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z3/src/nlsat/nlsat_interval_set.cpp
Nikolaj Bjorner 96e157e201 fix warnings for unused variables 
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2016-05-17 13:54:22 -07:00

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/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
nlsat_interval_set.cpp
Abstract:
Sets of disjoint infeasible intervals.
Author:
Leonardo de Moura (leonardo) 2012-01-11.
Revision History:
--*/
#include"nlsat_interval_set.h"
#include"algebraic_numbers.h"
#include"buffer.h"
namespace nlsat {
struct interval {
unsigned m_lower_open:1;
unsigned m_upper_open:1;
unsigned m_lower_inf:1;
unsigned m_upper_inf:1;
literal m_justification;
anum m_lower;
anum m_upper;
};
class interval_set {
public:
static unsigned get_obj_size(unsigned num) { return sizeof(interval_set) + num*sizeof(interval); }
unsigned m_num_intervals;
unsigned m_ref_count:31;
unsigned m_full:1;
interval m_intervals[0];
};
void display(std::ostream & out, anum_manager & am, interval const & curr) {
if (curr.m_lower_inf) {
out << "(-oo, ";
}
else {
if (curr.m_lower_open)
out << "(";
else
out << "[";
am.display_decimal(out, curr.m_lower);
out << ", ";
}
if (curr.m_justification.sign())
out << "~";
out << "p";
out << curr.m_justification.var() << ", ";
if (curr.m_upper_inf) {
out << "oo)";
}
else {
am.display_decimal(out, curr.m_upper);
if (curr.m_upper_open)
out << ")";
else
out << "]";
}
}
bool check_interval(anum_manager & am, interval const & i) {
if (i.m_lower_inf) {
SASSERT(i.m_lower_open);
}
if (i.m_upper_inf) {
SASSERT(i.m_upper_open);
}
if (!i.m_lower_inf && !i.m_upper_inf) {
int s = am.compare(i.m_lower, i.m_upper);
TRACE("nlsat_interval", tout << "lower: "; am.display_decimal(tout, i.m_lower); tout << ", upper: "; am.display_decimal(tout, i.m_upper);
tout << "\ns: " << s << "\n";);
SASSERT(s <= 0);
if (s == 0) {
SASSERT(!i.m_lower_open && !i.m_upper_open);
}
}
return true;
}
bool check_no_overlap(anum_manager & am, interval const & curr, interval const & next) {
SASSERT(!curr.m_upper_inf);
SASSERT(!next.m_lower_inf);
int sign = am.compare(curr.m_upper, next.m_lower);
CTRACE("nlsat", sign > 0, display(tout, am, curr); tout << " "; display(tout, am, next); tout << "\n";);
SASSERT(sign <= 0);
if (sign == 0) {
SASSERT(curr.m_upper_open || next.m_lower_open);
}
return true;
}
// Check if the intervals are valid, ordered, and are disjoint.
bool check_interval_set(anum_manager & am, unsigned sz, interval const * ints) {
DEBUG_CODE(
for (unsigned i = 0; i < sz; i++) {
interval const & curr = ints[i];
SASSERT(check_interval(am, curr));
if (i < sz - 1) {
SASSERT(check_no_overlap(am, curr, ints[i+1]));
}
});
return true;
}
interval_set_manager::interval_set_manager(anum_manager & m, small_object_allocator & a):
m_am(m),
m_allocator(a) {
}
interval_set_manager::~interval_set_manager() {
}
void interval_set_manager::del(interval_set * s) {
if (s == 0)
return;
unsigned num = s->m_num_intervals;
unsigned obj_sz = interval_set::get_obj_size(num);
for (unsigned i = 0; i < num; i++) {
m_am.del(s->m_intervals[i].m_lower);
m_am.del(s->m_intervals[i].m_upper);
}
s->~interval_set();
