From 4c1f1cad720a94226f7834874cf59478de35b74a Mon Sep 17 00:00:00 2001 From: Aina Niemetz Date: Thu, 30 Nov 2017 15:50:00 -0800 Subject: [PATCH] Add Gaussian Elimination as a preprocessing pass for BV. (#1342) This adds Gaussian Elimination as a preprocessing pass for BV. Gaussian Elimination is only applied if the given bit-width guarantees that no overflows can occur. --- src/Makefile.am | 2 + src/options/bv_options | 3 + src/smt/smt_engine.cpp | 15 +- src/theory/bv/bvgauss.cpp | 714 +++++ src/theory/bv/bvgauss.h | 151 + test/unit/Makefile.am | 1 + test/unit/theory/theory_bv_bvgauss_white.h | 2965 ++++++++++++++++++++ 7 files changed, 3850 insertions(+), 1 deletion(-) create mode 100644 src/theory/bv/bvgauss.cpp create mode 100644 src/theory/bv/bvgauss.h create mode 100644 test/unit/theory/theory_bv_bvgauss_white.h diff --git a/src/Makefile.am b/src/Makefile.am index f50893497..6a21251bd 100644 --- a/src/Makefile.am +++ b/src/Makefile.am @@ -306,6 +306,8 @@ libcvc4_la_SOURCES = \ theory/bv/bv_subtheory_inequality.h \ theory/bv/bv_to_bool.cpp \ theory/bv/bv_to_bool.h \ + theory/bv/bvgauss.cpp \ + theory/bv/bvgauss.h \ theory/bv/bvintropow2.cpp \ theory/bv/bvintropow2.h \ theory/bv/cd_set_collection.h \ diff --git a/src/options/bv_options b/src/options/bv_options index 035d6ae31..f434339b0 100644 --- a/src/options/bv_options +++ b/src/options/bv_options @@ -72,6 +72,9 @@ expert-option bitvectorQuickXplain --bv-quick-xplain bool :default false expert-option bvIntroducePow2 --bv-intro-pow2 bool :default false introduce bitvector powers of two as a preprocessing pass +expert-option bvGaussElim --bv-gauss-elim bool :default false + simplify formula via Gaussian Elimination if applicable + option bvLazyRewriteExtf --bv-lazy-rewrite-extf bool :default true :read-write lazily rewrite extended functions like bv2nat and int2bv diff --git a/src/smt/smt_engine.cpp b/src/smt/smt_engine.cpp index 3a0cb297e..f9d3c9909 100644 --- a/src/smt/smt_engine.cpp +++ b/src/smt/smt_engine.cpp @@ -86,6 +86,7 @@ #include "theory/arith/arith_msum.h" #include "theory/arith/pseudoboolean_proc.h" #include "theory/booleans/circuit_propagator.h" +#include "theory/bv/bvgauss.h" #include "theory/bv/bvintropow2.h" #include "theory/bv/theory_bv_rewriter.h" #include "theory/logic_info.h" @@ -185,6 +186,8 @@ public: };/* class AssertionPipeline */ struct SmtEngineStatistics { + /** time spent in gaussian elimination */ + TimerStat d_gaussElimTime; /** time spent in definition-expansion */ TimerStat d_definitionExpansionTime; /** time spent in non-clausal simplification */ @@ -232,6 +235,7 @@ struct SmtEngineStatistics { ReferenceStat d_resourceUnitsUsed; SmtEngineStatistics() : + d_gaussElimTime("smt::SmtEngine::gaussElimTime"), d_definitionExpansionTime("smt::SmtEngine::definitionExpansionTime"), d_nonclausalSimplificationTime("smt::SmtEngine::nonclausalSimplificationTime"), d_miplibPassTime("smt::SmtEngine::miplibPassTime"), @@ -256,6 +260,7 @@ struct SmtEngineStatistics { d_resourceUnitsUsed("smt::SmtEngine::resourceUnitsUsed") { + smtStatisticsRegistry()->registerStat(&d_gaussElimTime); smtStatisticsRegistry()->registerStat(&d_definitionExpansionTime); smtStatisticsRegistry()->registerStat(&d_nonclausalSimplificationTime); smtStatisticsRegistry()->registerStat(&d_miplibPassTime); @@ -281,6 +286,7 @@ struct SmtEngineStatistics { } ~SmtEngineStatistics() { + smtStatisticsRegistry()->unregisterStat(&d_gaussElimTime); smtStatisticsRegistry()->unregisterStat(&d_definitionExpansionTime); smtStatisticsRegistry()->unregisterStat(&d_nonclausalSimplificationTime); smtStatisticsRegistry()->unregisterStat(&d_miplibPassTime); @@ -1427,9 +1433,10 @@ void SmtEngine::setDefaults() { if(options::bvIntroducePow2.wasSetByUser()) { throw OptionException("bv-intro-pow2 not supported with unsat cores"); } - Notice() << "SmtEngine: turning off bv-introduce-pow2 to support unsat-cores" << endl; + Notice() << "SmtEngine: turning off bv-intro-pow2 to support unsat-cores" << endl; setOption("bv-intro-pow2", false); } + if(options::repeatSimp()) { if(options::repeatSimp.wasSetByUser()) { throw OptionException("repeat-simp not supported with unsat cores"); @@ -4006,6 +4013,12 @@ void SmtEnginePrivate::processAssertions() { return; } + if(options::bvGaussElim()) + { + TimerStat::CodeTimer gaussElimTimer(d_smt.d_stats->d_gaussElimTime); + theory::bv::BVGaussElim::gaussElimRewrite(d_assertions.ref()); + } + if (d_assertionsProcessed && options::incrementalSolving()) { // TODO(b/1255): Substitutions in incremental mode should be managed with a // proper data structure. diff --git a/src/theory/bv/bvgauss.cpp b/src/theory/bv/bvgauss.cpp new file mode 100644 index 000000000..cfdab57be --- /dev/null +++ b/src/theory/bv/bvgauss.cpp @@ -0,0 +1,714 @@ +/********************* */ +/*! \file bvgauss.cpp + ** \verbatim + ** Top contributors (to current version): + ** Aina Niemetz + ** This file is part of the CVC4 project. + ** Copyright (c) 2009-2017 by the authors listed in the file AUTHORS + ** in the top-level source directory) and their institutional affiliations. + ** All rights reserved. See the file COPYING in the top-level source + ** directory for licensing information.\endverbatim + ** + ** \brief Gaussian Elimination preprocessing pass. + ** + ** Simplify a given equation system modulo a (prime) number via Gaussian + ** Elimination if possible. + **/ + +#include "theory/bv/bvgauss.h" + +#include + +#include "theory/rewriter.h" +#include "theory/bv/theory_bv_utils.h" +#include "theory/bv/theory_bv_rewrite_rules_normalization.h" + +using namespace CVC4; + +namespace CVC4 { +namespace theory { +namespace bv { + +static bool is_bv_const(Node n) +{ + if (n.isConst()) { return true; } + return Rewriter::rewrite(n).getKind() == kind::CONST_BITVECTOR; +} + +static Node get_bv_const(Node n) +{ + Assert(is_bv_const(n)); + return Rewriter::rewrite(n); +} + +static Integer get_bv_const_value(Node n) +{ + Assert(is_bv_const(n)); + return get_bv_const(n).getConst().getValue(); +} + +/* Note: getMinBwExpr assumes that 'expr' is rewritten. + * + * If not, all operators that are removed via rewriting (e.g., ror, rol, ...) + * will be handled via the default case, which is not incorrect but also not + * necessarily the minimum. */ +unsigned BVGaussElim::getMinBwExpr(Node expr) +{ + std::vector visit; + /* Maps visited nodes to the determined minimum bit-width required. */ + std::unordered_map visited; + std::unordered_map::iterator it; + + visit.push_back(expr); + while (!visit.empty()) + { + Node n = visit.back(); + visit.pop_back(); + it = visited.find(n); + if (it == visited.end()) + { + if (is_bv_const(n)) + { + /* Rewrite const expr, overflows in consts are irrelevant. */ + visited[n] = get_bv_const(n).getConst().getValue().length(); + } + else + { + visited[n] = 0; + visit.push_back(n); + for (const Node &nn : n) { visit.push_back(nn); } + } + } + else if (it->second == 0) + { + Kind k = n.getKind(); + Assert(k != kind::CONST_BITVECTOR); + Assert(!is_bv_const(n)); + switch (k) + { + case kind::BITVECTOR_EXTRACT: + { + unsigned w = utils::getSize(n); + visited[n] = std::min( + w, std::max(visited[n[0]] - utils::getExtractLow(n), 0u)); + Assert(visited[n] <= visited[n[0]]); + break; + } + + case kind::BITVECTOR_ZERO_EXTEND: + { + visited[n] = visited[n[0]]; + break; + } + + case kind::BITVECTOR_MULT: + { + Integer maxval = Integer(1); + for (const Node& nn : n) + { + if (is_bv_const(nn)) + { + maxval *= get_bv_const_value(nn); + } + else + { + maxval *= utils::mkBitVectorOnes(visited[nn]).getValue(); + } + } + unsigned w = maxval.length(); + if (w > utils::getSize(n)) { return 0; } /* overflow */ + visited[n] = w; + break; + } + + case kind::BITVECTOR_CONCAT: + { + unsigned i, wnz, nc; + for (i = 0, wnz = 0, nc = n.getNumChildren() - 1; i < nc; ++i) + { + unsigned wni = utils::getSize(n[i]); + if (n[i] != utils::mkZero(wni)) { break; } + /* sum of all bit-widths of leading zero concats */ + wnz += wni; + } + /* Do not consider leading zero concats, i.e., + * min bw of current concat is determined as + * min bw of first non-zero term + * plus actual bw of all subsequent terms */ + visited[n] = utils::getSize(n) + + visited[n[i]] - utils::getSize(n[i]) + - wnz; + break; + } + + case kind::BITVECTOR_UREM_TOTAL: + case kind::BITVECTOR_LSHR: + case kind::BITVECTOR_ASHR: + { + visited[n] = visited[n[0]]; + break; + } + + case kind::BITVECTOR_OR: + case kind::BITVECTOR_NOR: + case kind::BITVECTOR_XOR: + case kind::BITVECTOR_XNOR: + case kind::BITVECTOR_AND: + case kind::BITVECTOR_NAND: + { + unsigned wmax = 0; + for (const Node &nn : n) + { + if (visited[nn] > wmax) + { + wmax = visited[nn]; + } + } + visited[n] = wmax; + break; + } + + case kind::BITVECTOR_PLUS: + { + Integer maxval = Integer(0); + for (const Node& nn : n) + { + if (is_bv_const(nn)) + { + maxval += get_bv_const_value(nn); + } + else + { + maxval += utils::mkBitVectorOnes(visited[nn]).getValue(); + } + } + unsigned w = maxval.length(); + if (w > utils::getSize(n)) { return 0; } /* overflow */ + visited[n] = w; + break; + } + + default: + { + /* BITVECTOR_UDIV_TOTAL (since x / 0 = -1) + * BITVECTOR_NOT + * BITVECTOR_NEG + * BITVECTOR_SHL */ + visited[n] = utils::getSize(n); + } + } + } + } + Assert(visited.find(expr) != visited.end()); + return