = isl_basic_map_universe(space);
3541
3542 bmap_context = isl_basic_map_intersect_domain(bmap_context, context);
3543 return isl_basic_map_gist(bmap, bmap_context);
3544}
3545
3546__isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
3547 __isl_take isl_setisl_map *context)
3548{
3549 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
3550 map_context = isl_map_intersect_domain(map_context, context);
3551 return isl_map_gist(map, map_context);
3552}
3553
3554__isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
3555 __isl_take isl_setisl_map *context)
3556{
3557 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
3558 map_context = isl_map_intersect_range(map_context, context);
3559 return isl_map_gist(map, map_context);
3560}
3561
3562__isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
3563 __isl_take isl_setisl_map *context)
3564{
3565 isl_map *map_context = isl_map_universe(isl_map_get_space(map));
3566 map_context = isl_map_intersect_params(map_context, context);
3567 return isl_map_gist(map, map_context);
3568}
3569
3570__isl_give isl_setisl_map *isl_set_gist_params(__isl_take isl_setisl_map *set,
3571 __isl_take isl_setisl_map *context)
3572{
3573 return isl_map_gist_params(set, context);
3574}
3575
3576/* Quick check to see if two basic maps are disjoint.
3577 * In particular, we reduce the equalities and inequalities of
3578 * one basic map in the context of the equalities of the other
3579 * basic map and check if we get a contradiction.
3580 */
3581isl_bool isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
3582 __isl_keep isl_basic_map *bmap2)
3583{
3584 struct isl_vec *v = NULL((void*)0);
3585 int *elim = NULL((void*)0);
3586 unsigned total;
3587 int i;
3588
3589 if (!bmap1 || !bmap2)
3590 return isl_bool_error;
3591 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),do { if (isl_space_is_equal(bmap1->dim, bmap2->dim)) break
; do { isl_handle_error(bmap1->ctx, isl_error_unknown, "Assertion \""
"isl_space_is_equal(bmap1->dim, bmap2->dim)" "\" failed"
, "/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 3592); return isl_bool_error; } while (0); } while (0)
3592 return isl_bool_error)do { if (isl_space_is_equal(bmap1->dim, bmap2->dim)) break
; do { isl_handle_error(bmap1->ctx, isl_error_unknown, "Assertion \""
"isl_space_is_equal(bmap1->dim, bmap2->dim)" "\" failed"
, "/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 3592); return isl_bool_error; } while (0); } while (0)
;
3593 if (bmap1->n_div || bmap2->n_div)
3594 return isl_bool_false;
3595 if (!bmap1->n_eq && !bmap2->n_eq)
3596 return isl_bool_false;
3597
3598 total = isl_space_dim(bmap1->dim, isl_dim_all);
3599 if (total == 0)
3600 return isl_bool_false;
3601 v = isl_vec_alloc(bmap1->ctx, 1 + total);
3602 if (!v)
3603 goto error;
3604 elim = isl_alloc_array(bmap1->ctx, int, total)((int *)isl_malloc_or_die(bmap1->ctx, (total)*sizeof(int))
)
;
3605 if (!elim)
3606 goto error;
3607 compute_elimination_index(bmap1, elim);
3608 for (i = 0; i < bmap2->n_eq; ++i) {
3609 int reduced;
3610 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
3611 bmap1, elim);
3612 if (reduced && !isl_int_is_zero(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) == 0) &&
3613 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
3614 goto disjoint;
3615 }
3616 for (i = 0; i < bmap2->n_ineq; ++i) {
3617 int reduced;
3618 reduced = reduced_using_equalities(v->block.data,
3619 bmap2->ineq[i], bmap1, elim);
3620 if (reduced && isl_int_is_neg(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) < 0) &&
3621 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
3622 goto disjoint;
3623 }
3624 compute_elimination_index(bmap2, elim);
3625 for (i = 0; i < bmap1->n_ineq; ++i) {
3626 int reduced;
3627 reduced = reduced_using_equalities(v->block.data,
3628 bmap1->ineq[i], bmap2, elim);
3629 if (reduced && isl_int_is_neg(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) < 0) &&
3630 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
3631 goto disjoint;
3632 }
3633 isl_vec_free(v);
3634 free(elim);
3635 return isl_bool_false;
3636disjoint:
3637 isl_vec_free(v);
3638 free(elim);
3639 return isl_bool_true;
3640error:
3641 isl_vec_free(v);
3642 free(elim);
3643 return isl_bool_error;
3644}
3645
3646int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_setisl_basic_map *bset1,
3647 __isl_keep isl_basic_setisl_basic_map *bset2)
3648{
3649 return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1),
3650 bset_to_bmap(bset2));
3651}
3652
3653/* Does "test" hold for all pairs of basic maps in "map1" and "map2"?
3654 */
3655static isl_bool all_pairs(__isl_keep isl_map *map1, __isl_keep isl_map *map2,
3656 isl_bool (*test)(__isl_keep isl_basic_map *bmap1,
3657 __isl_keep isl_basic_map *bmap2))
3658{
3659 int i, j;
3660
3661 if (!map1 || !map2)
3662 return isl_bool_error;
3663
3664 for (i = 0; i < map1->n; ++i) {
3665 for (j = 0; j < map2->n; ++j) {
3666 isl_bool d = test(map1->p[i], map2->p[j]);
3667 if (d != isl_bool_true)
3668 return d;
3669 }
3670 }
3671
3672 return isl_bool_true;
3673}
3674
3675/* Are "map1" and "map2" obviously disjoint, based on information
3676 * that can be derived without looking at the individual basic maps?
3677 *
3678 * In particular, if one of them is empty or if they live in different spaces
3679 * (ignoring parameters), then they are clearly disjoint.
3680 */
3681static isl_bool isl_map_plain_is_disjoint_global(__isl_keep isl_map *map1,
3682 __isl_keep isl_map *map2)
3683{
3684 isl_bool disjoint;
3685 isl_bool match;
3686
3687 if (!map1 || !map2)
3688 return isl_bool_error;
3689
3690 disjoint = isl_map_plain_is_empty(map1);
3691 if (disjoint < 0 || disjoint)
3692 return disjoint;
3693
3694 disjoint = isl_map_plain_is_empty(map2);
3695 if (disjoint < 0 || disjoint)
3696 return disjoint;
3697
3698 match = isl_space_tuple_is_equal(map1->dim, isl_dim_in,
3699 map2->dim, isl_dim_in);
3700 if (match < 0 || !match)
3701 return match < 0 ? isl_bool_error : isl_bool_true;
3702
3703 match = isl_space_tuple_is_equal(map1->dim, isl_dim_out,
3704 map2->dim, isl_dim_out);
3705 if (match < 0 || !match)
3706 return match < 0 ? isl_bool_error : isl_bool_true;
3707
3708 return isl_bool_false;
3709}
3710
3711/* Are "map1" and "map2" obviously disjoint?
3712 *
3713 * If one of them is empty or if they live in different spaces (ignoring
3714 * parameters), then they are clearly disjoint.
3715 * This is checked by isl_map_plain_is_disjoint_global.
3716 *
3717 * If they have different parameters, then we skip any further tests.
3718 *
3719 * If they are obviously equal, but not obviously empty, then we will
3720 * not be able to detect if they are disjoint.
3721 *
3722 * Otherwise we check if each basic map in "map1" is obviously disjoint
3723 * from each basic map in "map2".
3724 */
3725isl_bool isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
3726 __isl_keep isl_map *map2)
3727{
3728 isl_bool disjoint;
3729 isl_bool intersect;
3730 isl_bool match;
3731
3732 disjoint = isl_map_plain_is_disjoint_global(map1, map2);
3733 if (disjoint < 0 || disjoint)
3734 return disjoint;
3735
3736 match = isl_map_has_equal_params(map1, map2);
3737 if (match < 0 || !match)
3738 return match < 0 ? isl_bool_error : isl_bool_false;
3739
3740 intersect = isl_map_plain_is_equal(map1, map2);
3741 if (intersect < 0 || intersect)
3742 return intersect < 0 ? isl_bool_error : isl_bool_false;
3743
3744 return all_pairs(map1, map2, &isl_basic_map_plain_is_disjoint);
3745}
3746
3747/* Are "map1" and "map2" disjoint?
3748 * The parameters are assumed to have been aligned.
3749 *
3750 * In particular, check whether all pairs of basic maps are disjoint.
3751 */
3752static isl_bool isl_map_is_disjoint_aligned(__isl_keep isl_map *map1,
3753 __isl_keep isl_map *map2)
3754{
3755 return all_pairs(map1, map2, &isl_basic_map_is_disjoint);
3756}
3757
3758/* Are "map1" and "map2" disjoint?
3759 *
3760 * They are disjoint if they are "obviously disjoint" or if one of them
3761 * is empty. Otherwise, they are not disjoint if one of them is universal.
3762 * If the two inputs are (obviously) equal and not empty, then they are
3763 * not disjoint.
3764 * If none of these cases apply, then check if all pairs of basic maps
3765 * are disjoint after aligning the parameters.
3766 */
3767isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
3768{
3769 isl_bool disjoint;
3770 isl_bool intersect;
3771
3772 disjoint = isl_map_plain_is_disjoint_global(map1, map2);
3773 if (disjoint < 0 || disjoint)
3774 return disjoint;
3775
3776 disjoint = isl_map_is_empty(map1);
3777 if (disjoint < 0 || disjoint)
3778 return disjoint;
3779
3780 disjoint = isl_map_is_empty(map2);
3781 if (disjoint < 0 || disjoint)
3782 return disjoint;
3783
3784 intersect = isl_map_plain_is_universe(map1);
3785 if (intersect < 0 || intersect)
3786 return intersect < 0 ? isl_bool_error : isl_bool_false;
3787
3788 intersect = isl_map_plain_is_universe(map2);
3789 if (intersect < 0 || intersect)
3790 return intersect < 0 ? isl_bool_error : isl_bool_false;
3791
3792 intersect = isl_map_plain_is_equal(map1, map2);
3793 if (intersect < 0 || intersect)
3794 return isl_bool_not(intersect);
3795
3796 return isl_map_align_params_map_map_and_test(map1, map2,
3797 &isl_map_is_disjoint_aligned);
3798}
3799
3800/* Are "bmap1" and "bmap2" disjoint?
3801 *
3802 * They are disjoint if they are "obviously disjoint" or if one of them
3803 * is empty. Otherwise, they are not disjoint if one of them is universal.
3804 * If none of these cases apply, we compute the intersection and see if
3805 * the result is empty.
3806 */
3807isl_bool isl_basic_map_is_disjoint(__isl_keep isl_basic_map *bmap1,
3808 __isl_keep isl_basic_map *bmap2)
3809{
3810 isl_bool disjoint;
3811 isl_bool intersect;
3812 isl_basic_map *test;
3813
3814 disjoint = isl_basic_map_plain_is_disjoint(bmap1, bmap2);
3815 if (disjoint < 0 || disjoint)
3816 return disjoint;
3817
3818 disjoint = isl_basic_map_is_empty(bmap1);
3819 if (disjoint < 0 || disjoint)
3820 return disjoint;
3821
3822 disjoint = isl_basic_map_is_empty(bmap2);
3823 if (disjoint < 0 || disjoint)
3824 return disjoint;
3825
3826 intersect = isl_basic_map_plain_is_universe(bmap1);
3827 if (intersect < 0 || intersect)
3828 return intersect < 0 ? isl_bool_error : isl_bool_false;
3829
3830 intersect = isl_basic_map_plain_is_universe(bmap2);
3831 if (intersect < 0 || intersect)
3832 return intersect < 0 ? isl_bool_error : isl_bool_false;
3833
3834 test = isl_basic_map_intersect(isl_basic_map_copy(bmap1),
3835 isl_basic_map_copy(bmap2));
3836 disjoint = isl_basic_map_is_empty(test);
3837 isl_basic_map_free(test);
3838
3839 return disjoint;
3840}
3841
3842/* Are "bset1" and "bset2" disjoint?
3843 */
3844isl_bool isl_basic_set_is_disjoint(__isl_keep isl_basic_setisl_basic_map *bset1,
3845 __isl_keep isl_basic_setisl_basic_map *bset2)
3846{
3847 return isl_basic_map_is_disjoint(bset1, bset2);
3848}
3849
3850isl_bool isl_set_plain_is_disjoint(__isl_keep isl_setisl_map *set1,
3851 __isl_keep isl_setisl_map *set2)
3852{
3853 return isl_map_plain_is_disjoint(set_to_map(set1), set_to_map(set2));
3854}
3855
3856/* Are "set1" and "set2" disjoint?
3857 */
3858isl_bool isl_set_is_disjoint(__isl_keep isl_setisl_map *set1, __isl_keep isl_setisl_map *set2)
3859{
3860 return isl_map_is_disjoint(set1, set2);
3861}
3862
3863/* Is "v" equal to 0, 1 or -1?
3864 */
3865static int is_zero_or_one(isl_int v)
3866{
3867 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);
3868}
3869
3870/* Check if we can combine a given div with lower bound l and upper
3871 * bound u with some other div and if so return that other div.