m_allocator.deallocate(obj_sz, s);
}
void interval_set_manager::dec_ref(interval_set * s) {
SASSERT(s->m_ref_count > 0);
s->m_ref_count--;
if (s->m_ref_count == 0)
del(s);
}
void interval_set_manager::inc_ref(interval_set * s) {
s->m_ref_count++;
}
interval_set * interval_set_manager::mk(bool lower_open, bool lower_inf, anum const & lower,
bool upper_open, bool upper_inf, anum const & upper,
literal justification) {
void * mem = m_allocator.allocate(interval_set::get_obj_size(1));
interval_set * new_set = new (mem) interval_set();
new_set->m_num_intervals = 1;
new_set->m_ref_count = 0;
new_set->m_full = lower_inf && upper_inf;
interval * i = new (new_set->m_intervals) interval();
i->m_lower_open = lower_open;
i->m_lower_inf = lower_inf;
i->m_upper_open = upper_open;
i->m_upper_inf = upper_inf;
i->m_justification = justification;
if (!lower_inf)
m_am.set(i->m_lower, lower);
if (!upper_inf)
m_am.set(i->m_upper, upper);
SASSERT(check_interval_set(m_am, 1, new_set->m_intervals));
return new_set;
}
inline int compare_lower_lower(anum_manager & am, interval const & i1, interval const & i2) {
if (i1.m_lower_inf && i2.m_lower_inf)
return 0;
if (i1.m_lower_inf)
return -1;
if (i2.m_lower_inf)
return 1;
SASSERT(!i1.m_lower_inf && !i2.m_lower_inf);
int s = am.compare(i1.m_lower, i2.m_lower);
if (s != 0)
return s;
if (i1.m_lower_open == i2.m_lower_open)
return 0;
if (i1.m_lower_open)
return 1;
else
return -1;
}
inline int compare_upper_upper(anum_manager & am, interval const & i1, interval const & i2) {
if (i1.m_upper_inf && i2.m_upper_inf)
return 0;
if (i1.m_upper_inf)
return 1;
if (i2.m_upper_inf)
return -1;
SASSERT(!i1.m_upper_inf && !i2.m_upper_inf);
int s = am.compare(i1.m_upper, i2.m_upper);
if (s != 0)
return s;
if (i1.m_upper_open == i2.m_upper_open)
return 0;
if (i1.m_upper_open)
return -1;
else
return 1;
}
inline int compare_upper_lower(anum_manager & am, interval const & i1, interval const & i2) {
if (i1.m_upper_inf || i2.m_lower_inf)
return 1;
SASSERT(!i1.m_upper_inf && !i2.m_lower_inf);
int s = am.compare(i1.m_upper, i2.m_lower);
if (s != 0)
return s;
if (!i1.m_upper_open && !i2.m_lower_open)
return 0;
return -1;
}
typedef sbuffer<interval, 128> interval_buffer;
// Given two interval in an interval set s.t. curr occurs before next.
// We say curr and next are "adjacent" iff
// there is no "space" between them.
bool adjacent(anum_manager & am, interval const & curr, interval const & next) {
SASSERT(!curr.m_upper_inf);
SASSERT(!next.m_lower_inf);
int sign = am.compare(curr.m_upper, next.m_lower);
SASSERT(sign <= 0);
if (sign == 0) {
SASSERT(curr.m_upper_open || next.m_lower_open);
return !curr.m_upper_open || !next.m_lower_open;
}
return false;
}
inline void push_back(anum_manager & am, interval_buffer & buf,
bool lower_open, bool lower_inf, anum const & lower,
bool upper_open, bool upper_inf, anum const & upper,
literal justification) {
buf.push_back(interval());
interval & i = buf.back();
i.m_lower_open = lower_open;
i.m_lower_inf = lower_inf;
am.set(i.m_lower, lower);
i.m_upper_open = upper_open;
i.m_upper_inf = upper_inf;
am.set(i.m_upper, upper);
i.m_justification = justification;
SASSERT(check_interval(am, i));
