mirror of
https://github.com/Z3Prover/z3
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224 lines
8.1 KiB
C++
224 lines
8.1 KiB
C++
/*++
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Copyright (c) 2021 Microsoft Corporation
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Module Name:
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polysat intervals
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Author:
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Nikolaj Bjorner (nbjorner) 2021-03-19
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Jakob Rath 2021-04-6
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--*/
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#pragma once
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#include "sat/smt/polysat/types.h"
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#include <optional>
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namespace polysat {
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struct pdd_bounds {
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pdd lo; ///< lower bound, inclusive
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pdd hi; ///< upper bound, exclusive
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};
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/**
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* An interval is either [lo; hi[ (excl. upper bound) or the full domain Z_{2^w}.
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* If lo > hi, the interval wraps around, i.e., represents the union of [lo; 2^w[ and [0; hi[.
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* Membership test t \in [lo; hi[ is equivalent to t - lo < hi - lo.
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*/
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class interval {
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std::optional<pdd_bounds> m_bounds = std::nullopt;
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interval() = default;
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interval(pdd const& lo, pdd const& hi): m_bounds({lo, hi}) {}
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public:
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static interval empty(dd::pdd_manager& m) { return proper(m.zero(), m.zero()); }
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static interval full() { return {}; }
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static interval proper(pdd const& lo, pdd const& hi) { return {lo, hi}; }
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interval(interval const&) = default;
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interval(interval&&) = default;
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interval& operator=(interval const& other) {
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m_bounds = std::nullopt; // clear pdds first to allow changing pdd_manager (probably should change the PDD assignment operator; but for now I want to be able to detect manager confusions)
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m_bounds = other.m_bounds;
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return *this;
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}
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interval& operator=(interval&& other) {
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m_bounds = std::nullopt; // clear pdds first to allow changing pdd_manager
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m_bounds = std::move(other.m_bounds);
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return *this;
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}
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~interval() = default;
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bool is_full() const { return !m_bounds; }
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bool is_proper() const { return !!m_bounds; }
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bool is_always_empty() const { return is_proper() && lo() == hi(); }
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pdd const& lo() const { SASSERT(is_proper()); return m_bounds->lo; }
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pdd const& hi() const { SASSERT(is_proper()); return m_bounds->hi; }
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};
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inline std::ostream& operator<<(std::ostream& os, interval const& i) {
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if (i.is_full())
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return os << "full";
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else
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return os << "[" << i.lo() << " ; " << i.hi() << "[";
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}
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// distance from a to b, wrapping around at mod_value.
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// basically mod(b - a, mod_value), but distance(0, mod_value, mod_value) = mod_value.
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inline rational distance(rational const& a, rational const& b, rational const& mod_value) {
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SASSERT(mod_value.is_power_of_two());
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SASSERT(0 <= a && a < mod_value);
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SASSERT(0 <= b && b <= mod_value);
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rational x = b - a;
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if (x.is_neg())
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x += mod_value;
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return x;
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}
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class r_interval {
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rational m_lo;
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rational m_hi;
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r_interval(rational lo, rational hi)
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: m_lo(std::move(lo)), m_hi(std::move(hi))
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{}
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public:
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static r_interval empty() {
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return {rational::zero(), rational::zero()};
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}
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static r_interval full() {
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return {rational(-1), rational::zero()};
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}
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static r_interval proper(rational lo, rational hi) {
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SASSERT(0 <= lo);
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SASSERT(0 <= hi);
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return {std::move(lo), std::move(hi)};
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}
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bool is_full() const { return m_lo.is_neg(); }
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bool is_proper() const { return !is_full(); }
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bool is_empty() const { return is_proper() && lo() == hi(); }
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rational const& lo() const { SASSERT(is_proper()); return m_lo; }
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rational const& hi() const { SASSERT(is_proper()); return m_hi; }
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// this one also supports representing full intervals as [lo;mod_value[
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static rational len(rational const& lo, rational const& hi, rational const& mod_value) {
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SASSERT(mod_value.is_power_of_two());
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SASSERT(0 <= lo && lo < mod_value);
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SASSERT(0 <= hi && hi <= mod_value);
