/build/source/polly/lib/External/isl/isl_map

Bug Summary

File:	build/source/polly/lib/External/isl/isl_map_simplify.c
Warning:	line 743, column 41 Division by zero
Annotated Source Code

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clang -cc1 -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -clear-ast-before-backend -disable-llvm-verifier -discard-value-names -main-file-name isl_map_simplify.c -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -mframe-pointer=none -fmath-errno -ffp-contract=on -fno-rounding-math -mconstructor-aliases -funwind-tables=2 -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -fdebug-compilation-dir=/build/source/build-llvm/tools/clang/stage2-bins -fdebug-prefix-map=/build/source/build-llvm/tools/clang/stage2-bins=../../../../ -fdebug-prefix-map=/build/source/= -ffunction-sections -fdata-sections -fcoverage-compilation-dir=/build/source/build-llvm/tools/clang/stage2-bins -resource-dir /usr/lib/llvm-19/lib/clang/19 -I tools/polly/lib/External -I /build/source/polly/lib/External -I /build/source/polly/lib/External/isl -I /build/source/polly/lib/External/isl/include -I /build/source/polly/lib/External/isl/imath -I tools/polly/lib/External/isl -I tools/polly/include -I /build/source/polly/lib/External/pet/include -I tools/polly/lib/External/isl/include -I /build/source/polly/include -I include -I /build/source/llvm/include -D _DEBUG -D _GLIBCXX_ASSERTIONS -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -D _FORTIFY_SOURCE=2 -D NDEBUG -U NDEBUG -internal-isystem /usr/lib/llvm-19/lib/clang/19/include -internal-isystem /usr/local/include -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../x86_64-linux-gnu/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -fmacro-prefix-map=/build/source/build-llvm/tools/clang/stage2-bins=../../../../ -fmacro-prefix-map=/build/source/= -fcoverage-prefix-map=/build/source/build-llvm/tools/clang/stage2-bins=../../../../ -fcoverage-prefix-map=/build/source/= -O2 -Wno-unused-command-line-argument -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-comment -std=gnu99 -fconst-strings -ferror-limit 19 -stack-protector 2 -fgnuc-version=4.2.1 -fskip-odr-check-in-gmf -fcolor-diagnostics -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /tmp/scan-build-2024-04-02-020108-72015-1 -x c /build/source/polly/lib/External/isl/isl_map_simplify.c
1/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2012-2013 Ecole Normale Superieure
* Copyright 2014-2015 INRIA Rocquencourt
* Copyright 2016      Sven Verdoolaege
*
* Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
* and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
* and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
* B.P. 105 - 78153 Le Chesnay, France
*/

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>

26#include <bset_to_bmap.c>
27#include <bset_from_bmap.c>
28#include <set_to_map.c>
29#include <set_from_map.c>

31static void swap_equality(__isl_keep isl_basic_map *bmap, int a, int b)
32{
isl_int *t = bmap->eq[a];
bmap->eq[a] = bmap->eq[b];
bmap->eq[b] = t;
36}

38static void swap_inequality(__isl_keep isl_basic_map *bmap, int a, int b)
39{
if (a != b) {
isl_int *t = bmap->ineq[a];
bmap->ineq[a] = bmap->ineq[b];
bmap->ineq[b] = t;
}
45}

47__isl_give isl_basic_map *isl_basic_map_normalize_constraints(
__isl_take isl_basic_map *bmap)
49{
int i;
isl_int gcd;
isl_size total = isl_basic_map_dim(bmap, isl_dim_all);

if (total < 0)
return isl_basic_map_free(bmap);

isl_int_init(gcd)isl_sioimath_init((gcd));
for (i = bmap->n_eq - 1; i >= 0; --i) {
isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
if (isl_int_is_zero(gcd)(isl_sioimath_sgn(*(gcd)) == 0)) {
	if (!isl_int_is_zero(bmap->eq[i][0])(isl_sioimath_sgn(*(bmap->eq[i][0])) == 0)) {
		bmap = isl_basic_map_set_to_empty(bmap);
		break;
	}
	if (isl_basic_map_drop_equality(bmap, i) < 0)
		goto error;
	continue;
}
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4)))))
	isl_int_gcd(gcd, gcd, bmap->eq[i][0])isl_sioimath_gcd((gcd), *(gcd), *(bmap->eq[i][0]));
if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0))
	continue;
if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)isl_sioimath_is_divisible_by(*(bmap->eq[i][0]), *(gcd))) {
	bmap = isl_basic_map_set_to_empty(bmap);
	break;
}
isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
}

for (i = bmap->n_ineq - 1; i >= 0; --i) {
isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
if (isl_int_is_zero(gcd)(isl_sioimath_sgn(*(gcd)) == 0)) {
	if (isl_int_is_neg(bmap->ineq[i][0])(isl_sioimath_sgn(*(bmap->ineq[i][0])) < 0)) {
		bmap = isl_basic_map_set_to_empty(bmap);
		break;
	}
	if (isl_basic_map_drop_inequality(bmap, i) < 0)
		goto error;
	continue;
}
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4)))))
	isl_int_gcd(gcd, gcd, bmap->ineq[i][0])isl_sioimath_gcd((gcd), *(gcd), *(bmap->ineq[i][0]));
if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0))
	continue;
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));
isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
}
isl_int_clear(gcd)isl_sioimath_clear((gcd));

return bmap;
101error:
isl_int_clear(gcd)isl_sioimath_clear((gcd));
isl_basic_map_free(bmap);
return NULL((void*)0);
105}

107__isl_give isl_basic_setisl_basic_map *isl_basic_set_normalize_constraints(
__isl_take isl_basic_setisl_basic_map *bset)
109{
isl_basic_map *bmap = bset_to_bmap(bset);
return bset_from_bmap(isl_basic_map_normalize_constraints(bmap));
112}

114/* Reduce the coefficient of the variable at position "pos"
* in integer division "div", such that it lies in the half-open
* interval (1/2,1/2], extracting any excess value from this integer division.
* "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
* corresponds to the constant term.
*
* That is, the integer division is of the form
*
*	floor((... + (c * d + r) * x_pos + ...)/d)
*
* with -d < 2 * r <= d.
* Replace it by
*
*	floor((... + r * x_pos + ...)/d) + c * x_pos
*
* If 2 * ((c * d + r) % d) <= d, then c = floor((c * d + r)/d).
* Otherwise, c = floor((c * d + r)/d) + 1.
*
* This is the same normalization that is performed by isl_aff_floor.
*/
134static __isl_give isl_basic_map *reduce_coefficient_in_div(
__isl_take isl_basic_map *bmap, int div, int pos)
136{
isl_int shift;
int add_one;

isl_int_init(shift)isl_sioimath_init((shift));
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]));
isl_int_mul_ui(shift, shift, 2)isl_sioimath_mul_ui((shift), *(shift), 2);
add_one = isl_int_gt(shift, bmap->div[div][0])(isl_sioimath_cmp(*(shift), *(bmap->div[div][0])) > 0);
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]));
if (add_one)
isl_int_add_ui(shift, shift, 1)isl_sioimath_add_ui((shift), *(shift), 1);
isl_int_neg(shift, shift)isl_sioimath_neg((shift), *(shift));
bmap = isl_basic_map_shift_div(bmap, div, pos, shift);
isl_int_clear(shift)isl_sioimath_clear((shift));

return bmap;
152}

154/* Does the coefficient of the variable at position "pos"
* in integer division "div" need to be reduced?
* That is, does it lie outside the half-open interval (1/2,1/2]?
* The coefficient c/d lies outside this interval if abs(2 * c) >= d and
* 2 * c != d.
*/
160static isl_bool needs_reduction(__isl_keep isl_basic_map *bmap, int div,
int pos)
162{
isl_bool r;

if (isl_int_is_zero(bmap->div[div][1 + pos])(isl_sioimath_sgn(*(bmap->div[div][1 + pos])) == 0))
return isl_bool_false;

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);
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) &&
   !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);
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)
	    bmap->div[div][1 + pos], 2)isl_sioimath_tdiv_q_ui((bmap->div[div][1 + pos]), *(bmap->
div[div][1 + pos]), 2);

return r;
175}

177/* Reduce the coefficients (including the constant term) of
* integer division "div", if needed.
* In particular, make sure all coefficients lie in
* the half-open interval (1/2,1/2].
*/
182static __isl_give isl_basic_map *reduce_div_coefficients_of_div(
__isl_take isl_basic_map *bmap, int div)
184{
int i;
isl_size total;

total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);
for (i = 0; i < 1 + total; ++i) {
isl_bool reduce;

reduce = needs_reduction(bmap, div, i);
if (reduce < 0)
	return isl_basic_map_free(bmap);
if (!reduce)
	continue;
bmap = reduce_coefficient_in_div(bmap, div, i);
if (!bmap)
	break;
}

return bmap;
205}

207/* Reduce the coefficients (including the constant term) of
* the known integer divisions, if needed
* In particular, make sure all coefficients lie in
* the half-open interval (1/2,1/2].
*/
212static __isl_give isl_basic_map *reduce_div_coefficients(
__isl_take isl_basic_map *bmap)
214{
int i;

if (!bmap)
return NULL((void*)0);
if (bmap->n_div == 0)
return bmap;

for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
	continue;
bmap = reduce_div_coefficients_of_div(bmap, i);
if (!bmap)
	break;
}

return bmap;
231}

233/* Remove any common factor in numerator and denominator of the div expression,
* not taking into account the constant term.
* That is, if the div is of the form
*
*	floor((a + m f(x))/(m d))
*
* then replace it by
*
*	floor((floor(a/m) + f(x))/d)
*
* The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
* and can therefore not influence the result of the floor.
*/
246static __isl_give isl_basic_map *normalize_div_expression(
__isl_take isl_basic_map *bmap, int div)
248{
isl_size total = isl_basic_map_dim(bmap, isl_dim_all);
isl_ctx *ctx = bmap->ctx;

if (total < 0)
return isl_basic_map_free(bmap);
if (isl_int_is_zero(bmap->div[div][0])(isl_sioimath_sgn(*(bmap->div[div][0])) == 0))
return bmap;
isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd);
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]));
if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0))
return bmap;
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))
	ctx->normalize_gcd)isl_sioimath_fdiv_q((bmap->div[div][1]), *(bmap->div[div
][1]), *(ctx->normalize_gcd));
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))
	ctx->normalize_gcd)isl_sioimath_tdiv_q((bmap->div[div][0]), *(bmap->div[div
][0]), *(ctx->normalize_gcd));
isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2,
	ctx->normalize_gcd, total);

return bmap;
268}

270/* Remove any common factor in numerator and denominator of a div expression,
* not taking into account the constant term.
* That is, look for any div of the form
*
*	floor((a + m f(x))/(m d))
*
* and replace it by
*
*	floor((floor(a/m) + f(x))/d)
*
* The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
* and can therefore not influence the result of the floor.
*/
283static __isl_give isl_basic_map *normalize_div_expressions(
__isl_take isl_basic_map *bmap)
285{
int i;

if (!bmap)
return NULL((void*)0);
if (bmap->n_div == 0)
return bmap;

for (i = 0; i < bmap->n_div; ++i)
bmap = normalize_div_expression(bmap, i);

return bmap;
297}

299/* Assumes divs have been ordered if keep_divs is set.
*/
301static __isl_give isl_basic_map *eliminate_var_using_equality(
__isl_take isl_basic_map *bmap,
unsigned pos, isl_int *eq, int keep_divs, int *progress)
304{
isl_size total;
isl_size v_div;
int k;
int last_div;

total = isl_basic_map_dim(bmap, isl_dim_all);
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (total < 0 || v_div < 0)
return isl_basic_map_free(bmap);
last_div = isl_seq_last_non_zero(eq + 1 + v_div, bmap->n_div);
for (k = 0; k < bmap->n_eq; ++k) {
if (bmap->eq[k] == eq)
	continue;
if (isl_int_is_zero(bmap->eq[k][1+pos])(isl_sioimath_sgn(*(bmap->eq[k][1+pos])) == 0))
	continue;
if (progress)
	*progress = 1;
isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL((void*)0));
isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
}

for (k = 0; k < bmap->n_ineq; ++k) {
if (isl_int_is_zero(bmap->ineq[k][1+pos])(isl_sioimath_sgn(*(bmap->ineq[k][1+pos])) == 0))
	continue;
if (progress)
	*progress = 1;
isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL((void*)0));
isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT)(((bmap)->flags) &= ~((1 << 3)));
ISL_F_CLR(bmap, ISL_BASIC_MAP_SORTED)(((bmap)->flags) &= ~((1 << 5)));
}

for (k = 0; k < bmap->n_div; ++k) {
if (isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0))
	continue;
if (isl_int_is_zero(bmap->div[k][1+1+pos])(isl_sioimath_sgn(*(bmap->div[k][1+1+pos])) == 0))
	continue;
if (progress)
	*progress = 1;
/* We need to be careful about circular definitions,
 * so for now we just remove the definition of div k
 * if the equality contains any divs.
 * If keep_divs is set, then the divs have been ordered
 * and we can keep the definition as long as the result
 * is still ordered.
 */
if (last_div == -1 || (keep_divs && last_div < k)) {
	isl_seq_elim(bmap->div[k]+1, eq,
			1+pos, 1+total, &bmap->div[k][0]);
	bmap = normalize_div_expression(bmap, k);
	if (!bmap)
		return NULL((void*)0);
} else
	isl_seq_clr(bmap->div[k], 1 + total);
}

return bmap;
362}

364/* Assumes divs have been ordered if keep_divs is set.
*/
366static __isl_give isl_basic_map *eliminate_div(__isl_take isl_basic_map *bmap,
isl_int *eq, unsigned div, int keep_divs)
368{
isl_size v_div;
unsigned pos;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_basic_map_free(bmap);
pos = v_div + div;
bmap = eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL((void*)0));

bmap = isl_basic_map_drop_div(bmap, div);

return bmap;
381}

383/* Check if elimination of div "div" using equality "eq" would not
* result in a div depending on a later div.
*/
386static isl_bool ok_to_eliminate_div(__isl_keep isl_basic_map *bmap, isl_int *eq,
unsigned div)
388{
int k;
int last_div;
isl_size v_div;
unsigned pos;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_bool_error;
pos = v_div + div;

last_div = isl_seq_last_non_zero(eq + 1 + v_div, bmap->n_div);
if (last_div < 0 || last_div <= div)
return isl_bool_true;

for (k = 0; k <= last_div; ++k) {
if (isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0))
	continue;
if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos])(isl_sioimath_sgn(*(bmap->div[k][1 + 1 + pos])) == 0))
	return isl_bool_false;
}

return isl_bool_true;
411}

413/* Eliminate divs based on equalities
*/
415static __isl_give isl_basic_map *eliminate_divs_eq(
__isl_take isl_basic_map *bmap, int *progress)
417{
int d;
int i;
int modified = 0;
unsigned off;

bmap = isl_basic_map_order_divs(bmap);

if (!bmap)
return NULL((void*)0);

off = isl_basic_map_offset(bmap, isl_dim_div);

for (d = bmap->n_div - 1; d >= 0 ; --d) {
for (i = 0; i < bmap->n_eq; ++i) {
	isl_bool ok;

	if (!isl_int_is_one(bmap->eq[i][off + d])(isl_sioimath_cmp_si(*(bmap->eq[i][off + d]), 1) == 0) &&
	    !isl_int_is_negone(bmap->eq[i][off + d])(isl_sioimath_cmp_si(*(bmap->eq[i][off + d]), -1) == 0))
		continue;
	ok = ok_to_eliminate_div(bmap, bmap->eq[i], d);
	if (ok < 0)
		return isl_basic_map_free(bmap);
	if (!ok)
		continue;
	modified = 1;
	*progress = 1;
	bmap = eliminate_div(bmap, bmap->eq[i], d, 1);
	if (isl_basic_map_drop_equality(bmap, i) < 0)
		return isl_basic_map_free(bmap);
	break;
}
}
if (modified)
return eliminate_divs_eq(bmap, progress);
return bmap;
453}

455/* Eliminate divs based on inequalities
*/
457static __isl_give isl_basic_map *eliminate_divs_ineq(
__isl_take isl_basic_map *bmap, int *progress)
459{
int d;
int i;
unsigned off;
struct isl_ctx *ctx;

if (!bmap)
return NULL((void*)0);

ctx = bmap->ctx;
off = isl_basic_map_offset(bmap, isl_dim_div);

for (d = bmap->n_div - 1; d >= 0 ; --d) {
for (i = 0; i < bmap->n_eq; ++i)
	if (!isl_int_is_zero(bmap->eq[i][off + d])(isl_sioimath_sgn(*(bmap->eq[i][off + d])) == 0))
		break;
if (i < bmap->n_eq)
	continue;
for (i = 0; i < bmap->n_ineq; ++i)
	if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one)(isl_sioimath_abs_cmp(*(bmap->ineq[i][off + d]), *(ctx->
one)) > 0))
		break;
if (i < bmap->n_ineq)
	continue;
*progress = 1;
bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1)))))
	break;
bmap = isl_basic_map_drop_div(bmap, d);
if (!bmap)
	break;
}
return bmap;
491}

493/* Does the equality constraint at position "eq" in "bmap" involve
* any local variables in the range [first, first + n)
* that are not marked as having an explicit representation?
*/
497static isl_bool bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map *bmap,
int eq, unsigned first, unsigned n)
499{
unsigned o_div;
int i;

if (!bmap)
return isl_bool_error;

o_div = isl_basic_map_offset(bmap, isl_dim_div);
for (i = 0; i < n; ++i) {
isl_bool unknown;

if (isl_int_is_zero(bmap->eq[eq][o_div + first + i])(isl_sioimath_sgn(*(bmap->eq[eq][o_div + first + i])) == 0
))
	continue;
unknown = isl_basic_map_div_is_marked_unknown(bmap, first + i);
if (unknown < 0)
	return isl_bool_error;
if (unknown)
	return isl_bool_true;
}

return isl_bool_false;
520}

522/* The last local variable involved in the equality constraint
* at position "eq" in "bmap" is the local variable at position "div".
* It can therefore be used to extract an explicit representation
* for that variable.
* Do so unless the local variable already has an explicit representation or
* the explicit representation would involve any other local variables
* that in turn do not have an explicit representation.
* An equality constraint involving local variables without an explicit
* representation can be used in isl_basic_map_drop_redundant_divs
* to separate out an independent local variable.  Introducing
* an explicit representation here would block this transformation,
* while the partial explicit representation in itself is not very useful.
* Set *progress if anything is changed.
*
* The equality constraint is of the form
*
*	f(x) + n e >= 0
*
* with n a positive number.  The explicit representation derived from
* this constraint is
*
*	floor((-f(x))/n)
*/
545static __isl_give isl_basic_map *set_div_from_eq(__isl_take isl_basic_map *bmap,
int div, int eq, int *progress)
547{
isl_size total;
unsigned o_div;
isl_bool involves;

if (!bmap)
return NULL((void*)0);

if (!isl_int_is_zero(bmap->div[div][0])(isl_sioimath_sgn(*(bmap->div[div][0])) == 0))
return bmap;

involves = bmap_eq_involves_unknown_divs(bmap, eq, 0, div);
if (involves < 0)
return isl_basic_map_free(bmap);
if (involves)
return bmap;

total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);
o_div = isl_basic_map_offset(bmap, isl_dim_div);
isl_seq_neg(bmap->div[div] + 1, bmap->eq[eq], 1 + total);
isl_int_set_si(bmap->div[div][1 + o_div + div], 0)isl_sioimath_set_si((bmap->div[div][1 + o_div + div]), 0);
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]));
if (progress)
*progress = 1;

return bmap;
575}

577/* Perform fangcheng (Gaussian elimination) on the equality
* constraints of "bmap".
* That is, put them into row-echelon form, starting from the last column
* backward and use them to eliminate the corresponding coefficients
* from all constraints.
*
* If "progress" is not NULL, then it gets set if the elimination
* results in any changes.
* The elimination process may result in some equality constraints
* getting interchanged or removed.
* If "swap" or "drop" are not NULL, then they get called when
* two equality constraints get interchanged or
* when a number of final equality constraints get removed.
* As a special case, if the input turns out to be empty,
* then drop gets called with the number of removed equality
* constraints set to the total number of equality constraints.
* If "swap" or "drop" are not NULL, then the local variables (if any)
* are assumed to be in a valid order.
*/
596__isl_give isl_basic_map *isl_basic_map_gauss5(__isl_take isl_basic_map *bmap,
int *progress,
isl_stat (*swap)(unsigned a, unsigned b, void *user),
isl_stat (*drop)(unsigned n, void *user), void *user)
600{
int k;
int done;
int last_var;
unsigned total_var;
isl_size total;
unsigned n_drop;

if (!swap && !drop)
bmap = isl_basic_map_order_divs(bmap);

total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);

total_var = total - bmap->n_div;

last_var = total - 1;
for (done = 0; done < bmap->n_eq; ++done) {
for (; last_var >= 0; --last_var) {
	for (k = done; k < bmap->n_eq; ++k)
		if (!isl_int_is_zero(bmap->eq[k][1+last_var])(isl_sioimath_sgn(*(bmap->eq[k][1+last_var])) == 0))
			break;
	if (k < bmap->n_eq)
		break;
}
if (last_var < 0)
	break;
if (k != done) {
	swap_equality(bmap, k, done);
	if (swap && swap(k, done, user) < 0)
		return isl_basic_map_free(bmap);
}
if (isl_int_is_neg(bmap->eq[done][1+last_var])(isl_sioimath_sgn(*(bmap->eq[done][1+last_var])) < 0))
	isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);

bmap = eliminate_var_using_equality(bmap, last_var,
				bmap->eq[done], 1, progress);

if (last_var >= total_var)
	bmap = set_div_from_eq(bmap, last_var - total_var,
				done, progress);
if (!bmap)
	return NULL((void*)0);
}
if (done == bmap->n_eq)
return bmap;
for (k = done; k < bmap->n_eq; ++k) {
if (isl_int_is_zero(bmap->eq[k][0])(isl_sioimath_sgn(*(bmap->eq[k][0])) == 0))
	continue;
if (drop && drop(bmap->n_eq, user) < 0)
	return isl_basic_map_free(bmap);
return isl_basic_map_set_to_empty(bmap);
}
n_drop = bmap->n_eq - done;
bmap = isl_basic_map_free_equality(bmap, n_drop);
if (drop && drop(n_drop, user) < 0)
return isl_basic_map_free(bmap);
return bmap;
659}

661__isl_give isl_basic_map *isl_basic_map_gauss(__isl_take isl_basic_map *bmap,
int *progress)
663{
return isl_basic_map_gauss5(bmap, progress, NULL((void*)0), NULL((void*)0), NULL((void*)0));
665}

667__isl_give isl_basic_setisl_basic_map *isl_basic_set_gauss(
__isl_take isl_basic_setisl_basic_map *bset, int *progress)
669{
return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset),
					progress));
672}


675static unsigned int round_up(unsigned int v)
676{
int old_v = v;

while (v) {
61
←
Loop condition is false. Execution continues on line 683→
old_v = v;
v ^= v & -v;
}
return old_v << 1;
62
←
Returning zero→
684}

686/* Hash table of inequalities in a basic map.
* "index" is an array of addresses of inequalities in the basic map, some
* of which are NULL.  The inequalities are hashed on the coefficients
* except the constant term.
* "size" is the number of elements in the array and is always a power of two
* "bits" is the number of bits need to represent an index into the array.
* "total" is the total dimension of the basic map.
*/
694struct isl_constraint_index {
unsigned int size;
int bits;
isl_int ***index;
isl_size total;
699};

