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/****************************************************************************** |
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* Top contributors (to current version): |
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* Andrew Reynolds, Makai Mann, Gereon Kremer |
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* |
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* This file is part of the cvc5 project. |
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* |
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* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS |
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* in the top-level source directory and their institutional affiliations. |
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* All rights reserved. See the file COPYING in the top-level source |
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* directory for licensing information. |
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* **************************************************************************** |
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* |
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* Implementation of integer and (IAND) solver. |
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*/ |
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#include "theory/arith/nl/iand_solver.h" |
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#include "options/arith_options.h" |
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#include "options/smt_options.h" |
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#include "preprocessing/passes/bv_to_int.h" |
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#include "theory/arith/arith_msum.h" |
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#include "theory/arith/arith_state.h" |
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#include "theory/arith/arith_utilities.h" |
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#include "theory/arith/inference_manager.h" |
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#include "theory/arith/nl/nl_model.h" |
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#include "theory/rewriter.h" |
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#include "util/bitvector.h" |
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#include "util/iand.h" |
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using namespace cvc5::kind; |
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namespace cvc5 { |
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namespace theory { |
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namespace arith { |
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namespace nl { |
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IAndSolver::IAndSolver(Env& env, |
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InferenceManager& im, |
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ArithState& state, |
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NlModel& model) |
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: EnvObj(env), |
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d_im(im), |
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d_model(model), |
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d_astate(state), |
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d_initRefine(userContext()) |
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{ |
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NodeManager* nm = NodeManager::currentNM(); |
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d_false = nm->mkConst(false); |
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d_true = nm->mkConst(true); |
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d_zero = nm->mkConst(Rational(0)); |
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d_one = nm->mkConst(Rational(1)); |
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d_two = nm->mkConst(Rational(2)); |
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} |
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IAndSolver::~IAndSolver() {} |
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void IAndSolver::initLastCall(const std::vector<Node>& assertions, |
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const std::vector<Node>& false_asserts, |
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const std::vector<Node>& xts) |
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{ |
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d_iands.clear(); |
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Trace("iand-mv") << "IAND terms : " << std::endl; |
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for (const Node& a : xts) |
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{ |
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Kind ak = a.getKind(); |
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if (ak != IAND) |
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{ |
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// don't care about other terms |
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continue; |
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} |
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size_t bsize = a.getOperator().getConst<IntAnd>().d_size; |
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d_iands[bsize].push_back(a); |
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} |
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Trace("iand") << "We have " << d_iands.size() << " IAND terms." << std::endl; |
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} |
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void IAndSolver::checkInitialRefine() |
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{ |
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Trace("iand-check") << "IAndSolver::checkInitialRefine" << std::endl; |
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NodeManager* nm = NodeManager::currentNM(); |
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for (const std::pair<const unsigned, std::vector<Node> >& is : d_iands) |
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{ |
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// the reference bitwidth |
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unsigned k = is.first; |
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for (const Node& i : is.second) |
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{ |
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if (d_initRefine.find(i) != d_initRefine.end()) |
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{ |
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// already sent initial axioms for i in this user context |
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continue; |
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} |
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d_initRefine.insert(i); |
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Node op = i.getOperator(); |
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// initial refinement lemmas |
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std::vector<Node> conj; |
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// iand(x,y)=iand(y,x) is guaranteed by rewriting |
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Assert(i[0] <= i[1]); |
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// conj.push_back(i.eqNode(nm->mkNode(IAND, op, i[1], i[0]))); |
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// 0 <= iand(x,y) < 2^k |
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conj.push_back(nm->mkNode(LEQ, d_zero, i)); |
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conj.push_back(nm->mkNode(LT, i, d_iandUtils.twoToK(k))); |