3872 * Otherwise return -1.
3873 *
3874 * We first check that
3875 * - the bounds are opposites of each other (except for the constant
3876 * term)
3877 * - the bounds do not reference any other div
3878 * - no div is defined in terms of this div
3879 *
3880 * Let m be the size of the range allowed on the div by the bounds.
3881 * That is, the bounds are of the form
3882 *
3883 * e <= a <= e + m - 1
3884 *
3885 * with e some expression in the other variables.
3886 * We look for another div b such that no third div is defined in terms
3887 * of this second div b and such that in any constraint that contains
3888 * a (except for the given lower and upper bound), also contains b
3889 * with a coefficient that is m times that of b.
3890 * That is, all constraints (except for the lower and upper bound)
3891 * are of the form
3892 *
3893 * e + f (a + m b) >= 0
3894 *
3895 * Furthermore, in the constraints that only contain b, the coefficient
3896 * of b should be equal to 1 or -1.
3897 * If so, we return b so that "a + m b" can be replaced by
3898 * a single div "c = a + m b".
3899 */
3900static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
3901 unsigned div, unsigned l, unsigned u)
3902{
3903 int i, j;
3904 unsigned dim;
3905 int coalesce = -1;
3906
3907 if (bmap->n_div <= 1)
3908 return -1;
3909 dim = isl_space_dim(bmap->dim, isl_dim_all);
3910 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
3911 return -1;
3912 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
3913 bmap->n_div - div - 1) != -1)
3914 return -1;
3915 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
3916 dim + bmap->n_div))
3917 return -1;
3918
3919 for (i = 0; i < bmap->n_div; ++i) {
3920 if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
3921 continue;
3922 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div])(isl_sioimath_sgn(*(bmap->div[i][1 + 1 + dim + div])) == 0
)
)
3923 return -1;
3924 }
3925
3926 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]))
;
3927 if (isl_int_is_neg(bmap->ineq[l][0])(isl_sioimath_sgn(*(bmap->ineq[l][0])) < 0)) {
3928 isl_int_sub(bmap->ineq[l][0],isl_sioimath_sub((bmap->ineq[l][0]), *(bmap->ineq[l][0]
), *(bmap->ineq[u][0]))
3929 bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_sub((bmap->ineq[l][0]), *(bmap->ineq[l][0]
), *(bmap->ineq[u][0]))
;
3930 bmap = isl_basic_map_copy(bmap);
3931 bmap = isl_basic_map_set_to_empty(bmap);
3932 isl_basic_map_free(bmap);
3933 return -1;
3934 }
3935 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)
;
3936 for (i = 0; i < bmap->n_div; ++i) {
3937 if (i == div)
3938 continue;
3939 if (!pairs[i])
3940 continue;
3941 for (j = 0; j < bmap->n_div; ++j) {
3942 if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0))
3943 continue;
3944 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i])(isl_sioimath_sgn(*(bmap->div[j][1 + 1 + dim + i])) == 0))
3945 break;
3946 }
3947 if (j < bmap->n_div)
3948 continue;
3949 for (j = 0; j < bmap->n_ineq; ++j) {
3950 int valid;
3951 if (j == l || j == u)
3952 continue;
3953 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div])(isl_sioimath_sgn(*(bmap->ineq[j][1 + dim + div])) == 0)) {
3954 if (is_zero_or_one(bmap->ineq[j][1 + dim + i]))
3955 continue;
3956 break;
3957 }
3958 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + dim + i])) == 0))
3959 break;
3960 isl_int_mul(bmap->ineq[j][1 + dim + div],isl_sioimath_mul((bmap->ineq[j][1 + dim + div]), *(bmap->
ineq[j][1 + dim + div]), *(bmap->ineq[l][0]))
3961 bmap->ineq[j][1 + dim + div],isl_sioimath_mul((bmap->ineq[j][1 + dim + div]), *(bmap->
ineq[j][1 + dim + div]), *(bmap->ineq[l][0]))
3962 bmap->ineq[l][0])isl_sioimath_mul((bmap->ineq[j][1 + dim + div]), *(bmap->
ineq[j][1 + dim + div]), *(bmap->ineq[l][0]))
;
3963 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],(isl_sioimath_cmp(*(bmap->ineq[j][1 + dim + div]), *(bmap->
ineq[j][1 + dim + i])) == 0)
3964 bmap->ineq[j][1 + dim + i])(isl_sioimath_cmp(*(bmap->ineq[j][1 + dim + div]), *(bmap->
ineq[j][1 + dim + i])) == 0)
;
3965 isl_int_divexact(bmap->ineq[j][1 + dim + div],isl_sioimath_tdiv_q((bmap->ineq[j][1 + dim + div]), *(bmap
->ineq[j][1 + dim + div]), *(bmap->ineq[l][0]))
3966 bmap->ineq[j][1 + dim + div],isl_sioimath_tdiv_q((bmap->ineq[j][1 + dim + div]), *(bmap
->ineq[j][1 + dim + div]), *(bmap->ineq[l][0]))
3967 bmap->ineq[l][0])isl_sioimath_tdiv_q((bmap->ineq[j][1 + dim + div]), *(bmap
->ineq[j][1 + dim + div]), *(bmap->ineq[l][0]))
;
3968 if (!valid)
3969 break;
3970 }
3971 if (j < bmap->n_ineq)
3972 continue;
3973 coalesce = i;
3974 break;
3975 }
3976 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)
;
3977 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]))
;
3978 return coalesce;
3979}
3980
3981/* Internal data structure used during the construction and/or evaluation of
3982 * an inequality that ensures that a pair of bounds always allows
3983 * for an integer value.
3984 *
3985 * "tab" is the tableau in which the inequality is evaluated. It may
3986 * be NULL until it is actually needed.
3987 * "v" contains the inequality coefficients.
3988 * "g", "fl" and "fu" are temporary scalars used during the construction and
3989 * evaluation.
3990 */
3991struct test_ineq_data {
3992 struct isl_tab *tab;
3993 isl_vec *v;
3994 isl_int g;
3995 isl_int fl;
3996 isl_int fu;
3997};
3998
3999/* Free all the memory allocated by the fields of "data".
4000 */
4001static void test_ineq_data_clear(struct test_ineq_data *data)
4002{
4003 isl_tab_free(data->tab);
4004 isl_vec_free(data->v);
4005 isl_int_clear(data->g)isl_sioimath_clear((data->g));
4006 isl_int_clear(data->fl)isl_sioimath_clear((data->fl));
4007 isl_int_clear(data->fu)isl_sioimath_clear((data->fu));
4008}
4009
4010/* Is the inequality stored in data->v satisfied by "bmap"?
4011 * That is, does it only attain non-negative values?
4012 * data->tab is a tableau corresponding to "bmap".
4013 */
4014static isl_bool test_ineq_is_satisfied(__isl_keep isl_basic_map *bmap,
4015 struct test_ineq_data *data)
4016{
4017 isl_ctx *ctx;
4018 enum isl_lp_result res;
4019
4020 ctx = isl_basic_map_get_ctx(bmap);
4021 if (!data->tab)
4022 data->tab = isl_tab_from_basic_map(bmap, 0);
4023 res = isl_tab_min(data->tab, data->v->el, ctx->one, &data->g, NULL((void*)0), 0);
4024 if (res == isl_lp_error)
4025 return isl_bool_error;
4026 return res == isl_lp_ok && isl_int_is_nonneg(data->g)(isl_sioimath_sgn(*(data->g)) >= 0);
4027}
4028
4029/* Given a lower and an upper bound on div i, do they always allow
4030 * for an integer value of the given div?
4031 * Determine this property by constructing an inequality
4032 * such that the property is guaranteed when the inequality is nonnegative.
4033 * The lower bound is inequality l, while the upper bound is inequality u.
4034 * The constructed inequality is stored in data->v.
4035 *
4036 * Let the upper bound be
4037 *
4038 * -n_u a + e_u >= 0
4039 *
4040 * and the lower bound
4041 *
4042 * n_l a + e_l >= 0
4043 *
4044 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
4045 * We have
4046 *
4047 * - f_u e_l <= f_u f_l g a <= f_l e_u
4048 *
4049 * Since all variables are integer valued, this is equivalent to
4050 *
4051 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
4052 *
4053 * If this interval is at least f_u f_l g, then it contains at least
4054 * one integer value for a.
4055 * That is, the test constraint is
4056 *
4057 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
4058 *
4059 * or
4060 *
4061 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0
4062 *
4063 * If the coefficients of f_l e_u + f_u e_l have a common divisor g',
4064 * then the constraint can be scaled down by a factor g',
4065 * with the constant term replaced by
4066 * floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g').
4067 * Note that the result of applying Fourier-Motzkin to this pair
4068 * of constraints is
4069 *
4070 * f_l e_u + f_u e_l >= 0
4071 *
4072 * If the constant term of the scaled down version of this constraint,
4073 * i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant
4074 * term of the scaled down test constraint, then the test constraint
4075 * is known to hold and no explicit evaluation is required.
4076 * This is essentially the Omega test.
4077 *
4078 * If the test constraint consists of only a constant term, then
4079 * it is sufficient to look at the sign of this constant term.
4080 */
4081static isl_bool int_between_bounds(__isl_keep isl_basic_map *bmap, int i,
4082 int l, int u, struct test_ineq_data *data)
4083{
4084 unsigned offset, n_div;
4085 offset = isl_basic_map_offset(bmap, isl_dim_div);
4086 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4087
4088 isl_int_gcd(data->g,isl_sioimath_gcd((data->g), *(bmap->ineq[l][offset + i]
), *(bmap->ineq[u][offset + i]))
4089 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]))
;
4090 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))
;
4091 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))
;
4092 isl_int_neg(data->fu, data->fu)isl_sioimath_neg((data->fu), *(data->fu));
4093 isl_seq_combine(data->v->el, data->fl, bmap->ineq[u],
4094 data->fu, bmap->ineq[l], offset + n_div);
4095 isl_int_mul(data->g, data->g, data->fl)isl_sioimath_mul((data->g), *(data->g), *(data->fl));
4096 isl_int_mul(data->g, data->g, data->fu)isl_sioimath_mul((data->g), *(data->g), *(data->fu));
4097 isl_int_sub(data->g, data->g, data->fl)isl_sioimath_sub((data->g), *(data->g), *(data->fl));
4098 isl_int_sub(data->g, data->g, data->fu)isl_sioimath_sub((data->g), *(data->g), *(data->fu));
4099 isl_int_add_ui(data->g, data->g, 1)isl_sioimath_add_ui((data->g), *(data->g), 1);
4100 isl_int_sub(data->fl, data->v->el[0], data->g)isl_sioimath_sub((data->fl), *(data->v->el[0]), *(data
->g))
;
4101
4102 isl_seq_gcd(data->v->el + 1, offset - 1 + n_div, &data->g);
4103 if (isl_int_is_zero(data->g)(isl_sioimath_sgn(*(data->g)) == 0))
4104 return isl_int_is_nonneg(data->fl)(isl_sioimath_sgn(*(data->fl)) >= 0);
4105 if (isl_int_is_one(data->g)(isl_sioimath_cmp_si(*(data->g), 1) == 0)) {
4106 isl_int_set(data->v->el[0], data->fl)isl_sioimath_set((data->v->el[0]), *(data->fl));
4107 return test_ineq_is_satisfied(bmap, data);
4108 }
4109 isl_int_fdiv_q(data->fl, data->fl, data->g)isl_sioimath_fdiv_q((data->fl), *(data->fl), *(data->
g))
;
4110 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))
;
4111 if (isl_int_eq(data->fl, data->v->el[0])(isl_sioimath_cmp(*(data->fl), *(data->v->el[0])) ==
0)
)
4112 return isl_bool_true;
4113 isl_int_set(data->v->el[0], data->fl)isl_sioimath_set((data->v->el[0]), *(data->fl));
4114 isl_seq_scale_down(data->v->el + 1, data->v->el + 1, data->g,
4115 offset - 1 + n_div);
4116
4117 return test_ineq_is_satisfied(bmap, data);
4118}
4119
4120/* Remove more kinds of divs that are not strictly needed.
4121 * In particular, if all pairs of lower and upper bounds on a div
4122 * are such that they allow at least one integer value of the div,
4123 * then we can eliminate the div using Fourier-Motzkin without
4124 * introducing any spurious solutions.
4125 *
4126 * If at least one of the two constraints has a unit coefficient for the div,
4127 * then the presence of such a value is guaranteed so there is no need to check.
4128 * In particular, the value attained by the bound with unit coefficient
4129 * can serve as this intermediate value.