701/* Fill in the "ci" data structure for holding the inequalities of "bmap".
*/
703static isl_stat create_constraint_index(struct isl_constraint_index *ci,
__isl_keep isl_basic_map *bmap)
705{
isl_ctx *ctx;

ci->index = NULL((void*)0);
if (!bmap54.1
'bmap' is non-null
)
55
←
Taking false branch→
return isl_stat_error;
ci->total = isl_basic_map_dim(bmap, isl_dim_all);
if (ci->total < 0)
56
←
Assuming field 'total' is >= 0→
57
←
Taking false branch→
return isl_stat_error;
if (bmap->n_ineq == 0)
58
←
Assuming field 'n_ineq' is not equal to 0→
59
←
Taking false branch→
return isl_stat_ok;
ci->size = round_up(4 * (bmap->n_ineq + 1) / 3 - 1);
60
←
Calling 'round_up'→
63
←
Returning from 'round_up'→
64
←
The value 0 is assigned to 'ci.size'→
ci->bits = ffs(ci->size) - 1;
ctx = isl_basic_map_get_ctx(bmap);
ci->index = isl_calloc_array(ctx, isl_int **, ci->size)((isl_int ** *)isl_calloc_or_die(ctx, ci->size, sizeof(isl_int
 **)));
if (!ci->index)
65
←
Assuming field 'index' is non-null→
66
←
Taking false branch→
return isl_stat_error;

return isl_stat_ok;
724}

726/* Free the memory allocated by create_constraint_index.
*/
728static void constraint_index_free(struct isl_constraint_index *ci)
729{
free(ci->index);
731}

733/* Return the position in ci->index that contains the address of
* an inequality that is equal to *ineq up to the constant term,
* provided this address is not identical to "ineq".
* If there is no such inequality, then return the position where
* such an inequality should be inserted.
*/
739static int hash_index_ineq(struct isl_constraint_index *ci, isl_int **ineq)
740{
int h;
uint32_t hash = isl_seq_get_hash_bits((*ineq) + 1, ci->total, ci->bits);
for (h = hash; ci->index[h]; h = (h+1) % ci->size)
74
←
Division by zero
if (ineq != ci->index[h] &&
73
←
Assuming the condition is false→
    isl_seq_eq((*ineq) + 1, ci->index[h][0]+1, ci->total))
	break;
return h;
748}

750/* Return the position in ci->index that contains the address of
* an inequality that is equal to the k'th inequality of "bmap"
* up to the constant term, provided it does not point to the very
* same inequality.
* If there is no such inequality, then return the position where
* such an inequality should be inserted.
*/
757static int hash_index(struct isl_constraint_index *ci,
__isl_keep isl_basic_map *bmap, int k)
759{
return hash_index_ineq(ci, &bmap->ineq[k]);
72
←
Calling 'hash_index_ineq'→
761}

763static int set_hash_index(struct isl_constraint_index *ci,
__isl_keep isl_basic_setisl_basic_map *bset, int k)
765{
return hash_index(ci, bset, k);
767}

769/* Fill in the "ci" data structure with the inequalities of "bset".
*/
771static isl_stat setup_constraint_index(struct isl_constraint_index *ci,
__isl_keep isl_basic_setisl_basic_map *bset)
773{
int k, h;

if (create_constraint_index(ci, bset) < 0)
return isl_stat_error;

for (k = 0; k < bset->n_ineq; ++k) {
h = set_hash_index(ci, bset, k);
ci->index[h] = &bset->ineq[k];
}

return isl_stat_ok;
785}

787/* Is the inequality ineq (obviously) redundant with respect
* to the constraints in "ci"?
*
* Look for an inequality in "ci" with the same coefficients and then
* check if the contant term of "ineq" is greater than or equal
* to the constant term of that inequality.  If so, "ineq" is clearly
* redundant.
*
* Note that hash_index_ineq ignores a stored constraint if it has
* the same address as the passed inequality.  It is ok to pass
* the address of a local variable here since it will never be
* the same as the address of a constraint in "ci".
*/
800static isl_bool constraint_index_is_redundant(struct isl_constraint_index *ci,
isl_int *ineq)
802{
int h;

h = hash_index_ineq(ci, &ineq);
if (!ci->index[h])
return isl_bool_false;
return isl_int_ge(ineq[0], (*ci->index[h])[0])(isl_sioimath_cmp(*(ineq[0]), *((*ci->index[h])[0])) >=
 0);
809}

811/* If we can eliminate more than one div, then we need to make
* sure we do it from last div to first div, in order not to
* change the position of the other divs that still need to
* be removed.
*/
816static __isl_give isl_basic_map *remove_duplicate_divs(
__isl_take isl_basic_map *bmap, int *progress)
818{
unsigned int size;
int *index;
int *elim_for;
int k, l, h;
int bits;
struct isl_blk eq;
isl_size v_div;
unsigned total;
struct isl_ctx *ctx;

bmap = isl_basic_map_order_divs(bmap);
if (!bmap || bmap->n_div <= 1)
return bmap;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_basic_map_free(bmap);
total = v_div + bmap->n_div;

ctx = bmap->ctx;
for (k = bmap->n_div - 1; k >= 0; --k)
if (!isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0))
	break;
if (k <= 0)
return bmap;

size = round_up(4 * bmap->n_div / 3 - 1);
if (size == 0)
return bmap;
elim_for = isl_calloc_array(ctx, int, bmap->n_div)((int *)isl_calloc_or_die(ctx, bmap->n_div, sizeof(int)));
bits = ffs(size) - 1;
index = isl_calloc_array(ctx, int, size)((int *)isl_calloc_or_die(ctx, size, sizeof(int)));
if (!elim_for || !index)
goto out;
eq = isl_blk_alloc(ctx, 1+total);
if (isl_blk_is_error(eq))
goto out;

isl_seq_clr(eq.data, 1+total);
index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
for (--k; k >= 0; --k) {
uint32_t hash;

if (isl_int_is_zero(bmap->div[k][0])(isl_sioimath_sgn(*(bmap->div[k][0])) == 0))
	continue;

hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
for (h = hash; index[h]; h = (h+1) % size)
	if (isl_seq_eq(bmap->div[k],
		       bmap->div[index[h]-1], 2+total))
		break;
if (index[h]) {
	*progress = 1;
	l = index[h] - 1;
	elim_for[l] = k + 1;
}
index[h] = k+1;
}
for (l = bmap->n_div - 1; l >= 0; --l) {
if (!elim_for[l])
	continue;
k = elim_for[l] - 1;
isl_int_set_si(eq.data[1 + v_div + k], -1)isl_sioimath_set_si((eq.data[1 + v_div + k]), -1);
isl_int_set_si(eq.data[1 + v_div + l], 1)isl_sioimath_set_si((eq.data[1 + v_div + l]), 1);
bmap = eliminate_div(bmap, eq.data, l, 1);
if (!bmap)
	break;
isl_int_set_si(eq.data[1 + v_div + k], 0)isl_sioimath_set_si((eq.data[1 + v_div + k]), 0);
isl_int_set_si(eq.data[1 + v_div + l], 0)isl_sioimath_set_si((eq.data[1 + v_div + l]), 0);
}

isl_blk_free(ctx, eq);
891out:
free(index);
free(elim_for);
return bmap;
895}

897static int n_pure_div_eq(__isl_keep isl_basic_map *bmap)
898{
int i, j;
isl_size v_div;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return -1;
for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + v_div + j])(isl_sioimath_sgn(*(bmap->eq[i][1 + v_div + j])) == 0))
	--j;
if (j < 0)
	break;
if (isl_seq_first_non_zero(bmap->eq[i] + 1 + v_div, j) != -1)
	return 0;
}
return i;
914}

916/* Normalize divs that appear in equalities.
*
* In particular, we assume that bmap contains some equalities
* of the form
*
*	a x = m * e_i
*
* and we want to replace the set of e_i by a minimal set and
* such that the new e_i have a canonical representation in terms
* of the vector x.
* If any of the equalities involves more than one divs, then
* we currently simply bail out.
*
* Let us first additionally assume that all equalities involve
* a div.  The equalities then express modulo constraints on the
* remaining variables and we can use "parameter compression"
* to find a minimal set of constraints.  The result is a transformation
*
*	x = T(x') = x_0 + G x'
*
* with G a lower-triangular matrix with all elements below the diagonal
* non-negative and smaller than the diagonal element on the same row.
* We first normalize x_0 by making the same property hold in the affine
* T matrix.
* The rows i of G with a 1 on the diagonal do not impose any modulo
* constraint and simply express x_i = x'_i.
* For each of the remaining rows i, we introduce a div and a corresponding
* equality.  In particular
*
*	g_ii e_j = x_i - g_i(x')
*
* where each x'_k is replaced either by x_k (if g_kk = 1) or the
* corresponding div (if g_kk != 1).
*
* If there are any equalities not involving any div, then we
* first apply a variable compression on the variables x:
*
*	x = C x''	x'' = C_2 x
*
* and perform the above parameter compression on A C instead of on A.
* The resulting compression is then of the form
*
*	x'' = T(x') = x_0 + G x'
*
* and in constructing the new divs and the corresponding equalities,
* we have to replace each x'', i.e., the x'_k with (g_kk = 1),
* by the corresponding row from C_2.
*/
964static __isl_give isl_basic_map *normalize_divs(__isl_take isl_basic_map *bmap,
int *progress)
966{
int i, j, k;
isl_size v_div;
int div_eq;
struct isl_mat *B;
struct isl_vec *d;
struct isl_mat *T = NULL((void*)0);
struct isl_mat *C = NULL((void*)0);
struct isl_mat *C2 = NULL((void*)0);
isl_int v;
int *pos = NULL((void*)0);
int dropped, needed;

if (!bmap)
return NULL((void*)0);

if (bmap->n_div == 0)
return bmap;

if (bmap->n_eq == 0)
return bmap;

if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS)(!!(((bmap)->flags) & ((1 << 6)))))
return bmap;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
div_eq = n_pure_div_eq(bmap);
if (v_div < 0 || div_eq < 0)
return isl_basic_map_free(bmap);
if (div_eq == 0)
return bmap;

if (div_eq < bmap->n_eq) {
B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
			bmap->n_eq - div_eq, 0, 1 + v_div);
C = isl_mat_variable_compression(B, &C2);
if (!C || !C2)
	goto error;
if (C->n_col == 0) {
	bmap = isl_basic_map_set_to_empty(bmap);
	isl_mat_free(C);
	isl_mat_free(C2);
	goto done;
}
}

d = isl_vec_alloc(bmap->ctx, div_eq);
if (!d)
goto error;
for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + v_div + j])(isl_sioimath_sgn(*(bmap->eq[i][1 + v_div + j])) == 0))
	--j;
isl_int_set(d->block.data[i], bmap->eq[i][1 + v_div + j])isl_sioimath_set((d->block.data[i]), *(bmap->eq[i][1 + v_div
 + j]));
}
B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + v_div);

if (C) {
B = isl_mat_product(B, C);
C = NULL((void*)0);
}

T = isl_mat_parameter_compression(B, d);
if (!T)
goto error;
if (T->n_col == 0) {
bmap = isl_basic_map_set_to_empty(bmap);
isl_mat_free(C2);
isl_mat_free(T);
goto done;
}
isl_int_init(v)isl_sioimath_init((v));
for (i = 0; i < T->n_row - 1; ++i) {
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[
+ i][1 + i]));
if (isl_int_is_zero(v)(isl_sioimath_sgn(*(v)) == 0))
	continue;
isl_mat_col_submul(T, 0, v, 1 + i);
}
isl_int_clear(v)isl_sioimath_clear((v));
pos = isl_alloc_array(bmap->ctx, int, T->n_row)((int *)isl_malloc_or_die(bmap->ctx, (T->n_row)*sizeof(
int)));
if (!pos)
goto error;
/* We have to be careful because dropping equalities may reorder them */
dropped = 0;
for (j = bmap->n_div - 1; j >= 0; --j) {
for (i = 0; i < bmap->n_eq; ++i)
	if (!isl_int_is_zero(bmap->eq[i][1 + v_div + j])(isl_sioimath_sgn(*(bmap->eq[i][1 + v_div + j])) == 0))
		break;
if (i < bmap->n_eq) {
	bmap = isl_basic_map_drop_div(bmap, j);
	if (isl_basic_map_drop_equality(bmap, i) < 0)
		goto error;
	++dropped;
}
}
pos[0] = 0;
needed = 0;
for (i = 1; i < T->n_row; ++i) {
if (isl_int_is_one(T->row[i][i])(isl_sioimath_cmp_si(*(T->row[i][i]), 1) == 0))
	pos[i] = i;
else
	needed++;
}
if (needed > dropped) {
bmap = isl_basic_map_extend(bmap, needed, needed, 0);
if (!bmap)
	goto error;
}
for (i = 1; i < T->n_row; ++i) {
if (isl_int_is_one(T->row[i][i])(isl_sioimath_cmp_si(*(T->row[i][i]), 1) == 0))
	continue;
k = isl_basic_map_alloc_div(bmap);
pos[i] = 1 + v_div + k;
isl_seq_clr(bmap->div[k] + 1, 1 + v_div + bmap->n_div);
isl_int_set(bmap->div[k][0], T->row[i][i])isl_sioimath_set((bmap->div[k][0]), *(T->row[i][i]));
if (C2)
	isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + v_div);
else
	isl_int_set_si(bmap->div[k][1 + i], 1)isl_sioimath_set_si((bmap->div[k][1 + i]), 1);
for (j = 0; j < i; ++j) {
	if (isl_int_is_zero(T->row[i][j])(isl_sioimath_sgn(*(T->row[i][j])) == 0))
		continue;
	if (pos[j] < T->n_row && C2)
		isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
				C2->row[pos[j]], 1 + v_div);
	else
		isl_int_neg(bmap->div[k][1 + pos[j]],isl_sioimath_neg((bmap->div[k][1 + pos[j]]), *(T->row[i
][j]))
						T->row[i][j])isl_sioimath_neg((bmap->div[k][1 + pos[j]]), *(T->row[i
][j]));
}
j = isl_basic_map_alloc_equality(bmap);
isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+v_div+bmap->n_div);
isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0])isl_sioimath_set((bmap->eq[j][pos[i]]), *(bmap->div[k][
0]));
}
free(pos);
isl_mat_free(C2);
isl_mat_free(T);

if (progress)
*progress = 1;
1104done:
ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS)(((bmap)->flags) |= ((1 << 6)));

return bmap;
1108error:
free(pos);
isl_mat_free(C);
isl_mat_free(C2);
isl_mat_free(T);
isl_basic_map_free(bmap);
return NULL((void*)0);
1115}

1117static __isl_give isl_basic_map *set_div_from_lower_bound(
__isl_take isl_basic_map *bmap, int div, int ineq)
1119{
unsigned total = isl_basic_map_offset(bmap, isl_dim_div);

isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div])isl_sioimath_set((bmap->div[div][0]), *(bmap->ineq[ineq
][total + div]));
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]));
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);
isl_int_set_si(bmap->div[div][1 + total + div], 0)isl_sioimath_set_si((bmap->div[div][1 + total + div]), 0);

return bmap;
1129}

1131/* Check whether it is ok to define a div based on an inequality.
* To avoid the introduction of circular definitions of divs, we
* do not allow such a definition if the resulting expression would refer to
* any other undefined divs or if any known div is defined in
* terms of the unknown div.
*/
1137static isl_bool ok_to_set_div_from_bound(__isl_keep isl_basic_map *bmap,
int div, int ineq)
1139{
int j;
unsigned total = isl_basic_map_offset(bmap, isl_dim_div);

/* Not defined in terms of unknown divs */
for (j = 0; j < bmap->n_div; ++j) {
if (div == j)
	continue;
if (isl_int_is_zero(bmap->ineq[ineq][total + j])(isl_sioimath_sgn(*(bmap->ineq[ineq][total + j])) == 0))
	continue;
if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0))
	return isl_bool_false;
}

/* No other div defined in terms of this one => avoid loops */
for (j = 0; j < bmap->n_div; ++j) {
if (div == j)
	continue;
if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0))
	continue;
if (!isl_int_is_zero(bmap->div[j][1 + total + div])(isl_sioimath_sgn(*(bmap->div[j][1 + total + div])) == 0))
	return isl_bool_false;
}

return isl_bool_true;
1164}

1166/* Would an expression for div "div" based on inequality "ineq" of "bmap"
* be a better expression than the current one?
*
* If we do not have any expression yet, then any expression would be better.
* Otherwise we check if the last variable involved in the inequality
* (disregarding the div that it would define) is in an earlier position
* than the last variable involved in the current div expression.
*/
1174static isl_bool better_div_constraint(__isl_keep isl_basic_map *bmap,
int div, int ineq)
1176{
unsigned total = isl_basic_map_offset(bmap, isl_dim_div);
int last_div;
int last_ineq;

if (isl_int_is_zero(bmap->div[div][0])(isl_sioimath_sgn(*(bmap->div[div][0])) == 0))
return isl_bool_true;

if (isl_seq_last_non_zero(bmap->ineq[ineq] + total + div + 1,
		  bmap->n_div - (div + 1)) >= 0)
return isl_bool_false;

last_ineq = isl_seq_last_non_zero(bmap->ineq[ineq], total + div);
last_div = isl_seq_last_non_zero(bmap->div[div] + 1,
			 total + bmap->n_div);

return last_ineq < last_div;
1193}

1195/* Given two constraints "k" and "l" that are opposite to each other,
* except for the constant term, check if we can use them
* to obtain an expression for one of the hitherto unknown divs or
* a "better" expression for a div for which we already have an expression.
* "sum" is the sum of the constant terms of the constraints.
* If this sum is strictly smaller than the coefficient of one
* of the divs, then this pair can be used to define the div.
* To avoid the introduction of circular definitions of divs, we
* do not use the pair if the resulting expression would refer to
* any other undefined divs or if any known div is defined in
* terms of the unknown div.
*/
1207static __isl_give isl_basic_map *check_for_div_constraints(
__isl_take isl_basic_map *bmap, int k, int l, isl_int sum,
int *progress)
1210{
int i;
unsigned total = isl_basic_map_offset(bmap, isl_dim_div);

for (i = 0; i < bmap->n_div; ++i) {
isl_bool set_div;

if (isl_int_is_zero(bmap->ineq[k][total + i])(isl_sioimath_sgn(*(bmap->ineq[k][total + i])) == 0))
	continue;
if (isl_int_abs_ge(sum, bmap->ineq[k][total + i])(isl_sioimath_abs_cmp(*(sum), *(bmap->ineq[k][total + i]))
 >= 0))
	continue;
set_div = better_div_constraint(bmap, i, k);
if (set_div >= 0 && set_div)
	set_div = ok_to_set_div_from_bound(bmap, i, k);
if (set_div < 0)
	return isl_basic_map_free(bmap);
if (!set_div)
	break;
if (isl_int_is_pos(bmap->ineq[k][total + i])(isl_sioimath_sgn(*(bmap->ineq[k][total + i])) > 0))
	bmap = set_div_from_lower_bound(bmap, i, k);
else
	bmap = set_div_from_lower_bound(bmap, i, l);
if (progress)
	*progress = 1;
break;
}
return bmap;
1237}

1239__isl_give isl_basic_map *isl_basic_map_remove_duplicate_constraints(
__isl_take isl_basic_map *bmap, int *progress, int detect_divs)
1241{
struct isl_constraint_index ci;
int k, l, h;
isl_size total = isl_basic_map_dim(bmap, isl_dim_all);
isl_int sum;

if (total < 0 || bmap->n_ineq <= 1)
51
←
Assuming 'total' is >= 0→
52
←
Assuming field 'n_ineq' is > 1→
53
←
Taking false branch→
return bmap;

if (create_constraint_index(&ci, bmap) < 0)
54
←
Calling 'create_constraint_index'→
67
←
Returning from 'create_constraint_index'→
68
←
Taking false branch→
return bmap;

h = isl_seq_get_hash_bits(bmap->ineq[0] + 1, total, ci.bits);
ci.index[h] = &bmap->ineq[0];
for (k = 1; k < bmap->n_ineq; ++k) {
69
←
Assuming 'k' is < field 'n_ineq'→
70
←
Loop condition is true.  Entering loop body→
h = hash_index(&ci, bmap, k);
71
←
Calling 'hash_index'→
if (!ci.index[h]) {
	ci.index[h] = &bmap->ineq[k];
	continue;
}
if (progress)
	*progress = 1;
l = ci.index[h] - &bmap->ineq[0];
if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0])(isl_sioimath_cmp(*(bmap->ineq[k][0]), *(bmap->ineq[l][
0])) < 0))
	swap_inequality(bmap, k, l);
isl_basic_map_drop_inequality(bmap, k);
--k;
}
isl_int_init(sum)isl_sioimath_init((sum));
for (k = 0; bmap && k < bmap->n_ineq-1; ++k) {
isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
h = hash_index(&ci, bmap, k);
isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
if (!ci.index[h])
	continue;
l = ci.index[h] - &bmap->ineq[0];
isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0])isl_sioimath_add((sum), *(bmap->ineq[k][0]), *(bmap->ineq
[l][0]));
if (isl_int_is_pos(sum)(isl_sioimath_sgn(*(sum)) > 0)) {
	if (detect_divs)
		bmap = check_for_div_constraints(bmap, k, l,
						 sum, progress);
	continue;
}
if (isl_int_is_zero(sum)(isl_sioimath_sgn(*(sum)) == 0)) {
	/* We need to break out of the loop after these
	 * changes since the contents of the hash
	 * will no longer be valid.
	 * Plus, we probably we want to regauss first.
	 */
	if (progress)
		*progress = 1;
	isl_basic_map_drop_inequality(bmap, l);
	isl_basic_map_inequality_to_equality(bmap, k);
} else
	bmap = isl_basic_map_set_to_empty(bmap);
break;
}
isl_int_clear(sum)isl_sioimath_clear((sum));

constraint_index_free(&ci);
return bmap;
1302}

1304/* Detect all pairs of inequalities that form an equality.
*
* isl_basic_map_remove_duplicate_constraints detects at most one such pair.
* Call it repeatedly while it is making progress.
*/
1309__isl_give isl_basic_map *isl_basic_map_detect_inequality_pairs(
__isl_take isl_basic_map *bmap, int *progress)
1311{
int duplicate;

do {
duplicate = 0;
bmap = isl_basic_map_remove_duplicate_constraints(bmap,
50
←
Calling 'isl_basic_map_remove_duplicate_constraints'→
						&duplicate, 0);
if (progress && duplicate)
	*progress = 1;
} while (duplicate);

return bmap;
1323}

1325/* Given a known integer division "div" that is not integral
* (with denominator 1), eliminate it from the constraints in "bmap"
* where it appears with a (positive or negative) unit coefficient.
* If "progress" is not NULL, then it gets set if the elimination
* results in any changes.
*
* That is, replace
*
*	floor(e/m) + f >= 0
*
* by
*
*	e + m f >= 0
*
* and
*
*	-floor(e/m) + f >= 0
*
* by
*
*	-e + m f + m - 1 >= 0
*
* The first conversion is valid because floor(e/m) >= -f is equivalent
* to e/m >= -f because -f is an integral expression.
* The second conversion follows from the fact that
*
*	-floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
*
*
* Note that one of the div constraints may have been eliminated
* due to being redundant with respect to the constraint that is
* being modified by this function.  The modified constraint may
* no longer imply this div constraint, so we add it back to make
* sure we do not lose any information.
*/
1360static __isl_give isl_basic_map *eliminate_unit_div(
__isl_take isl_basic_map *bmap, int div, int *progress)
1362{
int j;
isl_size v_div, dim;
isl_ctx *ctx;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
dim = isl_basic_map_dim(bmap, isl_dim_all);
if (v_div < 0 || dim < 0)
return isl_basic_map_free(bmap);

ctx = isl_basic_map_get_ctx(bmap);

for (j = 0; j < bmap->n_ineq; ++j) {
int s;

if (!isl_int_is_one(bmap->ineq[j][1 + v_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[j][1 + v_div + div]), 1)
 == 0) &&
    !isl_int_is_negone(bmap->ineq[j][1 + v_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[j][1 + v_div + div]), -1
) == 0))
	continue;

if (progress)
	*progress = 1;

s = isl_int_sgn(bmap->ineq[j][1 + v_div + div])isl_sioimath_sgn(*(bmap->ineq[j][1 + v_div + div]));
isl_int_set_si(bmap->ineq[j][1 + v_div + div], 0)isl_sioimath_set_si((bmap->ineq[j][1 + v_div + div]), 0);
if (s < 0)
	isl_seq_combine(bmap->ineq[j],
		ctx->negone, bmap->div[div] + 1,
		bmap->div[div][0], bmap->ineq[j], 1 + dim);
else
	isl_seq_combine(bmap->ineq[j],
		ctx->one, bmap->div[div] + 1,
		bmap->div[div][0], bmap->ineq[j], 1 + dim);
if (s < 0) {
	isl_int_add(bmap->ineq[j][0],isl_sioimath_add((bmap->ineq[j][0]), *(bmap->ineq[j][0]
), *(bmap->div[div][0]))
		bmap->ineq[j][0], bmap->div[div][0])isl_sioimath_add((bmap->ineq[j][0]), *(bmap->ineq[j][0]
), *(bmap->div[div][0]));
	isl_int_sub_ui(bmap->ineq[j][0],isl_sioimath_sub_ui((bmap->ineq[j][0]), *(bmap->ineq[j]
[0]), 1)
		bmap->ineq[j][0], 1)isl_sioimath_sub_ui((bmap->ineq[j][0]), *(bmap->ineq[j]
[0]), 1);
}

bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
bmap = isl_basic_map_add_div_constraint(bmap, div, s);
if (!bmap)
	return NULL((void*)0);
}

return bmap;
1408}

1410/* Eliminate selected known divs from constraints where they appear with
* a (positive or negative) unit coefficient.
* In particular, only handle those for which "select" returns isl_bool_true.
* If "progress" is not NULL, then it gets set if the elimination
* results in any changes.
*
* We skip integral divs, i.e., those with denominator 1, as we would
* risk eliminating the div from the div constraints.  We do not need
* to handle those divs here anyway since the div constraints will turn
* out to form an equality and this equality can then be used to eliminate
* the div from all constraints.
*/
1422static __isl_give isl_basic_map *eliminate_selected_unit_divs(
__isl_take isl_basic_map *bmap,
isl_bool (*select)(__isl_keep isl_basic_map *bmap, int div),
int *progress)
1426{
int i;

if (!bmap)
return NULL((void*)0);

for (i = 0; i < bmap->n_div; ++i) {
isl_bool selected;

if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
	continue;
if (isl_int_is_one(bmap->div[i][0])(isl_sioimath_cmp_si(*(bmap->div[i][0]), 1) == 0))
	continue;
selected = select(bmap, i);
if (selected < 0)
	return isl_basic_map_free(bmap);
if (!selected)
	continue;
bmap = eliminate_unit_div(bmap, i, progress);
if (!bmap)
	return NULL((void*)0);
}

return bmap;
1450}

1452/* eliminate_selected_unit_divs callback that selects every
* integer division.
*/
1455static isl_bool is_any_div(__isl_keep isl_basic_map *bmap, int div)
1456{
return isl_bool_true;
1458}