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// iand(x,y)<=x |
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conj.push_back(nm->mkNode(LEQ, i, i[0])); |
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// iand(x,y)<=y |
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conj.push_back(nm->mkNode(LEQ, i, i[1])); |
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// x=y => iand(x,y)=x |
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conj.push_back(nm->mkNode(IMPLIES, i[0].eqNode(i[1]), i.eqNode(i[0]))); |
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Node lem = conj.size() == 1 ? conj[0] : nm->mkNode(AND, conj); |
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Trace("iand-lemma") << "IAndSolver::Lemma: " << lem << " ; INIT_REFINE" |
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<< std::endl; |
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d_im.addPendingLemma(lem, InferenceId::ARITH_NL_IAND_INIT_REFINE); |
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} |
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} |
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} |
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void IAndSolver::checkFullRefine() |
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{ |
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Trace("iand-check") << "IAndSolver::checkFullRefine"; |
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Trace("iand-check") << "IAND terms: " << std::endl; |
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for (const std::pair<const unsigned, std::vector<Node> >& is : d_iands) |
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{ |
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// the reference bitwidth |
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unsigned k = is.first; |
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for (const Node& i : is.second) |
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{ |
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Node valAndXY = d_model.computeAbstractModelValue(i); |
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Node valAndXYC = d_model.computeConcreteModelValue(i); |
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if (Trace.isOn("iand-check")) |
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{ |
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Node x = i[0]; |
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Node y = i[1]; |
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Node valX = d_model.computeConcreteModelValue(x); |
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Node valY = d_model.computeConcreteModelValue(y); |
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Trace("iand-check") |
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<< "* " << i << ", value = " << valAndXY << std::endl; |
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Trace("iand-check") << " actual (" << valX << ", " << valY |
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<< ") = " << valAndXYC << std::endl; |
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// print the bit-vector versions |
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Node bvalX = convertToBvK(k, valX); |
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Node bvalY = convertToBvK(k, valY); |
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Node bvalAndXY = convertToBvK(k, valAndXY); |
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Node bvalAndXYC = convertToBvK(k, valAndXYC); |
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Trace("iand-check") << " bv-value = " << bvalAndXY << std::endl; |
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Trace("iand-check") << " bv-actual (" << bvalX << ", " << bvalY |
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<< ") = " << bvalAndXYC << std::endl; |
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} |
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if (valAndXY == valAndXYC) |
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{ |
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Trace("iand-check") << "...already correct" << std::endl; |
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continue; |
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} |
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// ************* additional lemma schemas go here |
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if (options().smt.iandMode == options::IandMode::SUM) |
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{ |
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Node lem = sumBasedLemma(i); // add lemmas based on sum mode |
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Trace("iand-lemma") |
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<< "IAndSolver::Lemma: " << lem << " ; SUM_REFINE" << std::endl; |
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// note that lemma can contain div/mod, and will be preprocessed in the |
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// prop engine |
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d_im.addPendingLemma( |
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lem, InferenceId::ARITH_NL_IAND_SUM_REFINE, nullptr, true); |
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} |
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else if (options().smt.iandMode == options::IandMode::BITWISE) |
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{ |
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Node lem = bitwiseLemma(i); // check for violated bitwise axioms |
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Trace("iand-lemma") |
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<< "IAndSolver::Lemma: " << lem << " ; BITWISE_REFINE" << std::endl; |
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// note that lemma can contain div/mod, and will be preprocessed in the |
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// prop engine |
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d_im.addPendingLemma( |
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lem, InferenceId::ARITH_NL_IAND_BITWISE_REFINE, nullptr, true); |
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} |
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else |
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{ |
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// this is the most naive model-based schema based on model values |
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Node lem = valueBasedLemma(i); |
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Trace("iand-lemma") |
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<< "IAndSolver::Lemma: " << lem << " ; VALUE_REFINE" << std::endl; |
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// send the value lemma |
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d_im.addPendingLemma(lem, |
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InferenceId::ARITH_NL_IAND_VALUE_REFINE, |
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nullptr, |
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true); |
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} |
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} |
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} |
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} |
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Node IAndSolver::convertToBvK(unsigned k, Node n) const |
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{ |
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Assert(n.isConst() && n.getType().isInteger()); |
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NodeManager* nm = NodeManager::currentNM(); |