4130 */
4131static __isl_give isl_basic_map *drop_more_redundant_divs(
4132 __isl_take isl_basic_map *bmap, __isl_take int *pairs, int n)
4133{
4134 isl_ctx *ctx;
4135 struct test_ineq_data data = { NULL((void*)0), NULL((void*)0) };
4136 unsigned off, n_div;
4137 int remove = -1;
4138
4139 isl_int_init(data.g)isl_sioimath_init((data.g));
4140 isl_int_init(data.fl)isl_sioimath_init((data.fl));
4141 isl_int_init(data.fu)isl_sioimath_init((data.fu));
4142
4143 if (!bmap)
4144 goto error;
4145
4146 ctx = isl_basic_map_get_ctx(bmap);
4147 off = isl_basic_map_offset(bmap, isl_dim_div);
4148 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4149 data.v = isl_vec_alloc(ctx, off + n_div);
4150 if (!data.v)
4151 goto error;
4152
4153 while (n > 0) {
4154 int i, l, u;
4155 int best = -1;
4156 isl_bool has_int;
4157
4158 for (i = 0; i < n_div; ++i) {
4159 if (!pairs[i])
4160 continue;
4161 if (best >= 0 && pairs[best] <= pairs[i])
4162 continue;
4163 best = i;
4164 }
4165
4166 i = best;
4167 for (l = 0; l < bmap->n_ineq; ++l) {
4168 if (!isl_int_is_pos(bmap->ineq[l][off + i])(isl_sioimath_sgn(*(bmap->ineq[l][off + i])) > 0))
4169 continue;
4170 if (isl_int_is_one(bmap->ineq[l][off + i])(isl_sioimath_cmp_si(*(bmap->ineq[l][off + i]), 1) == 0))
4171 continue;
4172 for (u = 0; u < bmap->n_ineq; ++u) {
4173 if (!isl_int_is_neg(bmap->ineq[u][off + i])(isl_sioimath_sgn(*(bmap->ineq[u][off + i])) < 0))
4174 continue;
4175 if (isl_int_is_negone(bmap->ineq[u][off + i])(isl_sioimath_cmp_si(*(bmap->ineq[u][off + i]), -1) == 0))
4176 continue;
4177 has_int = int_between_bounds(bmap, i, l, u,
4178 &data);
4179 if (has_int < 0)
4180 goto error;
4181 if (data.tab && data.tab->empty)
4182 break;
4183 if (!has_int)
4184 break;
4185 }
4186 if (u < bmap->n_ineq)
4187 break;
4188 }
4189 if (data.tab && data.tab->empty) {
4190 bmap = isl_basic_map_set_to_empty(bmap);
4191 break;
4192 }
4193 if (l == bmap->n_ineq) {
4194 remove = i;
4195 break;
4196 }
4197 pairs[i] = 0;
4198 --n;
4199 }
4200
4201 test_ineq_data_clear(&data);
4202
4203 free(pairs);
4204
4205 if (remove < 0)
4206 return bmap;
4207
4208 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
4209 return isl_basic_map_drop_redundant_divs(bmap);
4210error:
4211 free(pairs);
4212 isl_basic_map_free(bmap);
4213 test_ineq_data_clear(&data);
4214 return NULL((void*)0);
4215}
4216
4217/* Given a pair of divs div1 and div2 such that, except for the lower bound l
4218 * and the upper bound u, div1 always occurs together with div2 in the form
4219 * (div1 + m div2), where m is the constant range on the variable div1
4220 * allowed by l and u, replace the pair div1 and div2 by a single
4221 * div that is equal to div1 + m div2.
4222 *
4223 * The new div will appear in the location that contains div2.
4224 * We need to modify all constraints that contain
4225 * div2 = (div - div1) / m
4226 * The coefficient of div2 is known to be equal to 1 or -1.
4227 * (If a constraint does not contain div2, it will also not contain div1.)
4228 * If the constraint also contains div1, then we know they appear
4229 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
4230 * i.e., the coefficient of div is f.
4231 *
4232 * Otherwise, we first need to introduce div1 into the constraint.
4233 * Let l be
4234 *
4235 * div1 + f >=0
4236 *
4237 * and u
4238 *
4239 * -div1 + f' >= 0
4240 *
4241 * A lower bound on div2
4242 *
4243 * div2 + t >= 0
4244 *
4245 * can be replaced by
4246 *
4247 * m div2 + div1 + m t + f >= 0
4248 *
4249 * An upper bound
4250 *
4251 * -div2 + t >= 0
4252 *
4253 * can be replaced by
4254 *
4255 * -(m div2 + div1) + m t + f' >= 0
4256 *
4257 * These constraint are those that we would obtain from eliminating
4258 * div1 using Fourier-Motzkin.
4259 *
4260 * After all constraints have been modified, we drop the lower and upper
4261 * bound and then drop div1.
4262 * Since the new div is only placed in the same location that used
4263 * to store div2, but otherwise has a different meaning, any possible
4264 * explicit representation of the original div2 is removed.
4265 */
4266static __isl_give isl_basic_map *coalesce_divs(__isl_take isl_basic_map *bmap,
4267 unsigned div1, unsigned div2, unsigned l, unsigned u)
4268{
4269 isl_ctx *ctx;
4270 isl_int m;
4271 unsigned dim, total;
4272 int i;
4273
4274 ctx = isl_basic_map_get_ctx(bmap);
4275
4276 dim = isl_space_dim(bmap->dim, isl_dim_all);
4277 total = 1 + dim + bmap->n_div;
4278
4279 isl_int_init(m)isl_sioimath_init((m));
4280 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_add((m), *(bmap->ineq[l][0]), *(bmap->ineq
[u][0]))
;
4281 isl_int_add_ui(m, m, 1)isl_sioimath_add_ui((m), *(m), 1);
4282
4283 for (i = 0; i < bmap->n_ineq; ++i) {
4284 if (i == l || i == u)
4285 continue;
4286 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2])(isl_sioimath_sgn(*(bmap->ineq[i][1 + dim + div2])) == 0))
4287 continue;
4288 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])(isl_sioimath_sgn(*(bmap->ineq[i][1 + dim + div1])) == 0)) {
4289 if (isl_int_is_pos(bmap->ineq[i][1 + dim + div2])(isl_sioimath_sgn(*(bmap->ineq[i][1 + dim + div2])) > 0
)
)
4290 isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i],
4291 ctx->one, bmap->ineq[l], total);
4292 else
4293 isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i],
4294 ctx->one, bmap->ineq[u], total);
4295 }
4296 isl_int_set(bmap->ineq[i][1 + dim + div2],isl_sioimath_set((bmap->ineq[i][1 + dim + div2]), *(bmap->
ineq[i][1 + dim + div1]))
4297 bmap->ineq[i][1 + dim + div1])isl_sioimath_set((bmap->ineq[i][1 + dim + div2]), *(bmap->
ineq[i][1 + dim + div1]))
;
4298 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0)isl_sioimath_set_si((bmap->ineq[i][1 + dim + div1]), 0);
4299 }
4300
4301 isl_int_clear(m)isl_sioimath_clear((m));
4302 if (l > u) {
4303 isl_basic_map_drop_inequality(bmap, l);
4304 isl_basic_map_drop_inequality(bmap, u);
4305 } else {
4306 isl_basic_map_drop_inequality(bmap, u);
4307 isl_basic_map_drop_inequality(bmap, l);
4308 }
4309 bmap = isl_basic_map_mark_div_unknown(bmap, div2);
4310 bmap = isl_basic_map_drop_div(bmap, div1);
4311 return bmap;
4312}
4313
4314/* First check if we can coalesce any pair of divs and
4315 * then continue with dropping more redundant divs.
4316 *
4317 * We loop over all pairs of lower and upper bounds on a div
4318 * with coefficient 1 and -1, respectively, check if there
4319 * is any other div "c" with which we can coalesce the div
4320 * and if so, perform the coalescing.
4321 */
4322static __isl_give isl_basic_map *coalesce_or_drop_more_redundant_divs(
4323 __isl_take isl_basic_map *bmap, int *pairs, int n)
4324{
4325 int i, l, u;
4326 unsigned dim;
4327
4328 dim = isl_space_dim(bmap->dim, isl_dim_all);
4329
4330 for (i = 0; i < bmap->n_div; ++i) {
4331 if (!pairs[i])
4332 continue;
4333 for (l = 0; l < bmap->n_ineq; ++l) {
4334 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i])(isl_sioimath_cmp_si(*(bmap->ineq[l][1 + dim + i]), 1) == 0
)
)
4335 continue;
4336 for (u = 0; u < bmap->n_ineq; ++u) {
4337 int c;
4338
4339 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i])(isl_sioimath_cmp_si(*(bmap->ineq[u][1+dim+i]), -1) == 0))
4340 continue;
4341 c = div_find_coalesce(bmap, pairs, i, l, u);
4342 if (c < 0)
4343 continue;
4344 free(pairs);
4345 bmap = coalesce_divs(bmap, i, c, l, u);
4346 return isl_basic_map_drop_redundant_divs(bmap);
4347 }
4348 }
4349 }
4350
4351 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1))))) {
4352 free(pairs);
4353 return bmap;
4354 }
4355
4356 return drop_more_redundant_divs(bmap, pairs, n);
4357}
4358
4359/* Are the "n" coefficients starting at "first" of inequality constraints
4360 * "i" and "j" of "bmap" equal to each other?
4361 */
4362static int is_parallel_part(__isl_keep isl_basic_map *bmap, int i, int j,
4363 int first, int n)
4364{
4365 return isl_seq_eq(bmap->ineq[i] + first, bmap->ineq[j] + first, n);
4366}
4367
4368/* Are the "n" coefficients starting at "first" of inequality constraints
4369 * "i" and "j" of "bmap" opposite to each other?
4370 */
4371static int is_opposite_part(__isl_keep isl_basic_map *bmap, int i, int j,
4372 int first, int n)
4373{
4374 return isl_seq_is_neg(bmap->ineq[i] + first, bmap->ineq[j] + first, n);
4375}
4376
4377/* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4378 * apart from the constant term?
4379 */
4380static isl_bool is_opposite(__isl_keep isl_basic_map *bmap, int i, int j)
4381{
4382 unsigned total;
4383
4384 total = isl_basic_map_dim(bmap, isl_dim_all);
4385 return is_opposite_part(bmap, i, j, 1, total);
4386}
4387
4388/* Are inequality constraints "i" and "j" of "bmap" equal to each other,
4389 * apart from the constant term and the coefficient at position "pos"?
4390 */
4391static int is_parallel_except(__isl_keep isl_basic_map *bmap, int i, int j,
4392 int pos)
4393{
4394 unsigned total;
4395
4396 total = isl_basic_map_dim(bmap, isl_dim_all);
4397 return is_parallel_part(bmap, i, j, 1, pos - 1) &&
4398 is_parallel_part(bmap, i, j, pos + 1, total - pos);
4399}
4400
4401/* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
4402 * apart from the constant term and the coefficient at position "pos"?
4403 */
4404static int is_opposite_except(__isl_keep isl_basic_map *bmap, int i, int j,
4405 int pos)
4406{
4407 unsigned total;
4408
4409 total = isl_basic_map_dim(bmap, isl_dim_all);
4410 return is_opposite_part(bmap, i, j, 1, pos - 1) &&
4411 is_opposite_part(bmap, i, j, pos + 1, total - pos);
4412}
4413
4414/* Restart isl_basic_map_drop_redundant_divs after "bmap" has
4415 * been modified, simplying it if "simplify" is set.
4416 * Free the temporary data structure "pairs" that was associated
4417 * to the old version of "bmap".
4418 */
4419static __isl_give isl_basic_map *drop_redundant_divs_again(
4420 __isl_take isl_basic_map *bmap, __isl_take int *pairs, int simplify)
4421{
4422 if (simplify)
4423 bmap = isl_basic_map_simplify(bmap);
4424 free(pairs);
4425 return isl_basic_map_drop_redundant_divs(bmap);
4426}
4427
4428/* Is "div" the single unknown existentially quantified variable
4429 * in inequality constraint "ineq" of "bmap"?
4430 * "div" is known to have a non-zero coefficient in "ineq".
4431 */
4432static isl_bool single_unknown(__isl_keep isl_basic_map *bmap, int ineq,
4433 int div)
4434{
4435 int i;
4436 unsigned n_div, o_div;
4437 isl_bool known;
4438
4439 known = isl_basic_map_div_is_known(bmap, div);
4440 if (known < 0 || known)
4441 return isl_bool_not(known);
4442 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4443 if (n_div == 1)
4444 return isl_bool_true;
4445 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4446 for (i = 0; i < n_div; ++i) {
4447 isl_bool known;
4448
4449 if (i == div)
4450 continue;
4451 if (isl_int_is_zero(bmap->ineq[ineq][o_div + i])(isl_sioimath_sgn(*(bmap->ineq[ineq][o_div + i])) == 0))
4452 continue;
4453 known = isl_basic_map_div_is_known(bmap, i);
4454 if (known < 0 || !known)
4455 return known;
4456 }
4457
4458 return isl_bool_true;
4459}
4460
4461/* Does integer division "div" have coefficient 1 in inequality constraint
4462 * "ineq" of "map"?
4463 */
4464static isl_bool has_coef_one(__isl_keep isl_basic_map *bmap, int div, int ineq)
4465{
4466 unsigned o_div;
4467
4468 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4469 if (isl_int_is_one(bmap->ineq[ineq][o_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[ineq][o_div + div]), 1) ==
0)
)
4470 return isl_bool_true;
4471
4472 return isl_bool_false;
4473}
4474
4475/* Turn inequality constraint "ineq" of "bmap" into an equality and
4476 * then try and drop redundant divs again,
4477 * freeing the temporary data structure "pairs" that was associated
4478 * to the old version of "bmap".