1460/* Eliminate known divs from constraints where they appear with
* a (positive or negative) unit coefficient.
* If "progress" is not NULL, then it gets set if the elimination
* results in any changes.
*/
1465static __isl_give isl_basic_map *eliminate_unit_divs(
__isl_take isl_basic_map *bmap, int *progress)
1467{
return eliminate_selected_unit_divs(bmap, &is_any_div, progress);
1469}

1471/* eliminate_selected_unit_divs callback that selects
* integer divisions that only appear with
* a (positive or negative) unit coefficient
* (outside their div constraints).
*/
1476static isl_bool is_pure_unit_div(__isl_keep isl_basic_map *bmap, int div)
1477{
int i;
isl_size v_div, n_ineq;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
n_ineq = isl_basic_map_n_inequality(bmap);
if (v_div < 0 || n_ineq < 0)
return isl_bool_error;

for (i = 0; i < n_ineq; ++i) {
isl_bool skip;

if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div])) == 0))
	continue;
skip = isl_basic_map_is_div_constraint(bmap,
					bmap->ineq[i], div);
if (skip < 0)
	return isl_bool_error;
if (skip)
	continue;
if (!isl_int_is_one(bmap->ineq[i][1 + v_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[i][1 + v_div + div]), 1)
 == 0) &&
    !isl_int_is_negone(bmap->ineq[i][1 + v_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[i][1 + v_div + div]), -1
) == 0))
	return isl_bool_false;
}

return isl_bool_true;
1503}

1505/* Eliminate known divs from constraints where they appear with
* a (positive or negative) unit coefficient,
* but only if they do not appear in any other constraints
* (other than the div constraints).
*/
1510__isl_give isl_basic_map *isl_basic_map_eliminate_pure_unit_divs(
__isl_take isl_basic_map *bmap)
1512{
return eliminate_selected_unit_divs(bmap, &is_pure_unit_div, NULL((void*)0));
1514}

1516__isl_give isl_basic_map *isl_basic_map_simplify(__isl_take isl_basic_map *bmap)
1517{
int progress = 1;
if (!bmap)
return NULL((void*)0);
while (progress) {
isl_bool empty;

progress = 0;
empty = isl_basic_map_plain_is_empty(bmap);
if (empty < 0)
	return isl_basic_map_free(bmap);
if (empty)
	break;
bmap = isl_basic_map_normalize_constraints(bmap);
bmap = reduce_div_coefficients(bmap);
bmap = normalize_div_expressions(bmap);
bmap = remove_duplicate_divs(bmap, &progress);
bmap = eliminate_unit_divs(bmap, &progress);
bmap = eliminate_divs_eq(bmap, &progress);
bmap = eliminate_divs_ineq(bmap, &progress);
bmap = isl_basic_map_gauss(bmap, &progress);
/* requires equalities in normal form */
bmap = normalize_divs(bmap, &progress);
bmap = isl_basic_map_remove_duplicate_constraints(bmap,
						&progress, 1);
if (bmap && progress)
	ISL_F_CLR(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(((bmap)->flags) &= ~((1 << 8)));
}
return bmap;
1546}

1548__isl_give isl_basic_setisl_basic_map *isl_basic_set_simplify(
__isl_take isl_basic_setisl_basic_map *bset)
1550{
return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset)));
1552}


1555isl_bool isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
isl_int *constraint, unsigned div)
1557{
unsigned pos;

if (!bmap)
return isl_bool_error;

pos = isl_basic_map_offset(bmap, isl_dim_div) + div;

if (isl_int_eq(constraint[pos], bmap->div[div][0])(isl_sioimath_cmp(*(constraint[pos]), *(bmap->div[div][0])
) == 0)) {
int neg;
isl_int_sub(bmap->div[div][1],isl_sioimath_sub((bmap->div[div][1]), *(bmap->div[div][
1]), *(bmap->div[div][0]))
		bmap->div[div][1], bmap->div[div][0])isl_sioimath_sub((bmap->div[div][1]), *(bmap->div[div][
1]), *(bmap->div[div][0]));
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);
neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
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);
isl_int_add(bmap->div[div][1],isl_sioimath_add((bmap->div[div][1]), *(bmap->div[div][
1]), *(bmap->div[div][0]))
		bmap->div[div][1], bmap->div[div][0])isl_sioimath_add((bmap->div[div][1]), *(bmap->div[div][
1]), *(bmap->div[div][0]));
if (!neg)
	return isl_bool_false;
if (isl_seq_first_non_zero(constraint+pos+1,
			    bmap->n_div-div-1) != -1)
	return isl_bool_false;
} else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])(isl_sioimath_abs_cmp(*(constraint[pos]), *(bmap->div[div]
[0])) == 0)) {
if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
	return isl_bool_false;
if (isl_seq_first_non_zero(constraint+pos+1,
			    bmap->n_div-div-1) != -1)
	return isl_bool_false;
} else
return isl_bool_false;

return isl_bool_true;
1589}

1591/* If the only constraints a div d=floor(f/m)
* appears in are its two defining constraints
*
*	f - m d >=0
*	-(f - (m - 1)) + m d >= 0
*
* then it can safely be removed.
*/
1599static isl_bool div_is_redundant(__isl_keep isl_basic_map *bmap, int div)
1600{
int i;
isl_size v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
unsigned pos = 1 + v_div + div;

if (v_div < 0)
return isl_bool_error;

for (i = 0; i < bmap->n_eq; ++i)
if (!isl_int_is_zero(bmap->eq[i][pos])(isl_sioimath_sgn(*(bmap->eq[i][pos])) == 0))
	return isl_bool_false;

for (i = 0; i < bmap->n_ineq; ++i) {
isl_bool red;

if (isl_int_is_zero(bmap->ineq[i][pos])(isl_sioimath_sgn(*(bmap->ineq[i][pos])) == 0))
	continue;
red = isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div);
if (red < 0 || !red)
	return red;
}

for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
	continue;
if (!isl_int_is_zero(bmap->div[i][1+pos])(isl_sioimath_sgn(*(bmap->div[i][1+pos])) == 0))
	return isl_bool_false;
}

return isl_bool_true;
1630}

1632/*
* Remove divs that don't occur in any of the constraints or other divs.
* These can arise when dropping constraints from a basic map or
* when the divs of a basic map have been temporarily aligned
* with the divs of another basic map.
*/
1638static __isl_give isl_basic_map *remove_redundant_divs(
__isl_take isl_basic_map *bmap)
1640{
int i;
isl_size v_div;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_basic_map_free(bmap);

for (i = bmap->n_div-1; i >= 0; --i) {
isl_bool redundant;

redundant = div_is_redundant(bmap, i);
if (redundant < 0)
	return isl_basic_map_free(bmap);
if (!redundant)
	continue;
bmap = isl_basic_map_drop_constraints_involving(bmap,
						v_div + i, 1);
bmap = isl_basic_map_drop_div(bmap, i);
}
return bmap;
1661}

1663/* Mark "bmap" as final, without checking for obviously redundant
* integer divisions.  This function should be used when "bmap"
* is known not to involve any such integer divisions.
*/
1667__isl_give isl_basic_map *isl_basic_map_mark_final(
__isl_take isl_basic_map *bmap)
1669{
if (!bmap)
return NULL((void*)0);
ISL_F_SET(bmap, ISL_BASIC_SET_FINAL)(((bmap)->flags) |= ((1 << 0)));
return bmap;
1674}

1676/* Mark "bmap" as final, after removing obviously redundant integer divisions.
*/
1678__isl_give isl_basic_map *isl_basic_map_finalize(__isl_take isl_basic_map *bmap)
1679{
bmap = remove_redundant_divs(bmap);
bmap = isl_basic_map_mark_final(bmap);
return bmap;
1683}

1685__isl_give isl_basic_setisl_basic_map *isl_basic_set_finalize(
__isl_take isl_basic_setisl_basic_map *bset)
1687{
return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset)));
1689}

1691/* Remove definition of any div that is defined in terms of the given variable.
* The div itself is not removed.  Functions such as
* eliminate_divs_ineq depend on the other divs remaining in place.
*/
1695static __isl_give isl_basic_map *remove_dependent_vars(
__isl_take isl_basic_map *bmap, int pos)
1697{
int i;

if (!bmap)
return NULL((void*)0);

for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
	continue;
if (isl_int_is_zero(bmap->div[i][1+1+pos])(isl_sioimath_sgn(*(bmap->div[i][1+1+pos])) == 0))
	continue;
bmap = isl_basic_map_mark_div_unknown(bmap, i);
if (!bmap)
	return NULL((void*)0);
}
return bmap;
1713}

1715/* Eliminate the specified variables from the constraints using
* Fourier-Motzkin.  The variables themselves are not removed.
*/
1718__isl_give isl_basic_map *isl_basic_map_eliminate_vars(
__isl_take isl_basic_map *bmap, unsigned pos, unsigned n)
1720{
int d;
int i, j, k;
isl_size total;
int need_gauss = 0;

if (n == 0)
return bmap;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);

bmap = isl_basic_map_cow(bmap);
for (d = pos + n - 1; d >= 0 && d >= pos; --d)
bmap = remove_dependent_vars(bmap, d);
if (!bmap)
return NULL((void*)0);

for (d = pos + n - 1;
    d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
int n_lower, n_upper;
if (!bmap)
	return NULL((void*)0);
for (i = 0; i < bmap->n_eq; ++i) {
	if (isl_int_is_zero(bmap->eq[i][1+d])(isl_sioimath_sgn(*(bmap->eq[i][1+d])) == 0))
		continue;
	bmap = eliminate_var_using_equality(bmap, d,
					bmap->eq[i], 0, NULL((void*)0));
	if (isl_basic_map_drop_equality(bmap, i) < 0)
		return isl_basic_map_free(bmap);
	need_gauss = 1;
	break;
}
if (i < bmap->n_eq)
	continue;
n_lower = 0;
n_upper = 0;
for (i = 0; i < bmap->n_ineq; ++i) {
	if (isl_int_is_pos(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) > 0))
		n_lower++;
	else if (isl_int_is_neg(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) < 0))
		n_upper++;
}
bmap = isl_basic_map_extend_constraints(bmap,
		0, n_lower * n_upper);
if (!bmap)
	goto error;
for (i = bmap->n_ineq - 1; i >= 0; --i) {
	int last;
	if (isl_int_is_zero(bmap->ineq[i][1+d])(isl_sioimath_sgn(*(bmap->ineq[i][1+d])) == 0))
		continue;
	last = -1;
	for (j = 0; j < i; ++j) {
		if (isl_int_is_zero(bmap->ineq[j][1+d])(isl_sioimath_sgn(*(bmap->ineq[j][1+d])) == 0))
			continue;
		last = j;
		if (isl_int_sgn(bmap->ineq[i][1+d])isl_sioimath_sgn(*(bmap->ineq[i][1+d])) ==
		    isl_int_sgn(bmap->ineq[j][1+d])isl_sioimath_sgn(*(bmap->ineq[j][1+d])))
			continue;
		k = isl_basic_map_alloc_inequality(bmap);
		if (k < 0)
			goto error;
		isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
				1+total);
		isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
				1+d, 1+total, NULL((void*)0));
	}
	isl_basic_map_drop_inequality(bmap, i);
	i = last + 1;
}
if (n_lower > 0 && n_upper > 0) {
	bmap = isl_basic_map_normalize_constraints(bmap);
	bmap = isl_basic_map_remove_duplicate_constraints(bmap,
						    NULL((void*)0), 0);
	bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
	bmap = isl_basic_map_remove_redundancies(bmap);
	need_gauss = 0;
	if (!bmap)
		goto error;
	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1)))))
		break;
}
}
if (need_gauss)
bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
return bmap;
1808error:
isl_basic_map_free(bmap);
return NULL((void*)0);
1811}

1813__isl_give isl_basic_setisl_basic_map *isl_basic_set_eliminate_vars(
__isl_take isl_basic_setisl_basic_map *bset, unsigned pos, unsigned n)
1815{
return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset),
						pos, n));
1818}

1820/* Eliminate the specified n dimensions starting at first from the
* constraints, without removing the dimensions from the space.
* If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
* Otherwise, they are projected out and the original space is restored.
*/
1825__isl_give isl_basic_map *isl_basic_map_eliminate(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, unsigned first, unsigned n)
1828{
isl_space *space;

if (!bmap)
return NULL((void*)0);
if (n == 0)
return bmap;

if (isl_basic_map_check_range(bmap, type, first, n) < 0)
return isl_basic_map_free(bmap);

if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4))))) {
first += isl_basic_map_offset(bmap, type) - 1;
bmap = isl_basic_map_eliminate_vars(bmap, first, n);
return isl_basic_map_finalize(bmap);
}

space = isl_basic_map_get_space(bmap);
bmap = isl_basic_map_project_out(bmap, type, first, n);
bmap = isl_basic_map_insert_dims(bmap, type, first, n);
bmap = isl_basic_map_reset_space(bmap, space);
return bmap;
1850}

1852__isl_give isl_basic_setisl_basic_map *isl_basic_set_eliminate(
__isl_take isl_basic_setisl_basic_map *bset,
enum isl_dim_type type, unsigned first, unsigned n)
1855{
return isl_basic_map_eliminate(bset, type, first, n);
1857}

1859/* Remove all constraints from "bmap" that reference any unknown local
* variables (directly or indirectly).
*
* Dropping all constraints on a local variable will make it redundant,
* so it will get removed implicitly by
* isl_basic_map_drop_constraints_involving_dims.  Some other local
* variables may also end up becoming redundant if they only appear
* in constraints together with the unknown local variable.
* Therefore, start over after calling
* isl_basic_map_drop_constraints_involving_dims.
*/
1870__isl_give isl_basic_map *isl_basic_map_drop_constraints_involving_unknown_divs(
__isl_take isl_basic_map *bmap)
1872{
isl_bool known;
isl_size n_div;
int i, o_div;

known = isl_basic_map_divs_known(bmap);
if (known < 0)
return isl_basic_map_free(bmap);
if (known)
return bmap;

n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
return isl_basic_map_free(bmap);
o_div = isl_basic_map_offset(bmap, isl_dim_div) - 1;

for (i = 0; i < n_div; ++i) {
known = isl_basic_map_div_is_known(bmap, i);
if (known < 0)
	return isl_basic_map_free(bmap);
if (known)
	continue;
bmap = remove_dependent_vars(bmap, o_div + i);
bmap = isl_basic_map_drop_constraints_involving_dims(bmap,
					    isl_dim_div, i, 1);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
	return isl_basic_map_free(bmap);
i = -1;
}

return bmap;
1904}

1906/* Remove all constraints from "bset" that reference any unknown local
* variables (directly or indirectly).
*/
1909__isl_give isl_basic_setisl_basic_map *isl_basic_set_drop_constraints_involving_unknown_divs(
__isl_take isl_basic_setisl_basic_map *bset)
1911{
isl_basic_map *bmap;

bmap = bset_to_bmap(bset);
bmap = isl_basic_map_drop_constraints_involving_unknown_divs(bmap);
return bset_from_bmap(bmap);
1917}

1919/* Remove all constraints from "map" that reference any unknown local
* variables (directly or indirectly).
*
* Since constraints may get dropped from the basic maps,
* they may no longer be disjoint from each other.
*/
1925__isl_give isl_map *isl_map_drop_constraints_involving_unknown_divs(
__isl_take isl_map *map)
1927{
int i;
isl_bool known;

known = isl_map_divs_known(map);
if (known < 0)
return isl_map_free(map);
if (known)
return map;

map = isl_map_cow(map);
if (!map)
return NULL((void*)0);

for (i = 0; i < map->n; ++i) {
map->p[i] =
    isl_basic_map_drop_constraints_involving_unknown_divs(
						    map->p[i]);
if (!map->p[i])
	return isl_map_free(map);
}

if (map->n > 1)
ISL_F_CLR(map, ISL_MAP_DISJOINT)(((map)->flags) &= ~((1 << 0)));

return map;
1953}

1955/* Don't assume equalities are in order, because align_divs
* may have changed the order of the divs.
*/
1958static void compute_elimination_index(__isl_keep isl_basic_map *bmap, int *elim,
unsigned len)
1960{
int d, i;

for (d = 0; d < len; ++d)
elim[d] = -1;
for (i = 0; i < bmap->n_eq; ++i) {
for (d = len - 1; d >= 0; --d) {
	if (isl_int_is_zero(bmap->eq[i][1+d])(isl_sioimath_sgn(*(bmap->eq[i][1+d])) == 0))
		continue;
	elim[d] = i;
	break;
}
}
1973}

1975static void set_compute_elimination_index(__isl_keep isl_basic_setisl_basic_map *bset,
int *elim, unsigned len)
1977{
compute_elimination_index(bset_to_bmap(bset), elim, len);
1979}

1981static int reduced_using_equalities(isl_int *dst, isl_int *src,
__isl_keep isl_basic_map *bmap, int *elim, unsigned total)
1983{
int d;
int copied = 0;

for (d = total - 1; d >= 0; --d) {
if (isl_int_is_zero(src[1+d])(isl_sioimath_sgn(*(src[1+d])) == 0))
	continue;
if (elim[d] == -1)
	continue;
if (!copied) {
	isl_seq_cpy(dst, src, 1 + total);
	copied = 1;
}
isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL((void*)0));
}
return copied;
1999}

2001static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
__isl_keep isl_basic_setisl_basic_map *bset, int *elim, unsigned total)
2003{
return reduced_using_equalities(dst, src,
			bset_to_bmap(bset), elim, total);
2006}

2008static __isl_give isl_basic_setisl_basic_map *isl_basic_set_reduce_using_equalities(
__isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context)
2010{
int i;
int *elim;
isl_size dim;

if (!bset || !context)
goto error;

if (context->n_eq == 0) {
isl_basic_set_free(context);
return bset;
}

bset = isl_basic_set_cow(bset);
dim = isl_basic_set_dim(bset, isl_dim_set);
if (dim < 0)
goto error;

elim = isl_alloc_array(bset->ctx, int, dim)((int *)isl_malloc_or_die(bset->ctx, (dim)*sizeof(int)));
if (!elim)
goto error;
set_compute_elimination_index(context, elim, dim);
for (i = 0; i < bset->n_eq; ++i)
set_reduced_using_equalities(bset->eq[i], bset->eq[i],
					context, elim, dim);
for (i = 0; i < bset->n_ineq; ++i)
set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
					context, elim, dim);
isl_basic_set_free(context);
free(elim);
bset = isl_basic_set_simplify(bset);
bset = isl_basic_set_finalize(bset);
return bset;
2043error:
isl_basic_set_free(bset);
isl_basic_set_free(context);
return NULL((void*)0);
2047}

2049/* For each inequality in "ineq" that is a shifted (more relaxed)
* copy of an inequality in "context", mark the corresponding entry
* in "row" with -1.
* If an inequality only has a non-negative constant term, then
* mark it as well.
*/
2055static isl_stat mark_shifted_constraints(__isl_keep isl_mat *ineq,
__isl_keep isl_basic_setisl_basic_map *context, int *row)
2057{
struct isl_constraint_index ci;
isl_size n_ineq, cols;
unsigned total;
int k;

if (!ineq || !context)
return isl_stat_error;
if (context->n_ineq == 0)
return isl_stat_ok;
if (setup_constraint_index(&ci, context) < 0)
return isl_stat_error;

n_ineq = isl_mat_rows(ineq);
cols = isl_mat_cols(ineq);
if (n_ineq < 0 || cols < 0)
return isl_stat_error;
total = cols - 1;
for (k = 0; k < n_ineq; ++k) {
int l;
isl_bool redundant;

l = isl_seq_first_non_zero(ineq->row[k] + 1, total);
if (l < 0 && isl_int_is_nonneg(ineq->row[k][0])(isl_sioimath_sgn(*(ineq->row[k][0])) >= 0)) {
	row[k] = -1;
	continue;
}
redundant = constraint_index_is_redundant(&ci, ineq->row[k]);
if (redundant < 0)
	goto error;
if (!redundant)
	continue;
row[k] = -1;
}
constraint_index_free(&ci);
return isl_stat_ok;
2093error:
constraint_index_free(&ci);
return isl_stat_error;
2096}

