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omega.c
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omega.c
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/* Source code for an implementation of the Omega test, an integer
programming algorithm for dependence analysis, by William Pugh,
appeared in Supercomputing '91 and CACM Aug 92.
This code has no license restrictions, and is considered public
domain.
Changes copyright (C) 2005, 2006, 2007, 2008, 2009,
2010 Free Software Foundation, Inc.
Contributed by Sebastian Pop <sebastian.pop@inria.fr>
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3. If not see
<http://www.gnu.org/licenses/>. */
/* For a detailed description, see "Constraint-Based Array Dependence
Analysis" William Pugh, David Wonnacott, TOPLAS'98 and David
Wonnacott's thesis:
ftp://ftp.cs.umd.edu/pub/omega/davewThesis/davewThesis.ps.gz
*/
#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tree.h"
#include "diagnostic-core.h"
#include "tree-pass.h"
#include "omega.h"
/* When set to true, keep substitution variables. When set to false,
resurrect substitution variables (convert substitutions back to EQs). */
static bool omega_reduce_with_subs = true;
/* When set to true, omega_simplify_problem checks for problem with no
solutions, calling verify_omega_pb. */
static bool omega_verify_simplification = false;
/* When set to true, only produce a single simplified result. */
static bool omega_single_result = false;
/* Set return_single_result to 1 when omega_single_result is true. */
static int return_single_result = 0;
/* Hash table for equations generated by the solver. */
#define HASH_TABLE_SIZE PARAM_VALUE (PARAM_OMEGA_HASH_TABLE_SIZE)
#define MAX_KEYS PARAM_VALUE (PARAM_OMEGA_MAX_KEYS)
static eqn hash_master;
static int next_key;
static int hash_version = 0;
/* Set to true for making the solver enter in approximation mode. */
static bool in_approximate_mode = false;
/* When set to zero, the solver is allowed to add new equalities to
the problem to be solved. */
static int conservative = 0;
/* Set to omega_true when the problem was successfully reduced, set to
omega_unknown when the solver is unable to determine an answer. */
static enum omega_result omega_found_reduction;
/* Set to true when the solver is allowed to add omega_red equations. */
static bool create_color = false;
/* Set to nonzero when the problem to be solved can be reduced. */
static int may_be_red = 0;
/* When false, there should be no substitution equations in the
simplified problem. */
static int please_no_equalities_in_simplified_problems = 0;
/* Variables names for pretty printing. */
static char wild_name[200][40];
/* Pointer to the void problem. */
static omega_pb no_problem = (omega_pb) 0;
/* Pointer to the problem to be solved. */
static omega_pb original_problem = (omega_pb) 0;
/* Return the integer A divided by B. */
static inline int
int_div (int a, int b)
{
if (a > 0)
return a/b;
else
return -((-a + b - 1)/b);
}
/* Return the integer A modulo B. */
static inline int
int_mod (int a, int b)
{
return a - b * int_div (a, b);
}
/* For X and Y positive integers, return X multiplied by Y and check
that the result does not overflow. */
static inline int
check_pos_mul (int x, int y)
{
if (x != 0)