4479 */
4480static __isl_give isl_basic_map *set_eq_and_try_again(
4481 __isl_take isl_basic_map *bmap, int ineq, __isl_take int *pairs)
4482{
4483 bmap = isl_basic_map_cow(bmap);
4484 isl_basic_map_inequality_to_equality(bmap, ineq);
4485 return drop_redundant_divs_again(bmap, pairs, 1);
4486}
4487
4488/* Drop the integer division at position "div", along with the two
4489 * inequality constraints "ineq1" and "ineq2" in which it appears
4490 * from "bmap" and then try and drop redundant divs again,
4491 * freeing the temporary data structure "pairs" that was associated
4492 * to the old version of "bmap".
4493 */
4494static __isl_give isl_basic_map *drop_div_and_try_again(
4495 __isl_take isl_basic_map *bmap, int div, int ineq1, int ineq2,
4496 __isl_take int *pairs)
4497{
4498 if (ineq1 > ineq2) {
4499 isl_basic_map_drop_inequality(bmap, ineq1);
4500 isl_basic_map_drop_inequality(bmap, ineq2);
4501 } else {
4502 isl_basic_map_drop_inequality(bmap, ineq2);
4503 isl_basic_map_drop_inequality(bmap, ineq1);
4504 }
4505 bmap = isl_basic_map_drop_div(bmap, div);
4506 return drop_redundant_divs_again(bmap, pairs, 0);
4507}
4508
4509/* Given two inequality constraints
4510 *
4511 * f(x) + n d + c >= 0, (ineq)
4512 *
4513 * with d the variable at position "pos", and
4514 *
4515 * f(x) + c0 >= 0, (lower)
4516 *
4517 * compute the maximal value of the lower bound ceil((-f(x) - c)/n)
4518 * determined by the first constraint.
4519 * That is, store
4520 *
4521 * ceil((c0 - c)/n)
4522 *
4523 * in *l.
4524 */
4525static void lower_bound_from_parallel(__isl_keep isl_basic_map *bmap,
4526 int ineq, int lower, int pos, isl_int *l)
4527{
4528 isl_int_neg(*l, bmap->ineq[ineq][0])isl_sioimath_neg((*l), *(bmap->ineq[ineq][0]));
4529 isl_int_add(*l, *l, bmap->ineq[lower][0])isl_sioimath_add((*l), *(*l), *(bmap->ineq[lower][0]));
4530 isl_int_cdiv_q(*l, *l, bmap->ineq[ineq][pos])isl_sioimath_cdiv_q((*l), *(*l), *(bmap->ineq[ineq][pos]));
4531}
4532
4533/* Given two inequality constraints
4534 *
4535 * f(x) + n d + c >= 0, (ineq)
4536 *
4537 * with d the variable at position "pos", and
4538 *
4539 * -f(x) - c0 >= 0, (upper)
4540 *
4541 * compute the minimal value of the lower bound ceil((-f(x) - c)/n)
4542 * determined by the first constraint.
4543 * That is, store
4544 *
4545 * ceil((-c1 - c)/n)
4546 *
4547 * in *u.
4548 */
4549static void lower_bound_from_opposite(__isl_keep isl_basic_map *bmap,
4550 int ineq, int upper, int pos, isl_int *u)
4551{
4552 isl_int_neg(*u, bmap->ineq[ineq][0])isl_sioimath_neg((*u), *(bmap->ineq[ineq][0]));
4553 isl_int_sub(*u, *u, bmap->ineq[upper][0])isl_sioimath_sub((*u), *(*u), *(bmap->ineq[upper][0]));
4554 isl_int_cdiv_q(*u, *u, bmap->ineq[ineq][pos])isl_sioimath_cdiv_q((*u), *(*u), *(bmap->ineq[ineq][pos]));
4555}
4556
4557/* Given a lower bound constraint "ineq" on "div" in "bmap",
4558 * does the corresponding lower bound have a fixed value in "bmap"?
4559 *
4560 * In particular, "ineq" is of the form
4561 *
4562 * f(x) + n d + c >= 0
4563 *
4564 * with n > 0, c the constant term and
4565 * d the existentially quantified variable "div".
4566 * That is, the lower bound is
4567 *
4568 * ceil((-f(x) - c)/n)
4569 *
4570 * Look for a pair of constraints
4571 *
4572 * f(x) + c0 >= 0
4573 * -f(x) + c1 >= 0
4574 *
4575 * i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value.
4576 * That is, check that
4577 *
4578 * ceil((-c1 - c)/n) = ceil((c0 - c)/n)
4579 *
4580 * If so, return the index of inequality f(x) + c0 >= 0.
4581 * Otherwise, return -1.
4582 */
4583static int lower_bound_is_cst(__isl_keep isl_basic_map *bmap, int div, int ineq)
4584{
4585 int i;
4586 int lower = -1, upper = -1;
4587 unsigned o_div;
4588 isl_int l, u;
4589 int equal;
4590
4591 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4592 for (i = 0; i < bmap->n_ineq && (lower < 0 || upper < 0); ++i) {
4593 if (i == ineq)
4594 continue;
4595 if (!isl_int_is_zero(bmap->ineq[i][o_div + div])(isl_sioimath_sgn(*(bmap->ineq[i][o_div + div])) == 0))
4596 continue;
4597 if (lower < 0 &&
4598 is_parallel_except(bmap, ineq, i, o_div + div)) {
4599 lower = i;
4600 continue;
4601 }
4602 if (upper < 0 &&
4603 is_opposite_except(bmap, ineq, i, o_div + div)) {
4604 upper = i;
4605 }
4606 }
4607
4608 if (lower < 0 || upper < 0)
4609 return -1;
4610
4611 isl_int_init(l)isl_sioimath_init((l));
4612 isl_int_init(u)isl_sioimath_init((u));
4613
4614 lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &l);
4615 lower_bound_from_opposite(bmap, ineq, upper, o_div + div, &u);
4616
4617 equal = isl_int_eq(l, u)(isl_sioimath_cmp(*(l), *(u)) == 0);
4618
4619 isl_int_clear(l)isl_sioimath_clear((l));
4620 isl_int_clear(u)isl_sioimath_clear((u));
4621
4622 return equal ? lower : -1;
4623}
4624
4625/* Given a lower bound constraint "ineq" on the existentially quantified
4626 * variable "div", such that the corresponding lower bound has
4627 * a fixed value in "bmap", assign this fixed value to the variable and
4628 * then try and drop redundant divs again,
4629 * freeing the temporary data structure "pairs" that was associated
4630 * to the old version of "bmap".
4631 * "lower" determines the constant value for the lower bound.
4632 *
4633 * In particular, "ineq" is of the form
4634 *
4635 * f(x) + n d + c >= 0,
4636 *
4637 * while "lower" is of the form
4638 *
4639 * f(x) + c0 >= 0
4640 *
4641 * The lower bound is ceil((-f(x) - c)/n) and its constant value
4642 * is ceil((c0 - c)/n).
4643 */
4644static __isl_give isl_basic_map *fix_cst_lower(__isl_take isl_basic_map *bmap,
4645 int div, int ineq, int lower, int *pairs)
4646{
4647 isl_int c;
4648 unsigned o_div;
4649
4650 isl_int_init(c)isl_sioimath_init((c));
4651
4652 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4653 lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &c);
4654 bmap = isl_basic_map_fix(bmap, isl_dim_div, div, c);
4655 free(pairs);
4656
4657 isl_int_clear(c)isl_sioimath_clear((c));
4658
4659 return isl_basic_map_drop_redundant_divs(bmap);
4660}
4661
4662/* Remove divs that are not strictly needed based on the inequality
4663 * constraints.
4664 * In particular, if a div only occurs positively (or negatively)
4665 * in constraints, then it can simply be dropped.
4666 * Also, if a div occurs in only two constraints and if moreover
4667 * those two constraints are opposite to each other, except for the constant
4668 * term and if the sum of the constant terms is such that for any value
4669 * of the other values, there is always at least one integer value of the
4670 * div, i.e., if one plus this sum is greater than or equal to
4671 * the (absolute value) of the coefficient of the div in the constraints,
4672 * then we can also simply drop the div.
4673 *
4674 * If an existentially quantified variable does not have an explicit
4675 * representation, appears in only a single lower bound that does not
4676 * involve any other such existentially quantified variables and appears
4677 * in this lower bound with coefficient 1,
4678 * then fix the variable to the value of the lower bound. That is,
4679 * turn the inequality into an equality.
4680 * If for any value of the other variables, there is any value
4681 * for the existentially quantified variable satisfying the constraints,
4682 * then this lower bound also satisfies the constraints.
4683 * It is therefore safe to pick this lower bound.
4684 *
4685 * The same reasoning holds even if the coefficient is not one.
4686 * However, fixing the variable to the value of the lower bound may
4687 * in general introduce an extra integer division, in which case
4688 * it may be better to pick another value.
4689 * If this integer division has a known constant value, then plugging
4690 * in this constant value removes the existentially quantified variable
4691 * completely. In particular, if the lower bound is of the form
4692 * ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and
4693 * -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n),
4694 * then the existentially quantified variable can be assigned this
4695 * shared value.
4696 *
4697 * We skip divs that appear in equalities or in the definition of other divs.
4698 * Divs that appear in the definition of other divs usually occur in at least
4699 * 4 constraints, but the constraints may have been simplified.
4700 *
4701 * If any divs are left after these simple checks then we move on
4702 * to more complicated cases in drop_more_redundant_divs.
4703 */
4704static __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs_ineq(
4705 __isl_take isl_basic_map *bmap)
4706{
4707 int i, j;
4708 unsigned off;
4709 int *pairs = NULL((void*)0);
4710 int n = 0;
4711
4712 if (!bmap)
4713 goto error;
4714 if (bmap->n_div == 0)
4715 return bmap;
4716
4717 off = isl_space_dim(bmap->dim, isl_dim_all);
4718 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div)((int *)isl_calloc_or_die(bmap->ctx, bmap->n_div, sizeof
(int)))
;
4719 if (!pairs)
4720 goto error;
4721
4722 for (i = 0; i < bmap->n_div; ++i) {
4723 int pos, neg;
4724 int last_pos, last_neg;
4725 int redundant;
4726 int defined;
4727 isl_bool opp, set_div;
4728
4729 defined = !isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0);
4730 for (j = i; j < bmap->n_div; ++j)
4731 if (!isl_int_is_zero(bmap->div[j][1 + 1 + off + i])(isl_sioimath_sgn(*(bmap->div[j][1 + 1 + off + i])) == 0))
4732 break;
4733 if (j < bmap->n_div)
4734 continue;
4735 for (j = 0; j < bmap->n_eq; ++j)
4736 if (!isl_int_is_zero(bmap->eq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->eq[j][1 + off + i])) == 0))
4737 break;
4738 if (j < bmap->n_eq)
4739 continue;
4740 ++n;
4741 pos = neg = 0;
4742 for (j = 0; j < bmap->n_ineq; ++j) {
4743 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + off + i])) > 0)) {
4744 last_pos = j;
4745 ++pos;
4746 }
4747 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + off + i])) < 0)) {
4748 last_neg = j;
4749 ++neg;
4750 }
4751 }
4752 pairs[i] = pos * neg;
4753 if (pairs[i] == 0) {
4754 for (j = bmap->n_ineq - 1; j >= 0; --j)
4755 if (!isl_int_is_zero(bmap->ineq[j][1+off+i])(isl_sioimath_sgn(*(bmap->ineq[j][1+off+i])) == 0))
4756 isl_basic_map_drop_inequality(bmap, j);
4757 bmap = isl_basic_map_drop_div(bmap, i);
4758 return drop_redundant_divs_again(bmap, pairs, 0);
4759 }
4760 if (pairs[i] != 1)
4761 opp = isl_bool_false;
4762 else
4763 opp = is_opposite(bmap, last_pos, last_neg);
4764 if (opp < 0)
4765 goto error;
4766 if (!opp) {
4767 int lower;
4768 isl_bool single, one;
4769
4770 if (pos != 1)
4771 continue;
4772 single = single_unknown(bmap, last_pos, i);
4773 if (single < 0)
4774 goto error;
4775 if (!single)
4776 continue;
4777 one = has_coef_one(bmap, i, last_pos);
4778 if (one < 0)
4779 goto error;
4780 if (one)
4781 return set_eq_and_try_again(bmap, last_pos,
4782 pairs);
4783 lower = lower_bound_is_cst(bmap, i, last_pos);
4784 if (lower >= 0)
4785 return fix_cst_lower(bmap, i, last_pos, lower,
4786 pairs);
4787 continue;
4788 }
4789
4790 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]))
4791 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]))
;
4792 isl_int_add_ui(bmap->ineq[last_pos][0],isl_sioimath_add_ui((bmap->ineq[last_pos][0]), *(bmap->
ineq[last_pos][0]), 1)
4793 bmap->ineq[last_pos][0], 1)isl_sioimath_add_ui((bmap->ineq[last_pos][0]), *(bmap->
ineq[last_pos][0]), 1)
;
4794 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)
4795 bmap->ineq[last_pos][1+off+i])(isl_sioimath_cmp(*(bmap->ineq[last_pos][0]), *(bmap->ineq
[last_pos][1+off+i])) >= 0)
;
4796 isl_int_sub_ui(bmap->ineq[last_pos][0],isl_sioimath_sub_ui((bmap->ineq[last_pos][0]), *(bmap->
ineq[last_pos][0]), 1)
4797 bmap->ineq[last_pos][0], 1)isl_sioimath_sub_ui((bmap->ineq[last_pos][0]), *(bmap->
ineq[last_pos][0]), 1)
;
4798 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]))
4799 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]))
;
4800 if (redundant)
4801 return drop_div_and_try_again(bmap, i,
4802 last_pos, last_neg, pairs);
4803 if (defined)
4804 set_div = isl_bool_false;
4805 else
4806 set_div = ok_to_set_div_from_bound(bmap, i, last_pos);
4807 if (set_div < 0)
4808 return isl_basic_map_free(bmap);
4809 if (set_div) {
4810 bmap = set_div_from_lower_bound(bmap, i, last_pos);
4811 return drop_redundant_divs_again(bmap, pairs, 1);
4812 }
4813 pairs[i] = 0;
4814 --n;
4815 }
4816
4817 if (n > 0)
4818 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
4819
4820 free(pairs);
4821 return bmap;
4822error:
4823 free(pairs);
4824 isl_basic_map_free(bmap);
4825 return NULL((void*)0);
4826}
4827
4828/* Consider the coefficients at "c" as a row vector and replace
4829 * them with their product with "T". "T" is assumed to be a square matrix.