visited[expr]; +} + +BVGaussElim::Result BVGaussElim::gaussElim( + Integer prime, + std::vector& rhs, + std::vector>& lhs) +{ + Assert(prime > 0); + Assert(lhs.size()); + Assert(lhs.size() == rhs.size()); + Assert(lhs.size() <= lhs[0].size()); + + /* special case: zero ring */ + if (prime == 1) + { + rhs = std::vector(rhs.size(), Integer(0)); + lhs = std::vector>( + lhs.size(), std::vector(lhs[0].size(), Integer(0))); + return BVGaussElim::Result::UNIQUE; + } + + size_t nrows = lhs.size(); + size_t ncols = lhs[0].size(); + + #ifdef CVC4_ASSERTIONS + for (size_t i = 1; i < nrows; ++i) Assert(lhs[i].size() == ncols); + #endif + /* (1) if element in pivot column is non-zero and != 1, divide row elements + * by element in pivot column modulo prime, i.e., multiply row with + * multiplicative inverse of element in pivot column modulo prime + * + * (2) subtract pivot row from all rows below pivot row + * + * (3) subtract (multiple of) current row from all rows above s.t. all + * elements in current pivot column above current row become equal to one + * + * Note: we do not normalize the given matrix to values modulo prime + * beforehand but on-the-fly. */ + + /* pivot = lhs[pcol][pcol] */ + for (size_t pcol = 0, prow = 0; pcol < ncols && prow < nrows; ++pcol, ++prow) + { + /* lhs[j][pcol]: element in pivot column */ + for (size_t j = prow; j < nrows; ++j) + { +#ifdef CVC4_ASSERTIONS + for (size_t k = 0; k < pcol; ++k) { Assert(lhs[j][k] == 0); } +#endif + /* normalize element in pivot column to modulo prime */ + lhs[j][pcol] = lhs[j][pcol].euclidianDivideRemainder(prime); + /* exchange rows if pivot elem is 0 */ + if (j == prow) + { + while (lhs[j][pcol] == 0) + { + for (size_t k = prow + 1; k < nrows; ++k) + { + lhs[k][pcol] = lhs[k][pcol].euclidianDivideRemainder(prime); + if (lhs[k][pcol] != 0) + { + std::swap(rhs[j], rhs[k]); + std::swap(lhs[j], lhs[k]); + break; + } + } + if (pcol >= ncols - 1) break; + if (lhs[j][pcol] == 0) + { + pcol += 1; + if (lhs[j][pcol] != 0) + lhs[j][pcol] = lhs[j][pcol].euclidianDivideRemainder(prime); + } + } + } + + if (lhs[j][pcol] != 0) + { + /* (1) */ + if (lhs[j][pcol] != 1) + { + Integer inv = lhs[j][pcol].modInverse(prime); + if (inv == -1) + { + return BVGaussElim::Result::INVALID; /* not coprime */ + } + for (size_t k = pcol; k < ncols; ++k) + { + lhs[j][k] = lhs[j][k].modMultiply(inv, prime); + if (j <= prow) continue; /* pivot */ + lhs[j][k] = lhs[j][k].modAdd(-lhs[prow][k], prime); + } + rhs[j] = rhs[j].modMultiply(inv, prime); + if (j > prow) { rhs[j] = rhs[j].modAdd(-rhs[prow], prime); } + } + /* (2) */ + else if (j != prow) + { + for (size_t k = pcol; k < ncols; ++k) + { + lhs[j][k] = lhs[j][k].modAdd(-lhs[prow][k], prime); + } + rhs[j] = rhs[j].modAdd(-rhs[prow], prime); + } + } + } + /* (3) */ + for (size_t j = 0; j < prow; ++j) + { + Integer mul = lhs[j][pcol]; + if (mul != 0) + { + for (size_t k = pcol; k < ncols; ++k) + { + lhs[j][k] = lhs[j][k].modAdd(-lhs[prow][k] * mul, prime); + } + rhs[j] = rhs[j].modAdd(-rhs[prow] * mul, prime); + } + } + } + + bool ispart = false; + for (size_t i = 0; i < nrows; ++i) + { + size_t pcol = i; + while (pcol < ncols && lhs[i][pcol] == 0) ++pcol; + if (pcol >= ncols) + { + rhs[i] = rhs[i].euclidianDivideRemainder(prime); + if (rhs[i] != 0) + { + /* no solution */ + return BVGaussElim::Result::NONE; + } + continue; + } + for (size_t j = i; j < ncols; ++j) + { + if (lhs[i][j] >= prime || lhs[i][j] <= -prime) + { + lhs[i][j] = lhs[i][j].euclidianDivideRemainder(prime); + } + if (j > pcol && lhs[i][j] != 0) + { + ispart = true; + } + } + } + + if (ispart) { return BVGaussElim::Result::PARTIAL; } + + return BVGaussElim::Result::UNIQUE; +} + +BVGaussElim::Result BVGaussElim::gaussElimRewriteForUrem( + const std::vector& equations, + std::unordered_map& res) +{ + Assert(res.empty()); + + Node prime; + Integer iprime; + std::unordered_map, NodeHashFunction> vars; + size_t neqs = equations.size(); + std::vector rhs; + std::vector> lhs = + std::vector>(neqs, std::vector()); + + res = std::unordered_map(); + + for (size_t i = 0; i < neqs; ++i) + { + Node eq = equations[i]; + Assert(eq.getKind() == kind::EQUAL); + Node urem, eqrhs; + + if (eq[0].getKind() == kind::BITVECTOR_UREM) + { + urem = eq[0]; + Assert(is_bv_const(eq[1])); + eqrhs = eq[1]; + } + else + { + Assert(eq[1].getKind() == kind::BITVECTOR_UREM); + urem = eq[1]; + Assert(is_bv_const(eq[0])); + eqrhs = eq[0]; + } + if (getMinBwExpr(Rewriter::rewrite(urem[0])) == 0) + { + Trace("bv-gauss-elim") + << "Minimum required bit-width exceeds given bit-width, " + "will not apply Gaussian Elimination." + << std::endl; + return BVGaussElim::Result::INVALID; + } + rhs.push_back(get_bv_const_value(eqrhs)); + + Assert(is_bv_const(urem[1])); + Assert(i == 0 || get_bv_const_value(urem[1]) == iprime); + if (i == 0) + { + prime = urem[1]; + iprime = get_bv_const_value(prime); + } + + std::unordered_map tmp; + std::vector stack; + stack.push_back(urem[0]); + while (!stack.empty()) + { + Node n = stack.back(); + stack.pop_back(); + + /* Subtract from rhs if const */ + if (is_bv_const(n)) + { + Integer val = get_bv_const_value(n); + if (val > 0) rhs.back() -= val; + continue; + } + + /* Split into matrix columns */ + Kind k = n.getKind(); + if (k == kind::BITVECTOR_PLUS) + { + for (const Node& nn : n) { stack.push_back(nn); } + } + else if (k == kind::BITVECTOR_MULT) + { + Node n0, n1; + /* Flatten mult expression. */ + n = RewriteRule::run(n); + /* Split operands into consts and non-consts */ + NodeBuilder<> nb_consts(NodeManager::currentNM(), k); + NodeBuilder<> nb_nonconsts(NodeManager::currentNM(), k); + for (const Node& nn : n) + { + Node nnrw = Rewriter::rewrite(nn); + if (is_bv_const(nnrw)) + { + nb_consts << nnrw; + } + else + { + nb_nonconsts << nnrw; + } + } + Assert(nb_nonconsts.getNumChildren() > 0); + /* n0 is const */ + unsigned nc = nb_consts.getNumChildren(); + if (nc > 1) + { + n0 = Rewriter::rewrite(nb_consts.constructNode()); + } + else if (nc == 1) + { + n0 = nb_consts[0]; + } + else + { + n0 = utils::mkOne(utils::getSize(n)); + } + /* n1 is a mult with non-const operands */ + if (nb_nonconsts.getNumChildren() > 1) + { + n1 = Rewriter::rewrite(nb_nonconsts.constructNode()); + } + else + { + n1 = nb_nonconsts[0]; + } + Assert(is_bv_const(n0)); + Assert(!is_bv_const(n1)); + tmp[n1] += get_bv_const_value(n0); + } + else + { + tmp[n] += Integer(1); + } + } + + /* Note: "var" is not necessarily a VARIABLE but can be an arbitrary expr */ + + for (const auto& p : tmp) + { + Node var = p.first; + Integer val = p.second; + if (i > 0 && vars.find(var) == vars.end()) + { + /* Add column and fill column elements of rows above with 0. */ + vars[var].insert(vars[var].end(), i, Integer(0)); + } + vars[var].push_back(val); + } + + for (const auto& p : vars) + { + if (tmp.find(p.first) == tmp.end()) + { + vars[p.first].push_back(Integer(0)); + } + } + } + + size_t nvars = vars.size(); + Assert(nvars); + size_t nrows = vars.begin()->second.size(); +#ifdef CVC4_ASSERTIONS + for (const auto& p : vars) { Assert(p.second.size() == nrows); } +#endif + + if (nrows < 1) + { + return BVGaussElim::Result::INVALID; + } + + for (size_t i = 0; i < nrows; ++i) + { + for (const auto& p : vars) + { + lhs[i].push_back(p.second[i]); + } + } + +#ifdef CVC4_ASSERTIONS + for (const auto& row : lhs) { Assert(row.size() == nvars); } + Assert(lhs.size() == rhs.size()); +#endif + + if (lhs.size() > lhs[0].size()) + { + return BVGaussElim::Result::INVALID; + } + + Trace("bv-gauss-elim") << "Applying Gaussian Elimination..." << std::endl; + Result ret = gaussElim(iprime, rhs, lhs); + + if (ret != BVGaussElim::Result::NONE && ret != BVGaussElim::Result::INVALID) + { + std::vector vvars; + for (const auto& p : vars) { vvars.push_back(p.first); } + Assert(nvars == vvars.size()); + Assert(nrows == lhs.size()); + Assert(nrows == rhs.size()); + NodeManager *nm = NodeManager::currentNM(); + if (ret == BVGaussElim::Result::UNIQUE) + { + for (size_t i = 0; i < nvars; ++i) + { + res[vvars[i]] = nm->mkConst( + BitVector(utils::getSize(vvars[i]), rhs[i])); + } + } + else + { + Assert(ret == BVGaussElim::Result::PARTIAL); + + for (size_t pcol = 0, prow = 0; pcol < nvars && prow < nrows; + ++pcol, ++prow) + { + Assert(lhs[prow][pcol] == 0 || lhs[prow][pcol] == 1); + while (pcol < nvars && lhs[prow][pcol] == 0) pcol += 1; + if (pcol >= nvars) + { + Assert(rhs[prow] == 0); + break; + } + if (lhs[prow][pcol] == 0) + { + Assert(rhs[prow] == 0); + continue; + } + Assert(lhs[prow][pcol] == 1); + std::vector stack; + for (size_t i = pcol + 1; i < nvars; ++i) + { + if (lhs[prow][i] == 0) continue; + /* Normalize (no negative numbers, hence no subtraction) + * e.g., x = 4 - 2y --> x = 4 + 9y (modulo 11) */ + Integer m = iprime - lhs[prow][i]; + Node bv = + nm->mkConst(BitVector(utils::getSize(vvars[i]), m)); + Node mult = nm->mkNode(kind::BITVECTOR_MULT, vvars[i], bv); + stack.push_back(mult); + } + + if (stack.empty()) + { + res[vvars[pcol]] = nm->mkConst( + BitVector(utils::getSize(vvars[pcol]), rhs[prow])); + } + else + { + Node tmp = stack.size() == 1 + ? stack[0] + : nm->mkNode(kind::BITVECTOR_PLUS, stack); + + if (rhs[prow] != 0) + { + tmp = nm->mkNode(kind::BITVECTOR_PLUS, + nm->mkConst(BitVector( + utils::getSize(vvars[pcol]), rhs[prow])), + tmp); + } + Assert(!is_bv_const(tmp)); + res[vvars[pcol]] = nm->mkNode(kind::BITVECTOR_UREM, tmp, prime); + } + } + } + } + return ret; +} + +void BVGaussElim::gaussElimRewrite(std::vector &assertionsToPreprocess) +{ + std::vector assertions(assertionsToPreprocess); + std::unordered_map, NodeHashFunction> equations; + + while (!assertions.empty()) + { + Node a = assertions.back(); + assertions.pop_back(); + CVC4::Kind k = a.getKind(); + + if (k == kind::AND) + { + for (const Node& aa : a) + { + assertions.push_back(aa); + } + } + else if (k == kind::EQUAL) + { + Node urem; + + if (is_bv_const(a[1]) && a[0].getKind() == kind::BITVECTOR_UREM) + { + urem = a[0]; + } + else if (is_bv_const(a[0]) && a[1].getKind() == kind::BITVECTOR_UREM) + { + urem = a[1]; + } + else + { + continue; + } + + if (urem[0].getKind() == kind::BITVECTOR_PLUS && is_bv_const(urem[1])) + { + equations[urem[1]].push_back(a); + } + } + } + + std::unordered_map subst; + + for (const auto& eq : equations) + { + if (eq.second.size() <= 1) { continue; } + + std::unordered_map res; + BVGaussElim::Result ret = gaussElimRewriteForUrem(eq.second, res); + Trace("bv-gauss-elim") << "result: " + << (ret == BVGaussElim::Result::INVALID + ? "INVALID" + : (ret == BVGaussElim::Result::UNIQUE + ? "UNIQUE" + : (ret == BVGaussElim::Result::PARTIAL + ? "PARTIAL" + : "NONE"))) + << std::endl; + if (ret != BVGaussElim::Result::INVALID) + { + NodeManager *nm = NodeManager::currentNM(); + if (ret == BVGaussElim::Result::NONE) + { + assertionsToPreprocess.clear(); + assertionsToPreprocess.push_back(nm->mkConst(false)); + } + else + { + for (const Node& e : eq.second) + { + subst[e] = nm->mkConst(true); + } + /* add resulting constraints */ + for (const auto& p : res) + { + Node a = nm->mkNode(kind::EQUAL, p.first, p.second); + Trace("bv-gauss-elim") << "added assertion: " << a << std::endl; + assertionsToPreprocess.push_back(a); + } + } + } + } + + if (!subst.empty()) + { + /* delete (= substitute with true) obsolete assertions */ + for (auto& a : assertionsToPreprocess) + { + a = a.substitute(subst.begin(), subst.end()); + } + } +} + +} // namespace bv +} // namespace theory +} // namespace CVC4 diff --git a/src/theory/bv/bvgauss.h b/src/theory/bv/bvgauss.h new file mode 100644 index 000000000..6cd80729d --- /dev/null +++ b/src/theory/bv/bvgauss.h @@ -0,0 +1,151 @@ +/********************* */ +/*! \file bvgauss.h + ** \verbatim + ** Top contributors (to current version): + ** Aina Niemetz + ** This file is part of the CVC4 project. + ** Copyright (c) 2009-2017 by the authors listed in the file AUTHORS + ** in the top-level source directory) and their institutional affiliations. + ** All rights reserved. See the file COPYING in the top-level source + ** directory for licensing information.\endverbatim + ** + ** \brief Gaussian Elimination preprocessing pass. + ** + ** Simplify a given equation system modulo a (prime) number via Gaussian + ** Elimination if possible. + **/ + +#include "cvc4_private.h" + +#ifndef __CVC4__THEORY__BV__BV_GAUSS_ELIM_H +#define __CVC4__THEORY__BV__BV_GAUSS_ELIM_H + +#include "expr/node.h" +#include "util/bitvector.h" + +#include +#include + +namespace CVC4 { +namespace theory { +namespace bv { + +class BVGaussElim +{ + public: + /** + * Apply Gaussian Elimination on (possibly multiple) set(s) of equations + * modulo some (prime) number given as bit-vector equations. + * + * Note that these sets of equations do not have to be modulo some prime + * but can be modulo any arbitrary number. However, GE is guaranteed to + * succeed modulo a prime number, which is not necessarily the case if a + * given set of equations is modulo a non-prime number. + */ + static void gaussElimRewrite(std::vector& assertionsToPreprocess); + + private: + /** + * Represents the result of Gaussian Elimination where the solution + * of the given equation system is + * + * INVALID ... i.e., NOT of the form c1*x1 + c2*x2 + ... % p = b, + * where ci, b and p are + * - bit-vector constants + * - extracts or zero extensions on bit-vector constants + * - of arbitrary nesting level + * and p is co-prime to all bit-vector constants for which + * a multiplicative inverse has to be computed. + * + * UNIQUE ... determined for all unknowns, e.g., x = 4 + * + * PARTIAL ... e.g., x = 4 - 2z + * + * NONE ... no solution + * + * Given a matrix A representing an equation system, the resulting + * matrix B after applying GE represents, e.g.: + * + * B = 1 0 0 2 <- UNIQUE + * 0 1 0 3 <- + * 0 0 1 1 <- + * + * B = 1 0 2 4 <- PARTIAL + * 0 1 3 2 <- + * 0 0 1 1 + * + * B = 1 0 0 1 NONE + * 0 1 1 2 + * 0 0 0 2 <- + */ + enum class Result + { + INVALID, + UNIQUE, + PARTIAL, + NONE + }; + + /** + * Determines if an overflow may occur in given 'expr'. + * + * Returns 0 if an overflow may occur, and the minimum required + * bit-width such that no overflow occurs, otherwise. + * + * Note that it would suffice for this function to be Boolean. + * However, it is handy to determine the minimum required bit-width for + * debugging purposes. + */ + static unsigned getMinBwExpr(Node expr); + + /** + * Apply Gaussian Elimination on a set of equations modulo some (prime) + * number given as bit-vector equations. + * + * IMPORTANT: Applying GE modulo some number (rather than modulo 2^bw) + * on a set of bit-vector equations is only sound if this set of equations + * has a solution that does not produce overflows. Consequently, we only + * apply GE if the given bit-width guarantees that no overflows can occur + * in the given set of equations. + * + * Note that the given set of equations does not have to be modulo a prime + * but can be modulo any arbitrary number. However, if it is indeed modulo + * prime, GE is guaranteed to succeed, which is not the case, otherwise. + * + * Returns INVALID if GE can not be applied, UNIQUE and PARTIAL if GE was + * successful, and NONE, otherwise. + * + * The resulting constraints are stored in 'res' as a mapping of unknown + * to result (modulo prime). These mapped results are added as constraints + * of the form 'unknown = mapped result' in gaussElimRewrite. + */ + static Result gaussElimRewriteForUrem( + const std::vector& equations, + std::unordered_map& res); + + /** + * Apply Gaussian Elimination modulo a (prime) number. + * The given equation system is represented as a matrix of Integers. + * + * Note that given 'prime' does not have to be prime but can be any + * arbitrary number. However, if 'prime' is indeed prime, GE is guaranteed + * to succeed, which is not the case, otherwise. + * + * Returns INVALID if GE can not be applied, UNIQUE and PARTIAL if GE was + * successful, and NONE, otherwise. + * + * Vectors 'rhs' and 'lhs' represent the right hand side and left hand side + * of the given matrix, respectively. The resulting matrix (in row echelon + * form) is stored in 'rhs' and 'lhs', i.e., the given matrix is overwritten + * with the resulting matrix. + */ + static Result gaussElim(Integer prime, + std::vector& rhs, + std::vector>& lhs); +}; + +} // namespace bv +} // namespace theory +} // namespace CVC4 + +#endif diff --git a/test/unit/Makefile.am b/test/unit/Makefile.am index 9640a059a..8c45eeb23 100644 --- a/test/unit/Makefile.am +++ b/test/unit/Makefile.am @@ -12,6 +12,7 @@ UNIT_TESTS += \ theory/theory_white \ theory/theory_arith_white \ theory/theory_bv_white \ + theory/theory_bv_bvgauss_white \ theory/type_enumerator_white \ expr/node_white \ expr/node_black \ diff --git a/test/unit/theory/theory_bv_bvgauss_white.h b/test/unit/theory/theory_bv_bvgauss_white.h new file mode 100644 index 000000000..a0e2b235b --- /dev/null +++ b/test/unit/theory/theory_bv_bvgauss_white.h @@ -0,0 +1,2965 @@ +/********************* */ +/*! \file theory_bv_bvgauss_white.h + ** \verbatim + ** Top contributors (to current version): + ** Aina Niemetz + ** This file is part of the CVC4 project. + ** Copyright (c) 2009-2017 by the authors listed in the file AUTHORS + ** in the top-level source directory) and their institutional affiliations. + ** All rights reserved. See the file COPYING in the top-level source + ** directory for licensing information.