}
inline void push_back(anum_manager & am, interval_buffer & buf, interval const & i) {
push_back(am, buf,
i.m_lower_open, i.m_lower_inf, i.m_lower,
i.m_upper_open, i.m_upper_inf, i.m_upper,
i.m_justification);
}
inline interval_set * mk_interval(small_object_allocator & allocator, interval_buffer & buf, bool full) {
unsigned sz = buf.size();
void * mem = allocator.allocate(interval_set::get_obj_size(sz));
interval_set * new_set = new (mem) interval_set();
new_set->m_full = full;
new_set->m_ref_count = 0;
new_set->m_num_intervals = sz;
memcpy(new_set->m_intervals, buf.c_ptr(), sizeof(interval)*sz);
return new_set;
}
interval_set * interval_set_manager::mk_union(interval_set const * s1, interval_set const * s2) {
TRACE("nlsat_interval", tout << "mk_union\ns1: "; display(tout, s1); tout << "\ns2: "; display(tout, s2); tout << "\n";);
if (s1 == 0 || s1 == s2)
return const_cast<interval_set*>(s2);
if (s2 == 0)
return const_cast<interval_set*>(s1);
if (s1->m_full)
return const_cast<interval_set*>(s1);
if (s2->m_full)
return const_cast<interval_set*>(s2);
interval_buffer result;
unsigned sz1 = s1->m_num_intervals;
unsigned sz2 = s2->m_num_intervals;
unsigned i1 = 0;
unsigned i2 = 0;
while (true) {
if (i1 >= sz1) {
while (i2 < sz2) {
TRACE("nlsat_interval", tout << "adding remaining intervals from s2: "; nlsat::display(tout, m_am, s2->m_intervals[i2]); tout << "\n";);
push_back(m_am, result, s2->m_intervals[i2]);
i2++;
}
break;
}
if (i2 >= sz2) {
while (i1 < sz1) {
TRACE("nlsat_interval", tout << "adding remaining intervals from s1: "; nlsat::display(tout, m_am, s1->m_intervals[i1]); tout << "\n";);
push_back(m_am, result, s1->m_intervals[i1]);
i1++;
}
break;
}
interval const & int1 = s1->m_intervals[i1];
interval const & int2 = s2->m_intervals[i2];
int l1_l2_sign = compare_lower_lower(m_am, int1, int2);
int u1_u2_sign = compare_upper_upper(m_am, int1, int2);
TRACE("nlsat_interval",
tout << "i1: " << i1 << ", i2: " << i2 << "\n";
tout << "int1: "; nlsat::display(tout, m_am, int1); tout << "\n";
tout << "int2: "; nlsat::display(tout, m_am, int2); tout << "\n";);
if (l1_l2_sign <= 0) {
if (u1_u2_sign == 0) {
// Cases:
// 1) [ ]
// [ ]
//
// 2) [ ]
// [ ]
//
TRACE("nlsat_interval", tout << "l1_l2_sign <= 0, u1_u2_sign == 0\n";);
push_back(m_am, result, int1);
i1++;
i2++;
}
else if (u1_u2_sign > 0) {
// Cases:
//
// 1) [ ]
// [ ]
//
// 2) [ ]
// [ ]
i2++;
TRACE("nlsat_interval", tout << "l1_l2_sign <= 0, u1_u2_sign > 0\n";);
// i1 may consume other intervals of s2
}
else {
SASSERT(u1_u2_sign < 0);
int u1_l2_sign = compare_upper_lower(m_am, int1, int2);
if (u1_l2_sign < 0) {
SASSERT(l1_l2_sign < 0);
// Cases:
// 1) [ ]
// [ ]
TRACE("nlsat_interval", tout << "l1_l2_sign <= 0, u1_u2_sign < 0, u1_l2_sign < 0\n";);
push_back(m_am, result, int1);
i1++;
}
else if (u1_l2_sign == 0) {
SASSERT(l1_l2_sign <= 0);
SASSERT(!int1.m_upper_open && !int2.m_lower_open);
SASSERT(!int2.m_lower_inf);
TRACE("nlsat_interval", tout << "l1_l2_sign <= 0, u1_u2_sign < 0, u1_l2_sign == 0\n";);
// Cases:
if (l1_l2_sign != 0) {
SASSERT(l1_l2_sign < 0);
// 1) [ ]
// [ ]
SASSERT(!int2.m_lower_open);
push_back(m_am, result,