gcc_assert ((INT_MAX) / x > y);
return x * y;
}
/* Return X multiplied by Y and check that the result does not
overflow. */
static inline int
check_mul (int x, int y)
{
if (x >= 0)
{
if (y >= 0)
return check_pos_mul (x, y);
else
return -check_pos_mul (x, -y);
}
else if (y >= 0)
return -check_pos_mul (-x, y);
else
return check_pos_mul (-x, -y);
}
/* Test whether equation E is red. */
static inline bool
omega_eqn_is_red (eqn e, int desired_res)
{
return (desired_res == omega_simplify && e->color == omega_red);
}
/* Return a string for VARIABLE. */
static inline char *
omega_var_to_str (int variable)
{
if (0 <= variable && variable <= 20)
return wild_name[variable];
if (-20 < variable && variable < 0)
return wild_name[40 + variable];
/* Collapse all the entries that would have overflowed. */
return wild_name[21];
}
/* Return a string for variable I in problem PB. */
static inline char *
omega_variable_to_str (omega_pb pb, int i)
{
return omega_var_to_str (pb->var[i]);
}
/* Do nothing function: used for default initializations. */
void
omega_no_procedure (omega_pb pb ATTRIBUTE_UNUSED)
{
}
void (*omega_when_reduced) (omega_pb) = omega_no_procedure;
/* Print to FILE from PB equation E with all its coefficients
multiplied by C. */
static void
omega_print_term (FILE *file, omega_pb pb, eqn e, int c)
{
int i;
bool first = true;
int n = pb->num_vars;
int went_first = -1;
for (i = 1; i <= n; i++)
if (c * e->coef[i] > 0)
{
first = false;
went_first = i;
if (c * e->coef[i] == 1)
fprintf (file, "%s", omega_variable_to_str (pb, i));
else
fprintf (file, "%d * %s", c * e->coef[i],
omega_variable_to_str (pb, i));
break;
}
for (i = 1; i <= n; i++)
if (i != went_first && c * e->coef[i] != 0)
{
if (!first && c * e->coef[i] > 0)
fprintf (file, " + ");
first = false;
if (c * e->coef[i] == 1)
fprintf (file, "%s", omega_variable_to_str (pb, i));
else if (c * e->coef[i] == -1)
fprintf (file, " - %s", omega_variable_to_str (pb, i));
else
fprintf (file, "%d * %s", c * e->coef[i],
omega_variable_to_str (pb, i));
}
if (!first && c * e->coef[0] > 0)
fprintf (file, " + ");
if (first || c * e->coef[0] != 0)
fprintf (file, "%d", c * e->coef[0]);
}
/* Print to FILE the equation E of problem PB. */
void
omega_print_eqn (FILE *file, omega_pb pb, eqn e, bool test, int extra)
{
int i;
int n = pb->num_vars + extra;
bool is_lt = test && e->coef[0] == -1;
bool first;
if (test)
{
if (e->touched)
fprintf (file, "!");
else if (e->key != 0)
fprintf (file, "%d: ", e->key);
}
if (e->color == omega_red)
fprintf (file, "[");
first = true;
for (i = is_lt ? 1 : 0; i <= n; i++)
if (e->coef[i] < 0)
{
if (!first)
fprintf (file, " + ");
else
first = false;
if (i == 0)
fprintf (file, "%d", -e->coef[i]);
else if (e->coef[i] == -1)
fprintf (file, "%s", omega_variable_to_str (pb, i));
else
fprintf (file, "%d * %s", -e->coef[i],
omega_variable_to_str (pb, i));
}
if (first)
{
if (is_lt)
{
fprintf (file, "1");
is_lt = false;
}
else
fprintf (file, "0");
}
if (test == 0)
fprintf (file, " = ");
else if (is_lt)
fprintf (file, " < ");
else
fprintf (file, " <= ");
first = true;
for (i = 0; i <= n; i++)
if (e->coef[i] > 0)
{
if (!first)
fprintf (file, " + ");
else
first = false;
if (i == 0)
fprintf (file, "%d", e->coef[i]);
else if (e->coef[i] == 1)
fprintf (file, "%s", omega_variable_to_str (pb, i));