4830 */
4831static isl_stat preimage(isl_int *c, __isl_keep isl_mat *T)
4832{
4833 int n;
4834 isl_ctx *ctx;
4835 isl_vec *v;
4836
4837 if (!T)
4838 return isl_stat_error;
4839 n = isl_mat_rows(T);
4840 if (isl_seq_first_non_zero(c, n) == -1)
4841 return isl_stat_ok;
4842 ctx = isl_mat_get_ctx(T);
4843 v = isl_vec_alloc(ctx, n);
4844 if (!v)
4845 return isl_stat_error;
4846 isl_seq_swp_or_cpy(v->el, c, n);
4847 v = isl_vec_mat_product(v, isl_mat_copy(T));
4848 if (!v)
4849 return isl_stat_error;
4850 isl_seq_swp_or_cpy(c, v->el, n);
4851 isl_vec_free(v);
4852
4853 return isl_stat_ok;
4854}
4855
4856/* Plug in T for the variables in "bmap" starting at "pos".
4857 * T is a linear unimodular matrix, i.e., without constant term.
4858 */
4859static __isl_give isl_basic_map *isl_basic_map_preimage_vars(
4860 __isl_take isl_basic_map *bmap, unsigned pos, __isl_take isl_mat *T)
4861{
4862 int i;
4863 unsigned n, total;
4864
4865 bmap = isl_basic_map_cow(bmap);
4866 if (!bmap || !T)
4867 goto error;
4868
4869 n = isl_mat_cols(T);
4870 if (n != isl_mat_rows(T))
4871 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-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 4872); goto error; } while (0)
4872 "expecting square matrix", goto error)do { isl_handle_error(isl_mat_get_ctx(T), isl_error_invalid, "expecting square matrix"
, "/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 4872); goto error; } while (0)
;
4873
4874 total = isl_basic_map_dim(bmap, isl_dim_all);
4875 if (pos + n > total || pos + n < pos)
4876 isl_die(isl_mat_get_ctx(T), isl_error_invalid,do { isl_handle_error(isl_mat_get_ctx(T), isl_error_invalid, "invalid range"
, "/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 4877); goto error; } while (0)
4877 "invalid range", goto error)do { isl_handle_error(isl_mat_get_ctx(T), isl_error_invalid, "invalid range"
, "/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_map_simplify.c"
, 4877); goto error; } while (0)
;
4878
4879 for (i = 0; i < bmap->n_eq; ++i)
4880 if (preimage(bmap->eq[i] + 1 + pos, T) < 0)
4881 goto error;
4882 for (i = 0; i < bmap->n_ineq; ++i)
4883 if (preimage(bmap->ineq[i] + 1 + pos, T) < 0)
4884 goto error;
4885 for (i = 0; i < bmap->n_div; ++i) {
4886 if (isl_basic_map_div_is_marked_unknown(bmap, i))
4887 continue;
4888 if (preimage(bmap->div[i] + 1 + 1 + pos, T) < 0)
4889 goto error;
4890 }
4891
4892 isl_mat_free(T);
4893 return bmap;
4894error:
4895 isl_basic_map_free(bmap);
4896 isl_mat_free(T);
4897 return NULL((void*)0);
4898}
4899
4900/* Remove divs that are not strictly needed.
4901 *
4902 * First look for an equality constraint involving two or more
4903 * existentially quantified variables without an explicit
4904 * representation. Replace the combination that appears
4905 * in the equality constraint by a single existentially quantified
4906 * variable such that the equality can be used to derive
4907 * an explicit representation for the variable.
4908 * If there are no more such equality constraints, then continue
4909 * with isl_basic_map_drop_redundant_divs_ineq.
4910 *
4911 * In particular, if the equality constraint is of the form
4912 *
4913 * f(x) + \sum_i c_i a_i = 0
4914 *
4915 * with a_i existentially quantified variable without explicit
4916 * representation, then apply a transformation on the existentially
4917 * quantified variables to turn the constraint into
4918 *
4919 * f(x) + g a_1' = 0
4920 *
4921 * with g the gcd of the c_i.
4922 * In order to easily identify which existentially quantified variables
4923 * have a complete explicit representation, i.e., without being defined
4924 * in terms of other existentially quantified variables without
4925 * an explicit representation, the existentially quantified variables
4926 * are first sorted.
4927 *
4928 * The variable transformation is computed by extending the row
4929 * [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation
4930 *
4931 * [a_1'] [c_1/g ... c_n/g] [ a_1 ]
4932 * [a_2'] [ a_2 ]
4933 * ... = U ....
4934 * [a_n'] [ a_n ]
4935 *
4936 * with [c_1/g ... c_n/g] representing the first row of U.
4937 * The inverse of U is then plugged into the original constraints.
4938 * The call to isl_basic_map_simplify makes sure the explicit
4939 * representation for a_1' is extracted from the equality constraint.
4940 */
4941__isl_give isl_basic_map *isl_basic_map_drop_redundant_divs(
4942 __isl_take isl_basic_map *bmap)
4943{
4944 int first;
4945 int i;
4946 unsigned o_div, n_div;
4947 int l;
4948 isl_ctx *ctx;
4949 isl_mat *T;
4950
4951 if (!bmap)
4952 return NULL((void*)0);
4953 if (isl_basic_map_divs_known(bmap))
4954 return isl_basic_map_drop_redundant_divs_ineq(bmap);
4955 if (bmap->n_eq == 0)
4956 return isl_basic_map_drop_redundant_divs_ineq(bmap);
4957 bmap = isl_basic_map_sort_divs(bmap);
4958 if (!bmap)
4959 return NULL((void*)0);
4960
4961 first = isl_basic_map_first_unknown_div(bmap);
4962 if (first < 0)
4963 return isl_basic_map_free(bmap);
4964
4965 o_div = isl_basic_map_offset(bmap, isl_dim_div);
4966 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4967
4968 for (i = 0; i < bmap->n_eq; ++i) {
4969 l = isl_seq_first_non_zero(bmap->eq[i] + o_div + first,
4970 n_div - (first));
4971 if (l < 0)
4972 continue;
4973 l += first;
4974 if (isl_seq_first_non_zero(bmap->eq[i] + o_div + l + 1,
4975 n_div - (l + 1)) == -1)
4976 continue;
4977 break;
4978 }
4979 if (i >= bmap->n_eq)
4980 return isl_basic_map_drop_redundant_divs_ineq(bmap);
4981
4982 ctx = isl_basic_map_get_ctx(bmap);
4983 T = isl_mat_alloc(ctx, n_div - l, n_div - l);
4984 if (!T)
4985 return isl_basic_map_free(bmap);
4986 isl_seq_cpy(T->row[0], bmap->eq[i] + o_div + l, n_div - l);
4987 T = isl_mat_normalize_row(T, 0);
4988 T = isl_mat_unimodular_complete(T, 1);
4989 T = isl_mat_right_inverse(T);
4990
4991 for (i = l; i < n_div; ++i)
4992 bmap = isl_basic_map_mark_div_unknown(bmap, i);
4993 bmap = isl_basic_map_preimage_vars(bmap, o_div - 1 + l, T);
4994 bmap = isl_basic_map_simplify(bmap);
4995
4996 return isl_basic_map_drop_redundant_divs(bmap);
4997}
4998
4999/* Does "bmap" satisfy any equality that involves more than 2 variables
5000 * and/or has coefficients different from -1 and 1?
5001 */
5002static int has_multiple_var_equality(__isl_keep isl_basic_map *bmap)
5003{
5004 int i;
5005 unsigned total;
5006
5007 total = isl_basic_map_dim(bmap, isl_dim_all);
5008
5009 for (i = 0; i < bmap->n_eq; ++i) {
10
Assuming 'i' is < field 'n_eq'
11
Loop condition is true. Entering loop body
5010 int j, k;
5011
5012 j = isl_seq_first_non_zero(bmap->eq[i] + 1, total);
5013 if (j < 0)
12
Assuming 'j' is >= 0
13
Taking false branch
5014 continue;
5015 if (!isl_int_is_one(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), 1) == 0) &&
14
Taking true branch
5016 !isl_int_is_negone(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), -1) == 0))
5017 return 1;
15
Returning the value 1, which participates in a condition later
5018
5019 j += 1;
5020 k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j);
5021 if (k < 0)
5022 continue;
5023 j += k;
5024 if (!isl_int_is_one(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), 1) == 0) &&
5025 !isl_int_is_negone(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), -1) == 0))
5026 return 1;
5027
5028 j += 1;
5029 k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j);
5030 if (k >= 0)
5031 return 1;
5032 }
5033
5034 return 0;
5035}
5036
5037/* Remove any common factor g from the constraint coefficients in "v".
5038 * The constant term is stored in the first position and is replaced
5039 * by floor(c/g). If any common factor is removed and if this results
5040 * in a tightening of the constraint, then set *tightened.
5041 */
5042static __isl_give isl_vec *normalize_constraint(__isl_take isl_vec *v,
5043 int *tightened)
5044{
5045 isl_ctx *ctx;
5046
5047 if (!v)
30
Assuming 'v' is non-null
31
Taking false branch
52
Assuming 'v' is null
53
Taking true branch
5048 return NULL((void*)0);
54
Returning without writing to '*tightened', which participates in a condition later
5049 ctx = isl_vec_get_ctx(v);
5050 isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd);
5051 if (isl_int_is_zero(ctx->normalize_gcd)(isl_sioimath_sgn(*(ctx->normalize_gcd)) == 0))
32
Assuming the condition is false
33
Taking false branch
5052 return v;
5053 if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0))
34
Assuming the condition is false
35
Taking false branch
5054 return v;
5055 v = isl_vec_cow(v);
5056 if (!v)
36
Assuming 'v' is non-null
37
Taking false branch
5057 return NULL((void*)0);
5058 if (tightened
37.1
'tightened' is non-null
37.1
'tightened' is non-null
&& !isl_int_is_divisible_by(v->el[0], ctx->normalize_gcd)isl_sioimath_is_divisible_by(*(v->el[0]), *(ctx->normalize_gcd
))
)
38
Calling 'isl_sioimath_is_divisible_by'
43
Returning from 'isl_sioimath_is_divisible_by'
44
Taking true branch
5059 *tightened = 1;
45
The value 1 is assigned to 'tightened', which participates in a condition later
5060 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))
;
5061 isl_seq_scale_down(v->el + 1, v->el + 1, ctx->normalize_gcd,
5062 v->size - 1);
5063 return v;
5064}
5065
5066/* If "bmap" is an integer set that satisfies any equality involving
5067 * more than 2 variables and/or has coefficients different from -1 and 1,
5068 * then use variable compression to reduce the coefficients by removing
5069 * any (hidden) common factor.
5070 * In particular, apply the variable compression to each constraint,
5071 * factor out any common factor in the non-constant coefficients and
5072 * then apply the inverse of the compression.
5073 * At the end, we mark the basic map as having reduced constants.
5074 * If this flag is still set on the next invocation of this function,
5075 * then we skip the computation.
5076 *
5077 * Removing a common factor may result in a tightening of some of
5078 * the constraints. If this happens, then we may end up with two
5079 * opposite inequalities that can be replaced by an equality.
5080 * We therefore call isl_basic_map_detect_inequality_pairs,
5081 * which checks for such pairs of inequalities as well as eliminate_divs_eq
5082 * and isl_basic_map_gauss if such a pair was found.