int1.m_lower_open, int1.m_lower_inf, int1.m_lower,
true /* open */, false /* not +oo */, int1.m_upper,
int1.m_justification);
i1++;
}
else {
SASSERT(l1_l2_sign == 0);
// 2) u <<< int1 is a singleton
// [ ]
// just consume int1
i1++;
}
}
else {
SASSERT(l1_l2_sign <= 0);
SASSERT(u1_u2_sign < 0);
SASSERT(u1_l2_sign > 0);
TRACE("nlsat_interval", tout << "l1_l2_sign <= 0, u1_u2_sign < 0, u1_l2_sign > 0\n";);
if (l1_l2_sign == 0) {
// Case:
// 1) [ ]
// [ ]
// just consume int1
i1++;
}
else {
SASSERT(l1_l2_sign < 0);
SASSERT(u1_u2_sign < 0);
SASSERT(u1_l2_sign > 0);
// 2) [ ]
// [ ]
push_back(m_am, result,
int1.m_lower_open, int1.m_lower_inf, int1.m_lower,
!int2.m_lower_open, false /* not +oo */, int2.m_lower,
int1.m_justification);
i1++;
}
}
}
}
else {
SASSERT(l1_l2_sign > 0);
if (u1_u2_sign == 0) {
TRACE("nlsat_interval", tout << "l1_l2_sign > 0, u1_u2_sign == 0\n";);
// Case:
// 1) [ ]
// [ ]
//
push_back(m_am, result, int2);
i1++;
i2++;
}
else if (u1_u2_sign < 0) {
TRACE("nlsat_interval", tout << "l1_l2_sign > 0, u1_u2_sign > 0\n";);
// Case:
// 1) [ ]
// [ ]
i1++;
// i2 may consume other intervals of s1
}
else {
int u2_l1_sign = compare_upper_lower(m_am, int2, int1);
if (u2_l1_sign < 0) {
TRACE("nlsat_interval", tout << "l1_l2_sign > 0, u1_u2_sign > 0, u2_l1_sign < 0\n";);
// Case:
// 1) [ ]
// [ ]
push_back(m_am, result, int2);
i2++;
}
else if (u2_l1_sign == 0) {
TRACE("nlsat_interval", tout << "l1_l2_sign > 0, u1_u2_sign > 0, u2_l1_sign == 0\n";);
SASSERT(!int1.m_lower_open && !int2.m_upper_open);
SASSERT(!int1.m_lower_inf);
// Case:
// [ ]
// [ ]
push_back(m_am, result,
int2.m_lower_open, int2.m_lower_inf, int2.m_lower,
true /* open */, false /* not +oo */, int2.m_upper,
int2.m_justification);
i2++;
}
else {
TRACE("nlsat_interval", tout << "l1_l2_sign > 0, u1_u2_sign > 0, u2_l1_sign > 0\n";);
SASSERT(l1_l2_sign > 0);
SASSERT(u1_u2_sign > 0);
SASSERT(u2_l1_sign > 0);
// Case:
// [ ]
// [ ]
push_back(m_am, result,
int2.m_lower_open, int2.m_lower_inf, int2.m_lower,
!int1.m_lower_open, false /* not +oo */, int1.m_lower,
int2.m_justification);
i2++;
}
}
}
SASSERT(result.size() <= 1 ||
check_no_overlap(m_am, result[result.size() - 2], result[result.size() - 1]));
}
SASSERT(!result.empty());
SASSERT(check_interval_set(m_am, result.size(), result.c_ptr()));
// Compress
// Remark: we only combine adjacent intervals when they have the same justification
unsigned j = 0;
unsigned sz = result.size();
for (unsigned i = 1; i < sz; i++) {
interval & curr = result[j];
interval & next = result[i];
if (curr.m_justification == next.m_justification &&
adjacent(m_am, curr, next)) {
// merge them
curr.m_upper_inf = next.m_upper_inf;
curr.m_upper_open = next.m_upper_open;
m_am.swap(curr.m_upper, next.m_upper);
}
else {
j++;
if (i != j) {
interval & next_curr = result[j];
next_curr.m_lower_inf = next.m_lower_inf;
next_curr.m_lower_open = next.m_lower_open;
m_am.swap(next_curr.m_lower, next.m_lower);
next_curr.m_upper_inf = next.m_upper_inf;
next_curr.m_upper_open = next.m_upper_open;
m_am.swap(next_curr.m_upper, next.m_upper);
next_curr.m_justification = next.m_justification;
}
}
}
j++;
for (unsigned i = j; i < sz; i++) {
interval & curr = result[i];