else
fprintf (file, "%d * %s", e->coef[i],
omega_variable_to_str (pb, i));
}
if (first)
fprintf (file, "0");
if (e->color == omega_red)
fprintf (file, "]");
}
/* Print to FILE all the variables of problem PB. */
static void
omega_print_vars (FILE *file, omega_pb pb)
{
int i;
fprintf (file, "variables = ");
if (pb->safe_vars > 0)
fprintf (file, "protected (");
for (i = 1; i <= pb->num_vars; i++)
{
fprintf (file, "%s", omega_variable_to_str (pb, i));
if (i == pb->safe_vars)
fprintf (file, ")");
if (i < pb->num_vars)
fprintf (file, ", ");
}
fprintf (file, "\n");
}
/* Debug problem PB. */
DEBUG_FUNCTION void
debug_omega_problem (omega_pb pb)
{
omega_print_problem (stderr, pb);
}
/* Print to FILE problem PB. */
void
omega_print_problem (FILE *file, omega_pb pb)
{
int e;
if (!pb->variables_initialized)
omega_initialize_variables (pb);
omega_print_vars (file, pb);
for (e = 0; e < pb->num_eqs; e++)
{
omega_print_eq (file, pb, &pb->eqs[e]);
fprintf (file, "\n");
}
fprintf (file, "Done with EQ\n");
for (e = 0; e < pb->num_geqs; e++)
{
omega_print_geq (file, pb, &pb->geqs[e]);
fprintf (file, "\n");
}
fprintf (file, "Done with GEQ\n");
for (e = 0; e < pb->num_subs; e++)
{
eqn eq = &pb->subs[e];
if (eq->color == omega_red)
fprintf (file, "[");
if (eq->key > 0)
fprintf (file, "%s := ", omega_var_to_str (eq->key));
else
fprintf (file, "#%d := ", eq->key);
omega_print_term (file, pb, eq, 1);
if (eq->color == omega_red)
fprintf (file, "]");
fprintf (file, "\n");
}
}
/* Return the number of equations in PB tagged omega_red. */
int
omega_count_red_equations (omega_pb pb)
{
int e, i;
int result = 0;
for (e = 0; e < pb->num_eqs; e++)
if (pb->eqs[e].color == omega_red)
{
for (i = pb->num_vars; i > 0; i--)
if (pb->geqs[e].coef[i])
break;
if (i == 0 && pb->geqs[e].coef[0] == 1)
return 0;
else
result += 2;
}
for (e = 0; e < pb->num_geqs; e++)
if (pb->geqs[e].color == omega_red)
result += 1;
for (e = 0; e < pb->num_subs; e++)
if (pb->subs[e].color == omega_red)
result += 2;
return result;
}
/* Print to FILE all the equations in PB that are tagged omega_red. */
void
omega_print_red_equations (FILE *file, omega_pb pb)
{
int e;
if (!pb->variables_initialized)
omega_initialize_variables (pb);
omega_print_vars (file, pb);
for (e = 0; e < pb->num_eqs; e++)
if (pb->eqs[e].color == omega_red)
{
omega_print_eq (file, pb, &pb->eqs[e]);
fprintf (file, "\n");
}
for (e = 0; e < pb->num_geqs; e++)
if (pb->geqs[e].color == omega_red)
{
omega_print_geq (file, pb, &pb->geqs[e]);
fprintf (file, "\n");
}
for (e = 0; e < pb->num_subs; e++)
if (pb->subs[e].color == omega_red)
{
eqn eq = &pb->subs[e];
fprintf (file, "[");
if (eq->key > 0)
fprintf (file, "%s := ", omega_var_to_str (eq->key));
else
fprintf (file, "#%d := ", eq->key);
omega_print_term (file, pb, eq, 1);
fprintf (file, "]\n");
}
}
/* Pretty print PB to FILE. */
void
omega_pretty_print_problem (FILE *file, omega_pb pb)
{
int e, v, v1, v2, v3, t;
bool *live = XNEWVEC (bool, OMEGA_MAX_GEQS);
int stuffPrinted = 0;
bool change;
typedef enum {
none, le, lt
} partial_order_type;
partial_order_type **po = XNEWVEC (partial_order_type *,
OMEGA_MAX_VARS * OMEGA_MAX_VARS);
int **po_eq = XNEWVEC (int *, OMEGA_MAX_VARS * OMEGA_MAX_VARS);
int *last_links = XNEWVEC (int, OMEGA_MAX_VARS);