5083 *
5084 * Note that this function may leave the result in an inconsistent state.
5085 * In particular, the constraints may not be gaussed.
5086 * Unfortunately, isl_map_coalesce actually depends on this inconsistent state
5087 * for some of the test cases to pass successfully.
5088 * Any potential modification of the representation is therefore only
5089 * performed on a single copy of the basic map.
5090 */
5091__isl_give isl_basic_map *isl_basic_map_reduce_coefficients(
5092 __isl_take isl_basic_map *bmap)
5093{
5094 unsigned total;
5095 isl_ctx *ctx;
5096 isl_vec *v;
5097 isl_mat *eq, *T, *T2;
5098 int i;
5099 int tightened;
5100
5101 if (!bmap)
1
Assuming 'bmap' is non-null
2
Taking false branch
5102 return NULL((void*)0);
5103 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(!!(((bmap)->flags) & ((1 << 8)))))
3
Assuming the condition is true
4
Taking false branch
5104 return bmap;
5105 if (isl_basic_map_is_rational(bmap))
5
Assuming the condition is false
6
Taking false branch
5106 return bmap;
5107 if (bmap->n_eq == 0)
7
Assuming field 'n_eq' is not equal to 0
8
Taking false branch
5108 return bmap;
5109 if (!has_multiple_var_equality(bmap))
9
Calling 'has_multiple_var_equality'
16
Returning from 'has_multiple_var_equality'
17
Taking false branch
5110 return bmap;
5111
5112 total = isl_basic_map_dim(bmap, isl_dim_all);
5113 ctx = isl_basic_map_get_ctx(bmap);
5114 v = isl_vec_alloc(ctx, 1 + total);
5115 if (!v)
18
Assuming 'v' is non-null
19
Taking false branch
5116 return isl_basic_map_free(bmap);
5117
5118 eq = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total);
5119 T = isl_mat_variable_compression(eq, &T2);
5120 if (!T || !T2)
20
Assuming 'T' is non-null
21
Assuming 'T2' is non-null
22
Taking false branch
5121 goto error;
5122 if (T->n_col == 0) {
23
Assuming field 'n_col' is not equal to 0
24
Taking false branch
5123 isl_mat_free(T);
5124 isl_mat_free(T2);
5125 isl_vec_free(v);
5126 return isl_basic_map_set_to_empty(bmap);
5127 }
5128
5129 bmap = isl_basic_map_cow(bmap);
5130 if (!bmap)
25
Assuming 'bmap' is non-null
26
Taking false branch
5131 goto error;
5132
5133 tightened = 0;
5134 for (i = 0; i < bmap->n_ineq; ++i) {
27
Assuming 'i' is < field 'n_ineq'
28
Loop condition is true. Entering loop body
49
Assuming 'i' is < field 'n_ineq'
50
Loop condition is true. Entering loop body
58
Assuming 'i' is >= field 'n_ineq'
59
Loop condition is false. Execution continues on line 5144
5135 isl_seq_cpy(v->el, bmap->ineq[i], 1 + total);
5136 v = isl_vec_mat_product(v, isl_mat_copy(T));
5137 v = normalize_constraint(v, &tightened);
29
Calling 'normalize_constraint'
46
Returning from 'normalize_constraint'
51
Calling 'normalize_constraint'
55
Returning from 'normalize_constraint'
5138 v = isl_vec_mat_product(v, isl_mat_copy(T2));
5139 if (!v)
47
Assuming 'v' is non-null
48
Taking false branch
56
Assuming 'v' is non-null
57
Taking false branch
5140 goto error;
5141 isl_seq_cpy(bmap->ineq[i], v->el, 1 + total);
5142 }
5143
5144 isl_mat_free(T);
5145 isl_mat_free(T2);
5146 isl_vec_free(v);
5147
5148 ISL_F_SET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(((bmap)->flags) |= ((1 << 8)));
5149
5150 if (tightened
59.1
'tightened' is 1
59.1
'tightened' is 1
) {
60
Taking true branch
5151 int progress = 0;
5152
5153 bmap = isl_basic_map_detect_inequality_pairs(bmap, &progress);
61
Calling 'isl_basic_map_detect_inequality_pairs'
5154 if (progress) {
5155 bmap = eliminate_divs_eq(bmap, &progress);
5156 bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
5157 }
5158 }
5159
5160 return bmap;
5161error:
5162 isl_mat_free(T);
5163 isl_mat_free(T2);
5164 isl_vec_free(v);
5165 return isl_basic_map_free(bmap);
5166}
5167
5168/* Shift the integer division at position "div" of "bmap"
5169 * by "shift" times the variable at position "pos".
5170 * "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
5171 * corresponds to the constant term.
5172 *
5173 * That is, if the integer division has the form
5174 *
5175 * floor(f(x)/d)
5176 *
5177 * then replace it by
5178 *
5179 * floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
5180 */
5181__isl_give isl_basic_map *isl_basic_map_shift_div(
5182 __isl_take isl_basic_map *bmap, int div, int pos, isl_int shift)
5183{
5184 int i;
5185 unsigned total;
5186
5187 if (isl_int_is_zero(shift)(isl_sioimath_sgn(*(shift)) == 0))
5188 return bmap;
5189 if (!bmap)
5190 return NULL((void*)0);
5191
5192 total = isl_basic_map_dim(bmap, isl_dim_all);
5193 total -= isl_basic_map_dim(bmap, isl_dim_div);
5194
5195 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]))
;
5196
5197 for (i = 0; i < bmap->n_eq; ++i) {
5198 if (isl_int_is_zero(bmap->eq[i][1 + total + div])(isl_sioimath_sgn(*(bmap->eq[i][1 + total + div])) == 0))
5199 continue;
5200 isl_int_submul(bmap->eq[i][pos],isl_sioimath_submul((bmap->eq[i][pos]), *(shift), *(bmap->
eq[i][1 + total + div]))
5201 shift, bmap->eq[i][1 + total + div])isl_sioimath_submul((bmap->eq[i][pos]), *(shift), *(bmap->
eq[i][1 + total + div]))
;
5202 }
5203 for (i = 0; i < bmap->n_ineq; ++i) {
5204 if (isl_int_is_zero(bmap->ineq[i][1 + total + div])(isl_sioimath_sgn(*(bmap->ineq[i][1 + total + div])) == 0))
5205 continue;
5206 isl_int_submul(bmap->ineq[i][pos],isl_sioimath_submul((bmap->ineq[i][pos]), *(shift), *(bmap
->ineq[i][1 + total + div]))
5207 shift, bmap->ineq[i][1 + total + div])isl_sioimath_submul((bmap->ineq[i][pos]), *(shift), *(bmap
->ineq[i][1 + total + div]))
;
5208 }
5209 for (i = 0; i < bmap->n_div; ++i) {
5210 if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
5211 continue;
5212 if (isl_int_is_zero(bmap->div[i][1 + 1 + total + div])(isl_sioimath_sgn(*(bmap->div[i][1 + 1 + total + div])) ==
0)
)
5213 continue;
5214 isl_int_submul(bmap->div[i][1 + pos],isl_sioimath_submul((bmap->div[i][1 + pos]), *(shift), *(bmap
->div[i][1 + 1 + total + div]))
5215 shift, bmap->div[i][1 + 1 + total + div])isl_sioimath_submul((bmap->div[i][1 + pos]), *(shift), *(bmap
->div[i][1 + 1 + total + div]))
;
5216 }
5217
5218 return bmap;
5219}

/build/llvm-toolchain-snapshot-10~svn374877/tools/polly/lib/External/isl/isl_int_sioimath.h

1/*
2 * Copyright 2015 INRIA Paris-Rocquencourt
3 *
4 * Use of this software is governed by the MIT license
5 *
6 * Written by Michael Kruse, INRIA Paris-Rocquencourt,
7 * Domaine de Voluceau, Rocquenqourt, B.P. 105,
8 * 78153 Le Chesnay Cedex France
9 */
10#ifndef ISL_INT_SIOIMATH_H
11#define ISL_INT_SIOIMATH_H
12
13#include <inttypes.h>
14#include <limits.h>
15#include <stdint.h>
16#include <stdlib.h>
17
18#include <isl_imath.h>
19#include <isl/hash.h>
20
21#define ARRAY_SIZE(array)(sizeof(array)/sizeof(*array)) (sizeof(array)/sizeof(*array))
22
23/* Visual Studio before VS2015 does not support the inline keyword when
24 * compiling in C mode because it was introduced in C99 which it does not
25 * officially support. Instead, it has a proprietary extension using __inline.
26 */
27#if defined(_MSC_VER) && (_MSC_VER < 1900)
28#define inline __inline
29#endif
30
31/* The type to represent integers optimized for small values. It is either a
32 * pointer to an mp_int ( = mpz_t*; big representation) or an int32_t (small
33 * represenation) with a discriminator at the least significant bit. In big
34 * representation it will be always zero because of heap alignment. It is set
35 * to 1 for small representation and use the 32 most significant bits for the
36 * int32_t.
37 *
38 * Structure on 64 bit machines, with 8-byte aligment (3 bits):
39 *
40 * Big representation:
41 * MSB LSB
42 * |------------------------------------------------------------000
43 * | mpz_t* |
44 * | != NULL |
45 *
46 * Small representation:
47 * MSB 32 LSB
48 * |------------------------------|00000000000000000000000000000001
49 * | int32_t |
50 * | 2147483647 ... -2147483647 |
51 * ^
52 * |
53 * discriminator bit
54 *
55 * On 32 bit machines isl_sioimath type is blown up to 8 bytes, i.e.
56 * isl_sioimath is guaranteed to be at least 8 bytes. This is to ensure the
57 * int32_t can be hidden in that type without data loss. In the future we might
58 * optimize this to use 31 hidden bits in a 32 bit pointer. We may also use 63
59 * bits on 64 bit machines, but this comes with the cost of additional overflow
60 * checks because there is no standardized 128 bit integer we could expand to.
61 *
62 * We use native integer types and avoid union structures to avoid assumptions
63 * on the machine's endianness.
64 *
65 * This implementation makes the following assumptions:
66 * - long can represent any int32_t
67 * - mp_small is signed long
68 * - mp_usmall is unsigned long
69 * - adresses returned by malloc are aligned to 2-byte boundaries (leastmost
70 * bit is zero)
71 */
72#if UINT64_MAX(18446744073709551615UL) > UINTPTR_MAX(18446744073709551615UL)
73typedef uint64_t isl_sioimath;
74#else
75typedef uintptr_t isl_sioimath;
76#endif
77
78/* The negation of the smallest possible number in int32_t, INT32_MIN
79 * (0x80000000u, -2147483648), cannot be represented in an int32_t, therefore
80 * every operation that may produce this value needs to special-case it.
81 * The operations are:
82 * abs(INT32_MIN)
83 * -INT32_MIN (negation)
84 * -1 * INT32_MIN (multiplication)
85 * INT32_MIN/-1 (any division: divexact, fdiv, cdiv, tdiv)
86 * To avoid checking these cases, we exclude INT32_MIN from small
87 * representation.
88 */
89#define ISL_SIOIMATH_SMALL_MIN(-(2147483647)) (-INT32_MAX(2147483647))
90
91/* Largest possible number in small representation */
92#define ISL_SIOIMATH_SMALL_MAX(2147483647) INT32_MAX(2147483647)
93
94/* Used for function parameters the function modifies. */
95typedef isl_sioimath *isl_sioimath_ptr;
96
97/* Used for function parameters that are read-only. */
98typedef isl_sioimath isl_sioimath_src;
99
100/* Return whether the argument is stored in small representation.
101 */
102inline int isl_sioimath_is_small(isl_sioimath val)
103{
104 return val & 0x00000001;
105}
106
107/* Return whether the argument is stored in big representation.
108 */
109inline int isl_sioimath_is_big(isl_sioimath val)
110{
111 return !isl_sioimath_is_small(val);
112}
113
114/* Get the number of an isl_int in small representation. Result is undefined if
115 * val is not stored in that format.
116 */
117inline int32_t isl_sioimath_get_small(isl_sioimath val)
118{
119 return val >> 32;
120}
121
122/* Get the number of an in isl_int in big representation. Result is undefined if
123 * val is not stored in that format.
124 */
125inline mp_int isl_sioimath_get_big(isl_sioimath val)
126{
127 return (mp_int)(uintptr_t) val;
128}
129
130/* Return 1 if val is stored in small representation and store its value to
131 * small. We rely on the compiler to optimize the isl_sioimath_get_small such
132 * that the shift is moved into the branch that executes in case of small
133 * representation. If there is no such branch, then a single shift is still
134 * cheaper than introducing branching code.
135 */
136inline int isl_sioimath_decode_small(isl_sioimath val, int32_t *small)
137{
138 *small = isl_sioimath_get_small(val);
139 return isl_sioimath_is_small(val);
140}
141
142/* Return 1 if val is stored in big representation and store its value to big.
143 */
144inline int isl_sioimath_decode_big(isl_sioimath val, mp_int *big)
145{
146 *big = isl_sioimath_get_big(val);
147 return isl_sioimath_is_big(val);
148}
149
150/* Encode a small representation into an isl_int.