2098static __isl_give isl_basic_setisl_basic_map *remove_shifted_constraints(
__isl_take isl_basic_setisl_basic_map *bset, __isl_keep isl_basic_setisl_basic_map *context)
2100{
struct isl_constraint_index ci;
int k;

if (!bset || !context)
return bset;

if (context->n_ineq == 0)
return bset;
if (setup_constraint_index(&ci, context) < 0)
return bset;

for (k = 0; k < bset->n_ineq; ++k) {
isl_bool redundant;

redundant = constraint_index_is_redundant(&ci, bset->ineq[k]);
if (redundant < 0)
	goto error;
if (!redundant)
	continue;
bset = isl_basic_set_cow(bset);
if (!bset)
	goto error;
isl_basic_set_drop_inequality(bset, k);
--k;
}
constraint_index_free(&ci);
return bset;
2128error:
constraint_index_free(&ci);
return bset;
2131}

2133/* Remove constraints from "bmap" that are identical to constraints
* in "context" or that are more relaxed (greater constant term).
*
* We perform the test for shifted copies on the pure constraints
* in remove_shifted_constraints.
*/
2139static __isl_give isl_basic_map *isl_basic_map_remove_shifted_constraints(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context)
2141{
isl_basic_setisl_basic_map *bset, *bset_context;

if (!bmap || !context)
goto error;

if (bmap->n_ineq == 0 || context->n_ineq == 0) {
isl_basic_map_free(context);
return bmap;
}

bmap = isl_basic_map_order_divs(bmap);
context = isl_basic_map_align_divs(context, bmap);
bmap = isl_basic_map_align_divs(bmap, context);

bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
bset_context = isl_basic_map_underlying_set(context);
bset = remove_shifted_constraints(bset, bset_context);
isl_basic_set_free(bset_context);

bmap = isl_basic_map_overlying_set(bset, bmap);

return bmap;
2164error:
isl_basic_map_free(bmap);
isl_basic_map_free(context);
return NULL((void*)0);
2168}

2170/* Does the (linear part of a) constraint "c" involve any of the "len"
* "relevant" dimensions?
*/
2173static int is_related(isl_int *c, int len, int *relevant)
2174{
int i;

for (i = 0; i < len; ++i) {
if (!relevant[i])
	continue;
if (!isl_int_is_zero(c[i])(isl_sioimath_sgn(*(c[i])) == 0))
	return 1;
}

return 0;
2185}

2187/* Drop constraints from "bmap" that do not involve any of
* the dimensions marked "relevant".
*/
2190static __isl_give isl_basic_map *drop_unrelated_constraints(
__isl_take isl_basic_map *bmap, int *relevant)
2192{
int i;
isl_size dim;

dim = isl_basic_map_dim(bmap, isl_dim_all);
if (dim < 0)
return isl_basic_map_free(bmap);
for (i = 0; i < dim; ++i)
if (!relevant[i])
	break;
if (i >= dim)
return bmap;

for (i = bmap->n_eq - 1; i >= 0; --i)
if (!is_related(bmap->eq[i] + 1, dim, relevant)) {
	bmap = isl_basic_map_cow(bmap);
	if (isl_basic_map_drop_equality(bmap, i) < 0)
		return isl_basic_map_free(bmap);
}

for (i = bmap->n_ineq - 1; i >= 0; --i)
if (!is_related(bmap->ineq[i] + 1, dim, relevant)) {
	bmap = isl_basic_map_cow(bmap);
	if (isl_basic_map_drop_inequality(bmap, i) < 0)
		return isl_basic_map_free(bmap);
}

return bmap;
2220}

2222/* Update the groups in "group" based on the (linear part of a) constraint "c".
*
* In particular, for any variable involved in the constraint,
* find the actual group id from before and replace the group
* of the corresponding variable by the minimal group of all
* the variables involved in the constraint considered so far
* (if this minimum is smaller) or replace the minimum by this group
* (if the minimum is larger).
*
* At the end, all the variables in "c" will (indirectly) point
* to the minimal of the groups that they referred to originally.
*/
2234static void update_groups(int dim, int *group, isl_int *c)
2235{
int j;
int min = dim;

for (j = 0; j < dim; ++j) {
if (isl_int_is_zero(c[j])(isl_sioimath_sgn(*(c[j])) == 0))
	continue;
while (group[j] >= 0 && group[group[j]] != group[j])
	group[j] = group[group[j]];
if (group[j] == min)
	continue;
if (group[j] < min) {
	if (min >= 0 && min < dim)
		group[min] = group[j];
	min = group[j];
} else
	group[group[j]] = min;
}
2253}

2255/* Allocate an array of groups of variables, one for each variable
* in "context", initialized to zero.
*/
2258static int *alloc_groups(__isl_keep isl_basic_setisl_basic_map *context)
2259{
isl_ctx *ctx;
isl_size dim;

dim = isl_basic_set_dim(context, isl_dim_set);
if (dim < 0)
return NULL((void*)0);
ctx = isl_basic_set_get_ctx(context);
return isl_calloc_array(ctx, int, dim)((int *)isl_calloc_or_die(ctx, dim, sizeof(int)));
2268}

2270/* Drop constraints from "bmap" that only involve variables that are
* not related to any of the variables marked with a "-1" in "group".
*
* We construct groups of variables that collect variables that
* (indirectly) appear in some common constraint of "bmap".
* Each group is identified by the first variable in the group,
* except for the special group of variables that was already identified
* in the input as -1 (or are related to those variables).
* If group[i] is equal to i (or -1), then the group of i is i (or -1),
* otherwise the group of i is the group of group[i].
*
* We first initialize groups for the remaining variables.
* Then we iterate over the constraints of "bmap" and update the
* group of the variables in the constraint by the smallest group.
* Finally, we resolve indirect references to groups by running over
* the variables.
*
* After computing the groups, we drop constraints that do not involve
* any variables in the -1 group.
*/
2290__isl_give isl_basic_map *isl_basic_map_drop_unrelated_constraints(
__isl_take isl_basic_map *bmap, __isl_take int *group)
2292{
isl_size dim;
int i;
int last;

dim = isl_basic_map_dim(bmap, isl_dim_all);
if (dim < 0)
return isl_basic_map_free(bmap);

last = -1;
for (i = 0; i < dim; ++i)
if (group[i] >= 0)
	last = group[i] = i;
if (last < 0) {
free(group);
return bmap;
}

for (i = 0; i < bmap->n_eq; ++i)
update_groups(dim, group, bmap->eq[i] + 1);
for (i = 0; i < bmap->n_ineq; ++i)
update_groups(dim, group, bmap->ineq[i] + 1);

for (i = 0; i < dim; ++i)
if (group[i] >= 0)
	group[i] = group[group[i]];

for (i = 0; i < dim; ++i)
group[i] = group[i] == -1;

bmap = drop_unrelated_constraints(bmap, group);

free(group);
return bmap;
2326}

2328/* Drop constraints from "context" that are irrelevant for computing
* the gist of "bset".
*
* In particular, drop constraints in variables that are not related
* to any of the variables involved in the constraints of "bset"
* in the sense that there is no sequence of constraints that connects them.
*
* We first mark all variables that appear in "bset" as belonging
* to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
*/
2338static __isl_give isl_basic_setisl_basic_map *drop_irrelevant_constraints(
__isl_take isl_basic_setisl_basic_map *context, __isl_keep isl_basic_setisl_basic_map *bset)
2340{
int *group;
isl_size dim;
int i, j;

dim = isl_basic_set_dim(bset, isl_dim_set);
if (!context || dim < 0)
return isl_basic_set_free(context);

group = alloc_groups(context);

if (!group)
return isl_basic_set_free(context);

for (i = 0; i < dim; ++i) {
for (j = 0; j < bset->n_eq; ++j)
	if (!isl_int_is_zero(bset->eq[j][1 + i])(isl_sioimath_sgn(*(bset->eq[j][1 + i])) == 0))
		break;
if (j < bset->n_eq) {
	group[i] = -1;
	continue;
}
for (j = 0; j < bset->n_ineq; ++j)
	if (!isl_int_is_zero(bset->ineq[j][1 + i])(isl_sioimath_sgn(*(bset->ineq[j][1 + i])) == 0))
		break;
if (j < bset->n_ineq)
	group[i] = -1;
}

return isl_basic_map_drop_unrelated_constraints(context, group);
2370}

2372/* Drop constraints from "context" that are irrelevant for computing
* the gist of the inequalities "ineq".
* Inequalities in "ineq" for which the corresponding element of row
* is set to -1 have already been marked for removal and should be ignored.
*
* In particular, drop constraints in variables that are not related
* to any of the variables involved in "ineq"
* in the sense that there is no sequence of constraints that connects them.
*
* We first mark all variables that appear in "bset" as belonging
* to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
*/
2384static __isl_give isl_basic_setisl_basic_map *drop_irrelevant_constraints_marked(
__isl_take isl_basic_setisl_basic_map *context, __isl_keep isl_mat *ineq, int *row)
2386{
int *group;
isl_size dim;
int i, j;
isl_size n;

dim = isl_basic_set_dim(context, isl_dim_set);
n = isl_mat_rows(ineq);
if (dim < 0 || n < 0)
return isl_basic_set_free(context);

group = alloc_groups(context);

if (!group)
return isl_basic_set_free(context);

for (i = 0; i < dim; ++i) {
for (j = 0; j < n; ++j) {
	if (row[j] < 0)
		continue;
	if (!isl_int_is_zero(ineq->row[j][1 + i])(isl_sioimath_sgn(*(ineq->row[j][1 + i])) == 0))
		break;
}
if (j < n)
	group[i] = -1;
}

return isl_basic_map_drop_unrelated_constraints(context, group);
2414}

2416/* Do all "n" entries of "row" contain a negative value?
*/
2418static int all_neg(int *row, int n)
2419{
int i;

for (i = 0; i < n; ++i)
if (row[i] >= 0)
	return 0;

return 1;
2427}

2429/* Update the inequalities in "bset" based on the information in "row"
* and "tab".
*
* In particular, the array "row" contains either -1, meaning that
* the corresponding inequality of "bset" is redundant, or the index
* of an inequality in "tab".
*
* If the row entry is -1, then drop the inequality.
* Otherwise, if the constraint is marked redundant in the tableau,
* then drop the inequality.  Similarly, if it is marked as an equality
* in the tableau, then turn the inequality into an equality and
* perform Gaussian elimination.
*/
2442static __isl_give isl_basic_setisl_basic_map *update_ineq(__isl_take isl_basic_setisl_basic_map *bset,
__isl_keep int *row, struct isl_tab *tab)
2444{
int i;
unsigned n_ineq;
unsigned n_eq;
int found_equality = 0;

if (!bset)
return NULL((void*)0);
if (tab && tab->empty)
return isl_basic_set_set_to_empty(bset);

n_ineq = bset->n_ineq;
for (i = n_ineq - 1; i >= 0; --i) {
if (row[i] < 0) {
	if (isl_basic_set_drop_inequality(bset, i) < 0)
		return isl_basic_set_free(bset);
	continue;
}
if (!tab)
	continue;
n_eq = tab->n_eq;
if (isl_tab_is_equality(tab, n_eq + row[i])) {
	isl_basic_map_inequality_to_equality(bset, i);
	found_equality = 1;
} else if (isl_tab_is_redundant(tab, n_eq + row[i])) {
	if (isl_basic_set_drop_inequality(bset, i) < 0)
		return isl_basic_set_free(bset);
}
}

if (found_equality)
bset = isl_basic_set_gauss(bset, NULL((void*)0));
bset = isl_basic_set_finalize(bset);
return bset;
2478}

2480/* Update the inequalities in "bset" based on the information in "row"
* and "tab" and free all arguments (other than "bset").
*/
2483static __isl_give isl_basic_setisl_basic_map *update_ineq_free(
__isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_mat *ineq,
__isl_take isl_basic_setisl_basic_map *context, __isl_take int *row,
struct isl_tab *tab)
2487{
isl_mat_free(ineq);
isl_basic_set_free(context);

bset = update_ineq(bset, row, tab);

free(row);
isl_tab_free(tab);
return bset;
2496}

2498/* Remove all information from bset that is redundant in the context
* of context.
* "ineq" contains the (possibly transformed) inequalities of "bset",
* in the same order.
* The (explicit) equalities of "bset" are assumed to have been taken
* into account by the transformation such that only the inequalities
* are relevant.
* "context" is assumed not to be empty.
*
* "row" keeps track of the constraint index of a "bset" inequality in "tab".
* A value of -1 means that the inequality is obviously redundant and may
* not even appear in  "tab".
*
* We first mark the inequalities of "bset"
* that are obviously redundant with respect to some inequality in "context".
* Then we remove those constraints from "context" that have become
* irrelevant for computing the gist of "bset".
* Note that this removal of constraints cannot be replaced by
* a factorization because factors in "bset" may still be connected
* to each other through constraints in "context".
*
* If there are any inequalities left, we construct a tableau for
* the context and then add the inequalities of "bset".
* Before adding these inequalities, we freeze all constraints such that
* they won't be considered redundant in terms of the constraints of "bset".
* Then we detect all redundant constraints (among the
* constraints that weren't frozen), first by checking for redundancy in the
* the tableau and then by checking if replacing a constraint by its negation
* would lead to an empty set.  This last step is fairly expensive
* and could be optimized by more reuse of the tableau.
* Finally, we update bset according to the results.
*/
2530static __isl_give isl_basic_setisl_basic_map *uset_gist_full(__isl_take isl_basic_setisl_basic_map *bset,
__isl_take isl_mat *ineq, __isl_take isl_basic_setisl_basic_map *context)
2532{
int i, r;
int *row = NULL((void*)0);
isl_ctx *ctx;
isl_basic_setisl_basic_map *combined = NULL((void*)0);
struct isl_tab *tab = NULL((void*)0);
unsigned n_eq, context_ineq;

if (!bset || !ineq || !context)
goto error;

if (bset->n_ineq == 0 || isl_basic_set_plain_is_universe(context)) {
isl_basic_set_free(context);
isl_mat_free(ineq);
return bset;
}

ctx = isl_basic_set_get_ctx(context);
row = isl_calloc_array(ctx, int, bset->n_ineq)((int *)isl_calloc_or_die(ctx, bset->n_ineq, sizeof(int)));
if (!row)
goto error;

if (mark_shifted_constraints(ineq, context, row) < 0)
goto error;
if (all_neg(row, bset->n_ineq))
return update_ineq_free(bset, ineq, context, row, NULL((void*)0));

context = drop_irrelevant_constraints_marked(context, ineq, row);
if (!context)
goto error;
if (isl_basic_set_plain_is_universe(context))
return update_ineq_free(bset, ineq, context, row, NULL((void*)0));

n_eq = context->n_eq;
context_ineq = context->n_ineq;
combined = isl_basic_set_cow(isl_basic_set_copy(context));
combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
tab = isl_tab_from_basic_set(combined, 0);
for (i = 0; i < context_ineq; ++i)
if (isl_tab_freeze_constraint(tab, n_eq + i) < 0)
	goto error;
if (isl_tab_extend_cons(tab, bset->n_ineq) < 0)
goto error;
r = context_ineq;
for (i = 0; i < bset->n_ineq; ++i) {
if (row[i] < 0)
	continue;
combined = isl_basic_set_add_ineq(combined, ineq->row[i]);
if (isl_tab_add_ineq(tab, ineq->row[i]) < 0)
	goto error;
row[i] = r++;
}
if (isl_tab_detect_implicit_equalities(tab) < 0)
goto error;
if (isl_tab_detect_redundant(tab) < 0)
goto error;
for (i = bset->n_ineq - 1; i >= 0; --i) {
isl_basic_setisl_basic_map *test;
int is_empty;

if (row[i] < 0)
	continue;
r = row[i];
if (tab->con[n_eq + r].is_redundant)
	continue;
test = isl_basic_set_dup(combined);
test = isl_inequality_negate(test, r);
test = isl_basic_set_update_from_tab(test, tab);
is_empty = isl_basic_set_is_empty(test);
isl_basic_set_free(test);
if (is_empty < 0)
	goto error;
if (is_empty)
	tab->con[n_eq + r].is_redundant = 1;
}
bset = update_ineq_free(bset, ineq, context, row, tab);
if (bset) {
ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) |= ((1 << 2)));
ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT)(((bset)->flags) |= ((1 << 3)));
}

isl_basic_set_free(combined);
return bset;
2615error:
free(row);
isl_mat_free(ineq);
isl_tab_free(tab);
isl_basic_set_free(combined);
isl_basic_set_free(context);
isl_basic_set_free(bset);
return NULL((void*)0);
2623}

2625/* Extract the inequalities of "bset" as an isl_mat.
*/
2627static __isl_give isl_mat *extract_ineq(__isl_keep isl_basic_setisl_basic_map *bset)
2628{
isl_size total;
isl_ctx *ctx;
isl_mat *ineq;

total = isl_basic_set_dim(bset, isl_dim_all);
if (total < 0)
return NULL((void*)0);

ctx = isl_basic_set_get_ctx(bset);
ineq = isl_mat_sub_alloc6(ctx, bset->ineq, 0, bset->n_ineq,
		    0, 1 + total);

return ineq;
2642}

2644/* Remove all information from "bset" that is redundant in the context
* of "context", for the case where both "bset" and "context" are
* full-dimensional.
*/
2648static __isl_give isl_basic_setisl_basic_map *uset_gist_uncompressed(
__isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context)
2650{
isl_mat *ineq;

ineq = extract_ineq(bset);
return uset_gist_full(bset, ineq, context);
2655}

2657/* Replace "bset" by an empty basic set in the same space.
*/
2659static __isl_give isl_basic_setisl_basic_map *replace_by_empty(
__isl_take isl_basic_setisl_basic_map *bset)
2661{
isl_space *space;

space = isl_basic_set_get_space(bset);
isl_basic_set_free(bset);
return isl_basic_set_empty(space);
2667}

2669/* Remove all information from "bset" that is redundant in the context
* of "context", for the case where the combined equalities of
* "bset" and "context" allow for a compression that can be obtained
* by preapplication of "T".
* If the compression of "context" is empty, meaning that "bset" and
* "context" do not intersect, then return the empty set.
*
* "bset" itself is not transformed by "T".  Instead, the inequalities
* are extracted from "bset" and those are transformed by "T".
* uset_gist_full then determines which of the transformed inequalities
* are redundant with respect to the transformed "context" and removes
* the corresponding inequalities from "bset".
*
* After preapplying "T" to the inequalities, any common factor is
* removed from the coefficients.  If this results in a tightening
* of the constant term, then the same tightening is applied to
* the corresponding untransformed inequality in "bset".
* That is, if after plugging in T, a constraint f(x) >= 0 is of the form
*
*	g f'(x) + r >= 0
*
* with 0 <= r < g, then it is equivalent to
*
*	f'(x) >= 0
*
* This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine
* subspace compressed by T since the latter would be transformed to
*
*	g f'(x) >= 0
*/
2699static __isl_give isl_basic_setisl_basic_map *uset_gist_compressed(
__isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *context,
__isl_take isl_mat *T)
2702{
isl_ctx *ctx;
isl_mat *ineq;
int i;
isl_size n_row, n_col;
isl_int rem;

ineq = extract_ineq(bset);
ineq = isl_mat_product(ineq, isl_mat_copy(T));
context = isl_basic_set_preimage(context, T);

if (!ineq || !context)
goto error;
if (isl_basic_set_plain_is_empty(context)) {
isl_mat_free(ineq);
isl_basic_set_free(context);
return replace_by_empty(bset);
}

ctx = isl_mat_get_ctx(ineq);
n_row = isl_mat_rows(ineq);
n_col = isl_mat_cols(ineq);
if (n_row < 0 || n_col < 0)
goto error;
isl_int_init(rem)isl_sioimath_init((rem));
for (i = 0; i < n_row; ++i) {
isl_seq_gcd(ineq->row[i] + 1, n_col - 1, &ctx->normalize_gcd);
if (isl_int_is_zero(ctx->normalize_gcd)(isl_sioimath_sgn(*(ctx->normalize_gcd)) == 0))
	continue;
if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0))
	continue;
isl_seq_scale_down(ineq->row[i] + 1, ineq->row[i] + 1,
		    ctx->normalize_gcd, n_col - 1);
isl_int_fdiv_r(rem, ineq->row[i][0], ctx->normalize_gcd)isl_sioimath_fdiv_r((rem), *(ineq->row[i][0]), *(ctx->normalize_gcd
));
isl_int_fdiv_q(ineq->row[i][0],isl_sioimath_fdiv_q((ineq->row[i][0]), *(ineq->row[i][0
]), *(ctx->normalize_gcd))
		ineq->row[i][0], ctx->normalize_gcd)isl_sioimath_fdiv_q((ineq->row[i][0]), *(ineq->row[i][0
]), *(ctx->normalize_gcd));
if (isl_int_is_zero(rem)(isl_sioimath_sgn(*(rem)) == 0))
	continue;
bset = isl_basic_set_cow(bset);
if (!bset)
	break;
isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], rem)isl_sioimath_sub((bset->ineq[i][0]), *(bset->ineq[i][0]
), *(rem));
}
isl_int_clear(rem)isl_sioimath_clear((rem));

return uset_gist_full(bset, ineq, context);
2748error:
isl_mat_free(ineq);
isl_basic_set_free(context);
isl_basic_set_free(bset);
return NULL((void*)0);
2753}

2755/* Project "bset" onto the variables that are involved in "template".
*/
2757static __isl_give isl_basic_setisl_basic_map *project_onto_involved(
__isl_take isl_basic_setisl_basic_map *bset, __isl_keep isl_basic_setisl_basic_map *template)
2759{
int i;
isl_size n;

n = isl_basic_set_dim(template, isl_dim_set);
if (n < 0 || !template)
return isl_basic_set_free(bset);

for (i = 0; i < n; ++i) {
isl_bool involved;

involved = isl_basic_set_involves_dims(template,
					isl_dim_set, i, 1);
if (involved < 0)
	return isl_basic_set_free(bset);
if (involved)
	continue;
bset = isl_basic_set_eliminate_vars(bset, i, 1);
}

return bset;
2780}

2782/* Remove all information from bset that is redundant in the context
* of context.  In particular, equalities that are linear combinations
* of those in context are removed.  Then the inequalities that are
* redundant in the context of the equalities and inequalities of
* context are removed.
*
* First of all, we drop those constraints from "context"
* that are irrelevant for computing the gist of "bset".
* Alternatively, we could factorize the intersection of "context" and "bset".
*
* We first compute the intersection of the integer affine hulls
* of "bset" and "context",
* compute the gist inside this intersection and then reduce
* the constraints with respect to the equalities of the context
* that only involve variables already involved in the input.
* If the intersection of the affine hulls turns out to be empty,
* then return the empty set.
*
* If two constraints are mutually redundant, then uset_gist_full
* will remove the second of those constraints.  We therefore first
* sort the constraints so that constraints not involving existentially
* quantified variables are given precedence over those that do.
* We have to perform this sorting before the variable compression,
* because that may effect the order of the variables.
*/
2807static __isl_give isl_basic_setisl_basic_map *uset_gist(__isl_take isl_basic_setisl_basic_map *bset,
__isl_take isl_basic_setisl_basic_map *context)
2809{
isl_mat *eq;
isl_mat *T;
isl_basic_setisl_basic_map *aff;
isl_basic_setisl_basic_map *aff_context;
isl_size total;

total = isl_basic_set_dim(bset, isl_dim_all);
if (total < 0 || !context)
goto error;

context = drop_irrelevant_constraints(context, bset);

bset = isl_basic_set_detect_equalities(bset);
aff = isl_basic_set_copy(bset);
aff = isl_basic_set_plain_affine_hull(aff);
context = isl_basic_set_detect_equalities(context);
aff_context = isl_basic_set_copy(context);
aff_context = isl_basic_set_plain_affine_hull(aff_context);
aff = isl_basic_set_intersect(aff, aff_context);
if (!aff)
goto error;
if (isl_basic_set_plain_is_empty(aff)) {
isl_basic_set_free(bset);
isl_basic_set_free(context);
return aff;
}
bset = isl_basic_set_sort_constraints(bset);
if (aff->n_eq == 0) {
isl_basic_set_free(aff);
return uset_gist_uncompressed(bset, context);
}
eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
eq = isl_mat_cow(eq);
T = isl_mat_variable_compression(eq, NULL((void*)0));
isl_basic_set_free(aff);
if (T && T->n_col == 0) {
isl_mat_free(T);
isl_basic_set_free(context);
return replace_by_empty(bset);
}

aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
aff_context = project_onto_involved(aff_context, bset);

bset = uset_gist_compressed(bset, context, T);
bset = isl_basic_set_reduce_using_equalities(bset, aff_context);

if (bset) {
ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) |= ((1 << 2)));
ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT)(((bset)->flags) |= ((1 << 3)));
}

return bset;
2863error:
isl_basic_set_free(bset);
isl_basic_set_free(context);
return NULL((void*)0);
2867}