int *first_links = XNEWVEC (int, OMEGA_MAX_VARS);
int *chain_length = XNEWVEC (int, OMEGA_MAX_VARS);
int *chain = XNEWVEC (int, OMEGA_MAX_VARS);
int i, m;
bool multiprint;
if (!pb->variables_initialized)
omega_initialize_variables (pb);
if (pb->num_vars > 0)
{
omega_eliminate_redundant (pb, false);
for (e = 0; e < pb->num_eqs; e++)
{
if (stuffPrinted)
fprintf (file, "; ");
stuffPrinted = 1;
omega_print_eq (file, pb, &pb->eqs[e]);
}
for (e = 0; e < pb->num_geqs; e++)
live[e] = true;
while (1)
{
for (v = 1; v <= pb->num_vars; v++)
{
last_links[v] = first_links[v] = 0;
chain_length[v] = 0;
for (v2 = 1; v2 <= pb->num_vars; v2++)
po[v][v2] = none;
}
for (e = 0; e < pb->num_geqs; e++)
if (live[e])
{
for (v = 1; v <= pb->num_vars; v++)
if (pb->geqs[e].coef[v] == 1)
first_links[v]++;
else if (pb->geqs[e].coef[v] == -1)
last_links[v]++;
v1 = pb->num_vars;
while (v1 > 0 && pb->geqs[e].coef[v1] == 0)
v1--;
v2 = v1 - 1;
while (v2 > 0 && pb->geqs[e].coef[v2] == 0)
v2--;
v3 = v2 - 1;
while (v3 > 0 && pb->geqs[e].coef[v3] == 0)
v3--;
if (pb->geqs[e].coef[0] > 0 || pb->geqs[e].coef[0] < -1
|| v2 <= 0 || v3 > 0
|| pb->geqs[e].coef[v1] * pb->geqs[e].coef[v2] != -1)
{
/* Not a partial order relation. */
}
else
{
if (pb->geqs[e].coef[v1] == 1)
{
v3 = v2;
v2 = v1;
v1 = v3;
}
/* Relation is v1 <= v2 or v1 < v2. */
po[v1][v2] = ((pb->geqs[e].coef[0] == 0) ? le : lt);
po_eq[v1][v2] = e;
}
}
for (v = 1; v <= pb->num_vars; v++)
chain_length[v] = last_links[v];
/* Just in case pb->num_vars <= 0. */
change = false;
for (t = 0; t < pb->num_vars; t++)
{
change = false;
for (v1 = 1; v1 <= pb->num_vars; v1++)
for (v2 = 1; v2 <= pb->num_vars; v2++)
if (po[v1][v2] != none &&
chain_length[v1] <= chain_length[v2])
{
chain_length[v1] = chain_length[v2] + 1;
change = true;
}
}
/* Caught in cycle. */
gcc_assert (!change);
for (v1 = 1; v1 <= pb->num_vars; v1++)
if (chain_length[v1] == 0)
first_links[v1] = 0;
v = 1;
for (v1 = 2; v1 <= pb->num_vars; v1++)
if (chain_length[v1] + first_links[v1] >
chain_length[v] + first_links[v])
v = v1;
if (chain_length[v] + first_links[v] == 0)
break;
if (stuffPrinted)
fprintf (file, "; ");
stuffPrinted = 1;
/* Chain starts at v. */
{
int tmp;
bool first = true;
for (e = 0; e < pb->num_geqs; e++)
if (live[e] && pb->geqs[e].coef[v] == 1)
{
if (!first)
fprintf (file, ", ");
tmp = pb->geqs[e].coef[v];
pb->geqs[e].coef[v] = 0;
omega_print_term (file, pb, &pb->geqs[e], -1);
pb->geqs[e].coef[v] = tmp;
live[e] = false;
first = false;
}
if (!first)
fprintf (file, " <= ");
}
/* Find chain. */
chain[0] = v;
m = 1;
while (1)
{
/* Print chain. */
for (v2 = 1; v2 <= pb->num_vars; v2++)
if (po[v][v2] && chain_length[v] == 1 + chain_length[v2])
break;
if (v2 > pb->num_vars)
break;
chain[m++] = v2;
v = v2;
}
fprintf (file, "%s", omega_variable_to_str (pb, chain[0]));
for (multiprint = false, i = 1; i < m; i++)
{
v = chain[i - 1];
v2 = chain[i];
if (po[v][v2] == le)
fprintf (file, " <= ");
else
fprintf (file, " < ");
fprintf (file, "%s", omega_variable_to_str (pb, v2));
live[po_eq[v][v2]] = false;
if (!multiprint && i < m - 1)
for (v3 = 1; v3 <= pb->num_vars; v3++)
{
if (v == v3 || v2 == v3
|| po[v][v2] != po[v][v3]
|| po[v2][chain[i + 1]] != po[v3][chain[i + 1]])
continue;
fprintf (file, ",%s", omega_variable_to_str (pb, v3));
live[po_eq[v][v3]] = false;