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SASSERT(hi != mod_value || lo == 0); // hi == mod_value only allowed when lo == 0
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rational len = hi - lo;
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if (len.is_neg())
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len += mod_value;
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return len;
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}
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rational len(rational const& mod_value) const {
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SASSERT(is_proper());
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return len(lo(), hi(), mod_value);
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}
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// deals only with proper intervals
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// but works with full intervals represented as [0;mod_value[ -- maybe we should just change representation of full intervals to this always
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static bool contains(rational const& lo, rational const& hi, rational const& val) {
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if (lo <= hi)
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return lo <= val && val < hi;
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else
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return val < hi || val >= lo;
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}
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bool contains(rational const& val) const {
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if (is_full())
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return true;
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else
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return contains(lo(), hi(), val);
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}
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};
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class eval_interval {
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interval m_symbolic;
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rational m_concrete_lo;
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rational m_concrete_hi;
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eval_interval(interval&& i, rational const& lo_val, rational const& hi_val):
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m_symbolic(std::move(i)), m_concrete_lo(lo_val), m_concrete_hi(hi_val) {}
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public:
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static eval_interval empty(dd::pdd_manager& m) {
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return {interval::empty(m), rational::zero(), rational::zero()};
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}
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static eval_interval full() {
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return {interval::full(), rational::zero(), rational::zero()};
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}
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static eval_interval proper(pdd const& lo, rational const& lo_val, pdd const& hi, rational const& hi_val) {
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SASSERT(0 <= lo_val && lo_val <= lo.manager().max_value());
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SASSERT(0 <= hi_val && hi_val <= hi.manager().max_value());
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return {interval::proper(lo, hi), lo_val, hi_val};
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}
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bool is_full() const { return m_symbolic.is_full(); }
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bool is_proper() const { return m_symbolic.is_proper(); }
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bool is_always_empty() const { return m_symbolic.is_always_empty(); }
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bool is_currently_empty() const { return is_proper() && lo_val() == hi_val(); }
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interval const& symbolic() const { return m_symbolic; }
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pdd const& lo() const { return m_symbolic.lo(); }
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pdd const& hi() const { return m_symbolic.hi(); }
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rational const& lo_val() const { SASSERT(is_proper()); return m_concrete_lo; }
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rational const& hi_val() const { SASSERT(is_proper()); return m_concrete_hi; }
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rational current_len() const {
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SASSERT(is_proper());
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return mod(hi_val() - lo_val(), lo().manager().two_to_N());
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}
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bool currently_contains(rational const& val) const {
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if (is_full())
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return true;
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else if (lo_val() <= hi_val())
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return lo_val() <= val && val < hi_val();
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else
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return val < hi_val() || val >= lo_val();
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}
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bool currently_contains(eval_interval const& other) const {
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if (is_full())
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return true;
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if (other.is_full())
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return false;
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// lo <= lo' <= hi' <= hi'
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if (lo_val() <= other.lo_val() && other.lo_val() <= other.hi_val() && other.hi_val() <= hi_val())
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return true;
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if (lo_val() <= hi_val())
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return false;
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// hi < lo <= lo' <= hi'
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if (lo_val() <= other.lo_val() && other.lo_val() <= other.hi_val())
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return true;
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// lo' <= hi' <= hi < lo
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if (other.lo_val() <= other.hi_val() && other.hi_val() <= hi_val())
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return true;
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// hi' <= hi < lo <= lo'
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if (other.hi_val() <= hi_val() && lo_val() <= other.lo_val())
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return true;
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return false;
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}
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}; // class eval_interval
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inline std::ostream& operator<<(std::ostream& os, eval_interval const& i) {
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if (i.is_full())
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return os << "full";
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else {
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auto& m = i.hi().manager();
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return os << i.symbolic() << " := [" << m.normalize(i.lo_val()) << ";" << m.normalize(i.hi_val()) << "[";
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}
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}
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}
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