2869/* Return the number of equality constraints in "bmap" that involve
* local variables.  This function assumes that Gaussian elimination
* has been applied to the equality constraints.
*/
2873static int n_div_eq(__isl_keep isl_basic_map *bmap)
2874{
int i;
isl_size total, n_div;

if (!bmap)
return -1;

if (bmap->n_eq == 0)
return 0;

total = isl_basic_map_dim(bmap, isl_dim_all);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (total < 0 || n_div < 0)
return -1;
total -= n_div;

for (i = 0; i < bmap->n_eq; ++i)
if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total,
			    n_div) == -1)
	return i;

return bmap->n_eq;
2896}

2898/* Construct a basic map in "space" defined by the equality constraints in "eq".
* The constraints are assumed not to involve any local variables.
*/
2901static __isl_give isl_basic_map *basic_map_from_equalities(
__isl_take isl_space *space, __isl_take isl_mat *eq)
2903{
int i, k;
isl_size total;
isl_basic_map *bmap = NULL((void*)0);

total = isl_space_dim(space, isl_dim_all);
if (total < 0 || !eq)
goto error;

if (1 + total != eq->n_col)
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", "polly/lib/External/isl/isl_map_simplify.c"
, 2914); goto error; } while (0)
	"unexpected number of columns", goto error)do { isl_handle_error(isl_space_get_ctx(space), isl_error_internal
, "unexpected number of columns", "polly/lib/External/isl/isl_map_simplify.c"
, 2914); goto error; } while (0);

bmap = isl_basic_map_alloc_space(isl_space_copy(space),
			    0, eq->n_row, 0);
for (i = 0; i < eq->n_row; ++i) {
k = isl_basic_map_alloc_equality(bmap);
if (k < 0)
	goto error;
isl_seq_cpy(bmap->eq[k], eq->row[i], eq->n_col);
}

isl_space_free(space);
isl_mat_free(eq);
return bmap;
2928error:
isl_space_free(space);
isl_mat_free(eq);
isl_basic_map_free(bmap);
return NULL((void*)0);
2933}

2935/* Construct and return a variable compression based on the equality
* constraints in "bmap1" and "bmap2" that do not involve the local variables.
* "n1" is the number of (initial) equality constraints in "bmap1"
* that do involve local variables.
* "n2" is the number of (initial) equality constraints in "bmap2"
* that do involve local variables.
* "total" is the total number of other variables.
* This function assumes that Gaussian elimination
* has been applied to the equality constraints in both "bmap1" and "bmap2"
* such that the equality constraints not involving local variables
* are those that start at "n1" or "n2".
*
* If either of "bmap1" and "bmap2" does not have such equality constraints,
* then simply compute the compression based on the equality constraints
* in the other basic map.
* Otherwise, combine the equality constraints from both into a new
* basic map such that Gaussian elimination can be applied to this combination
* and then construct a variable compression from the resulting
* equality constraints.
*/
2955static __isl_give isl_mat *combined_variable_compression(
__isl_keep isl_basic_map *bmap1, int n1,
__isl_keep isl_basic_map *bmap2, int n2, int total)
2958{
isl_ctx *ctx;
isl_mat *E1, *E2, *V;
isl_basic_map *bmap;

ctx = isl_basic_map_get_ctx(bmap1);
if (bmap1->n_eq == n1) {
E2 = isl_mat_sub_alloc6(ctx, bmap2->eq,
			n2, bmap2->n_eq - n2, 0, 1 + total);
return isl_mat_variable_compression(E2, NULL((void*)0));
}
if (bmap2->n_eq == n2) {
E1 = isl_mat_sub_alloc6(ctx, bmap1->eq,
			n1, bmap1->n_eq - n1, 0, 1 + total);
return isl_mat_variable_compression(E1, NULL((void*)0));
}
E1 = isl_mat_sub_alloc6(ctx, bmap1->eq,
		n1, bmap1->n_eq - n1, 0, 1 + total);
E2 = isl_mat_sub_alloc6(ctx, bmap2->eq,
		n2, bmap2->n_eq - n2, 0, 1 + total);
E1 = isl_mat_concat(E1, E2);
bmap = basic_map_from_equalities(isl_basic_map_get_space(bmap1), E1);
bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
if (!bmap)
return NULL((void*)0);
E1 = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total);
V = isl_mat_variable_compression(E1, NULL((void*)0));
isl_basic_map_free(bmap);

return V;
2988}

2990/* Extract the stride constraints from "bmap", compressed
* with respect to both the stride constraints in "context" and
* the remaining equality constraints in both "bmap" and "context".
* "bmap_n_eq" is the number of (initial) stride constraints in "bmap".
* "context_n_eq" is the number of (initial) stride constraints in "context".
*
* Let x be all variables in "bmap" (and "context") other than the local
* variables.  First compute a variable compression
*
*	x = V x'
*
* based on the non-stride equality constraints in "bmap" and "context".
* Consider the stride constraints of "context",
*
*	A(x) + B(y) = 0
*
* with y the local variables and plug in the variable compression,
* resulting in
*
*	A(V x') + B(y) = 0
*
* Use these constraints to compute a parameter compression on x'
*
*	x' = T x''
*
* Now consider the stride constraints of "bmap"
*
*	C(x) + D(y) = 0
*
* and plug in x = V*T x''.
* That is, return A = [C*V*T D].
*/
3022static __isl_give isl_mat *extract_compressed_stride_constraints(
__isl_keep isl_basic_map *bmap, int bmap_n_eq,
__isl_keep isl_basic_map *context, int context_n_eq)
3025{
isl_size total, n_div;
isl_ctx *ctx;
isl_mat *A, *B, *T, *V;

total = isl_basic_map_dim(context, isl_dim_all);
n_div = isl_basic_map_dim(context, isl_dim_div);
if (total < 0 || n_div < 0)
return NULL((void*)0);
total -= n_div;

ctx = isl_basic_map_get_ctx(bmap);

V = combined_variable_compression(bmap, bmap_n_eq,
				context, context_n_eq, total);

A = isl_mat_sub_alloc6(ctx, context->eq, 0, context_n_eq, 0, 1 + total);
B = isl_mat_sub_alloc6(ctx, context->eq,
		0, context_n_eq, 1 + total, n_div);
A = isl_mat_product(A, isl_mat_copy(V));
T = isl_mat_parameter_compression_ext(A, B);
T = isl_mat_product(V, T);

n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
T = isl_mat_free(T);
else
T = isl_mat_diagonal(T, isl_mat_identity(ctx, n_div));

A = isl_mat_sub_alloc6(ctx, bmap->eq,
		0, bmap_n_eq, 0, 1 + total + n_div);
A = isl_mat_product(A, T);

return A;
3059}

3061/* Remove the prime factors from *g that have an exponent that
* is strictly smaller than the exponent in "c".
* All exponents in *g are known to be smaller than or equal
* to those in "c".
*
* That is, if *g is equal to
*
*	p_1^{e_1} p_2^{e_2} ... p_n^{e_n}
*
* and "c" is equal to
*
*	p_1^{f_1} p_2^{f_2} ... p_n^{f_n}
*
* then update *g to
*
*	p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ...
*		p_n^{e_n * (e_n = f_n)}
*
* If e_i = f_i, then c / *g does not have any p_i factors and therefore
* neither does the gcd of *g and c / *g.
* If e_i < f_i, then the gcd of *g and c / *g has a positive
* power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors.
* Dividing *g by this gcd therefore strictly reduces the exponent
* of the prime factors that need to be removed, while leaving the
* other prime factors untouched.
* Repeating this process until gcd(*g, c / *g) = 1 therefore
* removes all undesired factors, without removing any others.
*/
3089static void remove_incomplete_powers(isl_int *g, isl_int c)
3090{
isl_int t;

isl_int_init(t)isl_sioimath_init((t));
for (;;) {
isl_int_divexact(t, c, *g)isl_sioimath_tdiv_q((t), *(c), *(*g));
isl_int_gcd(t, t, *g)isl_sioimath_gcd((t), *(t), *(*g));
if (isl_int_is_one(t)(isl_sioimath_cmp_si(*(t), 1) == 0))
	break;
isl_int_divexact(*g, *g, t)isl_sioimath_tdiv_q((*g), *(*g), *(t));
}
isl_int_clear(t)isl_sioimath_clear((t));
3102}

3104/* Reduce the "n" stride constraints in "bmap" based on a copy "A"
* of the same stride constraints in a compressed space that exploits
* all equalities in the context and the other equalities in "bmap".
*
* If the stride constraints of "bmap" are of the form
*
*	C(x) + D(y) = 0
*
* then A is of the form
*
*	B(x') + D(y) = 0
*
* If any of these constraints involves only a single local variable y,
* then the constraint appears as
*
*	f(x) + m y_i = 0
*
* in "bmap" and as
*
*	h(x') + m y_i = 0
*
* in "A".
*
* Let g be the gcd of m and the coefficients of h.
* Then, in particular, g is a divisor of the coefficients of h and
*
*	f(x) = h(x')
*
* is known to be a multiple of g.
* If some prime factor in m appears with the same exponent in g,
* then it can be removed from m because f(x) is already known
* to be a multiple of g and therefore in particular of this power
* of the prime factors.
* Prime factors that appear with a smaller exponent in g cannot
* be removed from m.
* Let g' be the divisor of g containing all prime factors that
* appear with the same exponent in m and g, then
*
*	f(x) + m y_i = 0
*
* can be replaced by
*
*	f(x) + m/g' y_i' = 0
*
* Note that (if g' != 1) this changes the explicit representation
* of y_i to that of y_i', so the integer division at position i
* is marked unknown and later recomputed by a call to
* isl_basic_map_gauss.
*/
3153static __isl_give isl_basic_map *reduce_stride_constraints(
__isl_take isl_basic_map *bmap, int n, __isl_keep isl_mat *A)
3155{
int i;
isl_size total, n_div;
int any = 0;
isl_int gcd;

total = isl_basic_map_dim(bmap, isl_dim_all);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (total < 0 || n_div < 0 || !A)
return isl_basic_map_free(bmap);
total -= n_div;

isl_int_init(gcd)isl_sioimath_init((gcd));
for (i = 0; i < n; ++i) {
int div;

div = isl_seq_first_non_zero(bmap->eq[i] + 1 + total, n_div);
if (div < 0)
	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", "polly/lib/External/isl/isl_map_simplify.c"
, 3175); goto error; } while (0)
		"equality constraints modified unexpectedly",do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_internal
, "equality constraints modified unexpectedly", "polly/lib/External/isl/isl_map_simplify.c"
, 3175); goto error; } while (0)
		goto error)do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_internal
, "equality constraints modified unexpectedly", "polly/lib/External/isl/isl_map_simplify.c"
, 3175); goto error; } while (0);
if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total + div + 1,
				n_div - div - 1) != -1)
	continue;
if (isl_mat_row_gcd(A, i, &gcd) < 0)
	goto error;
if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0))
	continue;
remove_incomplete_powers(&gcd, bmap->eq[i][1 + total + div]);
if (isl_int_is_one(gcd)(isl_sioimath_cmp_si(*(gcd), 1) == 0))
	continue;
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))
		bmap->eq[i][1 + total + div], gcd)isl_sioimath_tdiv_q((bmap->eq[i][1 + total + div]), *(bmap
->eq[i][1 + total + div]), *(gcd));
bmap = isl_basic_map_mark_div_unknown(bmap, div);
if (!bmap)
	goto error;
any = 1;
}
isl_int_clear(gcd)isl_sioimath_clear((gcd));

if (any)
bmap = isl_basic_map_gauss(bmap, NULL((void*)0));

return bmap;
3199error:
isl_int_clear(gcd)isl_sioimath_clear((gcd));
isl_basic_map_free(bmap);
return NULL((void*)0);
3203}

3205/* Simplify the stride constraints in "bmap" based on
* the remaining equality constraints in "bmap" and all equality
* constraints in "context".
* Only do this if both "bmap" and "context" have stride constraints.
*
* First extract a copy of the stride constraints in "bmap" in a compressed
* space exploiting all the other equality constraints and then
* use this compressed copy to simplify the original stride constraints.
*/
3214static __isl_give isl_basic_map *gist_strides(__isl_take isl_basic_map *bmap,
__isl_keep isl_basic_map *context)
3216{
int bmap_n_eq, context_n_eq;
isl_mat *A;

if (!bmap || !context)
return isl_basic_map_free(bmap);

bmap_n_eq = n_div_eq(bmap);
context_n_eq = n_div_eq(context);

if (bmap_n_eq < 0 || context_n_eq < 0)
return isl_basic_map_free(bmap);
if (bmap_n_eq == 0 || context_n_eq == 0)
return bmap;

A = extract_compressed_stride_constraints(bmap, bmap_n_eq,
				    context, context_n_eq);
bmap = reduce_stride_constraints(bmap, bmap_n_eq, A);

isl_mat_free(A);

return bmap;
3238}

3240/* Return a basic map that has the same intersection with "context" as "bmap"
* and that is as "simple" as possible.
*
* The core computation is performed on the pure constraints.
* When we add back the meaning of the integer divisions, we need
* to (re)introduce the div constraints.  If we happen to have
* discovered that some of these integer divisions are equal to
* some affine combination of other variables, then these div
* constraints may end up getting simplified in terms of the equalities,
* resulting in extra inequalities on the other variables that
* may have been removed already or that may not even have been
* part of the input.  We try and remove those constraints of
* this form that are most obviously redundant with respect to
* the context.  We also remove those div constraints that are
* redundant with respect to the other constraints in the result.
*
* The stride constraints among the equality constraints in "bmap" are
* also simplified with respecting to the other equality constraints
* in "bmap" and with respect to all equality constraints in "context".
*/
3260__isl_give isl_basic_map *isl_basic_map_gist(__isl_take isl_basic_map *bmap,
__isl_take isl_basic_map *context)
3262{
isl_basic_setisl_basic_map *bset, *eq;
isl_basic_map *eq_bmap;
isl_size total, n_div, n_div_bmap;
unsigned extra, n_eq, n_ineq;

if (!bmap || !context)
goto error;

if (isl_basic_map_plain_is_universe(bmap)) {
isl_basic_map_free(context);
return bmap;
}
if (isl_basic_map_plain_is_empty(context)) {
isl_space *space = isl_basic_map_get_space(bmap);
isl_basic_map_free(bmap);
isl_basic_map_free(context);
return isl_basic_map_universe(space);
}
if (isl_basic_map_plain_is_empty(bmap)) {
isl_basic_map_free(context);
return bmap;
}

bmap = isl_basic_map_remove_redundancies(bmap);
context = isl_basic_map_remove_redundancies(context);
bmap = isl_basic_map_order_divs(bmap);
context = isl_basic_map_align_divs(context, bmap);

n_div = isl_basic_map_dim(context, isl_dim_div);
total = isl_basic_map_dim(bmap, isl_dim_all);
n_div_bmap = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0 || total < 0 || n_div_bmap < 0)
goto error;
extra = n_div - n_div_bmap;

bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
bset = isl_basic_set_add_dims(bset, isl_dim_set, extra);
bset = uset_gist(bset,
    isl_basic_map_underlying_set(isl_basic_map_copy(context)));
bset = isl_basic_set_project_out(bset, isl_dim_set, total, extra);

if (!bset || bset->n_eq == 0 || n_div == 0 ||
   isl_basic_set_plain_is_empty(bset)) {
isl_basic_map_free(context);
return isl_basic_map_overlying_set(bset, bmap);
}

n_eq = bset->n_eq;
n_ineq = bset->n_ineq;
eq = isl_basic_set_copy(bset);
eq = isl_basic_set_cow(eq);
eq = isl_basic_set_free_inequality(eq, n_ineq);
bset = isl_basic_set_free_equality(bset, n_eq);

eq_bmap = isl_basic_map_overlying_set(eq, isl_basic_map_copy(bmap));
eq_bmap = gist_strides(eq_bmap, context);
eq_bmap = isl_basic_map_remove_shifted_constraints(eq_bmap, context);
bmap = isl_basic_map_overlying_set(bset, bmap);
bmap = isl_basic_map_intersect(bmap, eq_bmap);
bmap = isl_basic_map_remove_redundancies(bmap);

return bmap;
3325error:
isl_basic_map_free(bmap);
isl_basic_map_free(context);
return NULL((void*)0);
3329}

3331/*
* Assumes context has no implicit divs.
*/
3334__isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
__isl_take isl_basic_map *context)
3336{
int i;

if (!map || !context)
goto error;

if (isl_basic_map_plain_is_empty(context)) {
isl_space *space = isl_map_get_space(map);
isl_map_free(map);
isl_basic_map_free(context);
return isl_map_universe(space);
}

context = isl_basic_map_remove_redundancies(context);
map = isl_map_cow(map);
if (isl_map_basic_map_check_equal_space(map, context) < 0)
goto error;
map = isl_map_compute_divs(map);
if (!map)
goto error;
for (i = map->n - 1; i >= 0; --i) {
map->p[i] = isl_basic_map_gist(map->p[i],
				isl_basic_map_copy(context));
if (!map->p[i])
	goto error;
if (isl_basic_map_plain_is_empty(map->p[i])) {
	isl_basic_map_free(map->p[i]);
	if (i != map->n - 1)
		map->p[i] = map->p[map->n - 1];
	map->n--;
}
}
isl_basic_map_free(context);
ISL_F_CLR(map, ISL_MAP_NORMALIZED)(((map)->flags) &= ~((1 << 1)));
return map;
3371error:
isl_map_free(map);
isl_basic_map_free(context);
return NULL((void*)0);
3375}

3377/* Drop all inequalities from "bmap" that also appear in "context".
* "context" is assumed to have only known local variables and
* the initial local variables of "bmap" are assumed to be the same
* as those of "context".
* The constraints of both "bmap" and "context" are assumed
* to have been sorted using isl_basic_map_sort_constraints.
*
* Run through the inequality constraints of "bmap" and "context"
* in sorted order.
* If a constraint of "bmap" involves variables not in "context",
* then it cannot appear in "context".
* If a matching constraint is found, it is removed from "bmap".
*/
3390static __isl_give isl_basic_map *drop_inequalities(
__isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context)
3392{
int i1, i2;
isl_size total, bmap_total;
unsigned extra;

total = isl_basic_map_dim(context, isl_dim_all);
bmap_total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0 || bmap_total < 0)
return isl_basic_map_free(bmap);

extra = bmap_total - total;

i1 = bmap->n_ineq - 1;
i2 = context->n_ineq - 1;
while (bmap && i1 >= 0 && i2 >= 0) {
int cmp;

if (isl_seq_first_non_zero(bmap->ineq[i1] + 1 + total,
			    extra) != -1) {
	--i1;
	continue;
}
cmp = isl_basic_map_constraint_cmp(context, bmap->ineq[i1],
					context->ineq[i2]);
if (cmp < 0) {
	--i2;
	continue;
}
if (cmp > 0) {
	--i1;
	continue;
}
if (isl_int_eq(bmap->ineq[i1][0], context->ineq[i2][0])(isl_sioimath_cmp(*(bmap->ineq[i1][0]), *(context->ineq
[i2][0])) == 0)) {
	bmap = isl_basic_map_cow(bmap);
	if (isl_basic_map_drop_inequality(bmap, i1) < 0)
		bmap = isl_basic_map_free(bmap);
}
--i1;
--i2;
}

return bmap;
3434}

3436/* Drop all equalities from "bmap" that also appear in "context".
* "context" is assumed to have only known local variables and
* the initial local variables of "bmap" are assumed to be the same
* as those of "context".
*
* Run through the equality constraints of "bmap" and "context"
* in sorted order.
* If a constraint of "bmap" involves variables not in "context",
* then it cannot appear in "context".
* If a matching constraint is found, it is removed from "bmap".
*/
3447static __isl_give isl_basic_map *drop_equalities(
__isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context)
3449{
int i1, i2;
isl_size total, bmap_total;
unsigned extra;

total = isl_basic_map_dim(context, isl_dim_all);
bmap_total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0 || bmap_total < 0)
return isl_basic_map_free(bmap);

extra = bmap_total - total;

i1 = bmap->n_eq - 1;
i2 = context->n_eq - 1;

while (bmap && i1 >= 0 && i2 >= 0) {
int last1, last2;

if (isl_seq_first_non_zero(bmap->eq[i1] + 1 + total,
			    extra) != -1)
	break;
last1 = isl_seq_last_non_zero(bmap->eq[i1] + 1, total);
last2 = isl_seq_last_non_zero(context->eq[i2] + 1, total);
if (last1 > last2) {
	--i2;
	continue;
}
if (last1 < last2) {
	--i1;
	continue;
}
if (isl_seq_eq(bmap->eq[i1], context->eq[i2], 1 + total)) {
	bmap = isl_basic_map_cow(bmap);
	if (isl_basic_map_drop_equality(bmap, i1) < 0)
		bmap = isl_basic_map_free(bmap);
}
--i1;
--i2;
}

return bmap;
3490}

3492/* Remove the constraints in "context" from "bmap".
* "context" is assumed to have explicit representations
* for all local variables.
*
* First align the divs of "bmap" to those of "context" and
* sort the constraints.  Then drop all constraints from "bmap"
* that appear in "context".
*/
3500__isl_give isl_basic_map *isl_basic_map_plain_gist(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context)
3502{
isl_bool done, known;

done = isl_basic_map_plain_is_universe(context);
if (done == isl_bool_false)
done = isl_basic_map_plain_is_universe(bmap);
if (done == isl_bool_false)
done = isl_basic_map_plain_is_empty(context);
if (done == isl_bool_false)
done = isl_basic_map_plain_is_empty(bmap);
if (done < 0)
goto error;
if (done) {
isl_basic_map_free(context);
return bmap;
}
known = isl_basic_map_divs_known(context);
if (known < 0)
goto error;
if (!known)
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", "polly/lib/External/isl/isl_map_simplify.c"
, 3523); goto error; } while (0)
	"context has unknown divs", goto error)do { isl_handle_error(isl_basic_map_get_ctx(bmap), isl_error_invalid
, "context has unknown divs", "polly/lib/External/isl/isl_map_simplify.c"
, 3523); goto error; } while (0);

context = isl_basic_map_order_divs(context);
bmap = isl_basic_map_align_divs(bmap, context);
bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
bmap = isl_basic_map_sort_constraints(bmap);
context = isl_basic_map_sort_constraints(context);

bmap = drop_inequalities(bmap, context);
bmap = drop_equalities(bmap, context);

isl_basic_map_free(context);
bmap = isl_basic_map_finalize(bmap);
return bmap;
3537error:
isl_basic_map_free(bmap);
isl_basic_map_free(context);
return NULL((void*)0);
3541}

3543/* Replace "map" by the disjunct at position "pos" and free "context".
*/
3545static __isl_give isl_map *replace_by_disjunct(__isl_take isl_map *map,
int pos, __isl_take isl_basic_map *context)
3547{
isl_basic_map *bmap;

bmap = isl_basic_map_copy(map->p[pos]);
isl_map_free(map);
isl_basic_map_free(context);
return isl_map_from_basic_map(bmap);
3554}