\endverbatim + ** + ** \brief Unit tests for Gaussian Elimination preprocessing pass. + ** + ** Unit tests for Gaussian Elimination preprocessing pass. + **/ + +#include "expr/node.h" +#include "expr/node_manager.h" +#include "smt/smt_engine.h" +#include "smt/smt_engine_scope.h" +#include "theory/rewriter.h" +#include "theory/bv/bvgauss.h" +#include "theory/bv/theory_bv_utils.h" +#include "util/bitvector.h" + +#include +#include +#include + +using namespace CVC4; +using namespace CVC4::theory; +using namespace CVC4::theory::bv; +using namespace CVC4::theory::bv::utils; +using namespace CVC4::smt; + +static void print_matrix_dbg(std::vector &rhs, + std::vector> &lhs) +{ + for (size_t m = 0, nrows = lhs.size(), ncols = lhs[0].size(); m < nrows; ++m) + { + for (size_t n = 0; n < ncols; ++n) + { + std::cout << " " << lhs[m][n]; + } + std::cout << " " << rhs[m]; + std::cout << std::endl; + } +} + +static void testGaussElimX(Integer prime, + std::vector rhs, + std::vector> lhs, + BVGaussElim::Result expected, + std::vector *rrhs = nullptr, + std::vector> *rlhs = nullptr) +{ + size_t nrows = lhs.size(); + size_t ncols = lhs[0].size(); + BVGaussElim::Result ret; + std::vector resrhs = std::vector(rhs); + std::vector> reslhs = + std::vector>(lhs); + + std::cout << "Input: " << std::endl; + print_matrix_dbg(rhs, lhs); + + ret = BVGaussElim::gaussElim(prime, resrhs, reslhs); + + std::cout << "Result: " + << (ret == BVGaussElim::Result::INVALID + ? "INVALID" + : (ret == BVGaussElim::Result::UNIQUE + ? "UNIQUE" + : (ret == BVGaussElim::Result::PARTIAL ? "PARTIAL" + : "NONE"))) + << std::endl; + print_matrix_dbg(resrhs, reslhs); + + TS_ASSERT_EQUALS(expected, ret); + + if (expected == BVGaussElim::Result::UNIQUE) + { + /* map result value to column index + * e.g.: + * 1 0 0 2 -> res = { 2, 0, 3} + * 0 0 1 3 */ + std::vector res = std::vector(ncols, Integer(0)); + for (size_t i = 0; i < nrows; ++i) + for (size_t j = 0; j < ncols; ++j) + { + if (reslhs[i][j] == 1) + res[j] = resrhs[i]; + else + TS_ASSERT(reslhs[i][j] == 0); + } + + for (size_t i = 0; i < nrows; ++i) + { + Integer tmp = Integer(0); + for (size_t j = 0; j < ncols; ++j) + tmp = tmp.modAdd(lhs[i][j].modMultiply(res[j], prime), prime); + TS_ASSERT(tmp == rhs[i].euclidianDivideRemainder(prime)); + } + } + if (rrhs != nullptr && rlhs != nullptr) + { + for (size_t i = 0; i < nrows; ++i) + { + for (size_t j = 0; j < ncols; ++j) + { + TS_ASSERT(reslhs[i][j] == (*rlhs)[i][j]); + } + TS_ASSERT(resrhs[i] == (*rrhs)[i]); + } + } +} + +template +static void testGaussElimT(Integer prime, + std::vector rhs, + std::vector> lhs) +{ + TS_ASSERT_THROWS(BVGaussElim::gaussElim(prime, rhs, lhs), T); +} + +class TheoryBVGaussWhite : public CxxTest::TestSuite +{ + ExprManager *d_em; + NodeManager *d_nm; + SmtEngine *d_smt; + SmtScope *d_scope; + Node d_p; + Node d_x; + Node d_y; + Node d_z; + Node d_zero; + Node d_one; + Node d_two; + Node d_three; + Node d_four; + Node d_five; + Node d_six; + Node d_seven; + Node d_eight; + Node d_nine; + Node d_ten; + Node d_twelve; + Node d_eighteen; + Node d_twentyfour; + Node d_thirty; + Node d_one32; + Node d_two32; + Node d_three32; + Node d_four32; + Node d_five32; + Node d_six32; + Node d_seven32; + Node d_eight32; + Node d_nine32; + Node d_ten32; + Node d_x_mul_one; + Node d_x_mul_two; + Node d_x_mul_four; + Node d_y_mul_one; + Node d_y_mul_three; + Node d_y_mul_four; + Node d_y_mul_five; + Node d_y_mul_seven; + Node d_z_mul_one; + Node d_z_mul_three; + Node d_z_mul_five; + Node d_z_mul_twelve; + Node d_z_mul_six; + Node d_z_mul_nine; + + public: + TheoryBVGaussWhite() {} + + void setUp() + { + d_em = new ExprManager(); + d_nm = NodeManager::fromExprManager(d_em); + d_smt = new SmtEngine(d_em); + d_scope = new SmtScope(d_smt); + + d_zero = mkZero(16); + + d_p = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 11u))); + d_x = mkConcat(d_zero, d_nm->mkVar("x", d_nm->mkBitVectorType(16))); + d_y = mkConcat(d_zero, d_nm->mkVar("y", d_nm->mkBitVectorType(16))); + d_z = mkConcat(d_zero, d_nm->mkVar("z", d_nm->mkBitVectorType(16))); + + d_one = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 1u))); + d_two = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 2u))); + d_three = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 3u))); + d_four = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 4u))); + d_five = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 5u))); + d_six = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 6u))); + d_seven = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 7u))); + d_eight = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 8u))); + d_nine = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 9u))); + d_ten = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 10u))); + d_twelve = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 12u))); + d_eighteen = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 18u))); + d_twentyfour = + mkConcat(d_zero, d_nm->mkConst(BitVector(16, 24u))); + d_thirty = mkConcat(d_zero, d_nm->mkConst(BitVector(16, 30u))); + + d_one32 = d_nm->mkConst(BitVector(32, 1u)); + d_two32 = d_nm->mkConst(BitVector(32, 2u)); + d_three32 = d_nm->mkConst(BitVector(32, 3u)); + d_four32 = d_nm->mkConst(BitVector(32, 4u)); + d_five32 = d_nm->mkConst(BitVector(32, 5u)); + d_six32 = d_nm->mkConst(BitVector(32, 6u)); + d_seven32 = d_nm->mkConst(BitVector(32, 7u)); + d_eight32 = d_nm->mkConst(BitVector(32, 8u)); + d_nine32 = d_nm->mkConst(BitVector(32, 9u)); + d_ten32 = d_nm->mkConst(BitVector(32, 10u)); + + d_x_mul_one = d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_one); + d_x_mul_two = d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_two); + d_x_mul_four = d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_four); + d_y_mul_three = d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_three); + d_y_mul_one = d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_one); + d_y_mul_four = d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_four); + d_y_mul_five = d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_five); + d_y_mul_seven = d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_seven); + d_z_mul_one = d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_one); + d_z_mul_three = d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_three); + d_z_mul_five = d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_five); + d_z_mul_six = d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_six); + d_z_mul_twelve = d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_twelve); + d_z_mul_nine = d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_nine); + } + + void tearDown() + { + (void)d_scope; + d_p = Node::null(); + d_x = Node::null(); + d_y = Node::null(); + d_z = Node::null(); + d_zero = Node::null(); + d_one = Node::null(); + d_two = Node::null(); + d_three = Node::null(); + d_four = Node::null(); + d_five = Node::null(); + d_six = Node::null(); + d_seven = Node::null(); + d_eight = Node::null(); + d_nine = Node::null(); + d_ten = Node::null(); + d_twelve = Node::null(); + d_eighteen = Node::null(); + d_twentyfour = Node::null(); + d_thirty = Node::null(); + d_one32 = Node::null(); + d_two32 = Node::null(); + d_three32 = Node::null(); + d_four32 = Node::null(); + d_five32 = Node::null(); + d_six32 = Node::null(); + d_seven32 = Node::null(); + d_eight32 = Node::null(); + d_nine32 = Node::null(); + d_ten32 = Node::null(); + d_x_mul_one = Node::null(); + d_x_mul_two = Node::null(); + d_x_mul_four = Node::null(); + d_y_mul_one = Node::null(); + d_y_mul_four = Node::null(); + d_y_mul_seven = Node::null(); + d_y_mul_five = Node::null(); + d_y_mul_three = Node::null(); + d_z_mul_one = Node::null(); + d_z_mul_three = Node::null(); + d_z_mul_five = Node::null(); + d_z_mul_six = Node::null(); + d_z_mul_twelve = Node::null(); + d_z_mul_nine = Node::null(); + delete d_scope; + delete d_smt; + delete d_em; + } + + void testGaussElimMod() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs modulo { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 } + * --^-- ^ + * 1 1 1 5 + * 2 3 5 8 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8), Integer(2)}; + lhs = {{Integer(1), Integer(1), Integer(1)}, + {Integer(2), Integer(3), Integer(5)}, + {Integer(4), Integer(0), Integer(5)}}; + std::cout << "matrix 0, modulo 0" << std::endl; // throws + testGaussElimT(Integer(0), rhs, lhs); + std::cout << "matrix 0, modulo 1" << std::endl; + testGaussElimX(Integer(1), rhs, lhs, BVGaussElim::Result::UNIQUE); + std::cout << "matrix 0, modulo 2" << std::endl; + testGaussElimX(Integer(2), rhs, lhs, BVGaussElim::Result::UNIQUE); + std::cout << "matrix 0, modulo 3" << std::endl; + testGaussElimX(Integer(3), rhs, lhs, BVGaussElim::Result::UNIQUE); + std::cout << "matrix 0, modulo 4" << std::endl; // no inverse + testGaussElimX(Integer(4), rhs, lhs, BVGaussElim::Result::INVALID); + std::cout << "matrix 0, modulo 5" << std::endl; + testGaussElimX(Integer(5), rhs, lhs, BVGaussElim::Result::UNIQUE); + std::cout << "matrix 0, modulo 6" << std::endl; // no inverse + testGaussElimX(Integer(6), rhs, lhs, BVGaussElim::Result::INVALID); + std::cout << "matrix 0, modulo 7" << std::endl; + testGaussElimX(Integer(7), rhs, lhs, BVGaussElim::Result::UNIQUE); + std::cout << "matrix 0, modulo 8" << std::endl; // no inverse + testGaussElimX(Integer(8), rhs, lhs, BVGaussElim::Result::INVALID); + std::cout << "matrix 0, modulo 9" << std::endl; + testGaussElimX(Integer(9), rhs, lhs, BVGaussElim::Result::UNIQUE); + std::cout << "matrix 0, modulo 10" << std::endl; // no inverse + testGaussElimX(Integer(10), rhs, lhs, BVGaussElim::Result::INVALID); + std::cout << "matrix 0, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + } + + void testGaussElimUniqueDone() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 17 + * --^--- ^ --^-- ^ + * 1 0 0 4 --> 1 0 0 4 + * 0 1 0 15 0 1 0 15 + * 0 0 1 3 0 0 1 3 + * ------------------------------------------------------------------- */ + rhs = {Integer(4), Integer(15), Integer(3)}; + lhs = {{Integer(1), Integer(0), Integer(0)}, + {Integer(0), Integer(1), Integer(0)}, + {Integer(0), Integer(0), Integer(1)}}; + std::cout << "matrix 1, modulo 17" << std::endl; + testGaussElimX(Integer(17), rhs, lhs, BVGaussElim::Result::UNIQUE); + } + + void testGaussElimUnique() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs modulo { 11,17,59 } + * --^--- ^ + * 2 4 6 18 + * 4 5 6 24 + * 3 1 -2 4 + * ------------------------------------------------------------------- */ + rhs = {Integer(18), Integer(24), Integer(4)}; + lhs = {{Integer(2), Integer(4), Integer(6)}, + {Integer(4), Integer(5), Integer(6)}, + {Integer(3), Integer(1), Integer(-2)}}; + std::cout << "matrix 2, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + std::cout << "matrix 2, modulo 17" << std::endl; + testGaussElimX(Integer(17), rhs, lhs, BVGaussElim::Result::UNIQUE); + std::cout << "matrix 2, modulo 59" << std::endl; + testGaussElimX(Integer(59), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * -----^----- ^ ---^--- ^ + * 1 1 2 0 1 --> 1 0 0 0 1 + * 2 -1 0 1 -2 0 1 0 0 2 + * 1 -1 -1 -2 4 0 0 1 0 -1 + * 2 -1 2 -1 0 0 0 0 1 -2 + * ------------------------------------------------------------------- */ + rhs = {Integer(1), Integer(-2), Integer(4), Integer(0)}; + lhs = {{Integer(1), Integer(1), Integer(2), Integer(0)}, + {Integer(2), Integer(-1), Integer(0), Integer(1)}, + {Integer(1), Integer(-1), Integer(-1), Integer(-2)}, + {Integer(2), Integer(-1), Integer(2), Integer(-1)}}; + std::cout << "matrix 3, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + } + + void testGaussElimUniqueZero1() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 0 4 5 2 --> 1 0 0 4 + * 1 1 1 5 0 1 0 3 + * 3 2 5 8 0 0 1 9 + * ------------------------------------------------------------------- */ + rhs = {Integer(2), Integer(5), Integer(8)}; + lhs = {{Integer(0), Integer(4), Integer(5)}, + {Integer(1), Integer(1), Integer(1)}, + {Integer(3), Integer(2), Integer(5)}}; + std::cout << "matrix 4, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 1 1 5 --> 1 0 0 4 + * 0 4 5 2 0 1 0 3 + * 3 2 5 8 0 0 1 9 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(2), Integer(8)}; + lhs = {{Integer(1), Integer(1), Integer(1)}, + {Integer(0), Integer(4), Integer(5)}, + {Integer(3), Integer(2), Integer(5)}}; + std::cout << "matrix 5, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 1 1 5 --> 1 0 0 4 + * 3 2 5 8 0 1 0 9 + * 0 4 5 2 0 0 1 3 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8), Integer(2)}; + lhs = {{Integer(1), Integer(1), Integer(1)}, + {Integer(3), Integer(2), Integer(5)}, + {Integer(0), Integer(4), Integer(5)}}; + std::cout << "matrix 6, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + } + + void testGaussElimUniqueZero2() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 0 0 5 2 1 0 0 10 + * 1 1 1 5 --> 0 1 0 10 + * 3 2 5 8 0 0 1 7 + * ------------------------------------------------------------------- */ + rhs = {Integer(2), Integer(5), Integer(8)}; + lhs = {{Integer(0), Integer(0), Integer(5)}, + {Integer(1), Integer(1), Integer(1)}, + {Integer(3), Integer(2), Integer(5)}}; + std::cout << "matrix 7, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 1 1 5 --> 1 0 0 10 + * 0 0 5 2 0 1 0 10 + * 3 2 5 8 0 0 1 7 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(2), Integer(8)}; + lhs = {{Integer(1), Integer(1), Integer(1)}, + {Integer(0), Integer(0), Integer(5)}, + {Integer(3), Integer(2), Integer(5)}}; + std::cout << "matrix 8, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 1 1 5 --> 1 0 0 10 + * 3 2 5 8 0 1 0 10 + * 0 0 5 2 0 0 1 7 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8), Integer(2)}; + lhs = {{Integer(1), Integer(1), Integer(1)}, + {Integer(3), Integer(2), Integer(5)}, + {Integer(0), Integer(0), Integer(5)}}; + std::cout << "matrix 9, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + } + + void testGaussElimUniqueZero3() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 7 + * --^-- ^ --^-- ^ + * 2 0 6 4 1 0 0 3 + * 0 0 0 0 --> 0 0 0 0 + * 4 0 6 3 0 0 1 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(4), Integer(0), Integer(3)}; + lhs = {{Integer(2), Integer(0), Integer(6)}, + {Integer(0), Integer(0), Integer(0)}, + {Integer(4), Integer(0), Integer(6)}}; + std::cout << "matrix 10, modulo 7" << std::endl; + testGaussElimX(Integer(7), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 7 + * --^-- ^ --^-- ^ + * 2 6 0 4 1 0 0 3 + * 0 0 0 0 --> 0 0 0 0 + * 4 6 0 3 0 0 1 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(4), Integer(0), Integer(3)}; + lhs = {{Integer(2), Integer(6), Integer(0)}, + {Integer(0), Integer(0), Integer(0)}, + {Integer(4), Integer(6), Integer(0)}}; + std::cout << "matrix 11, modulo 7" << std::endl; + testGaussElimX(Integer(7), rhs, lhs, BVGaussElim::Result::UNIQUE); + } + + void testGaussElimUniqueZero4() + { + std::vector rhs, resrhs; + std::vector> lhs, reslhs; + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 0 1 1 5 + * 0 0 0 0 + * 0 0 5 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(0), Integer(2)}; + lhs = {{Integer(0), Integer(1), Integer(1)}, + {Integer(0), Integer(0), Integer(0)}, + {Integer(0), Integer(0), Integer(5)}}; + std::cout << "matrix 12, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 0 1 1 5 + * 0 3 5 8 + * 0 0 0 0 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8), Integer(0)}; + lhs = {{Integer(0), Integer(1), Integer(1)}, + {Integer(0), Integer(3), Integer(5)}, + {Integer(0), Integer(0), Integer(0)}}; + std::cout << "matrix 13, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 0 0 0 0 + * 0 3 5 8 + * 0 0 5 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(0), Integer(8), Integer(2)}; + lhs = {{Integer(0), Integer(0), Integer(0)}, + {Integer(0), Integer(3), Integer(5)}, + {Integer(0), Integer(0), Integer(5)}}; + std::cout << "matrix 14, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 0 1 5 + * 0 0 0 0 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(0), Integer(2)}; + lhs = {{Integer(1), Integer(0), Integer(1)}, + {Integer(0), Integer(0), Integer(0)}, + {Integer(4), Integer(0), Integer(5)}}; + std::cout << "matrix 15, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 0 1 5 + * 2 0 5 8 + * 0 0 0 0 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8), Integer(0)}; + lhs = {{Integer(1), Integer(0), Integer(1)}, + {Integer(2), Integer(0), Integer(5)}, + {Integer(0), Integer(0), Integer(0)}}; + std::cout << "matrix 16, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 0 0 0 0 + * 2 0 5 8 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(0), Integer(8), Integer(2)}; + lhs = {{Integer(0), Integer(0), Integer(0)}, + {Integer(2), Integer(0), Integer(5)}, + {Integer(4), Integer(0), Integer(5)}}; + std::cout << "matrix 17, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 1 0 5 + * 0 0 0 0 + * 4 0 0 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(0), Integer(2)}; + lhs = {{Integer(1), Integer(1), Integer(0)}, + {Integer(0), Integer(0), Integer(0)}, + {Integer(4), Integer(0), Integer(0)}}; + std::cout << "matrix 18, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 1 0 5 + * 2 3 0 8 + * 0 0 0 0 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8), Integer(0)}; + lhs = {{Integer(1), Integer(1), Integer(0)}, + {Integer(2), Integer(3), Integer(0)}, + {Integer(0), Integer(0), Integer(0)}}; + std::cout << "matrix 18, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 0 0 0 0 + * 2 3 0 8 + * 4 0 0 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(0), Integer(8), Integer(2)}; + lhs = {{Integer(0), Integer(0), Integer(0)}, + {Integer(2), Integer(3), Integer(0)}, + {Integer(4), Integer(0), Integer(0)}}; + std::cout << "matrix 19, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 2 + * ----^--- ^ + * 2 4 6 18 0 0 0 0 + * 4 5 6 24 = 0 1 0 0 + * 2 7 12 30 0 1 0 0 + * ------------------------------------------------------------------- */ + rhs = {Integer(18), Integer(24), Integer(30)}; + lhs = {{Integer(2), Integer(4), Integer(6)}, + {Integer(4), Integer(5), Integer(6)}, + {Integer(2), Integer(7), Integer(12)}}; + std::cout << "matrix 20, modulo 2" << std::endl; + resrhs = {Integer(0), Integer(0), Integer(0)}; + reslhs = {{Integer(0), Integer(1), Integer(0)}, + {Integer(0), Integer(0), Integer(0)}, + {Integer(0), Integer(0), Integer(0)}}; + testGaussElimX( + Integer(2), rhs, lhs, BVGaussElim::Result::UNIQUE, &resrhs, &reslhs); + } + + void testGaussElimUniquePartial() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 7 + * --^-- ^ --^-- ^ + * 2 0 6 4 1 0 0 3 + * 4 0 6 3 0 0 1 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(4), Integer(3)}; + lhs = {{Integer(2), Integer(0), Integer(6)}, + {Integer(4), Integer(0), Integer(6)}}; + std::cout << "matrix 21, modulo 7" << std::endl; + testGaussElimX(Integer(7), rhs, lhs, BVGaussElim::Result::UNIQUE); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 7 + * --^-- ^ --^-- ^ + * 2 6 0 4 1 0 0 3 + * 4 6 0 3 0 1 0 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(4), Integer(3)}; + lhs = {{Integer(2), Integer(6), Integer(0)}, + {Integer(4), Integer(6), Integer(0)}}; + std::cout << "matrix 22, modulo 7" << std::endl; + testGaussElimX(Integer(7), rhs, lhs, BVGaussElim::Result::UNIQUE); + } + + void testGaussElimNone() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs modulo 9 + * --^--- ^ + * 2 4 6 18 --> not coprime (no inverse) + * 4 5 6 24 + * 3 1 -2 4 + * ------------------------------------------------------------------- */ + rhs = {Integer(18), Integer(24), Integer(4)}; + lhs = {{Integer(2), Integer(4), Integer(6)}, + {Integer(4), Integer(5), Integer(6)}, + {Integer(3), Integer(1), Integer(-2)}}; + std::cout << "matrix 23, modulo 9" << std::endl; + testGaussElimX(Integer(9), rhs, lhs, BVGaussElim::Result::INVALID); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 59 + * ----^--- ^ + * 1 -2 -6 12 --> no solution + * 2 4 12 -17 + * 1 -4 -12 22 + * ------------------------------------------------------------------- */ + rhs = {Integer(12), Integer(-17), Integer(22)}; + lhs = {{Integer(1), Integer(-2), Integer(-6)}, + {Integer(2), Integer(4), Integer(12)}, + {Integer(1), Integer(-4), Integer(-12)}}; + std::cout << "matrix 24, modulo 59" << std::endl; + testGaussElimX(Integer(59), rhs, lhs, BVGaussElim::Result::NONE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 9 + * ----^--- ^ + * 2 4 6 18 --> not coprime (no inverse) + * 4 5 6 24 + * 2 7 12 30 + * ------------------------------------------------------------------- */ + rhs = {Integer(18), Integer(24), Integer(30)}; + lhs = {{Integer(2), Integer(4), Integer(6)}, + {Integer(4), Integer(5), Integer(6)}, + {Integer(2), Integer(7), Integer(12)}}; + std::cout << "matrix 25, modulo 9" << std::endl; + testGaussElimX(Integer(9), rhs, lhs, BVGaussElim::Result::INVALID); + } + + void testGaussElimNoneZero() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 0 1 1 5 + * 0 3 5 8 + * 0 0 5 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8), Integer(2)}; + lhs = {{Integer(0), Integer(1), Integer(1)}, + {Integer(0), Integer(3), Integer(5)}, + {Integer(0), Integer(0), Integer(5)}}; + std::cout << "matrix 26, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::NONE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 0 1 5 + * 2 0 5 8 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8), Integer(2)}; + lhs = {{Integer(1), Integer(0), Integer(1)}, + {Integer(2), Integer(0), Integer(5)}, + {Integer(4), Integer(0), Integer(5)}}; + std::cout << "matrix 27, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::NONE); + + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 1 0 5 + * 2 3 0 8 + * 4 0 0 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8), Integer(2)}; + lhs = {{Integer(1), Integer(1), Integer(0)}, + {Integer(2), Integer(3), Integer(0)}, + {Integer(4), Integer(0), Integer(0)}}; + std::cout << "matrix 28, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::NONE); + } + + void testGaussElimPartial1() + { + std::vector rhs, resrhs; + std::vector> lhs, reslhs; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * ------------------------------------------------------------------- */ + rhs = {Integer(7), Integer(9)}; + lhs = {{Integer(1), Integer(0), Integer(9)}, + {Integer(0), Integer(1), Integer(3)}}; + std::cout << "matrix 29, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::PARTIAL); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 3 0 7 --> 1 3 0 7 + * 0 0 1 9 0 0 1 9 + * ------------------------------------------------------------------- */ + rhs = {Integer(7), Integer(9)}; + lhs = {{Integer(1), Integer(3), Integer(0)}, + {Integer(0), Integer(0), Integer(1)}}; + std::cout << "matrix 30, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::PARTIAL); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 1 1 5 --> 1 0 9 7 + * 2 3 5 8 0 1 3 9 + * ------------------------------------------------------------------- */ + rhs = {Integer(5), Integer(8)}; + lhs = {{Integer(1), Integer(1), Integer(1)}, + {Integer(2), Integer(3), Integer(5)}}; + std::cout << "matrix 31, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::PARTIAL); + + /* ------------------------------------------------------------------- + * lhs rhs modulo { 3, 5, 7, 11, 17, 31, 59 } + * ----^--- ^ + * 2 4 6 18 + * 4 5 6 24 + * 2 7 12 30 + * ------------------------------------------------------------------- */ + rhs = {Integer(18), Integer(24), Integer(30)}; + lhs = {{Integer(2), Integer(4), Integer(6)}, + {Integer(4), Integer(5), Integer(6)}, + {Integer(2), Integer(7), Integer(12)}}; + std::cout << "matrix 32, modulo 3" << std::endl; + resrhs = {Integer(0), Integer(0), Integer(0)}; + reslhs = {{Integer(1), Integer(2), Integer(0)}, + {Integer(0), Integer(0), Integer(0)}, + {Integer(0), Integer(0), Integer(0)}}; + testGaussElimX( + Integer(3), rhs, lhs, BVGaussElim::Result::PARTIAL, &resrhs, &reslhs); + resrhs = {Integer(1), Integer(4), Integer(0)}; + std::cout << "matrix 32, modulo 5" << std::endl; + reslhs = {{Integer(1), Integer(0), Integer(4)}, + {Integer(0), Integer(1), Integer(2)}, + {Integer(0), Integer(0), Integer(0)}}; + testGaussElimX( + Integer(5), rhs, lhs, BVGaussElim::Result::PARTIAL, &resrhs, &reslhs); + std::cout << "matrix 32, modulo 7" << std::endl; + reslhs = {{Integer(1), Integer(0), Integer(6)}, + {Integer(0), Integer(1), Integer(2)}, + {Integer(0), Integer(0), Integer(0)}}; + testGaussElimX( + Integer(7), rhs, lhs, BVGaussElim::Result::PARTIAL, &resrhs, &reslhs); + std::cout << "matrix 32, modulo 11" << std::endl; + reslhs = {{Integer(1), Integer(0), Integer(10)}, + {Integer(0), Integer(1), Integer(2)}, + {Integer(0), Integer(0), Integer(0)}}; + testGaussElimX( + Integer(11), rhs, lhs, BVGaussElim::Result::PARTIAL, &resrhs, &reslhs); + std::cout << "matrix 32, modulo 17" << std::endl; + reslhs = {{Integer(1), Integer(0), Integer(16)}, + {Integer(0), Integer(1), Integer(2)}, + {Integer(0), Integer(0), Integer(0)}}; + testGaussElimX( + Integer(17), rhs, lhs, BVGaussElim::Result::PARTIAL, &resrhs, &reslhs); + std::cout << "matrix 32, modulo 59" << std::endl; + reslhs = {{Integer(1), Integer(0), Integer(58)}, + {Integer(0), Integer(1), Integer(2)}, + {Integer(0), Integer(0), Integer(0)}}; + testGaussElimX( + Integer(59), rhs, lhs, BVGaussElim::Result::PARTIAL, &resrhs, &reslhs); + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 3 + * ----^--- ^ --^-- ^ + * 4 6 2 18 --> 1 0 2 0 + * 5 6 4 24 0 0 0 0 + * 7 12 2 30 0 0 0 0 + * ------------------------------------------------------------------- */ + rhs = {Integer(18), Integer(24), Integer(30)}; + lhs = {{Integer(4), Integer(6), Integer(2)}, + {Integer(5), Integer(6), Integer(4)}, + {Integer(7), Integer(12), Integer(2)}}; + std::cout << "matrix 33, modulo 3" << std::endl; + resrhs = {Integer(0), Integer(0), Integer(0)}; + reslhs = {{Integer(1), Integer(0), Integer(2)}, + {Integer(0), Integer(0), Integer(0)}, + {Integer(0), Integer(0), Integer(0)}}; + testGaussElimX( + Integer(3), rhs, lhs, BVGaussElim::Result::PARTIAL, &resrhs, &reslhs); + } + + void testGaussElimPartial2() + { + std::vector rhs; + std::vector> lhs; + + /* ------------------------------------------------------------------- + * lhs rhs --> lhs rhs modulo 11 + * ---^--- ^ ---^--- ^ + * x y z w x y z w + * 1 2 0 6 2 1 2 0 0 1 + * 0 0 2 2 2 0 0 1 0 10 + * 0 0 0 1 2 0 0 0 1 2 + * ------------------------------------------------------------------- */ + rhs = {Integer(2), Integer(2), Integer(2)}; + lhs = {{Integer(1), Integer(2), Integer(6), Integer(0)}, + {Integer(0), Integer(0), Integer(2), Integer(2)}, + {Integer(0), Integer(0), Integer(1), Integer(0)}}; + std::cout << "matrix 34, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGaussElim::Result::PARTIAL); + } + void testGaussElimRewriteForUremUnique1() + { + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 1 1 5 + * 2 3 5 8 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_one, d_y_mul_one), + d_z_mul_one), + d_p), + d_five); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_three), + d_z_mul_five), + d_p), + d_eight); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_four, d_z_mul_five), + d_p), + d_two); + + std::vector eqs = {eq1, eq2, eq3}; + std::unordered_map res; + BVGaussElim::Result ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::UNIQUE); + TS_ASSERT(res.size() == 3); + TS_ASSERT(res[d_x] == d_three32); + TS_ASSERT(res[d_y] == d_four32); + TS_ASSERT(res[d_z] == d_nine32); + } + + void testGaussElimRewriteForUremUnique2() + { + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 1 1 5 + * 2 3 5 8 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + + Node zextop6 = d_nm->mkConst(BitVectorZeroExtend(6)); + + Node p = d_nm->mkNode(zextop6, mkConcat(mkZero(6), + d_nm->mkNode(kind::BITVECTOR_PLUS, mkConst(20, 7), mkConst(20, 4)))); + + Node x_mul_one = d_nm->mkNode(kind::BITVECTOR_MULT, + d_nm->mkNode(kind::BITVECTOR_SUB, d_five, d_four), d_x); + Node y_mul_one = d_nm->mkNode(kind::BITVECTOR_MULT, + d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, d_one, d_five), d_y); + Node z_mul_one = d_nm->mkNode(kind::BITVECTOR_MULT, mkOne(32), d_z); + + Node x_mul_two = d_nm->mkNode(kind::BITVECTOR_MULT, + d_nm->mkNode(kind::BITVECTOR_SHL, mkOne(32), mkOne(32)), d_x); + Node y_mul_three = d_nm->mkNode(kind::BITVECTOR_MULT, + d_nm->mkNode(kind::BITVECTOR_LSHR, mkOnes(32), mkConst(32, 30)), d_y); + Node z_mul_five = d_nm->mkNode(kind::BITVECTOR_MULT, + mkExtract( + d_nm->mkNode( + zextop6, d_nm->mkNode(kind::BITVECTOR_PLUS, d_three, d_two)), + 31, 0), + d_z); + + Node x_mul_four = d_nm->mkNode(kind::BITVECTOR_MULT, + d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_MULT, + mkConst(32, 4), + mkConst(32, 5)), + mkConst(32, 4)), + mkConst(32, 6)), + d_x); + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, + x_mul_one, + y_mul_one), + z_mul_one), + p), + d_five); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, x_mul_two, y_mul_three), + z_mul_five), + p), + d_eight); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, x_mul_four, z_mul_five), + d_p), + d_two); + + std::vector