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Node iToBvOp = nm->mkConst(IntToBitVector(k)); |
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Node bn = nm->mkNode(kind::INT_TO_BITVECTOR, iToBvOp, n); |
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return Rewriter::rewrite(bn); |
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} |
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Node IAndSolver::mkIAnd(unsigned k, Node x, Node y) const |
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{ |
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NodeManager* nm = NodeManager::currentNM(); |
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Node iAndOp = nm->mkConst(IntAnd(k)); |
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Node ret = nm->mkNode(IAND, iAndOp, x, y); |
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ret = Rewriter::rewrite(ret); |
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return ret; |
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} |
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Node IAndSolver::mkIOr(unsigned k, Node x, Node y) const |
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{ |
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Node ret = mkINot(k, mkIAnd(k, mkINot(k, x), mkINot(k, y))); |
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ret = Rewriter::rewrite(ret); |
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return ret; |
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} |
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Node IAndSolver::mkINot(unsigned k, Node x) const |
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{ |
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NodeManager* nm = NodeManager::currentNM(); |
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Node ret = nm->mkNode(MINUS, d_iandUtils.twoToKMinusOne(k), x); |
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ret = Rewriter::rewrite(ret); |
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return ret; |
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} |
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Node IAndSolver::valueBasedLemma(Node i) |
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{ |
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Assert(i.getKind() == IAND); |
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Node x = i[0]; |
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Node y = i[1]; |
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Node valX = d_model.computeConcreteModelValue(x); |
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Node valY = d_model.computeConcreteModelValue(y); |
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NodeManager* nm = NodeManager::currentNM(); |
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Node valC = nm->mkNode(IAND, i.getOperator(), valX, valY); |
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valC = Rewriter::rewrite(valC); |
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Node lem = nm->mkNode( |
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IMPLIES, nm->mkNode(AND, x.eqNode(valX), y.eqNode(valY)), i.eqNode(valC)); |
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return lem; |
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} |
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Node IAndSolver::sumBasedLemma(Node i) |
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{ |
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Assert(i.getKind() == IAND); |
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Node x = i[0]; |
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Node y = i[1]; |
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size_t bvsize = i.getOperator().getConst<IntAnd>().d_size; |
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uint64_t granularity = options().smt.BVAndIntegerGranularity; |
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NodeManager* nm = NodeManager::currentNM(); |
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Node lem = nm->mkNode( |
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EQUAL, i, d_iandUtils.createSumNode(x, y, bvsize, granularity)); |
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return lem; |
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} |
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Node IAndSolver::bitwiseLemma(Node i) |
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{ |
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Assert(i.getKind() == IAND); |
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Node x = i[0]; |
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Node y = i[1]; |
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unsigned bvsize = i.getOperator().getConst<IntAnd>().d_size; |
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uint64_t granularity = options().smt.BVAndIntegerGranularity; |
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Rational absI = d_model.computeAbstractModelValue(i).getConst<Rational>(); |
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Rational concI = d_model.computeConcreteModelValue(i).getConst<Rational>(); |
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Assert(absI.isIntegral()); |
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Assert(concI.isIntegral()); |
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BitVector bvAbsI = BitVector(bvsize, absI.getNumerator()); |
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BitVector bvConcI = BitVector(bvsize, concI.getNumerator()); |
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NodeManager* nm = NodeManager::currentNM(); |
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Node lem = d_true; |
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// compare each bit to bvI |
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Node cond; |
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Node bitIAnd; |
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unsigned high_bit; |
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for (unsigned j = 0; j < bvsize; j += granularity) |
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{ |
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high_bit = j + granularity - 1; |
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// don't let high_bit pass bvsize |
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if (high_bit >= bvsize) |
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{ |
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high_bit = bvsize - 1; |
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} |
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// check if the abstraction differs from the concrete one on these bits |
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if (bvAbsI.extract(high_bit, j) != bvConcI.extract(high_bit, j)) |
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{ |
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bitIAnd = d_iandUtils.createBitwiseIAndNode(x, y, high_bit, j); |
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// enforce bitwise equality |
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lem = nm->mkNode( |
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AND, lem, d_iandUtils.iextract(high_bit, j, i).eqNode(bitIAnd)); |
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} |
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} |
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return lem; |
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} |
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} // namespace nl |
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} // namespace arith |
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} // namespace theory |
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} // namespace cvc5 |