151 */
152inline isl_sioimath isl_sioimath_encode_small(int32_t val)
153{
154 return ((isl_sioimath) val) << 32 | 0x00000001;
155}
156
157/* Encode a big representation.
158 */
159inline isl_sioimath isl_sioimath_encode_big(mp_int val)
160{
161 return (isl_sioimath)(uintptr_t) val;
162}
163
164/* A common situation is to call an IMath function with at least one argument
165 * that is currently in small representation or an integer parameter, i.e. a big
166 * representation of the same number is required. Promoting the original
167 * argument comes with multiple problems, such as modifying a read-only
168 * argument, the responsibility of deallocation and the execution cost. Instead,
169 * we make a copy by 'faking' the IMath internal structure.
170 *
171 * We reserve the maximum number of required digits on the stack to avoid heap
172 * allocations.
173 *
174 * mp_digit can be uint32_t or uint16_t. This code must work for little and big
175 * endian digits. The structure for an uint64_t argument and 32-bit mp_digits is
176 * sketched below.
177 *
178 * |----------------------------|
179 * uint64_t
180 *
181 * |-------------||-------------|
182 * mp_digit mp_digit
183 * digits[1] digits[0]
184 * Most sig digit Least sig digit
185 */
186typedef struct {
187 mpz_t big;
188 mp_digit digits[(sizeof(uintmax_t) + sizeof(mp_digit) - 1) /
189 sizeof(mp_digit)];
190} isl_sioimath_scratchspace_t;
191
192/* Convert a native integer to IMath's digit representation. A native integer
193 * might be big- or little endian, but IMath always stores the least significant
194 * digit in the lowest array indices. memcpy therefore is not possible.
195 *
196 * We also have to consider that long and mp_digit can be of different sizes,
197 * depending on the compiler (LP64, LLP64) and IMath's USE_64BIT_WORDS. This
198 * macro should work for all of them.
199 *
200 * "used" is set to the number of written digits. It must be minimal (IMath
201 * checks zeroness using the used field), but always at least one. Also note
202 * that the result of num>>(sizeof(num)*CHAR_BIT) is undefined.
203 */
204#define ISL_SIOIMATH_TO_DIGITS(num, digits, used)do { int i = 0; do { (digits)[i] = ((num) >> (sizeof(mp_digit
) * 8 * i)); i += 1; if (i >= (sizeof(num) + sizeof(mp_digit
) - 1) / sizeof(mp_digit)) break; if (((num) >> (sizeof
(mp_digit) * 8 * i)) == 0) break; } while (1); (used) = i; } while
(0)
\
205 do { \
206 int i = 0; \
207 do { \
208 (digits)[i] = \
209 ((num) >> (sizeof(mp_digit) * CHAR_BIT8 * i)); \
210 i += 1; \
211 if (i >= (sizeof(num) + sizeof(mp_digit) - 1) / \
212 sizeof(mp_digit)) \
213 break; \
214 if (((num) >> (sizeof(mp_digit) * CHAR_BIT8 * i)) == 0) \
215 break; \
216 } while (1); \
217 (used) = i; \
218 } while (0)
219
220inline void isl_siomath_uint32_to_digits(uint32_t num, mp_digit *digits,
221 mp_size *used)
222{
223 ISL_SIOIMATH_TO_DIGITS(num, digits, *used)do { int i = 0; do { (digits)[i] = ((num) >> (sizeof(mp_digit
) * 8 * i)); i += 1; if (i >= (sizeof(num) + sizeof(mp_digit
) - 1) / sizeof(mp_digit)) break; if (((num) >> (sizeof
(mp_digit) * 8 * i)) == 0) break; } while (1); (*used) = i; }
while (0)
;
224}
225
226inline void isl_siomath_ulong_to_digits(unsigned long num, mp_digit *digits,
227 mp_size *used)
228{
229 ISL_SIOIMATH_TO_DIGITS(num, digits, *used)do { int i = 0; do { (digits)[i] = ((num) >> (sizeof(mp_digit
) * 8 * i)); i += 1; if (i >= (sizeof(num) + sizeof(mp_digit
) - 1) / sizeof(mp_digit)) break; if (((num) >> (sizeof
(mp_digit) * 8 * i)) == 0) break; } while (1); (*used) = i; }
while (0)
;
230}
231
232inline void isl_siomath_uint64_to_digits(uint64_t num, mp_digit *digits,
233 mp_size *used)
234{
235 ISL_SIOIMATH_TO_DIGITS(num, digits, *used)do { int i = 0; do { (digits)[i] = ((num) >> (sizeof(mp_digit
) * 8 * i)); i += 1; if (i >= (sizeof(num) + sizeof(mp_digit
) - 1) / sizeof(mp_digit)) break; if (((num) >> (sizeof
(mp_digit) * 8 * i)) == 0) break; } while (1); (*used) = i; }
while (0)
;
236}
237
238/* Get the IMath representation of an isl_int without modifying it.
239 * For the case it is not in big representation yet, pass some scratch space we
240 * can use to store the big representation in.
241 * In order to avoid requiring init and free on the scratch space, we directly
242 * modify the internal representation.
243 *
244 * The name derives from its indented use: getting the big representation of an
245 * input (src) argument.
246 */
247inline mp_int isl_sioimath_bigarg_src(isl_sioimath arg,
248 isl_sioimath_scratchspace_t *scratch)
249{
250 mp_int big;
251 int32_t small;
252 uint32_t num;
253
254 if (isl_sioimath_decode_big(arg, &big))
255 return big;
256
257 small = isl_sioimath_get_small(arg);
258 scratch->big.digits = scratch->digits;
259 scratch->big.alloc = ARRAY_SIZE(scratch->digits)(sizeof(scratch->digits)/sizeof(*scratch->digits));
260 if (small >= 0) {
261 scratch->big.sign = MP_ZPOS;
262 num = small;
263 } else {
264 scratch->big.sign = MP_NEG;
265 num = -small;
266 }
267
268 isl_siomath_uint32_to_digits(num, scratch->digits, &scratch->big.used);
269 return &scratch->big;
270}
271
272/* Create a temporary IMath mp_int for a signed long.
273 */
274inline mp_int isl_sioimath_siarg_src(signed long arg,
275 isl_sioimath_scratchspace_t *scratch)
276{
277 unsigned long num;
278
279 scratch->big.digits = scratch->digits;
280 scratch->big.alloc = ARRAY_SIZE(scratch->digits)(sizeof(scratch->digits)/sizeof(*scratch->digits));
281 if (arg >= 0) {
282 scratch->big.sign = MP_ZPOS;
283 num = arg;
284 } else {
285 scratch->big.sign = MP_NEG;
286 num = (arg == LONG_MIN(-9223372036854775807L -1L)) ? ((unsigned long) LONG_MAX9223372036854775807L) + 1 : -arg;
287 }
288
289 isl_siomath_ulong_to_digits(num, scratch->digits, &scratch->big.used);
290 return &scratch->big;
291}
292
293/* Create a temporary IMath mp_int for an int64_t.
294 */
295inline mp_int isl_sioimath_si64arg_src(int64_t arg,
296 isl_sioimath_scratchspace_t *scratch)
297{
298 uint64_t num;
299
300 scratch->big.digits = scratch->digits;
301 scratch->big.alloc = ARRAY_SIZE(scratch->digits)(sizeof(scratch->digits)/sizeof(*scratch->digits));
302 if (arg >= 0) {
303 scratch->big.sign = MP_ZPOS;
304 num = arg;
305 } else {
306 scratch->big.sign = MP_NEG;
307 num = (arg == INT64_MIN(-9223372036854775807L -1)) ? ((uint64_t) INT64_MAX(9223372036854775807L)) + 1 : -arg;
308 }
309
310 isl_siomath_uint64_to_digits(num, scratch->digits, &scratch->big.used);
311 return &scratch->big;
312}
313
314/* Create a temporary IMath mp_int for an unsigned long.
315 */
316inline mp_int isl_sioimath_uiarg_src(unsigned long arg,
317 isl_sioimath_scratchspace_t *scratch)
318{
319 scratch->big.digits = scratch->digits;
320 scratch->big.alloc = ARRAY_SIZE(scratch->digits)(sizeof(scratch->digits)/sizeof(*scratch->digits));
321 scratch->big.sign = MP_ZPOS;
322
323 isl_siomath_ulong_to_digits(arg, scratch->digits, &scratch->big.used);
324 return &scratch->big;
325}
326
327/* Ensure big representation. Does not preserve the current number.
328 * Callers may use the fact that the value _is_ preserved if the presentation
329 * was big before.
330 */
331inline mp_int isl_sioimath_reinit_big(isl_sioimath_ptr ptr)
332{
333 if (isl_sioimath_is_small(*ptr))
334 *ptr = isl_sioimath_encode_big(mp_int_alloc());
335 return isl_sioimath_get_big(*ptr);
336}
337
338/* Set ptr to a number in small representation.
339 */
340inline void isl_sioimath_set_small(isl_sioimath_ptr ptr, int32_t val)
341{
342 if (isl_sioimath_is_big(*ptr))
343 mp_int_free(isl_sioimath_get_big(*ptr));
344 *ptr = isl_sioimath_encode_small(val);
345}
346
347/* Set ptr to val, choosing small representation if possible.
348 */
349inline void isl_sioimath_set_int32(isl_sioimath_ptr ptr, int32_t val)
350{
351 if (ISL_SIOIMATH_SMALL_MIN(-(2147483647)) <= val && val <= ISL_SIOIMATH_SMALL_MAX(2147483647)) {
352 isl_sioimath_set_small(ptr, val);
353 return;
354 }
355
356 mp_int_init_value(isl_sioimath_reinit_big(ptr), val);
357}
358
359/* Assign an int64_t number using small representation if possible.
360 */
361inline void isl_sioimath_set_int64(isl_sioimath_ptr ptr, int64_t val)
362{
363 if (ISL_SIOIMATH_SMALL_MIN(-(2147483647)) <= val && val <= ISL_SIOIMATH_SMALL_MAX(2147483647)) {
364 isl_sioimath_set_small(ptr, val);
365 return;
366 }
367
368 isl_sioimath_scratchspace_t scratch;
369 mp_int_copy(isl_sioimath_si64arg_src(val, &scratch),
370 isl_sioimath_reinit_big(ptr));
371}
372
373/* Convert to big representation while preserving the current number.
374 */
375inline void isl_sioimath_promote(isl_sioimath_ptr dst)
376{
377 int32_t small;
378
379 if (isl_sioimath_is_big(*dst))
380 return;
381
382 small = isl_sioimath_get_small(*dst);
383 mp_int_set_value(isl_sioimath_reinit_big(dst), small);
384}
385
386/* Convert to small representation while preserving the current number. Does
387 * nothing if dst doesn't fit small representation.
388 */
389inline void isl_sioimath_try_demote(isl_sioimath_ptr dst)
390{
391 mp_small small;
392
393 if (isl_sioimath_is_small(*dst))
394 return;
395
396 if (mp_int_to_int(isl_sioimath_get_big(*dst), &small) != MP_OK)
397 return;
398
399 if (ISL_SIOIMATH_SMALL_MIN(-(2147483647)) <= small && small <= ISL_SIOIMATH_SMALL_MAX(2147483647))
400 isl_sioimath_set_small(dst, small);
401}
402
403/* Initialize an isl_int. The implicit value is 0 in small representation.
404 */
405inline void isl_sioimath_init(isl_sioimath_ptr dst)
406{
407 *dst = isl_sioimath_encode_small(0);
408}
409
410/* Free the resources taken by an isl_int.
411 */
412inline void isl_sioimath_clear(isl_sioimath_ptr dst)
413{
414 if (isl_sioimath_is_small(*dst))
415 return;
416
417 mp_int_free(isl_sioimath_get_big(*dst));
418}
419
420/* Copy the value of one isl_int to another.
421 */
422inline void isl_sioimath_set(isl_sioimath_ptr dst, isl_sioimath_src val)
423{
424 if (isl_sioimath_is_small(val)) {
425 isl_sioimath_set_small(dst, isl_sioimath_get_small(val));
426 return;
427 }
428
429 mp_int_copy(isl_sioimath_get_big(val), isl_sioimath_reinit_big(dst));
430}
431
432/* Store a signed long into an isl_int.
433 */
434inline void isl_sioimath_set_si(isl_sioimath_ptr dst, long val)
435{
436 if (ISL_SIOIMATH_SMALL_MIN(-(2147483647)) <= val && val <= ISL_SIOIMATH_SMALL_MAX(2147483647)) {
437 isl_sioimath_set_small(dst, val);
438 return;
439 }
440
441 mp_int_set_value(isl_sioimath_reinit_big(dst), val);
442}
443
444/* Store an unsigned long into an isl_int.
445 */
446inline void isl_sioimath_set_ui(isl_sioimath_ptr dst, unsigned long val)
447{
448 if (val <= ISL_SIOIMATH_SMALL_MAX(2147483647)) {
449 isl_sioimath_set_small(dst, val);
450 return;
451 }
452
453 mp_int_set_uvalue(isl_sioimath_reinit_big(dst), val);
454}
455
456/* Return whether a number can be represented by a signed long.