eqs = {eq1, eq2, eq3}; + std::unordered_map res; + BVGaussElim::Result ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::UNIQUE); + TS_ASSERT(res.size() == 3); + TS_ASSERT(res[d_x] == d_three32); + TS_ASSERT(res[d_y] == d_four32); + TS_ASSERT(res[d_z] == d_nine32); + } + + void testGaussElimRewriteForUremPartial1() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_one, d_z_mul_nine), + d_p), + d_seven); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_y_mul_one, d_z_mul_three), + d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::PARTIAL); + TS_ASSERT(res.size() == 2); + + Node x1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_seven32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)), + d_p); + Node y1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nine32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)), + d_p); + + Node x2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)), + d_p); + Node z2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)), + d_p); + + Node y3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)), + d_p); + Node z3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_six32)), + d_p); + + /* result depends on order of variables in matrix */ + if (res.find(d_x) == res.end()) + { + /* + * y z x y z x + * 0 9 1 7 --> 1 0 7 3 + * 1 3 0 9 0 1 5 2 + * + * z y x z y x + * 9 0 1 7 --> 1 0 5 2 + * 3 1 0 9 0 1 7 3 + */ + TS_ASSERT(res[d_y] == y3); + TS_ASSERT(res[d_z] == z3); + } + else if (res.find(d_y) == res.end()) + { + /* + * x z y x z y + * 1 9 0 7 --> 1 0 8 2 + * 0 3 1 9 0 1 4 3 + * + * z x y z x y + * 9 1 0 7 --> 1 0 4 3 + * 3 0 1 9 0 1 8 2 + */ + TS_ASSERT(res[d_x] == x2); + TS_ASSERT(res[d_z] == z2); + } + else + { + TS_ASSERT(res.find(d_z) == res.end()); + /* + * x y z x y z + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * + * y x z y x z + * 0 1 9 7 --> 1 0 3 9 + * 1 0 3 9 0 1 9 7 + */ + TS_ASSERT(res[d_x] == x1); + TS_ASSERT(res[d_y] == y1); + } + } + + void testGaussElimRewriteForUremPartial1a() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x, d_z_mul_nine), + d_p), + d_seven); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_y, d_z_mul_three), + d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::PARTIAL); + TS_ASSERT(res.size() == 2); + + Node x1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_seven32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)), + d_p); + Node y1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nine32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)), + d_p); + + Node x2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)), + d_p); + Node z2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)), + d_p); + + Node y3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)), + d_p); + Node z3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_six32)), + d_p); + + /* result depends on order of variables in matrix */ + if (res.find(d_x) == res.end()) + { + /* + * y z x y z x + * 0 9 1 7 --> 1 0 7 3 + * 1 3 0 9 0 1 5 2 + * + * z y x z y x + * 9 0 1 7 --> 1 0 5 2 + * 3 1 0 9 0 1 7 3 + */ + TS_ASSERT(res[d_y] == y3); + TS_ASSERT(res[d_z] == z3); + } + else if (res.find(d_y) == res.end()) + { + /* + * x z y x z y + * 1 9 0 7 --> 1 0 8 2 + * 0 3 1 9 0 1 4 3 + * + * z x y z x y + * 9 1 0 7 --> 1 0 4 3 + * 3 0 1 9 0 1 8 2 + */ + TS_ASSERT(res[d_x] == x2); + TS_ASSERT(res[d_z] == z2); + } + else + { + TS_ASSERT(res.find(d_z) == res.end()); + /* + * x y z x y z + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * + * y x z y x z + * 0 1 9 7 --> 1 0 3 9 + * 1 0 3 9 0 1 9 7 + */ + TS_ASSERT(res[d_x] == x1); + TS_ASSERT(res[d_y] == y1); + } + } + + void testGaussElimRewriteForUremPartial2() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 3 0 7 --> 1 3 0 7 + * 0 0 1 9 0 0 1 9 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_one, d_y_mul_three), + d_p), + d_seven); + + Node eq2 = + d_nm->mkNode(kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, d_z_mul_one, d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::PARTIAL); + TS_ASSERT(res.size() == 2); + + Node x1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_seven32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_eight32)), + d_p); + Node y2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_six32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_seven32)), + d_p); + + /* result depends on order of variables in matrix */ + if (res.find(d_x) == res.end()) + { + /* + * x y z x y z + * 1 3 0 7 --> 1 3 0 7 + * 0 0 1 9 0 0 1 9 + * + * x z y x z y + * 1 0 3 7 --> 1 0 3 7 + * 0 1 0 9 0 1 0 9 + * + * z x y z x y + * 0 1 3 7 --> 1 0 0 9 + * 1 0 0 9 0 1 3 7 + */ + TS_ASSERT(res[d_y] == y2); + TS_ASSERT(res[d_z] == d_nine32); + } + else if (res.find(d_y) == res.end()) + { + /* + * z y x z y x + * 0 3 1 7 --> 1 0 0 9 + * 1 0 0 9 0 1 4 6 + * + * y x z y x z + * 3 1 0 7 --> 1 4 0 6 + * 0 0 1 9 0 0 1 9 + * + * y z x y z x + * 3 0 1 7 --> 1 0 4 6 + * 0 1 0 9 0 1 0 9 + */ + TS_ASSERT(res[d_x] == x1); + TS_ASSERT(res[d_z] == d_nine32); + } + else + { + TS_ASSERT(false); + } + } + + void testGaussElimRewriteForUremPartial3() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 1 1 5 --> 1 0 9 7 + * 2 3 5 8 0 1 3 9 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_one, d_y), + d_z_mul_one), + d_p), + d_five); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_three), + d_z_mul_five), + d_p), + d_eight); + + std::vector eqs = {eq1, eq2}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::PARTIAL); + TS_ASSERT(res.size() == 2); + + Node x1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_seven32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)), + d_p); + Node y1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nine32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)), + d_p); + Node x2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)), + d_p); + Node z2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)), + d_p); + Node y3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)), + d_p); + Node z3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_six32)), + d_p); + + /* result depends on order of variables in matrix */ + if (res.find(d_x) == res.end()) + { + /* + * y z x y z x + * 1 1 1 5 --> 1 0 7 3 + * 3 5 2 8 0 1 5 2 + * + * z y x z y x + * 1 1 1 5 --> 1 0 5 2 + * 5 3 2 8 0 1 7 3 + */ + TS_ASSERT(res[d_y] == y3); + TS_ASSERT(res[d_z] == z3); + } + else if (res.find(d_y) == res.end()) + { + /* + * x z y x z y + * 1 1 1 5 --> 1 0 8 2 + * 2 5 3 8 0 1 4 3 + * + * z x y z x y + * 1 1 1 5 --> 1 0 4 3 + * 5 2 3 9 0 1 8 2 + */ + TS_ASSERT(res[d_x] == x2); + TS_ASSERT(res[d_z] == z2); + } + else + { + TS_ASSERT(res.find(d_z) == res.end()); + /* + * x y z x y z + * 1 1 1 5 --> 1 0 9 7 + * 2 3 5 8 0 1 3 9 + * + * y x z y x z + * 1 1 1 5 --> 1 0 3 9 + * 3 2 5 8 0 1 9 7 + */ + TS_ASSERT(res[d_x] == x1); + TS_ASSERT(res[d_y] == y1); + } + } + + void testGaussElimRewriteForUremPartial4() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * ----^--- ^ ---^--- ^ + * 2 4 6 18 --> 1 0 10 1 + * 4 5 6 24 0 1 2 4 + * 2 7 12 30 0 0 0 0 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_four), + d_z_mul_six), + d_p), + d_eighteen); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_four, d_y_mul_five), + d_z_mul_six), + d_p), + d_twentyfour); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_seven), + d_z_mul_twelve), + d_p), + d_thirty); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::PARTIAL); + TS_ASSERT(res.size() == 2); + + Node x1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_one32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_one32)), + d_p); + Node y1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_four32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_nine32)), + d_p); + Node x2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_five32)), + d_p); + Node z2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_five32)), + d_p); + Node y3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_six32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_nine32)), + d_p); + Node z3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_ten32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_one32)), + d_p); + + /* result depends on order of variables in matrix */ + if (res.find(d_x) == res.end()) + { + /* + * y z x y z x + * 4 6 2 18 --> 1 0 2 6 + * 5 6 4 24 0 1 10 10 + * 7 12 2 30 0 0 0 0 + * + * z y x z y x + * 6 4 2 18 --> 1 0 10 10 + * 6 5 4 24 0 1 2 6 + * 12 12 2 30 0 0 0 0 + * + */ + TS_ASSERT(res[d_y] == y3); + TS_ASSERT(res[d_z] == z3); + } + else if (res.find(d_y) == res.end()) + { + /* + * x z y x z y + * 2 6 4 18 --> 1 0 6 3 + * 4 6 5 24 0 1 6 2 + * 2 12 7 30 0 0 0 0 + * + * z x y z x y + * 6 2 4 18 --> 1 0 6 2 + * 6 4 5 24 0 1 6 3 + * 12 2 12 30 0 0 0 0 + * + */ + TS_ASSERT(res[d_x] == x2); + TS_ASSERT(res[d_z] == z2); + } + else + { + TS_ASSERT(res.find(d_z) == res.end()); + /* + * x y z x y z + * 2 4 6 18 --> 1 0 10 1 + * 4 5 6 24 0 1 2 4 + * 2 7 12 30 0 0 0 0 + * + * y x z y x z + * 4 2 6 18 --> 1 0 2 49 + * 5 4 6 24 0 1 10 1 + * 7 2 12 30 0 0 0 0 + */ + TS_ASSERT(res[d_x] == x1); + TS_ASSERT(res[d_y] == y1); + } + } + + void