m_am.del(curr.m_lower);
m_am.del(curr.m_upper);
}
result.shrink(j);
SASSERT(check_interval_set(m_am, result.size(), result.c_ptr()));
sz = j;
SASSERT(sz >= 1);
bool found_slack = !result[0].m_lower_inf || !result[sz-1].m_upper_inf;
// Check if full
for (unsigned i = 0; i < sz - 1 && !found_slack; i++) {
if (!adjacent(m_am, result[i], result[i+1]))
found_slack = true;
}
// Create new interval set
interval_set * new_set = mk_interval(m_allocator, result, !found_slack);
SASSERT(check_interval_set(m_am, sz, new_set->m_intervals));
return new_set;
}
bool interval_set_manager::is_full(interval_set const * s) {
if (s == 0)
return false;
return s->m_full == 1;
}
unsigned interval_set_manager::num_intervals(interval_set const * s) const {
if (s == 0) return 0;
return s->m_num_intervals;
}
bool interval_set_manager::subset(interval_set const * s1, interval_set const * s2) {
if (s1 == s2)
return true;
if (s1 == 0)
return true;
if (s2 == 0)
return false;
if (s2->m_full)
return true;
if (s1->m_full)
return false;
unsigned sz1 = s1->m_num_intervals;
unsigned sz2 = s2->m_num_intervals;
SASSERT(sz1 > 0 && sz2 > 0);
unsigned i1 = 0;
unsigned i2 = 0;
while (i1 < sz1 && i2 < sz2) {
interval const & int1 = s1->m_intervals[i1];
interval const & int2 = s2->m_intervals[i2];
TRACE("nlsat_interval", tout << "subset main loop, i1: " << i1 << ", i2: " << i2 << "\n";
tout << "int1: "; nlsat::display(tout, m_am, int1); tout << "\n";
tout << "int2: "; nlsat::display(tout, m_am, int2); tout << "\n";);
if (compare_lower_lower(m_am, int1, int2) < 0) {
TRACE("nlsat_interval", tout << "done\n";);
// interval [int1.lower1, int2.lower2] is not in s2
// s1: [ ...
// s2: [ ...
return false;
}
while (i2 < sz2) {
interval const & int2 = s2->m_intervals[i2];
TRACE("nlsat_interval", tout << "inner loop, i2: " << i2 << "\n";
tout << "int2: "; nlsat::display(tout, m_am, int2); tout << "\n";);
int u1_u2_sign = compare_upper_upper(m_am, int1, int2);
if (u1_u2_sign == 0) {
TRACE("nlsat_interval", tout << "case 1, break\n";);
// consume both
// s1: ... ]
// s2: ... ]
i1++;
i2++;
break;
}
else if (u1_u2_sign < 0) {
TRACE("nlsat_interval", tout << "case 2, break\n";);
// consume only int1, int2 may cover other intervals of s1
// s1: ... ]
// s2: ... ]
i1++;
break;
}
else {
SASSERT(u1_u2_sign > 0);
int u2_l1_sign = compare_upper_lower(m_am, int2, int1);
TRACE("nlsat_interval", tout << "subset, u2_l1_sign: " << u2_l1_sign << "\n";);
if (u2_l1_sign < 0) {
TRACE("nlsat_interval", tout << "case 3, break\n";);
// s1: [ ...
// s2: [ ... ] ...
i2++;
break;
}
SASSERT(u2_l1_sign >= 0);
// s1: [ ... ]
// s2: [ ... ]
if (i2 == sz2 - 1) {
TRACE("nlsat_interval", tout << "case 4, done\n";);
// s1: ... ]
// s2: ...]
// the interval [int2.upper, int1.upper] is not in s2
return false; // last interval of s2
}
interval const & next2 = s2->m_intervals[i2+1];
if (!adjacent(m_am, int2, next2)) {
TRACE("nlsat_interval", tout << "not adjacent, done\n";);
// s1: ... ]
// s2: ... ] [
// the interval [int2.upper, min(int1.upper, next2.lower)] is not in s2
return false;
}
TRACE("nlsat_interval", tout << "continue..\n";);
// continue with adjacent interval of s2
// s1: ... ]
// s2: ..][ ...