3556/* Remove the constraints in "context" from "map".
* If any of the disjuncts in the result turns out to be the universe,
* then return this universe.
* "context" is assumed to have explicit representations
* for all local variables.
*/
3562__isl_give isl_map *isl_map_plain_gist_basic_map(__isl_take isl_map *map,
__isl_take isl_basic_map *context)
3564{
int i;
isl_bool univ, known;

univ = isl_basic_map_plain_is_universe(context);
if (univ < 0)
goto error;
if (univ) {
isl_basic_map_free(context);
return map;
}
known = isl_basic_map_divs_known(context);
if (known < 0)
goto error;
if (!known)
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", "polly/lib/External/isl/isl_map_simplify.c"
, 3580); goto error; } while (0)
	"context has unknown divs", goto error)do { isl_handle_error(isl_map_get_ctx(map), isl_error_invalid
, "context has unknown divs", "polly/lib/External/isl/isl_map_simplify.c"
, 3580); goto error; } while (0);

map = isl_map_cow(map);
if (!map)
goto error;
for (i = 0; i < map->n; ++i) {
map->p[i] = isl_basic_map_plain_gist(map->p[i],
				isl_basic_map_copy(context));
univ = isl_basic_map_plain_is_universe(map->p[i]);
if (univ < 0)
	goto error;
if (univ && map->n > 1)
	return replace_by_disjunct(map, i, context);
}

isl_basic_map_free(context);
ISL_F_CLR(map, ISL_MAP_NORMALIZED)(((map)->flags) &= ~((1 << 1)));
if (map->n > 1)
ISL_F_CLR(map, ISL_MAP_DISJOINT)(((map)->flags) &= ~((1 << 0)));
return map;
3600error:
isl_map_free(map);
isl_basic_map_free(context);
return NULL((void*)0);
3604}

3606/* Remove the constraints in "context" from "set".
* If any of the disjuncts in the result turns out to be the universe,
* then return this universe.
* "context" is assumed to have explicit representations
* for all local variables.
*/
3612__isl_give isl_setisl_map *isl_set_plain_gist_basic_set(__isl_take isl_setisl_map *set,
__isl_take isl_basic_setisl_basic_map *context)
3614{
return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set),
					bset_to_bmap(context)));
3617}

3619/* Remove the constraints in "context" from "map".
* If any of the disjuncts in the result turns out to be the universe,
* then return this universe.
* "context" is assumed to consist of a single disjunct and
* to have explicit representations for all local variables.
*/
3625__isl_give isl_map *isl_map_plain_gist(__isl_take isl_map *map,
__isl_take isl_map *context)
3627{
isl_basic_map *hull;

hull = isl_map_unshifted_simple_hull(context);
return isl_map_plain_gist_basic_map(map, hull);
3632}

3634/* Replace "map" by a universe map in the same space and free "drop".
*/
3636static __isl_give isl_map *replace_by_universe(__isl_take isl_map *map,
__isl_take isl_map *drop)
3638{
isl_map *res;

res = isl_map_universe(isl_map_get_space(map));
isl_map_free(map);
isl_map_free(drop);
return res;
3645}

3647/* Return a map that has the same intersection with "context" as "map"
* and that is as "simple" as possible.
*
* If "map" is already the universe, then we cannot make it any simpler.
* Similarly, if "context" is the universe, then we cannot exploit it
* to simplify "map"
* If "map" and "context" are identical to each other, then we can
* return the corresponding universe.
*
* If either "map" or "context" consists of multiple disjuncts,
* then check if "context" happens to be a subset of "map",
* in which case all constraints can be removed.
* In case of multiple disjuncts, the standard procedure
* may not be able to detect that all constraints can be removed.
*
* If none of these cases apply, we have to work a bit harder.
* During this computation, we make use of a single disjunct context,
* so if the original context consists of more than one disjunct
* then we need to approximate the context by a single disjunct set.
* Simply taking the simple hull may drop constraints that are
* only implicitly available in each disjunct.  We therefore also
* look for constraints among those defining "map" that are valid
* for the context.  These can then be used to simplify away
* the corresponding constraints in "map".
*/
3672__isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
__isl_take isl_map *context)
3674{
int equal;
int is_universe;
isl_size n_disjunct_map, n_disjunct_context;
isl_bool subset;
isl_basic_map *hull;

is_universe = isl_map_plain_is_universe(map);
if (is_universe >= 0 && !is_universe)
is_universe = isl_map_plain_is_universe(context);
if (is_universe < 0)
goto error;
if (is_universe) {
isl_map_free(context);
return map;
}

isl_map_align_params_bin(&map, &context);
equal = isl_map_plain_is_equal(map, context);
if (equal < 0)
goto error;
if (equal)
return replace_by_universe(map, context);

n_disjunct_map = isl_map_n_basic_map(map);
n_disjunct_context = isl_map_n_basic_map(context);
if (n_disjunct_map < 0 || n_disjunct_context < 0)
goto error;
if (n_disjunct_map != 1 || n_disjunct_context != 1) {
subset = isl_map_is_subset(context, map);
if (subset < 0)
	goto error;
if (subset)
	return replace_by_universe(map, context);
}

context = isl_map_compute_divs(context);
if (!context)
goto error;
if (n_disjunct_context == 1) {
hull = isl_map_simple_hull(context);
} else {
isl_ctx *ctx;
isl_map_list *list;

ctx = isl_map_get_ctx(map);
list = isl_map_list_alloc(ctx, 2);
list = isl_map_list_add(list, isl_map_copy(context));
list = isl_map_list_add(list, isl_map_copy(map));
hull = isl_map_unshifted_simple_hull_from_map_list(context,
						    list);
}
return isl_map_gist_basic_map(map, hull);
3727error:
isl_map_free(map);
isl_map_free(context);
return NULL((void*)0);
3731}

3733__isl_give isl_basic_setisl_basic_map *isl_basic_set_gist(__isl_take isl_basic_setisl_basic_map *bset,
__isl_take isl_basic_setisl_basic_map *context)
3735{
return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset),
				bset_to_bmap(context)));
3738}

3740__isl_give isl_setisl_map *isl_set_gist_basic_set(__isl_take isl_setisl_map *set,
__isl_take isl_basic_setisl_basic_map *context)
3742{
return set_from_map(isl_map_gist_basic_map(set_to_map(set),
			bset_to_bmap(context)));
3745}

3747__isl_give isl_setisl_map *isl_set_gist_params_basic_set(__isl_take isl_setisl_map *set,
__isl_take isl_basic_setisl_basic_map *context)
3749{
isl_space *space = isl_set_get_space(set);
isl_basic_setisl_basic_map *dom_context = isl_basic_set_universe(space);
dom_context = isl_basic_set_intersect_params(dom_context, context);
return isl_set_gist_basic_set(set, dom_context);
3754}

3756__isl_give isl_setisl_map *isl_set_gist(__isl_take isl_setisl_map *set,
__isl_take isl_setisl_map *context)
3758{
return set_from_map(isl_map_gist(set_to_map(set), set_to_map(context)));
3760}

3762/* Compute the gist of "bmap" with respect to the constraints "context"
* on the domain.
*/
3765__isl_give isl_basic_map *isl_basic_map_gist_domain(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_setisl_basic_map *context)
3767{
isl_space *space = isl_basic_map_get_space(bmap);
isl_basic_map *bmap_context = isl_basic_map_universe(space);

bmap_context = isl_basic_map_intersect_domain(bmap_context, context);
return isl_basic_map_gist(bmap, bmap_context);
3773}

3775__isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
__isl_take isl_setisl_map *context)
3777{
isl_map *map_context = isl_map_universe(isl_map_get_space(map));
map_context = isl_map_intersect_domain(map_context, context);
return isl_map_gist(map, map_context);
3781}

3783__isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
__isl_take isl_setisl_map *context)
3785{
isl_map *map_context = isl_map_universe(isl_map_get_space(map));
map_context = isl_map_intersect_range(map_context, context);
return isl_map_gist(map, map_context);
3789}

3791__isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
__isl_take isl_setisl_map *context)
3793{
isl_map *map_context = isl_map_universe(isl_map_get_space(map));
map_context = isl_map_intersect_params(map_context, context);
return isl_map_gist(map, map_context);
3797}

3799__isl_give isl_setisl_map *isl_set_gist_params(__isl_take isl_setisl_map *set,
__isl_take isl_setisl_map *context)
3801{
return isl_map_gist_params(set, context);
3803}

3805/* Quick check to see if two basic maps are disjoint.
* In particular, we reduce the equalities and inequalities of
* one basic map in the context of the equalities of the other
* basic map and check if we get a contradiction.
*/
3810isl_bool isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2)
3812{
struct isl_vec *v = NULL((void*)0);
int *elim = NULL((void*)0);
isl_size total;
int i;

if (isl_basic_map_check_equal_space(bmap1, bmap2) < 0)
return isl_bool_error;
if (bmap1->n_div || bmap2->n_div)
return isl_bool_false;
if (!bmap1->n_eq && !bmap2->n_eq)
return isl_bool_false;

total = isl_space_dim(bmap1->dim, isl_dim_all);
if (total < 0)
return isl_bool_error;
if (total == 0)
return isl_bool_false;
v = isl_vec_alloc(bmap1->ctx, 1 + total);
if (!v)
goto error;
elim = isl_alloc_array(bmap1->ctx, int, total)((int *)isl_malloc_or_die(bmap1->ctx, (total)*sizeof(int))
);
if (!elim)
goto error;
compute_elimination_index(bmap1, elim, total);
for (i = 0; i < bmap2->n_eq; ++i) {
int reduced;
reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
					bmap1, elim, total);
if (reduced && !isl_int_is_zero(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) == 0) &&
    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
	goto disjoint;
}
for (i = 0; i < bmap2->n_ineq; ++i) {
int reduced;
reduced = reduced_using_equalities(v->block.data,
			bmap2->ineq[i], bmap1, elim, total);
if (reduced && isl_int_is_neg(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) < 0) &&
    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
	goto disjoint;
}
compute_elimination_index(bmap2, elim, total);
for (i = 0; i < bmap1->n_ineq; ++i) {
int reduced;
reduced = reduced_using_equalities(v->block.data,
			bmap1->ineq[i], bmap2, elim, total);
if (reduced && isl_int_is_neg(v->block.data[0])(isl_sioimath_sgn(*(v->block.data[0])) < 0) &&
    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
	goto disjoint;
}
isl_vec_free(v);
free(elim);
return isl_bool_false;
3865disjoint:
isl_vec_free(v);
free(elim);
return isl_bool_true;
3869error:
isl_vec_free(v);
free(elim);
return isl_bool_error;
3873}

3875int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_setisl_basic_map *bset1,
__isl_keep isl_basic_setisl_basic_map *bset2)
3877{
return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1),
			      bset_to_bmap(bset2));
3880}

3882/* Does "test" hold for all pairs of basic maps in "map1" and "map2"?
*/
3884static isl_bool all_pairs(__isl_keep isl_map *map1, __isl_keep isl_map *map2,
isl_bool (*test)(__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2))
3887{
int i, j;

if (!map1 || !map2)
return isl_bool_error;

for (i = 0; i < map1->n; ++i) {
for (j = 0; j < map2->n; ++j) {
	isl_bool d = test(map1->p[i], map2->p[j]);
	if (d != isl_bool_true)
		return d;
}
}

return isl_bool_true;
3902}

3904/* Are "map1" and "map2" obviously disjoint, based on information
* that can be derived without looking at the individual basic maps?
*
* In particular, if one of them is empty or if they live in different spaces
* (ignoring parameters), then they are clearly disjoint.
*/
3910static isl_bool isl_map_plain_is_disjoint_global(__isl_keep isl_map *map1,
__isl_keep isl_map *map2)
3912{
isl_bool disjoint;
isl_bool match;

if (!map1 || !map2)
return isl_bool_error;

disjoint = isl_map_plain_is_empty(map1);
if (disjoint < 0 || disjoint)
return disjoint;

disjoint = isl_map_plain_is_empty(map2);
if (disjoint < 0 || disjoint)
return disjoint;

match = isl_map_tuple_is_equal(map1, isl_dim_in, map2, isl_dim_in);
if (match < 0 || !match)
return match < 0 ? isl_bool_error : isl_bool_true;

match = isl_map_tuple_is_equal(map1, isl_dim_out, map2, isl_dim_out);
if (match < 0 || !match)
return match < 0 ? isl_bool_error : isl_bool_true;

return isl_bool_false;
3936}

3938/* Are "map1" and "map2" obviously disjoint?
*
* If one of them is empty or if they live in different spaces (ignoring
* parameters), then they are clearly disjoint.
* This is checked by isl_map_plain_is_disjoint_global.
*
* If they have different parameters, then we skip any further tests.
*
* If they are obviously equal, but not obviously empty, then we will
* not be able to detect if they are disjoint.
*
* Otherwise we check if each basic map in "map1" is obviously disjoint
* from each basic map in "map2".
*/
3952isl_bool isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
__isl_keep isl_map *map2)
3954{
isl_bool disjoint;
isl_bool intersect;
isl_bool match;

disjoint = isl_map_plain_is_disjoint_global(map1, map2);
if (disjoint < 0 || disjoint)
return disjoint;

match = isl_map_has_equal_params(map1, map2);
if (match < 0 || !match)
return match < 0 ? isl_bool_error : isl_bool_false;

intersect = isl_map_plain_is_equal(map1, map2);
if (intersect < 0 || intersect)
return intersect < 0 ? isl_bool_error : isl_bool_false;

return all_pairs(map1, map2, &isl_basic_map_plain_is_disjoint);
3972}

3974/* Are "map1" and "map2" disjoint?
* The parameters are assumed to have been aligned.
*
* In particular, check whether all pairs of basic maps are disjoint.
*/
3979static isl_bool isl_map_is_disjoint_aligned(__isl_keep isl_map *map1,
__isl_keep isl_map *map2)
3981{
return all_pairs(map1, map2, &isl_basic_map_is_disjoint);
3983}

3985/* Are "map1" and "map2" disjoint?
*
* They are disjoint if they are "obviously disjoint" or if one of them
* is empty.  Otherwise, they are not disjoint if one of them is universal.
* If the two inputs are (obviously) equal and not empty, then they are
* not disjoint.
* If none of these cases apply, then check if all pairs of basic maps
* are disjoint after aligning the parameters.
*/
3994isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
3995{
isl_bool disjoint;
isl_bool intersect;

disjoint = isl_map_plain_is_disjoint_global(map1, map2);
if (disjoint < 0 || disjoint)
return disjoint;

disjoint = isl_map_is_empty(map1);
if (disjoint < 0 || disjoint)
return disjoint;

disjoint = isl_map_is_empty(map2);
if (disjoint < 0 || disjoint)
return disjoint;

intersect = isl_map_plain_is_universe(map1);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);

intersect = isl_map_plain_is_universe(map2);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);

intersect = isl_map_plain_is_equal(map1, map2);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);

return isl_map_align_params_map_map_and_test(map1, map2,
				&isl_map_is_disjoint_aligned);
4025}

4027/* Are "bmap1" and "bmap2" disjoint?
*
* They are disjoint if they are "obviously disjoint" or if one of them
* is empty.  Otherwise, they are not disjoint if one of them is universal.
* If none of these cases apply, we compute the intersection and see if
* the result is empty.
*/
4034isl_bool isl_basic_map_is_disjoint(__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2)
4036{
isl_bool disjoint;
isl_bool intersect;
isl_basic_map *test;

disjoint = isl_basic_map_plain_is_disjoint(bmap1, bmap2);
if (disjoint < 0 || disjoint)
return disjoint;

disjoint = isl_basic_map_is_empty(bmap1);
if (disjoint < 0 || disjoint)
return disjoint;

disjoint = isl_basic_map_is_empty(bmap2);
if (disjoint < 0 || disjoint)
return disjoint;

intersect = isl_basic_map_plain_is_universe(bmap1);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);

intersect = isl_basic_map_plain_is_universe(bmap2);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);

test = isl_basic_map_intersect(isl_basic_map_copy(bmap1),
isl_basic_map_copy(bmap2));
disjoint = isl_basic_map_is_empty(test);
isl_basic_map_free(test);

return disjoint;
4067}

4069/* Are "bset1" and "bset2" disjoint?
*/
4071isl_bool isl_basic_set_is_disjoint(__isl_keep isl_basic_setisl_basic_map *bset1,
__isl_keep isl_basic_setisl_basic_map *bset2)
4073{
return isl_basic_map_is_disjoint(bset1, bset2);
4075}

4077isl_bool isl_set_plain_is_disjoint(__isl_keep isl_setisl_map *set1,
__isl_keep isl_setisl_map *set2)
4079{
return isl_map_plain_is_disjoint(set_to_map(set1), set_to_map(set2));
4081}

4083/* Are "set1" and "set2" disjoint?
*/
4085isl_bool isl_set_is_disjoint(__isl_keep isl_setisl_map *set1, __isl_keep isl_setisl_map *set2)
4086{
return isl_map_is_disjoint(set1, set2);
4088}

4090/* Is "v" equal to 0, 1 or -1?
*/
4092static int is_zero_or_one(isl_int v)
4093{
return isl_int_is_zero(v)(isl_sioimath_sgn(*(v)) == 0) || isl_int_is_one(v)(isl_sioimath_cmp_si(*(v), 1) == 0) || isl_int_is_negone(v)(isl_sioimath_cmp_si(*(v), -1) == 0);
4095}

4097/* Are the "n" coefficients starting at "first" of inequality constraints
* "i" and "j" of "bmap" opposite to each other?
*/
4100static int is_opposite_part(__isl_keep isl_basic_map *bmap, int i, int j,
int first, int n)
4102{
return isl_seq_is_neg(bmap->ineq[i] + first, bmap->ineq[j] + first, n);
4104}

4106/* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
* apart from the constant term?
*/
4109static isl_bool is_opposite(__isl_keep isl_basic_map *bmap, int i, int j)
4110{
isl_size total;

total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_bool_error;
return is_opposite_part(bmap, i, j, 1, total);
4117}

4119/* Check if we can combine a given div with lower bound l and upper
* bound u with some other div and if so return that other div.
* Otherwise, return a position beyond the integer divisions.
* Return -1 on error.
*
* We first check that
*	- the bounds are opposites of each other (except for the constant
*	  term)
*	- the bounds do not reference any other div
*	- no div is defined in terms of this div
*
* Let m be the size of the range allowed on the div by the bounds.
* That is, the bounds are of the form
*
*	e <= a <= e + m - 1
*
* with e some expression in the other variables.
* We look for another div b such that no third div is defined in terms
* of this second div b and such that in any constraint that contains
* a (except for the given lower and upper bound), also contains b
* with a coefficient that is m times that of b.
* That is, all constraints (except for the lower and upper bound)
* are of the form
*
*	e + f (a + m b) >= 0
*
* Furthermore, in the constraints that only contain b, the coefficient
* of b should be equal to 1 or -1.
* If so, we return b so that "a + m b" can be replaced by
* a single div "c = a + m b".
*/
4150static int div_find_coalesce(__isl_keep isl_basic_map *bmap, int *pairs,
unsigned div, unsigned l, unsigned u)
4152{
int i, j;
unsigned n_div;
isl_size v_div;
int coalesce;
isl_bool opp;

n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div <= 1)
return n_div;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return -1;
if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + v_div, div) != -1)
return n_div;
if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + v_div + div + 1,
		   n_div - div - 1) != -1)
return n_div;
opp = is_opposite(bmap, l, u);
if (opp < 0 || !opp)
return opp < 0 ? -1 : n_div;

for (i = 0; i < n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
	continue;
if (!isl_int_is_zero(bmap->div[i][1 + 1 + v_div + div])(isl_sioimath_sgn(*(bmap->div[i][1 + 1 + v_div + div])) ==
 0))
	return n_div;
}

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]));
if (isl_int_is_neg(bmap->ineq[l][0])(isl_sioimath_sgn(*(bmap->ineq[l][0])) < 0)) {
isl_int_sub(bmap->ineq[l][0],isl_sioimath_sub((bmap->ineq[l][0]), *(bmap->ineq[l][0]
), *(bmap->ineq[u][0]))
	    bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_sub((bmap->ineq[l][0]), *(bmap->ineq[l][0]
), *(bmap->ineq[u][0]));
bmap = isl_basic_map_copy(bmap);
bmap = isl_basic_map_set_to_empty(bmap);
isl_basic_map_free(bmap);
return n_div;
}
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);
coalesce = n_div;
for (i = 0; i < n_div; ++i) {
if (i == div)
	continue;
if (!pairs[i])
	continue;
for (j = 0; j < n_div; ++j) {
	if (isl_int_is_zero(bmap->div[j][0])(isl_sioimath_sgn(*(bmap->div[j][0])) == 0))
		continue;
	if (!isl_int_is_zero(bmap->div[j][1 + 1 + v_div + i])(isl_sioimath_sgn(*(bmap->div[j][1 + 1 + v_div + i])) == 0
))
		break;
}
if (j < n_div)
	continue;
for (j = 0; j < bmap->n_ineq; ++j) {
	int valid;
	if (j == l || j == u)
		continue;
	if (isl_int_is_zero(bmap->ineq[j][1 + v_div + div])(isl_sioimath_sgn(*(bmap->ineq[j][1 + v_div + div])) == 0)) {
		if (is_zero_or_one(bmap->ineq[j][1 + v_div + i]))
			continue;
		break;
	}
	if (isl_int_is_zero(bmap->ineq[j][1 + v_div + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + v_div + i])) == 0))
		break;
	isl_int_mul(bmap->ineq[j][1 + v_div + div],isl_sioimath_mul((bmap->ineq[j][1 + v_div + div]), *(bmap->
ineq[j][1 + v_div + div]), *(bmap->ineq[l][0]))
		    bmap->ineq[j][1 + v_div + div],isl_sioimath_mul((bmap->ineq[j][1 + v_div + div]), *(bmap->
ineq[j][1 + v_div + div]), *(bmap->ineq[l][0]))
		    bmap->ineq[l][0])isl_sioimath_mul((bmap->ineq[j][1 + v_div + div]), *(bmap->
ineq[j][1 + v_div + div]), *(bmap->ineq[l][0]));
	valid = isl_int_eq(bmap->ineq[j][1 + v_div + div],(isl_sioimath_cmp(*(bmap->ineq[j][1 + v_div + div]), *(bmap
->ineq[j][1 + v_div + i])) == 0)
			   bmap->ineq[j][1 + v_div + i])(isl_sioimath_cmp(*(bmap->ineq[j][1 + v_div + div]), *(bmap
->ineq[j][1 + v_div + i])) == 0);
	isl_int_divexact(bmap->ineq[j][1 + v_div + div],isl_sioimath_tdiv_q((bmap->ineq[j][1 + v_div + div]), *(bmap
->ineq[j][1 + v_div + div]), *(bmap->ineq[l][0]))
			 bmap->ineq[j][1 + v_div + div],isl_sioimath_tdiv_q((bmap->ineq[j][1 + v_div + div]), *(bmap
->ineq[j][1 + v_div + div]), *(bmap->ineq[l][0]))
			 bmap->ineq[l][0])isl_sioimath_tdiv_q((bmap->ineq[j][1 + v_div + div]), *(bmap
->ineq[j][1 + v_div + div]), *(bmap->ineq[l][0]));
	if (!valid)
		break;
}
if (j < bmap->n_ineq)
	continue;
coalesce = i;
break;
}
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);
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]));
return coalesce;
4235}