live[po_eq[v3][chain[i + 1]]] = false;
multiprint = true;
}
else
multiprint = false;
}
v = chain[m - 1];
/* Print last_links. */
{
int tmp;
bool first = true;
for (e = 0; e < pb->num_geqs; e++)
if (live[e] && pb->geqs[e].coef[v] == -1)
{
if (!first)
fprintf (file, ", ");
else
fprintf (file, " <= ");
tmp = pb->geqs[e].coef[v];
pb->geqs[e].coef[v] = 0;
omega_print_term (file, pb, &pb->geqs[e], 1);
pb->geqs[e].coef[v] = tmp;
live[e] = false;
first = false;
}
}
}
for (e = 0; e < pb->num_geqs; e++)
if (live[e])
{
if (stuffPrinted)
fprintf (file, "; ");
stuffPrinted = 1;
omega_print_geq (file, pb, &pb->geqs[e]);
}
for (e = 0; e < pb->num_subs; e++)
{
eqn eq = &pb->subs[e];
if (stuffPrinted)
fprintf (file, "; ");
stuffPrinted = 1;
if (eq->key > 0)
fprintf (file, "%s := ", omega_var_to_str (eq->key));
else
fprintf (file, "#%d := ", eq->key);
omega_print_term (file, pb, eq, 1);
}
}
free (live);
free (po);
free (po_eq);
free (last_links);
free (first_links);
free (chain_length);
free (chain);
}
/* Assign to variable I in PB the next wildcard name. The name of a
wildcard is a negative number. */
static int next_wild_card = 0;
static void
omega_name_wild_card (omega_pb pb, int i)
{
--next_wild_card;
if (next_wild_card < -PARAM_VALUE (PARAM_OMEGA_MAX_WILD_CARDS))
next_wild_card = -1;
pb->var[i] = next_wild_card;
}
/* Return the index of the last protected (or safe) variable in PB,
after having added a new wildcard variable. */
static int
omega_add_new_wild_card (omega_pb pb)
{
int e;
int i = ++pb->safe_vars;
pb->num_vars++;
/* Make a free place in the protected (safe) variables, by moving
the non protected variable pointed by "I" at the end, ie. at
offset pb->num_vars. */
if (pb->num_vars != i)
{
/* Move "I" for all the inequalities. */
for (e = pb->num_geqs - 1; e >= 0; e--)
{
if (pb->geqs[e].coef[i])
pb->geqs[e].touched = 1;
pb->geqs[e].coef[pb->num_vars] = pb->geqs[e].coef[i];
}
/* Move "I" for all the equalities. */
for (e = pb->num_eqs - 1; e >= 0; e--)
pb->eqs[e].coef[pb->num_vars] = pb->eqs[e].coef[i];
/* Move "I" for all the substitutions. */
for (e = pb->num_subs - 1; e >= 0; e--)
pb->subs[e].coef[pb->num_vars] = pb->subs[e].coef[i];
/* Move the identifier. */
pb->var[pb->num_vars] = pb->var[i];
}
/* Initialize at zero all the coefficients */
for (e = pb->num_geqs - 1; e >= 0; e--)
pb->geqs[e].coef[i] = 0;
for (e = pb->num_eqs - 1; e >= 0; e--)
pb->eqs[e].coef[i] = 0;
for (e = pb->num_subs - 1; e >= 0; e--)
pb->subs[e].coef[i] = 0;
/* And give it a name. */
omega_name_wild_card (pb, i);
return i;
}
/* Delete inequality E from problem PB that has N_VARS variables. */
static void
omega_delete_geq (omega_pb pb, int e, int n_vars)
{
if (dump_file && (dump_flags & TDF_DETAILS))
{
fprintf (dump_file, "Deleting %d (last:%d): ", e, pb->num_geqs - 1);
omega_print_geq (dump_file, pb, &pb->geqs[e]);
fprintf (dump_file, "\n");
}
if (e < pb->num_geqs - 1)
omega_copy_eqn (&pb->geqs[e], &pb->geqs[pb->num_geqs - 1], n_vars);
pb->num_geqs--;
}
/* Delete extra inequality E from problem PB that has N_VARS
variables. */
static void
omega_delete_geq_extra (omega_pb pb, int e, int n_vars)
{
if (dump_file && (dump_flags & TDF_DETAILS))
{
fprintf (dump_file, "Deleting %d: ",e);
omega_print_geq_extra (dump_file, pb, &pb->geqs[e]);