i2++;
}
}
}
return i1 == sz1;
}
bool interval_set_manager::set_eq(interval_set const * s1, interval_set const * s2) {
if (s1 == 0 || s2 == 0)
return s1 == s2;
if (s1->m_full || s2->m_full)
return s1->m_full == s2->m_full;
// TODO: check if bottleneck, then replace simple implementation
return subset(s1, s2) && subset(s2, s1);
}
bool interval_set_manager::eq(interval_set const * s1, interval_set const * s2) {
if (s1 == 0 || s2 == 0)
return s1 == s2;
if (s1->m_num_intervals != s2->m_num_intervals)
return false;
for (unsigned i = 0; i < s1->m_num_intervals; i++) {
interval const & int1 = s1->m_intervals[i];
interval const & int2 = s2->m_intervals[i];
if (int1.m_lower_inf != int2.m_lower_inf ||
int1.m_lower_open != int2.m_lower_open ||
int1.m_upper_inf != int2.m_upper_inf ||
int1.m_upper_open != int2.m_upper_open ||
int1.m_justification != int2.m_justification ||
!m_am.eq(int1.m_lower, int2.m_lower) ||
!m_am.eq(int1.m_upper, int2.m_upper))
return false;
}
return true;
}
void interval_set_manager::get_justifications(interval_set const * s, literal_vector & js) {
js.reset();
unsigned num = num_intervals(s);
for (unsigned i = 0; i < num; i++) {
literal l = s->m_intervals[i].m_justification;
unsigned lidx = l.index();
if (m_already_visited.get(lidx, false))
continue;
m_already_visited.setx(lidx, true, false);
js.push_back(l);
}
for (unsigned i = 0; i < num; i++) {
literal l = s->m_intervals[i].m_justification;
unsigned lidx = l.index();
m_already_visited[lidx] = false;
}
}
interval_set * interval_set_manager::get_interval(interval_set const * s, unsigned idx) const {
SASSERT(idx < num_intervals(s));
interval_buffer result;
push_back(m_am, result, s->m_intervals[idx]);
bool found_slack = !result[0].m_lower_inf || !result[0].m_upper_inf;
interval_set * new_set = mk_interval(m_allocator, result, !found_slack);
SASSERT(check_interval_set(m_am, result.size(), new_set->m_intervals));
return new_set;
}
void interval_set_manager::peek_in_complement(interval_set const * s, anum & w, bool randomize) {
SASSERT(!is_full(s));
if (s == 0) {
if (randomize) {
int num = m_rand() % 2 == 0 ? 1 : -1;
#define MAX_RANDOM_DEN_K 4
int den_k = (m_rand() % MAX_RANDOM_DEN_K);
int den = 1 << den_k;
scoped_mpq _w(m_am.qm());
m_am.qm().set(_w, num, den);
m_am.set(w, _w);
return;
}
else {
m_am.set(w, 0);
return;
}
}
unsigned n = 0;
unsigned num = num_intervals(s);
if (!s->m_intervals[0].m_lower_inf) {
// lower is not -oo
n++;
m_am.int_lt(s->m_intervals[0].m_lower, w);
if (!randomize)
return;
}
if (!s->m_intervals[num-1].m_upper_inf) {
// upper is not oo
n++;
if (n == 1 || m_rand()%n == 0)
m_am.int_gt(s->m_intervals[num-1].m_upper, w);
if (!randomize)
return;
}
// Try to find a gap that is not an unit.
for (unsigned i = 1; i < num; i++) {
if (m_am.lt(s->m_intervals[i-1].m_upper, s->m_intervals[i].m_lower)) {
n++;
if (n == 1 || m_rand()%n == 0)
m_am.select(s->m_intervals[i-1].m_upper, s->m_intervals[i].m_lower, w);
if (!randomize)
return;
}
}
if (n > 0)
return;
// Try to find a rational
unsigned irrational_i = UINT_MAX;
for (unsigned i = 1; i < num; i++) {
if (s->m_intervals[i-1].m_upper_open && s->m_intervals[i].m_lower_open) {
SASSERT(m_am.eq(s->m_intervals[i-1].m_upper, s->m_intervals[i].m_lower)); // otherwise we would have found it in the previous step
if (m_am.is_rational(s->m_intervals[i-1].m_upper)) {
m_am.set(w, s->m_intervals[i-1].m_upper);
return;
}
if (irrational_i == UINT_MAX)
irrational_i = i-1;
}
}
SASSERT(irrational_i != UINT_MAX);
// Last option: peek irrational witness :-(
SASSERT(s->m_intervals[irrational_i].m_upper_open && s->m_intervals[irrational_i+1].m_lower_open);
m_am.set(w, s->m_intervals[irrational_i].m_upper);
}
void interval_set_manager::display(std::ostream & out, interval_set const * s) const {
if (s == 0) {
out << "{}";
return;
}
out << "{";
for (unsigned i = 0; i < s->m_num_intervals; i++) {
if (i > 0)
out << ", ";
nlsat::display(out, m_am, s->m_intervals[i]);
}
out << "}";
if (s->m_full)
out << "*";
}
};
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