4237/* Internal data structure used during the construction and/or evaluation of
* an inequality that ensures that a pair of bounds always allows
* for an integer value.
*
* "tab" is the tableau in which the inequality is evaluated.  It may
* be NULL until it is actually needed.
* "v" contains the inequality coefficients.
* "g", "fl" and "fu" are temporary scalars used during the construction and
* evaluation.
*/
4247struct test_ineq_data {
struct isl_tab *tab;
isl_vec *v;
isl_int g;
isl_int fl;
isl_int fu;
4253};

4255/* Free all the memory allocated by the fields of "data".
*/
4257static void test_ineq_data_clear(struct test_ineq_data *data)
4258{
isl_tab_free(data->tab);
isl_vec_free(data->v);
isl_int_clear(data->g)isl_sioimath_clear((data->g));
isl_int_clear(data->fl)isl_sioimath_clear((data->fl));
isl_int_clear(data->fu)isl_sioimath_clear((data->fu));
4264}

4266/* Is the inequality stored in data->v satisfied by "bmap"?
* That is, does it only attain non-negative values?
* data->tab is a tableau corresponding to "bmap".
*/
4270static isl_bool test_ineq_is_satisfied(__isl_keep isl_basic_map *bmap,
struct test_ineq_data *data)
4272{
isl_ctx *ctx;
enum isl_lp_result res;

ctx = isl_basic_map_get_ctx(bmap);
if (!data->tab)
data->tab = isl_tab_from_basic_map(bmap, 0);
res = isl_tab_min(data->tab, data->v->el, ctx->one, &data->g, NULL((void*)0), 0);
if (res == isl_lp_error)
return isl_bool_error;
return res == isl_lp_ok && isl_int_is_nonneg(data->g)(isl_sioimath_sgn(*(data->g)) >= 0);
4283}

4285/* Given a lower and an upper bound on div i, do they always allow
* for an integer value of the given div?
* Determine this property by constructing an inequality
* such that the property is guaranteed when the inequality is nonnegative.
* The lower bound is inequality l, while the upper bound is inequality u.
* The constructed inequality is stored in data->v.
*
* Let the upper bound be
*
*	-n_u a + e_u >= 0
*
* and the lower bound
*
*	n_l a + e_l >= 0
*
* Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
* We have
*
*	- f_u e_l <= f_u f_l g a <= f_l e_u
*
* Since all variables are integer valued, this is equivalent to
*
*	- f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
*
* If this interval is at least f_u f_l g, then it contains at least
* one integer value for a.
* That is, the test constraint is
*
*	f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
*
* or
*
*	f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0
*
* If the coefficients of f_l e_u + f_u e_l have a common divisor g',
* then the constraint can be scaled down by a factor g',
* with the constant term replaced by
* floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g').
* Note that the result of applying Fourier-Motzkin to this pair
* of constraints is
*
*	f_l e_u + f_u e_l >= 0
*
* If the constant term of the scaled down version of this constraint,
* i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant
* term of the scaled down test constraint, then the test constraint
* is known to hold and no explicit evaluation is required.
* This is essentially the Omega test.
*
* If the test constraint consists of only a constant term, then
* it is sufficient to look at the sign of this constant term.
*/
4337static isl_bool int_between_bounds(__isl_keep isl_basic_map *bmap, int i,
int l, int u, struct test_ineq_data *data)
4339{
unsigned offset;
isl_size n_div;

offset = isl_basic_map_offset(bmap, isl_dim_div);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
return isl_bool_error;

isl_int_gcd(data->g,isl_sioimath_gcd((data->g), *(bmap->ineq[l][offset + i]
), *(bmap->ineq[u][offset + i]))
    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]));
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));
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));
isl_int_neg(data->fu, data->fu)isl_sioimath_neg((data->fu), *(data->fu));
isl_seq_combine(data->v->el, data->fl, bmap->ineq[u],
	data->fu, bmap->ineq[l], offset + n_div);
isl_int_mul(data->g, data->g, data->fl)isl_sioimath_mul((data->g), *(data->g), *(data->fl));
isl_int_mul(data->g, data->g, data->fu)isl_sioimath_mul((data->g), *(data->g), *(data->fu));
isl_int_sub(data->g, data->g, data->fl)isl_sioimath_sub((data->g), *(data->g), *(data->fl));
isl_int_sub(data->g, data->g, data->fu)isl_sioimath_sub((data->g), *(data->g), *(data->fu));
isl_int_add_ui(data->g, data->g, 1)isl_sioimath_add_ui((data->g), *(data->g), 1);
isl_int_sub(data->fl, data->v->el[0], data->g)isl_sioimath_sub((data->fl), *(data->v->el[0]), *(data
->g));

isl_seq_gcd(data->v->el + 1, offset - 1 + n_div, &data->g);
if (isl_int_is_zero(data->g)(isl_sioimath_sgn(*(data->g)) == 0))
return isl_int_is_nonneg(data->fl)(isl_sioimath_sgn(*(data->fl)) >= 0);
if (isl_int_is_one(data->g)(isl_sioimath_cmp_si(*(data->g), 1) == 0)) {
isl_int_set(data->v->el[0], data->fl)isl_sioimath_set((data->v->el[0]), *(data->fl));
return test_ineq_is_satisfied(bmap, data);
}
isl_int_fdiv_q(data->fl, data->fl, data->g)isl_sioimath_fdiv_q((data->fl), *(data->fl), *(data->
g));
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));
if (isl_int_eq(data->fl, data->v->el[0])(isl_sioimath_cmp(*(data->fl), *(data->v->el[0])) ==
 0))
return isl_bool_true;
isl_int_set(data->v->el[0], data->fl)isl_sioimath_set((data->v->el[0]), *(data->fl));
isl_seq_scale_down(data->v->el + 1, data->v->el + 1, data->g,
	    offset - 1 + n_div);

return test_ineq_is_satisfied(bmap, data);
4378}

4380/* Remove more kinds of divs that are not strictly needed.
* In particular, if all pairs of lower and upper bounds on a div
* are such that they allow at least one integer value of the div,
* then we can eliminate the div using Fourier-Motzkin without
* introducing any spurious solutions.
*
* If at least one of the two constraints has a unit coefficient for the div,
* then the presence of such a value is guaranteed so there is no need to check.
* In particular, the value attained by the bound with unit coefficient
* can serve as this intermediate value.
*/
4391static __isl_give isl_basic_map *drop_more_redundant_divs(
__isl_take isl_basic_map *bmap, __isl_take int *pairs, int n)
4393{
isl_ctx *ctx;
struct test_ineq_data data = { NULL((void*)0), NULL((void*)0) };
unsigned off;
isl_size n_div;
int remove = -1;

isl_int_init(data.g)isl_sioimath_init((data.g));
isl_int_init(data.fl)isl_sioimath_init((data.fl));
isl_int_init(data.fu)isl_sioimath_init((data.fu));

n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
goto error;

ctx = isl_basic_map_get_ctx(bmap);
off = isl_basic_map_offset(bmap, isl_dim_div);
data.v = isl_vec_alloc(ctx, off + n_div);
if (!data.v)
goto error;

while (n > 0) {
int i, l, u;
int best = -1;
isl_bool has_int;

for (i = 0; i < n_div; ++i) {
	if (!pairs[i])
		continue;
	if (best >= 0 && pairs[best] <= pairs[i])
		continue;
	best = i;
}

i = best;
for (l = 0; l < bmap->n_ineq; ++l) {
	if (!isl_int_is_pos(bmap->ineq[l][off + i])(isl_sioimath_sgn(*(bmap->ineq[l][off + i])) > 0))
		continue;
	if (isl_int_is_one(bmap->ineq[l][off + i])(isl_sioimath_cmp_si(*(bmap->ineq[l][off + i]), 1) == 0))
		continue;
	for (u = 0; u < bmap->n_ineq; ++u) {
		if (!isl_int_is_neg(bmap->ineq[u][off + i])(isl_sioimath_sgn(*(bmap->ineq[u][off + i])) < 0))
			continue;
		if (isl_int_is_negone(bmap->ineq[u][off + i])(isl_sioimath_cmp_si(*(bmap->ineq[u][off + i]), -1) == 0))
			continue;
		has_int = int_between_bounds(bmap, i, l, u,
						&data);
		if (has_int < 0)
			goto error;
		if (data.tab && data.tab->empty)
			break;
		if (!has_int)
			break;
	}
	if (u < bmap->n_ineq)
		break;
}
if (data.tab && data.tab->empty) {
	bmap = isl_basic_map_set_to_empty(bmap);
	break;
}
if (l == bmap->n_ineq) {
	remove = i;
	break;
}
pairs[i] = 0;
--n;
}

test_ineq_data_clear(&data);

free(pairs);

if (remove < 0)
return bmap;

bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
return isl_basic_map_drop_redundant_divs(bmap);
4471error:
free(pairs);
isl_basic_map_free(bmap);
test_ineq_data_clear(&data);
return NULL((void*)0);
4476}

4478/* Given a pair of divs div1 and div2 such that, except for the lower bound l
* and the upper bound u, div1 always occurs together with div2 in the form
* (div1 + m div2), where m is the constant range on the variable div1
* allowed by l and u, replace the pair div1 and div2 by a single
* div that is equal to div1 + m div2.
*
* The new div will appear in the location that contains div2.
* We need to modify all constraints that contain
* div2 = (div - div1) / m
* The coefficient of div2 is known to be equal to 1 or -1.
* (If a constraint does not contain div2, it will also not contain div1.)
* If the constraint also contains div1, then we know they appear
* as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
* i.e., the coefficient of div is f.
*
* Otherwise, we first need to introduce div1 into the constraint.
* Let l be
*
*	div1 + f >=0
*
* and u
*
*	-div1 + f' >= 0
*
* A lower bound on div2
*
*	div2 + t >= 0
*
* can be replaced by
*
*	m div2 + div1 + m t + f >= 0
*
* An upper bound
*
*	-div2 + t >= 0
*
* can be replaced by
*
*	-(m div2 + div1) + m t + f' >= 0
*
* These constraint are those that we would obtain from eliminating
* div1 using Fourier-Motzkin.
*
* After all constraints have been modified, we drop the lower and upper
* bound and then drop div1.
* Since the new div is only placed in the same location that used
* to store div2, but otherwise has a different meaning, any possible
* explicit representation of the original div2 is removed.
*/
4527static __isl_give isl_basic_map *coalesce_divs(__isl_take isl_basic_map *bmap,
unsigned div1, unsigned div2, unsigned l, unsigned u)
4529{
isl_ctx *ctx;
isl_int m;
isl_size v_div;
unsigned total;
int i;

ctx = isl_basic_map_get_ctx(bmap);

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_basic_map_free(bmap);
total = 1 + v_div + bmap->n_div;

isl_int_init(m)isl_sioimath_init((m));
isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0])isl_sioimath_add((m), *(bmap->ineq[l][0]), *(bmap->ineq
[u][0]));
isl_int_add_ui(m, m, 1)isl_sioimath_add_ui((m), *(m), 1);

for (i = 0; i < bmap->n_ineq; ++i) {
if (i == l || i == u)
	continue;
if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div2])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div2])) == 0
))
	continue;
if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div1])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div1])) == 0
)) {
	if (isl_int_is_pos(bmap->ineq[i][1 + v_div + div2])(isl_sioimath_sgn(*(bmap->ineq[i][1 + v_div + div2])) >
 0))
		isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i],
				ctx->one, bmap->ineq[l], total);
	else
		isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i],
				ctx->one, bmap->ineq[u], total);
}
isl_int_set(bmap->ineq[i][1 + v_div + div2],isl_sioimath_set((bmap->ineq[i][1 + v_div + div2]), *(bmap
->ineq[i][1 + v_div + div1]))
	    bmap->ineq[i][1 + v_div + div1])isl_sioimath_set((bmap->ineq[i][1 + v_div + div2]), *(bmap
->ineq[i][1 + v_div + div1]));
isl_int_set_si(bmap->ineq[i][1 + v_div + div1], 0)isl_sioimath_set_si((bmap->ineq[i][1 + v_div + div1]), 0);
}

isl_int_clear(m)isl_sioimath_clear((m));
if (l > u) {
isl_basic_map_drop_inequality(bmap, l);
isl_basic_map_drop_inequality(bmap, u);
} else {
isl_basic_map_drop_inequality(bmap, u);
isl_basic_map_drop_inequality(bmap, l);
}
bmap = isl_basic_map_mark_div_unknown(bmap, div2);
bmap = isl_basic_map_drop_div(bmap, div1);
return bmap;
4576}

4578/* First check if we can coalesce any pair of divs and
* then continue with dropping more redundant divs.
*
* We loop over all pairs of lower and upper bounds on a div
* with coefficient 1 and -1, respectively, check if there
* is any other div "c" with which we can coalesce the div
* and if so, perform the coalescing.
*/
4586static __isl_give isl_basic_map *coalesce_or_drop_more_redundant_divs(
__isl_take isl_basic_map *bmap, int *pairs, int n)
4588{
int i, l, u;
isl_size v_div;
isl_size n_div;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (v_div < 0 || n_div < 0)
return isl_basic_map_free(bmap);

for (i = 0; i < n_div; ++i) {
if (!pairs[i])
	continue;
for (l = 0; l < bmap->n_ineq; ++l) {
	if (!isl_int_is_one(bmap->ineq[l][1 + v_div + i])(isl_sioimath_cmp_si(*(bmap->ineq[l][1 + v_div + i]), 1) ==
 0))
		continue;
	for (u = 0; u < bmap->n_ineq; ++u) {
		int c;

		if (!isl_int_is_negone(bmap->ineq[u][1+v_div+i])(isl_sioimath_cmp_si(*(bmap->ineq[u][1+v_div+i]), -1) == 0
))
			continue;
		c = div_find_coalesce(bmap, pairs, i, l, u);
		if (c < 0)
			goto error;
		if (c >= n_div)
			continue;
		free(pairs);
		bmap = coalesce_divs(bmap, i, c, l, u);
		return isl_basic_map_drop_redundant_divs(bmap);
	}
}
}

if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1))))) {
free(pairs);
return bmap;
}

return drop_more_redundant_divs(bmap, pairs, n);
4627error:
free(pairs);
isl_basic_map_free(bmap);
return NULL((void*)0);
4631}

4633/* Are the "n" coefficients starting at "first" of inequality constraints
* "i" and "j" of "bmap" equal to each other?
*/
4636static int is_parallel_part(__isl_keep isl_basic_map *bmap, int i, int j,
int first, int n)
4638{
return isl_seq_eq(bmap->ineq[i] + first, bmap->ineq[j] + first, n);
4640}

4642/* Are inequality constraints "i" and "j" of "bmap" equal to each other,
* apart from the constant term and the coefficient at position "pos"?
*/
4645static isl_bool is_parallel_except(__isl_keep isl_basic_map *bmap, int i, int j,
int pos)
4647{
isl_size total;

total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_bool_error;
return is_parallel_part(bmap, i, j, 1, pos - 1) &&
is_parallel_part(bmap, i, j, pos + 1, total - pos);
4655}

4657/* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
* apart from the constant term and the coefficient at position "pos"?
*/
4660static isl_bool is_opposite_except(__isl_keep isl_basic_map *bmap, int i, int j,
int pos)
4662{
isl_size total;

total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_bool_error;
return is_opposite_part(bmap, i, j, 1, pos - 1) &&
is_opposite_part(bmap, i, j, pos + 1, total - pos);
4670}

4672/* Restart isl_basic_map_drop_redundant_divs after "bmap" has
* been modified, simplying it if "simplify" is set.
* Free the temporary data structure "pairs" that was associated
* to the old version of "bmap".
*/
4677static __isl_give isl_basic_map *drop_redundant_divs_again(
__isl_take isl_basic_map *bmap, __isl_take int *pairs, int simplify)
4679{
if (simplify)
bmap = isl_basic_map_simplify(bmap);
free(pairs);
return isl_basic_map_drop_redundant_divs(bmap);
4684}

4686/* Is "div" the single unknown existentially quantified variable
* in inequality constraint "ineq" of "bmap"?
* "div" is known to have a non-zero coefficient in "ineq".
*/
4690static isl_bool single_unknown(__isl_keep isl_basic_map *bmap, int ineq,
int div)
4692{
int i;
isl_size n_div;
unsigned o_div;
isl_bool known;

known = isl_basic_map_div_is_known(bmap, div);
if (known < 0 || known)
return isl_bool_not(known);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
return isl_bool_error;
if (n_div == 1)
return isl_bool_true;
o_div = isl_basic_map_offset(bmap, isl_dim_div);
for (i = 0; i < n_div; ++i) {
isl_bool known;

if (i == div)
	continue;
if (isl_int_is_zero(bmap->ineq[ineq][o_div + i])(isl_sioimath_sgn(*(bmap->ineq[ineq][o_div + i])) == 0))
	continue;
known = isl_basic_map_div_is_known(bmap, i);
if (known < 0 || !known)
	return known;
}

return isl_bool_true;
4720}

4722/* Does integer division "div" have coefficient 1 in inequality constraint
* "ineq" of "map"?
*/
4725static isl_bool has_coef_one(__isl_keep isl_basic_map *bmap, int div, int ineq)
4726{
unsigned o_div;

o_div = isl_basic_map_offset(bmap, isl_dim_div);
if (isl_int_is_one(bmap->ineq[ineq][o_div + div])(isl_sioimath_cmp_si(*(bmap->ineq[ineq][o_div + div]), 1) ==
 0))
return isl_bool_true;

return isl_bool_false;
4734}

4736/* Turn inequality constraint "ineq" of "bmap" into an equality and
* then try and drop redundant divs again,
* freeing the temporary data structure "pairs" that was associated
* to the old version of "bmap".
*/
4741static __isl_give isl_basic_map *set_eq_and_try_again(
__isl_take isl_basic_map *bmap, int ineq, __isl_take int *pairs)
4743{
bmap = isl_basic_map_cow(bmap);
isl_basic_map_inequality_to_equality(bmap, ineq);
return drop_redundant_divs_again(bmap, pairs, 1);
4747}

4749/* Drop the integer division at position "div", along with the two
* inequality constraints "ineq1" and "ineq2" in which it appears
* from "bmap" and then try and drop redundant divs again,
* freeing the temporary data structure "pairs" that was associated
* to the old version of "bmap".
*/
4755static __isl_give isl_basic_map *drop_div_and_try_again(
__isl_take isl_basic_map *bmap, int div, int ineq1, int ineq2,
__isl_take int *pairs)
4758{
if (ineq1 > ineq2) {
isl_basic_map_drop_inequality(bmap, ineq1);
isl_basic_map_drop_inequality(bmap, ineq2);
} else {
isl_basic_map_drop_inequality(bmap, ineq2);
isl_basic_map_drop_inequality(bmap, ineq1);
}
bmap = isl_basic_map_drop_div(bmap, div);
return drop_redundant_divs_again(bmap, pairs, 0);
4768}

4770/* Given two inequality constraints
*
*	f(x) + n d + c >= 0,		(ineq)
*
* with d the variable at position "pos", and
*
*	f(x) + c0 >= 0,			(lower)
*
* compute the maximal value of the lower bound ceil((-f(x) - c)/n)
* determined by the first constraint.
* That is, store
*
*	ceil((c0 - c)/n)
*
* in *l.
*/
4786static void lower_bound_from_parallel(__isl_keep isl_basic_map *bmap,
int ineq, int lower, int pos, isl_int *l)
4788{
isl_int_neg(*l, bmap->ineq[ineq][0])isl_sioimath_neg((*l), *(bmap->ineq[ineq][0]));
isl_int_add(*l, *l, bmap->ineq[lower][0])isl_sioimath_add((*l), *(*l), *(bmap->ineq[lower][0]));
isl_int_cdiv_q(*l, *l, bmap->ineq[ineq][pos])isl_sioimath_cdiv_q((*l), *(*l), *(bmap->ineq[ineq][pos]));
4792}

4794/* Given two inequality constraints
*
*	f(x) + n d + c >= 0,		(ineq)
*
* with d the variable at position "pos", and
*
*	-f(x) - c0 >= 0,		(upper)
*
* compute the minimal value of the lower bound ceil((-f(x) - c)/n)
* determined by the first constraint.
* That is, store
*
*	ceil((-c1 - c)/n)
*
* in *u.
*/
4810static void lower_bound_from_opposite(__isl_keep isl_basic_map *bmap,
int ineq, int upper, int pos, isl_int *u)
4812{
isl_int_neg(*u, bmap->ineq[ineq][0])isl_sioimath_neg((*u), *(bmap->ineq[ineq][0]));
isl_int_sub(*u, *u, bmap->ineq[upper][0])isl_sioimath_sub((*u), *(*u), *(bmap->ineq[upper][0]));
isl_int_cdiv_q(*u, *u, bmap->ineq[ineq][pos])isl_sioimath_cdiv_q((*u), *(*u), *(bmap->ineq[ineq][pos]));
4816}