fprintf (dump_file, "\n");
}
if (e < pb->num_geqs - 1)
omega_copy_eqn (&pb->geqs[e], &pb->geqs[pb->num_geqs - 1], n_vars);
pb->num_geqs--;
}
/* Remove variable I from problem PB. */
static void
omega_delete_variable (omega_pb pb, int i)
{
int n_vars = pb->num_vars;
int e;
if (omega_safe_var_p (pb, i))
{
int j = pb->safe_vars;
for (e = pb->num_geqs - 1; e >= 0; e--)
{
pb->geqs[e].touched = 1;
pb->geqs[e].coef[i] = pb->geqs[e].coef[j];
pb->geqs[e].coef[j] = pb->geqs[e].coef[n_vars];
}
for (e = pb->num_eqs - 1; e >= 0; e--)
{
pb->eqs[e].coef[i] = pb->eqs[e].coef[j];
pb->eqs[e].coef[j] = pb->eqs[e].coef[n_vars];
}
for (e = pb->num_subs - 1; e >= 0; e--)
{
pb->subs[e].coef[i] = pb->subs[e].coef[j];
pb->subs[e].coef[j] = pb->subs[e].coef[n_vars];
}
pb->var[i] = pb->var[j];
pb->var[j] = pb->var[n_vars];
}
else if (i < n_vars)
{
for (e = pb->num_geqs - 1; e >= 0; e--)
if (pb->geqs[e].coef[n_vars])
{
pb->geqs[e].coef[i] = pb->geqs[e].coef[n_vars];
pb->geqs[e].touched = 1;
}
for (e = pb->num_eqs - 1; e >= 0; e--)
pb->eqs[e].coef[i] = pb->eqs[e].coef[n_vars];
for (e = pb->num_subs - 1; e >= 0; e--)
pb->subs[e].coef[i] = pb->subs[e].coef[n_vars];
pb->var[i] = pb->var[n_vars];
}
if (omega_safe_var_p (pb, i))
pb->safe_vars--;
pb->num_vars--;
}
/* Because the coefficients of an equation are sparse, PACKING records
indices for non null coefficients. */
static int *packing;
/* Set up the coefficients of PACKING, following the coefficients of
equation EQN that has NUM_VARS variables. */
static inline int
setup_packing (eqn eqn, int num_vars)
{
int k;
int n = 0;
for (k = num_vars; k >= 0; k--)
if (eqn->coef[k])
packing[n++] = k;
return n;
}
/* Computes a linear combination of EQ and SUB at VAR with coefficient
C, such that EQ->coef[VAR] is set to 0. TOP_VAR is the number of
non null indices of SUB stored in PACKING. */
static inline void
omega_substitute_red_1 (eqn eq, eqn sub, int var, int c, bool *found_black,
int top_var)
{
if (eq->coef[var] != 0)
{
if (eq->color == omega_black)
*found_black = true;
else
{
int j, k = eq->coef[var];
eq->coef[var] = 0;
for (j = top_var; j >= 0; j--)
eq->coef[packing[j]] -= sub->coef[packing[j]] * k * c;
}
}
}
/* Substitute in PB variable VAR with "C * SUB". */
static void
omega_substitute_red (omega_pb pb, eqn sub, int var, int c, bool *found_black)
{
int e, top_var = setup_packing (sub, pb->num_vars);
*found_black = false;
if (dump_file && (dump_flags & TDF_DETAILS))
{
if (sub->color == omega_red)
fprintf (dump_file, "[");
fprintf (dump_file, "substituting using %s := ",
omega_variable_to_str (pb, var));
omega_print_term (dump_file, pb, sub, -c);
if (sub->color == omega_red)
fprintf (dump_file, "]");
fprintf (dump_file, "\n");
omega_print_vars (dump_file, pb);
}
for (e = pb->num_eqs - 1; e >= 0; e--)
{
eqn eqn = &(pb->eqs[e]);
omega_substitute_red_1 (eqn, sub, var, c, found_black, top_var);
if (dump_file && (dump_flags & TDF_DETAILS))
{
omega_print_eq (dump_file, pb, eqn);
fprintf (dump_file, "\n");
}
}
for (e = pb->num_geqs - 1; e >= 0; e--)
{
eqn eqn = &(pb->geqs[e]);
omega_substitute_red_1 (eqn, sub, var, c, found_black, top_var);
if (eqn->coef[var] && eqn->color == omega_red)
eqn->touched = 1;
if (dump_file && (dump_flags & TDF_DETAILS))
{
omega_print_geq (dump_file, pb, eqn);
fprintf (dump_file, "\n");