457 */
458inline int isl_sioimath_fits_slong(isl_sioimath_src val)
459{
460 mp_small dummy;
461
462 if (isl_sioimath_is_small(val))
463 return 1;
464
465 return mp_int_to_int(isl_sioimath_get_big(val), &dummy) == MP_OK;
466}
467
468/* Return a number as signed long. Result is undefined if the number cannot be
469 * represented as long.
470 */
471inline long isl_sioimath_get_si(isl_sioimath_src val)
472{
473 mp_small result;
474
475 if (isl_sioimath_is_small(val))
476 return isl_sioimath_get_small(val);
477
478 mp_int_to_int(isl_sioimath_get_big(val), &result);
479 return result;
480}
481
482/* Return whether a number can be represented as unsigned long.
483 */
484inline int isl_sioimath_fits_ulong(isl_sioimath_src val)
485{
486 mp_usmall dummy;
487
488 if (isl_sioimath_is_small(val))
489 return isl_sioimath_get_small(val) >= 0;
490
491 return mp_int_to_uint(isl_sioimath_get_big(val), &dummy) == MP_OK;
492}
493
494/* Return a number as unsigned long. Result is undefined if the number cannot be
495 * represented as unsigned long.
496 */
497inline unsigned long isl_sioimath_get_ui(isl_sioimath_src val)
498{
499 mp_usmall result;
500
501 if (isl_sioimath_is_small(val))
502 return isl_sioimath_get_small(val);
503
504 mp_int_to_uint(isl_sioimath_get_big(val), &result);
505 return result;
506}
507
508/* Return a number as floating point value.
509 */
510inline double isl_sioimath_get_d(isl_sioimath_src val)
511{
512 mp_int big;
513 double result = 0;
514 int i;
515
516 if (isl_sioimath_is_small(val))
517 return isl_sioimath_get_small(val);
518
519 big = isl_sioimath_get_big(val);
520 for (i = 0; i < big->used; ++i)
521 result = result * (double) ((uintmax_t) MP_DIGIT_MAX((4294967295U) * 1UL) + 1) +
522 (double) big->digits[i];
523
524 if (big->sign == MP_NEG)
525 result = -result;
526
527 return result;
528}
529
530/* Format a number as decimal string.
531 *
532 * The largest possible string from small representation is 12 characters
533 * ("-2147483647").
534 */
535inline char *isl_sioimath_get_str(isl_sioimath_src val)
536{
537 char *result;
538
539 if (isl_sioimath_is_small(val)) {
540 result = malloc(12);
541 snprintf(result, 12, "%" PRIi32"i", isl_sioimath_get_small(val));
542 return result;
543 }
544
545 return impz_get_str(NULL((void*)0), 10, isl_sioimath_get_big(val));
546}
547
548/* Return the absolute value.
549 */
550inline void isl_sioimath_abs(isl_sioimath_ptr dst, isl_sioimath_src arg)
551{
552 if (isl_sioimath_is_small(arg)) {
553 isl_sioimath_set_small(dst, labs(isl_sioimath_get_small(arg)));
554 return;
555 }
556
557 mp_int_abs(isl_sioimath_get_big(arg), isl_sioimath_reinit_big(dst));
558}
559
560/* Return the negation of a number.
561 */
562inline void isl_sioimath_neg(isl_sioimath_ptr dst, isl_sioimath_src arg)
563{
564 if (isl_sioimath_is_small(arg)) {
565 isl_sioimath_set_small(dst, -isl_sioimath_get_small(arg));
566 return;
567 }
568
569 mp_int_neg(isl_sioimath_get_big(arg), isl_sioimath_reinit_big(dst));
570}
571
572/* Swap two isl_ints.
573 *
574 * isl_sioimath can be copied bytewise; nothing depends on its address. It can
575 * also be stored in a CPU register.
576 */
577inline void isl_sioimath_swap(isl_sioimath_ptr lhs, isl_sioimath_ptr rhs)
578{
579 isl_sioimath tmp = *lhs;
580 *lhs = *rhs;
581 *rhs = tmp;
582}
583
584/* Add an unsigned long to the number.
585 *
586 * On LP64 unsigned long exceeds the range of an int64_t, therefore we check in
587 * advance whether small representation possibly overflows.
588 */
589inline void isl_sioimath_add_ui(isl_sioimath_ptr dst, isl_sioimath lhs,
590 unsigned long rhs)
591{
592 int32_t smalllhs;
593 isl_sioimath_scratchspace_t lhsscratch;
594
595 if (isl_sioimath_decode_small(lhs, &smalllhs) &&
596 (rhs <= (uint64_t) INT64_MAX(9223372036854775807L) - (uint64_t) ISL_SIOIMATH_SMALL_MAX(2147483647))) {
597 isl_sioimath_set_int64(dst, (int64_t) smalllhs + rhs);
598 return;
599 }
600
601 impz_add_ui(isl_sioimath_reinit_big(dst),
602 isl_sioimath_bigarg_src(lhs, &lhsscratch), rhs);
603 isl_sioimath_try_demote(dst);
604}
605
606/* Subtract an unsigned long.
607 *
608 * On LP64 unsigned long exceeds the range of an int64_t. If
609 * ISL_SIOIMATH_SMALL_MIN-rhs>=INT64_MIN we can do the calculation using int64_t
610 * without risking an overflow.
611 */
612inline void isl_sioimath_sub_ui(isl_sioimath_ptr dst, isl_sioimath lhs,
613 unsigned long rhs)
614{
615 int32_t smalllhs;
616 isl_sioimath_scratchspace_t lhsscratch;
617
618 if (isl_sioimath_decode_small(lhs, &smalllhs) &&
619 (rhs < (uint64_t) INT64_MIN(-9223372036854775807L -1) - (uint64_t) ISL_SIOIMATH_SMALL_MIN(-(2147483647)))) {
620 isl_sioimath_set_int64(dst, (int64_t) smalllhs - rhs);
621 return;
622 }
623
624 impz_sub_ui(isl_sioimath_reinit_big(dst),
625 isl_sioimath_bigarg_src(lhs, &lhsscratch), rhs);
626 isl_sioimath_try_demote(dst);
627}
628
629/* Sum of two isl_ints.
630 */
631inline void isl_sioimath_add(isl_sioimath_ptr dst, isl_sioimath_src lhs,
632 isl_sioimath_src rhs)
633{
634 isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
635 int32_t smalllhs, smallrhs;
636
637 if (isl_sioimath_decode_small(lhs, &smalllhs) &&
638 isl_sioimath_decode_small(rhs, &smallrhs)) {
639 isl_sioimath_set_int64(
640 dst, (int64_t) smalllhs + (int64_t) smallrhs);
641 return;
642 }
643
644 mp_int_add(isl_sioimath_bigarg_src(lhs, &scratchlhs),
645 isl_sioimath_bigarg_src(rhs, &scratchrhs),
646 isl_sioimath_reinit_big(dst));
647 isl_sioimath_try_demote(dst);
648}
649
650/* Subtract two isl_ints.
651 */
652inline void isl_sioimath_sub(isl_sioimath_ptr dst, isl_sioimath_src lhs,
653 isl_sioimath_src rhs)
654{
655 isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
656 int32_t smalllhs, smallrhs;
657
658 if (isl_sioimath_decode_small(lhs, &smalllhs) &&
659 isl_sioimath_decode_small(rhs, &smallrhs)) {
660 isl_sioimath_set_int64(
661 dst, (int64_t) smalllhs - (int64_t) smallrhs);
662 return;
663 }
664
665 mp_int_sub(isl_sioimath_bigarg_src(lhs, &scratchlhs),
666 isl_sioimath_bigarg_src(rhs, &scratchrhs),
667 isl_sioimath_reinit_big(dst));
668 isl_sioimath_try_demote(dst);
669}
670
671/* Multiply two isl_ints.
672 */
673inline void isl_sioimath_mul(isl_sioimath_ptr dst, isl_sioimath_src lhs,
674 isl_sioimath_src rhs)
675{
676 isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
677 int32_t smalllhs, smallrhs;
678
679 if (isl_sioimath_decode_small(lhs, &smalllhs) &&
680 isl_sioimath_decode_small(rhs, &smallrhs)) {
681 isl_sioimath_set_int64(
682 dst, (int64_t) smalllhs * (int64_t) smallrhs);
683 return;
684 }
685
686 mp_int_mul(isl_sioimath_bigarg_src(lhs, &scratchlhs),
687 isl_sioimath_bigarg_src(rhs, &scratchrhs),
688 isl_sioimath_reinit_big(dst));
689 isl_sioimath_try_demote(dst);
690}
691
692/* Shift lhs by rhs bits to the left and store the result in dst. Effectively,
693 * this operation computes 'lhs * 2^rhs'.
694 */
695inline void isl_sioimath_mul_2exp(isl_sioimath_ptr dst, isl_sioimath lhs,
696 unsigned long rhs)
697{
698 isl_sioimath_scratchspace_t scratchlhs;
699 int32_t smalllhs;
700
701 if (isl_sioimath_decode_small(lhs, &smalllhs) && (rhs <= 32ul)) {
702 isl_sioimath_set_int64(dst, ((int64_t) smalllhs) << rhs);
703 return;
704 }
705
706 mp_int_mul_pow2(isl_sioimath_bigarg_src(lhs, &scratchlhs), rhs,
707 isl_sioimath_reinit_big(dst));
708}
709
710/* Multiply an isl_int and a signed long.
711 */
712inline void isl_sioimath_mul_si(isl_sioimath_ptr dst, isl_sioimath lhs,
713 signed long rhs)
714{
715 isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
716 int32_t smalllhs;
717
718 if (isl_sioimath_decode_small(lhs, &smalllhs) && (rhs > LONG_MIN(-9223372036854775807L -1L)) &&
719 (labs(rhs) <= UINT32_MAX(4294967295U))) {
720 isl_sioimath_set_int64(dst, (int64_t) smalllhs * (int64_t) rhs);
721 return;
722 }
723
724 mp_int_mul(isl_sioimath_bigarg_src(lhs, &scratchlhs),
725 isl_sioimath_siarg_src(rhs, &scratchrhs),
726 isl_sioimath_reinit_big(dst));
727 isl_sioimath_try_demote(dst);
728}
729
730/* Multiply an isl_int and an unsigned long.
731 */
732inline void isl_sioimath_mul_ui(isl_sioimath_ptr dst, isl_sioimath lhs,
733 unsigned long rhs)
734{
735 isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
736 int32_t smalllhs;
737
738 if (isl_sioimath_decode_small(lhs, &smalllhs) && (rhs <= UINT32_MAX(4294967295U))) {
739 isl_sioimath_set_int64(dst, (int64_t) smalllhs * (int64_t) rhs);
740 return;
741 }
742
743 mp_int_mul(isl_sioimath_bigarg_src(lhs, &scratchlhs),
744 isl_sioimath_uiarg_src(rhs, &scratchrhs),
745 isl_sioimath_reinit_big(dst));
746 isl_sioimath_try_demote(dst);
747}
748
749/* Compute the power of an isl_int to an unsigned long.
750 * Always let IMath do it; the result is unlikely to be small except in some
751 * special cases.
752 * Note: 0^0 == 1
753 */
754inline void isl_sioimath_pow_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs,
755 unsigned long rhs)
756{
757 isl_sioimath_scratchspace_t scratchlhs, scratchrhs;
758 int32_t smalllhs;
759
760 switch (rhs) {
761 case 0:
762 isl_sioimath_set_small(dst, 1);
763 return;
764 case 1:
765 isl_sioimath_set(dst, lhs);
766 return;
767 case 2:
768 isl_sioimath_mul(dst, lhs, lhs);
769 return;
770 }
771
772 if (isl_sioimath_decode_small(lhs, &smalllhs)) {
773 switch (smalllhs) {
774 case 0:
775 isl_sioimath_set_small(dst, 0);
776 return;
777 case 1:
778 isl_sioimath_set_small(dst, 1);
779 return;
780 case 2:
781 isl_sioimath_set_small(dst, 1);
782 isl_sioimath_mul_2exp(dst, *dst, rhs);
783 return;
784 default:
785 if ((MP_SMALL_MIN(-9223372036854775807L -1L) <= rhs) && (rhs <= MP_SMALL_MAX9223372036854775807L)) {
786 mp_int_expt_value(smalllhs, rhs,
787 isl_sioimath_reinit_big(dst));
788 isl_sioimath_try_demote(dst);
789 return;
790 }
791 }
792 }
793
794 mp_int_expt_full(isl_sioimath_bigarg_src(lhs, &scratchlhs),
795 isl_sioimath_uiarg_src(rhs, &scratchrhs),
796 isl_sioimath_reinit_big(dst));
797 isl_sioimath_try_demote(dst);
798}
799
800/* Fused multiply-add.
801 */
802inline void isl_sioimath_addmul(isl_sioimath_ptr dst, isl_sioimath_src lhs,
803 isl_sioimath_src rhs)
804{
805 isl_sioimath tmp;
806 isl_sioimath_init(&t