4818/* Given a lower bound constraint "ineq" on "div" in "bmap",
* does the corresponding lower bound have a fixed value in "bmap"?
*
* In particular, "ineq" is of the form
*
*	f(x) + n d + c >= 0
*
* with n > 0, c the constant term and
* d the existentially quantified variable "div".
* That is, the lower bound is
*
*	ceil((-f(x) - c)/n)
*
* Look for a pair of constraints
*
*	f(x) + c0 >= 0
*	-f(x) + c1 >= 0
*
* i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value.
* That is, check that
*
*	ceil((-c1 - c)/n) = ceil((c0 - c)/n)
*
* If so, return the index of inequality f(x) + c0 >= 0.
* Otherwise, return bmap->n_ineq.
* Return -1 on error.
*/
4845static int lower_bound_is_cst(__isl_keep isl_basic_map *bmap, int div, int ineq)
4846{
int i;
int lower = -1, upper = -1;
unsigned o_div;
isl_int l, u;
int equal;

o_div = isl_basic_map_offset(bmap, isl_dim_div);
for (i = 0; i < bmap->n_ineq && (lower < 0 || upper < 0); ++i) {
isl_bool par, opp;

if (i == ineq)
	continue;
if (!isl_int_is_zero(bmap->ineq[i][o_div + div])(isl_sioimath_sgn(*(bmap->ineq[i][o_div + div])) == 0))
	continue;
par = isl_bool_false;
if (lower < 0)
	par = is_parallel_except(bmap, ineq, i, o_div + div);
if (par < 0)
	return -1;
if (par) {
	lower = i;
	continue;
}
opp = isl_bool_false;
if (upper < 0)
	opp = is_opposite_except(bmap, ineq, i, o_div + div);
if (opp < 0)
	return -1;
if (opp)
	upper = i;
}

if (lower < 0 || upper < 0)
return bmap->n_ineq;

isl_int_init(l)isl_sioimath_init((l));
isl_int_init(u)isl_sioimath_init((u));

lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &l);
lower_bound_from_opposite(bmap, ineq, upper, o_div + div, &u);

equal = isl_int_eq(l, u)(isl_sioimath_cmp(*(l), *(u)) == 0);

isl_int_clear(l)isl_sioimath_clear((l));
isl_int_clear(u)isl_sioimath_clear((u));

return equal ? lower : bmap->n_ineq;
4894}

4896/* Given a lower bound constraint "ineq" on the existentially quantified
* variable "div", such that the corresponding lower bound has
* a fixed value in "bmap", assign this fixed value to the variable and
* then try and drop redundant divs again,
* freeing the temporary data structure "pairs" that was associated
* to the old version of "bmap".
* "lower" determines the constant value for the lower bound.
*
* In particular, "ineq" is of the form
*
*	f(x) + n d + c >= 0,
*
* while "lower" is of the form
*
*	f(x) + c0 >= 0
*
* The lower bound is ceil((-f(x) - c)/n) and its constant value
* is ceil((c0 - c)/n).
*/
4915static __isl_give isl_basic_map *fix_cst_lower(__isl_take isl_basic_map *bmap,
int div, int ineq, int lower, int *pairs)
4917{
isl_int c;
unsigned o_div;

isl_int_init(c)isl_sioimath_init((c));

o_div = isl_basic_map_offset(bmap, isl_dim_div);
lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &c);
bmap = isl_basic_map_fix(bmap, isl_dim_div, div, c);
free(pairs);

isl_int_clear(c)isl_sioimath_clear((c));

return isl_basic_map_drop_redundant_divs(bmap);
4931}

4933/* Do any of the integer divisions of "bmap" involve integer division "div"?
*
* The integer division "div" could only ever appear in any later
* integer division (with an explicit representation).
*/
4938static isl_bool any_div_involves_div(__isl_keep isl_basic_map *bmap, int div)
4939{
int i;
isl_size v_div, n_div;

v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (v_div < 0 || n_div < 0)
return isl_bool_error;

for (i = div + 1; i < n_div; ++i) {
isl_bool unknown;

unknown = isl_basic_map_div_is_marked_unknown(bmap, i);
if (unknown < 0)
	return isl_bool_error;
if (unknown)
	continue;
if (!isl_int_is_zero(bmap->div[i][1 + 1 + v_div + div])(isl_sioimath_sgn(*(bmap->div[i][1 + 1 + v_div + div])) ==
 0))
	return isl_bool_true;
}

return isl_bool_false;
4961}

4963/* Remove divs that are not strictly needed based on the inequality
* constraints.
* In particular, if a div only occurs positively (or negatively)
* in constraints, then it can simply be dropped.
* Also, if a div occurs in only two constraints and if moreover
* those two constraints are opposite to each other, except for the constant
* term and if the sum of the constant terms is such that for any value
* of the other values, there is always at least one integer value of the
* div, i.e., if one plus this sum is greater than or equal to
* the (absolute value) of the coefficient of the div in the constraints,
* then we can also simply drop the div.
*
* If an existentially quantified variable does not have an explicit
* representation, appears in only a single lower bound that does not
* involve any other such existentially quantified variables and appears
* in this lower bound with coefficient 1,
* then fix the variable to the value of the lower bound.  That is,
* turn the inequality into an equality.
* If for any value of the other variables, there is any value
* for the existentially quantified variable satisfying the constraints,
* then this lower bound also satisfies the constraints.
* It is therefore safe to pick this lower bound.
*
* The same reasoning holds even if the coefficient is not one.
* However, fixing the variable to the value of the lower bound may
* in general introduce an extra integer division, in which case
* it may be better to pick another value.
* If this integer division has a known constant value, then plugging
* in this constant value removes the existentially quantified variable
* completely.  In particular, if the lower bound is of the form
* ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and
* -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n),
* then the existentially quantified variable can be assigned this
* shared value.
*
* We skip divs that appear in equalities or in the definition of other divs.
* Divs that appear in the definition of other divs usually occur in at least
* 4 constraints, but the constraints may have been simplified.
*
* If any divs are left after these simple checks then we move on
* to more complicated cases in drop_more_redundant_divs.
*/
5005static __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs_ineq(
__isl_take isl_basic_map *bmap)
5007{
int i, j;
isl_size off;
int *pairs = NULL((void*)0);
int n = 0;
isl_size n_ineq;

if (!bmap)
goto error;
if (bmap->n_div == 0)
return bmap;

off = isl_basic_map_var_offset(bmap, isl_dim_div);
if (off < 0)
return isl_basic_map_free(bmap);
pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div)((int *)isl_calloc_or_die(bmap->ctx, bmap->n_div, sizeof
(int)));
if (!pairs)
goto error;

n_ineq = isl_basic_map_n_inequality(bmap);
if (n_ineq < 0)
goto error;
for (i = 0; i < bmap->n_div; ++i) {
int pos, neg;
int last_pos, last_neg;
int redundant;
int defined;
isl_bool involves, opp, set_div;

defined = !isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0);
involves = any_div_involves_div(bmap, i);
if (involves < 0)
	goto error;
if (involves)
	continue;
for (j = 0; j < bmap->n_eq; ++j)
	if (!isl_int_is_zero(bmap->eq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->eq[j][1 + off + i])) == 0))
		break;
if (j < bmap->n_eq)
	continue;
++n;
pos = neg = 0;
for (j = 0; j < bmap->n_ineq; ++j) {
	if (isl_int_is_pos(bmap->ineq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + off + i])) > 0)) {
		last_pos = j;
		++pos;
	}
	if (isl_int_is_neg(bmap->ineq[j][1 + off + i])(isl_sioimath_sgn(*(bmap->ineq[j][1 + off + i])) < 0)) {
		last_neg = j;
		++neg;
	}
}
pairs[i] = pos * neg;
if (pairs[i] == 0) {
	for (j = bmap->n_ineq - 1; j >= 0; --j)
		if (!isl_int_is_zero(bmap->ineq[j][1+off+i])(isl_sioimath_sgn(*(bmap->ineq[j][1+off+i])) == 0))
			isl_basic_map_drop_inequality(bmap, j);
	bmap = isl_basic_map_drop_div(bmap, i);
	return drop_redundant_divs_again(bmap, pairs, 0);
}
if (pairs[i] != 1)
	opp = isl_bool_false;
else
	opp = is_opposite(bmap, last_pos, last_neg);
if (opp < 0)
	goto error;
if (!opp) {
	int lower;
	isl_bool single, one;

	if (pos != 1)
		continue;
	single = single_unknown(bmap, last_pos, i);
	if (single < 0)
		goto error;
	if (!single)
		continue;
	one = has_coef_one(bmap, i, last_pos);
	if (one < 0)
		goto error;
	if (one)
		return set_eq_and_try_again(bmap, last_pos,
					    pairs);
	lower = lower_bound_is_cst(bmap, i, last_pos);
	if (lower < 0)
		goto error;
	if (lower < n_ineq)
		return fix_cst_lower(bmap, i, last_pos, lower,
				pairs);
	continue;
}

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]))
	    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]));
isl_int_add_ui(bmap->ineq[last_pos][0],isl_sioimath_add_ui((bmap->ineq[last_pos][0]), *(bmap->
ineq[last_pos][0]), 1)
	       bmap->ineq[last_pos][0], 1)isl_sioimath_add_ui((bmap->ineq[last_pos][0]), *(bmap->
ineq[last_pos][0]), 1);
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)
		bmap->ineq[last_pos][1+off+i])(isl_sioimath_cmp(*(bmap->ineq[last_pos][0]), *(bmap->ineq
[last_pos][1+off+i])) >= 0);
isl_int_sub_ui(bmap->ineq[last_pos][0],isl_sioimath_sub_ui((bmap->ineq[last_pos][0]), *(bmap->
ineq[last_pos][0]), 1)
	       bmap->ineq[last_pos][0], 1)isl_sioimath_sub_ui((bmap->ineq[last_pos][0]), *(bmap->
ineq[last_pos][0]), 1);
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]))
	    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]));
if (redundant)
	return drop_div_and_try_again(bmap, i,
				    last_pos, last_neg, pairs);
if (defined)
	set_div = isl_bool_false;
else
	set_div = ok_to_set_div_from_bound(bmap, i, last_pos);
if (set_div < 0)
	return isl_basic_map_free(bmap);
if (set_div) {
	bmap = set_div_from_lower_bound(bmap, i, last_pos);
	return drop_redundant_divs_again(bmap, pairs, 1);
}
pairs[i] = 0;
--n;
}

if (n > 0)
return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);

free(pairs);
return bmap;
5131error:
free(pairs);
isl_basic_map_free(bmap);
return NULL((void*)0);
5135}

5137/* Consider the coefficients at "c" as a row vector and replace
* them with their product with "T".  "T" is assumed to be a square matrix.
*/
5140static isl_stat preimage(isl_int *c, __isl_keep isl_mat *T)
5141{
isl_size n;
isl_ctx *ctx;
isl_vec *v;

n = isl_mat_rows(T);
if (n < 0)
return isl_stat_error;
if (isl_seq_first_non_zero(c, n) == -1)
return isl_stat_ok;
ctx = isl_mat_get_ctx(T);
v = isl_vec_alloc(ctx, n);
if (!v)
return isl_stat_error;
isl_seq_swp_or_cpy(v->el, c, n);
v = isl_vec_mat_product(v, isl_mat_copy(T));
if (!v)
return isl_stat_error;
isl_seq_swp_or_cpy(c, v->el, n);
isl_vec_free(v);

return isl_stat_ok;
5163}

5165/* Plug in T for the variables in "bmap" starting at "pos".
* T is a linear unimodular matrix, i.e., without constant term.
*/
5168static __isl_give isl_basic_map *isl_basic_map_preimage_vars(
__isl_take isl_basic_map *bmap, unsigned pos, __isl_take isl_mat *T)
5170{
int i;
isl_size n_row, n_col;

bmap = isl_basic_map_cow(bmap);
n_row = isl_mat_rows(T);
n_col = isl_mat_cols(T);
if (!bmap || n_row < 0 || n_col < 0)
goto error;

if (n_col != n_row)
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"
, "polly/lib/External/isl/isl_map_simplify.c", 5182); goto error
; } while (0)
	"expecting square matrix", goto error)do { isl_handle_error(isl_mat_get_ctx(T), isl_error_invalid, "expecting square matrix"
, "polly/lib/External/isl/isl_map_simplify.c", 5182); goto error
; } while (0);

if (isl_basic_map_check_range(bmap, isl_dim_all, pos, n_col) < 0)
goto error;

for (i = 0; i < bmap->n_eq; ++i)
if (preimage(bmap->eq[i] + 1 + pos, T) < 0)
	goto error;
for (i = 0; i < bmap->n_ineq; ++i)
if (preimage(bmap->ineq[i] + 1 + pos, T) < 0)
	goto error;
for (i = 0; i < bmap->n_div; ++i) {
if (isl_basic_map_div_is_marked_unknown(bmap, i))
	continue;
if (preimage(bmap->div[i] + 1 + 1 + pos, T) < 0)
	goto error;
}

isl_mat_free(T);
return bmap;
5202error:
isl_basic_map_free(bmap);
isl_mat_free(T);
return NULL((void*)0);
5206}

5208/* Remove divs that are not strictly needed.
*
* First look for an equality constraint involving two or more
* existentially quantified variables without an explicit
* representation.  Replace the combination that appears
* in the equality constraint by a single existentially quantified
* variable such that the equality can be used to derive
* an explicit representation for the variable.
* If there are no more such equality constraints, then continue
* with isl_basic_map_drop_redundant_divs_ineq.
*
* In particular, if the equality constraint is of the form
*
*	f(x) + \sum_i c_i a_i = 0
*
* with a_i existentially quantified variable without explicit
* representation, then apply a transformation on the existentially
* quantified variables to turn the constraint into
*
*	f(x) + g a_1' = 0
*
* with g the gcd of the c_i.
* In order to easily identify which existentially quantified variables
* have a complete explicit representation, i.e., without being defined
* in terms of other existentially quantified variables without
* an explicit representation, the existentially quantified variables
* are first sorted.
*
* The variable transformation is computed by extending the row
* [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation
*
*	[a_1']   [c_1/g ... c_n/g]   [ a_1 ]
*	[a_2']                       [ a_2 ]
*	 ...   =         U             ....
*	[a_n']            	     [ a_n ]
*
* with [c_1/g ... c_n/g] representing the first row of U.
* The inverse of U is then plugged into the original constraints.
* The call to isl_basic_map_simplify makes sure the explicit
* representation for a_1' is extracted from the equality constraint.
*/
5249__isl_give isl_basic_map *isl_basic_map_drop_redundant_divs(
__isl_take isl_basic_map *bmap)
5251{
int first;
int i;
unsigned o_div;
isl_size n_div;
int l;
isl_ctx *ctx;
isl_mat *T;

if (!bmap)
return NULL((void*)0);
if (isl_basic_map_divs_known(bmap))
return isl_basic_map_drop_redundant_divs_ineq(bmap);
if (bmap->n_eq == 0)
return isl_basic_map_drop_redundant_divs_ineq(bmap);
bmap = isl_basic_map_sort_divs(bmap);
if (!bmap)
return NULL((void*)0);

first = isl_basic_map_first_unknown_div(bmap);
if (first < 0)
return isl_basic_map_free(bmap);

o_div = isl_basic_map_offset(bmap, isl_dim_div);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
return isl_basic_map_free(bmap);

for (i = 0; i < bmap->n_eq; ++i) {
l = isl_seq_first_non_zero(bmap->eq[i] + o_div + first,
			    n_div - (first));
if (l < 0)
	continue;
l += first;
if (isl_seq_first_non_zero(bmap->eq[i] + o_div + l + 1,
			    n_div - (l + 1)) == -1)
	continue;
break;
}
if (i >= bmap->n_eq)
return isl_basic_map_drop_redundant_divs_ineq(bmap);

ctx = isl_basic_map_get_ctx(bmap);
T = isl_mat_alloc(ctx, n_div - l, n_div - l);
if (!T)
return isl_basic_map_free(bmap);
isl_seq_cpy(T->row[0], bmap->eq[i] + o_div + l, n_div - l);
T = isl_mat_normalize_row(T, 0);
T = isl_mat_unimodular_complete(T, 1);
T = isl_mat_right_inverse(T);

for (i = l; i < n_div; ++i)
bmap = isl_basic_map_mark_div_unknown(bmap, i);
bmap = isl_basic_map_preimage_vars(bmap, o_div - 1 + l, T);
bmap = isl_basic_map_simplify(bmap);

return isl_basic_map_drop_redundant_divs(bmap);
5308}

5310/* Does "bmap" satisfy any equality that involves more than 2 variables
* and/or has coefficients different from -1 and 1?
*/
5313static isl_bool has_multiple_var_equality(__isl_keep isl_basic_map *bmap)
5314{
int i;
isl_size total;

total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
10
←
Assuming 'total' is >= 0→
11
←
Taking false branch→
return isl_bool_error;

for (i = 0; i < bmap->n_eq; ++i) {
12
←
Assuming 'i' is < field 'n_eq'→
13
←
Loop condition is true.  Entering loop body→
int j, k;

j = isl_seq_first_non_zero(bmap->eq[i] + 1, total);
if (j < 0)
14
←
Assuming 'j' is >= 0→
	continue;
if (!isl_int_is_one(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), 1) == 0) &&
15
←
Taking true branch→
    !isl_int_is_negone(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), -1) == 0))
	return isl_bool_true;
16
←
Returning the value 1, which participates in a condition later→

j += 1;
k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j);
if (k < 0)
	continue;
j += k;
if (!isl_int_is_one(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), 1) == 0) &&
    !isl_int_is_negone(bmap->eq[i][1 + j])(isl_sioimath_cmp_si(*(bmap->eq[i][1 + j]), -1) == 0))
	return isl_bool_true;

j += 1;
k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j);
if (k >= 0)
	return isl_bool_true;
}

return isl_bool_false;
5348}

5350/* Remove any common factor g from the constraint coefficients in "v".
* The constant term is stored in the first position and is replaced
* by floor(c/g).  If any common factor is removed and if this results
* in a tightening of the constraint, then set *tightened.
*/
5355static __isl_give isl_vec *normalize_constraint(__isl_take isl_vec *v,
int *tightened)
5357{
isl_ctx *ctx;

if (!v)
34
←
Assuming 'v' is non-null→
35
←
Taking false branch→
return NULL((void*)0);
ctx = isl_vec_get_ctx(v);
isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd);
if (isl_int_is_zero(ctx->normalize_gcd)(isl_sioimath_sgn(*(ctx->normalize_gcd)) == 0))
36
←
Assuming the condition is false→
37
←
Taking false branch→
return v;
if (isl_int_is_one(ctx->normalize_gcd)(isl_sioimath_cmp_si(*(ctx->normalize_gcd), 1) == 0))
38
←
Assuming the condition is false→
39
←
Taking false branch→
return v;
v = isl_vec_cow(v);
if (!v)
40
←
Assuming 'v' is non-null→
return NULL((void*)0);
if (tightened40.1
'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
)))
41
←
Taking true branch→
*tightened = 1;
42
←
The value 1 is assigned to 'tightened', which participates in a condition later→
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));
isl_seq_scale_down(v->el + 1, v->el + 1, ctx->normalize_gcd,
		v->size - 1);
return v;
5377}

5379/* If "bmap" is an integer set that satisfies any equality involving
* more than 2 variables and/or has coefficients different from -1 and 1,
* then use variable compression to reduce the coefficients by removing
* any (hidden) common factor.
* In particular, apply the variable compression to each constraint,
* factor out any common factor in the non-constant coefficients and
* then apply the inverse of the compression.
* At the end, we mark the basic map as having reduced constants.
* If this flag is still set on the next invocation of this function,
* then we skip the computation.
*
* Removing a common factor may result in a tightening of some of
* the constraints.  If this happens, then we may end up with two
* opposite inequalities that can be replaced by an equality.
* We therefore call isl_basic_map_detect_inequality_pairs,
* which checks for such pairs of inequalities as well as eliminate_divs_eq
* and isl_basic_map_gauss if such a pair was found.
*
* Tightening may also result in some other constraints becoming
* (rationally) redundant with respect to the tightened constraint
* (in combination with other constraints).  The basic map may
* therefore no longer be assumed to have no redundant constraints.
*
* Note that this function may leave the result in an inconsistent state.
* In particular, the constraints may not be gaussed.
* Unfortunately, isl_map_coalesce actually depends on this inconsistent state
* for some of the test cases to pass successfully.
* Any potential modification of the representation is therefore only
* performed on a single copy of the basic map.
*/
5409__isl_give isl_basic_map *isl_basic_map_reduce_coefficients(
__isl_take isl_basic_map *bmap)
5411{
isl_size total;
isl_bool multi;
isl_ctx *ctx;
isl_vec *v;
isl_mat *eq, *T, *T2;
int i;
int tightened;

if (!bmap)
1
Assuming 'bmap' is non-null→
2
←
Taking false branch→
return NULL((void*)0);
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(!!(((bmap)->flags) & ((1 << 8)))))
3
←
Assuming the condition is true→
4
←
Taking false branch→
return bmap;
if (isl_basic_map_is_rational(bmap))
5
←
Assuming the condition is false→
6
←
Taking false branch→
return bmap;
if (bmap->n_eq == 0)
7
←
Assuming field 'n_eq' is not equal to 0→
8
←
Taking false branch→
return bmap;
multi = has_multiple_var_equality(bmap);
9
←
Calling 'has_multiple_var_equality'→
17
←
Returning from 'has_multiple_var_equality'→
if (multi17.1
'multi' is >= 0
 < 0)
18
←
Taking false branch→
return isl_basic_map_free(bmap);
if (!multi18.1
'multi' is 1
)
19
←
Taking false branch→
return bmap;

total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
20
←
Assuming 'total' is >= 0→
21
←
Taking false branch→
return isl_basic_map_free(bmap);
ctx = isl_basic_map_get_ctx(bmap);
v = isl_vec_alloc(ctx, 1 + total);
if (!v)
22
←
Assuming 'v' is non-null→
23
←
Taking false branch→
return isl_basic_map_free(bmap);

eq = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total);
T = isl_mat_variable_compression(eq, &T2);
if (!T || !T2)
24
←
Assuming 'T' is non-null→
25
←
Assuming 'T2' is non-null→
26
←
Taking false branch→
goto error;
if (T->n_col == 0) {
27
←
Assuming field 'n_col' is not equal to 0→
28
←
Taking false branch→
isl_mat_free(T);
isl_mat_free(T2);
isl_vec_free(v);
return isl_basic_map_set_to_empty(bmap);
}

bmap = isl_basic_map_cow(bmap);
if (!bmap)
29
←
Assuming 'bmap' is non-null→
30
←
Taking false branch→
goto error;

tightened = 0;
for (i = 0; i < bmap->n_ineq; ++i) {
31
←
Assuming 'i' is < field 'n_ineq'→
32
←
Loop condition is true.  Entering loop body→
46
←
Assuming 'i' is >= field 'n_ineq'→
47
←
Loop condition is false. Execution continues on line 5468→
isl_seq_cpy(v->el, bmap->ineq[i], 1 + total);
v = isl_vec_mat_product(v, isl_mat_copy(T));
v = normalize_constraint(v, &tightened);
33
←
Calling 'normalize_constraint'→
43
←
Returning from 'normalize_constraint'→
v = isl_vec_mat_product(v, isl_mat_copy(T2));
if (!v)
44
←
Assuming 'v' is non-null→
45
←
Taking false branch→
	goto error;
isl_seq_cpy(bmap->ineq[i], v->el, 1 + total);
}

isl_mat_free(T);
isl_mat_free(T2);
isl_vec_free(v);

ISL_F_SET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS)(((bmap)->flags) |= ((1 << 8)));

if (tightened47.1
'tightened' is 1
) {
48
←
Taking true branch→
int progress = 0;

ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT)(((bmap)->flags) &= ~((1 << 3)));
bmap = isl_basic_map_detect_inequality_pairs(bmap, &progress);
49
←
Calling 'isl_basic_map_detect_inequality_pairs'→
if (progress) {
	bmap = eliminate_divs_eq(bmap, &progress);
	bmap = isl_basic_map_gauss(bmap, NULL((void*)0));
}
}

return bmap;
5486error:
isl_mat_free(T);
isl_mat_free(T2);
isl_vec_free(v);
return isl_basic_map_free(bmap);
5491}

5493/* Shift the integer division at position "div" of "bmap"
* by "shift" times the variable at position "pos".
* "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
* corresponds to the constant term.
*
* That is, if the integer division has the form
*
*	floor(f(x)/d)
*
* then replace it by
*
*	floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
*/
5506__isl_give isl_basic_map *isl_basic_map_shift_div(
__isl_take isl_basic_map *bmap, int div, int pos, isl_int shift)
5508{
int i;
isl_size total, n_div;

if (isl_int_is_zero(shift)(isl_sioimath_sgn(*(shift)) == 0))
return bmap;
total = isl_basic_map_dim(bmap, isl_dim_all);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
total -= n_div;
if (total < 0 || n_div < 0)
return isl_basic_map_free(bmap);

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]));

for (i = 0; i < bmap->n_eq; ++i) {
if (isl_int_is_zero(bmap->eq[i][1 + total + div])(isl_sioimath_sgn(*(bmap->eq[i][1 + total + div])) == 0))
	continue;
isl_int_submul(bmap->eq[i][pos],isl_sioimath_submul((bmap->eq[i][pos]), *(shift), *(bmap->
eq[i][1 + total + div]))
		shift, bmap->eq[i][1 + total + div])isl_sioimath_submul((bmap->eq[i][pos]), *(shift), *(bmap->
eq[i][1 + total + div]));
}
for (i = 0; i < bmap->n_ineq; ++i) {
if (isl_int_is_zero(bmap->ineq[i][1 + total + div])(isl_sioimath_sgn(*(bmap->ineq[i][1 + total + div])) == 0))
	continue;
isl_int_submul(bmap->ineq[i][pos],isl_sioimath_submul((bmap->ineq[i][pos]), *(shift), *(bmap
->ineq[i][1 + total + div]))
		shift, bmap->ineq[i][1 + total + div])isl_sioimath_submul((bmap->ineq[i][pos]), *(shift), *(bmap
->ineq[i][1 + total + div]));
}
for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0])(isl_sioimath_sgn(*(bmap->div[i][0])) == 0))
	continue;
if (isl_int_is_zero(bmap->div[i][1 + 1 + total + div])(isl_sioimath_sgn(*(bmap->div[i][1 + 1 + total + div])) ==
 0))
	continue;
isl_int_submul(bmap->div[i][1 + pos],isl_sioimath_submul((bmap->div[i][1 + pos]), *(shift), *(bmap
->div[i][1 + 1 + total + div]))
		shift, bmap->div[i][1 + 1 + total + div])isl_sioimath_submul((bmap->div[i][1 + pos]), *(shift), *(bmap
->div[i][1 + 1 + total + div]));
}

return bmap;
5544}