testGaussElimRewriteForUremPartial5() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 3 + * ----^--- ^ --^-- ^ + * 2 4 6 18 --> 1 2 0 0 + * 4 5 6 24 0 0 0 0 + * 2 7 12 30 0 0 0 0 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_four), + d_z_mul_six), + d_three), + d_eighteen); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_four, d_y_mul_five), + d_z_mul_six), + d_three), + d_twentyfour); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_seven), + d_z_mul_twelve), + d_three), + d_thirty); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::PARTIAL); + TS_ASSERT(res.size() == 1); + + Node x1 = d_nm->mkNode(kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_one32), + d_three); + Node y2 = d_nm->mkNode(kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_one32), + d_three); + + /* result depends on order of variables in matrix */ + if (res.find(d_x) == res.end()) + { + /* + * y x z y x z + * 4 2 6 18 --> 1 2 0 0 + * 5 4 6 24 0 0 0 0 + * 7 2 12 30 0 0 0 0 + * + * y z x y z x + * 4 6 2 18 --> 1 0 2 0 + * 5 6 4 24 0 0 0 0 + * 7 12 2 30 0 0 0 0 + * + * z y x z y x + * 6 4 2 18 --> 0 1 2 0 + * 6 5 4 24 0 0 0 0 + * 12 12 2 30 0 0 0 0 + * + */ + TS_ASSERT(res[d_y] == y2); + } + else if (res.find(d_y) == res.end()) + { + /* + * x y z x y z + * 2 4 6 18 --> 1 2 0 0 + * 4 5 6 24 0 0 0 0 + * 2 7 12 30 0 0 0 0 + * + * x z y x z y + * 2 6 4 18 --> 1 0 2 0 + * 4 6 5 24 0 0 0 0 + * 2 12 7 30 0 0 0 0 + * + * z x y z x y + * 6 2 4 18 --> 0 1 2 0 + * 6 4 5 24 0 0 0 0 + * 12 2 12 30 0 0 0 0 + * + */ + TS_ASSERT(res[d_x] == x1); + } + else + { + TS_ASSERT(false); + } + } + + void testGaussElimRewriteForUremPartial6() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * lhs rhs --> lhs rhs modulo 11 + * ---^--- ^ ---^--- ^ + * x y z w x y z w + * 1 2 0 6 2 1 2 0 6 2 + * 0 0 2 2 2 0 0 1 1 1 + * 0 0 0 1 2 0 0 0 1 2 + * ------------------------------------------------------------------- */ + + Node y_mul_two = d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_two); + Node z_mul_two = d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_two); + Node w = mkConcat(d_zero, d_nm->mkVar("w", d_nm->mkBitVectorType(16))); + Node w_mul_six = d_nm->mkNode(kind::BITVECTOR_MULT, w, d_six); + Node w_mul_two = d_nm->mkNode(kind::BITVECTOR_MULT, w, d_two); + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_one, y_mul_two), + w_mul_six), + d_p), + d_two); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, z_mul_two, w_mul_two), + d_p), + d_two); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, w, d_p), + d_two); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::PARTIAL); + TS_ASSERT(res.size() == 3); + + Node x1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_one32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_nine32)), + d_p); + Node z1 = d_ten32; + Node w1 = d_two32; + + Node y2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_six32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_five32)), + d_p); + Node z2 = d_ten32; + Node w2 = d_two32; + + /* result depends on order of variables in matrix */ + if (res.find(d_x) == res.end()) + { + TS_ASSERT(res[d_y] == y2); + TS_ASSERT(res[d_z] == z2); + TS_ASSERT(res[w] == w2); + } + else if (res.find(d_y) == res.end()) + { + TS_ASSERT(res[d_x] == x1); + TS_ASSERT(res[d_z] == z1); + TS_ASSERT(res[w] == w1); + } + else + { + TS_ASSERT(false); + } + } + + void testGaussElimRewriteForUremWithExprPartial() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * ------------------------------------------------------------------- */ + + Node zero = mkZero(8); + Node xx = d_nm->mkVar("xx", d_nm->mkBitVectorType(8)); + Node yy = d_nm->mkVar("yy", d_nm->mkBitVectorType(8)); + Node zz = d_nm->mkVar("zz", d_nm->mkBitVectorType(8)); + + Node x = + mkConcat(d_zero, mkConcat(zero, mkExtract(mkConcat(zero, xx), 7, 0))); + Node y = + mkConcat(d_zero, mkConcat(zero, mkExtract(mkConcat(zero, yy), 7, 0))); + Node z = + mkConcat(d_zero, mkConcat(zero, mkExtract(mkConcat(zero, zz), 7, 0))); + Node x_mul_one = d_nm->mkNode(kind::BITVECTOR_MULT, x, d_one32); + Node nine_mul_z = d_nm->mkNode(kind::BITVECTOR_MULT, d_nine32, z); + Node one_mul_y = d_nm->mkNode(kind::BITVECTOR_MULT, d_one, y); + Node z_mul_three = d_nm->mkNode(kind::BITVECTOR_MULT, z, d_three); + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, x_mul_one, nine_mul_z), + d_p), + d_seven); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, one_mul_y, z_mul_three), + d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::PARTIAL); + TS_ASSERT(res.size() == 2); + + x = Rewriter::rewrite(x); + y = Rewriter::rewrite(y); + z = Rewriter::rewrite(z); + + Node x1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_seven32, + d_nm->mkNode(kind::BITVECTOR_MULT, z, d_two32)), + d_p); + Node y1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nine32, + d_nm->mkNode(kind::BITVECTOR_MULT, z, d_eight32)), + d_p); + + Node x2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, y, d_three32)), + d_p); + Node z2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, y, d_seven32)), + d_p); + + Node y3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, x, d_four32)), + d_p); + Node z3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, x, d_six32)), + d_p); + + /* result depends on order of variables in matrix */ + if (res.find(x) == res.end()) + { + /* + * y z x y z x + * 0 9 1 7 --> 1 0 7 3 + * 1 3 0 9 0 1 5 2 + * + * z y x z y x + * 9 0 1 7 --> 1 0 5 2 + * 3 1 0 9 0 1 7 3 + */ + TS_ASSERT(res[Rewriter::rewrite(y)] == y3); + TS_ASSERT(res[Rewriter::rewrite(z)] == z3); + } + else if (res.find(y) == res.end()) + { + /* + * x z y x z y + * 1 9 0 7 --> 1 0 8 2 + * 0 3 1 9 0 1 4 3 + * + * z x y z x y + * 9 1 0 7 --> 1 0 4 3 + * 3 0 1 9 0 1 8 2 + */ + TS_ASSERT(res[x] == x2); + TS_ASSERT(res[z] == z2); + } + else + { + TS_ASSERT(res.find(z) == res.end()); + /* + * x y z x y z + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * + * y x z y x z + * 0 1 9 7 --> 1 0 3 9 + * 1 0 3 9 0 1 9 7 + */ + TS_ASSERT(res[x] == x1); + TS_ASSERT(res[y] == y1); + } + } + + void testGaussElimRewriteForUremNAryPartial() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * ------------------------------------------------------------------- */ + + Node zero = mkZero(8); + Node xx = d_nm->mkVar("xx", d_nm->mkBitVectorType(8)); + Node yy = d_nm->mkVar("yy", d_nm->mkBitVectorType(8)); + Node zz = d_nm->mkVar("zz", d_nm->mkBitVectorType(8)); + + Node x = mkConcat( + d_zero, + mkConcat( + zero, + mkExtract(d_nm->mkNode(kind::BITVECTOR_CONCAT, zero, xx), 7, 0))); + Node y = mkConcat( + d_zero, + mkConcat( + zero, + mkExtract(d_nm->mkNode(kind::BITVECTOR_CONCAT, zero, yy), 7, 0))); + Node z = mkConcat( + d_zero, + mkConcat( + zero, + mkExtract(d_nm->mkNode(kind::BITVECTOR_CONCAT, zero, zz), 7, 0))); + + NodeBuilder<> nbx(d_nm, kind::BITVECTOR_MULT); + nbx << d_x << d_one << x; + Node x_mul_one_mul_xx = nbx.constructNode(); + NodeBuilder<> nby(d_nm, kind::BITVECTOR_MULT); + nby << d_y << y << d_one; + Node y_mul_yy_mul_one = nby.constructNode(); + NodeBuilder<> nbz(d_nm, kind::BITVECTOR_MULT); + nbz << d_three << d_z << z; + Node three_mul_z_mul_zz = nbz.constructNode(); + NodeBuilder<> nbz2(d_nm, kind::BITVECTOR_MULT); + nbz2 << d_z << d_nine << z; + Node z_mul_nine_mul_zz = nbz2.constructNode(); + + Node x_mul_xx = d_nm->mkNode(kind::BITVECTOR_MULT, d_x, x); + Node y_mul_yy = d_nm->mkNode(kind::BITVECTOR_MULT, d_y, y); + Node z_mul_zz = d_nm->mkNode(kind::BITVECTOR_MULT, d_z, z); + + Node eq1 = d_nm->mkNode(kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + x_mul_one_mul_xx, + z_mul_nine_mul_zz), + d_p), + d_seven); + + Node eq2 = d_nm->mkNode(kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + y_mul_yy_mul_one, + three_mul_z_mul_zz), + d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::PARTIAL); + TS_ASSERT(res.size() == 2); + + x_mul_xx = Rewriter::rewrite(x_mul_xx); + y_mul_yy = Rewriter::rewrite(y_mul_yy); + z_mul_zz = Rewriter::rewrite(z_mul_zz); + + Node x1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_seven32, + d_nm->mkNode(kind::BITVECTOR_MULT, z_mul_zz, d_two32)), + d_p); + Node y1 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nine32, + d_nm->mkNode(kind::BITVECTOR_MULT, z_mul_zz, d_eight32)), + d_p); + + Node x2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, y_mul_yy, d_three32)), + d_p); + Node z2 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, y_mul_yy, d_seven32)), + d_p); + + Node y3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, x_mul_xx, d_four32)), + d_p); + Node z3 = d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, x_mul_xx, d_six32)), + d_p); + + /* result depends on order of variables in matrix */ + if (res.find(x_mul_xx) == res.end()) + { + /* + * y z x y z x + * 0 9 1 7 --> 1 0 7 3 + * 1 3 0 9 0 1 5 2 + * + * z y x z y x + * 9 0 1 7 --> 1 0 5 2 + * 3 1 0 9 0 1 7 3 + */ + TS_ASSERT(res[y_mul_yy] == y3); + TS_ASSERT(res[z_mul_zz] == z3); + } + else if (res.find(y_mul_yy) == res.end()) + { + /* + * x z y x z y + * 1 9 0 7 --> 1 0 8 2 + * 0 3 1 9 0 1 4 3 + * + * z x y z x y + * 9 1 0 7 --> 1 0 4 3 + * 3 0 1 9 0 1 8 2 + */ + TS_ASSERT(res[x_mul_xx] == x2); + TS_ASSERT(res[z_mul_zz] == z2); + } + else + { + TS_ASSERT(res.find(z_mul_zz) == res.end()); + /* + * x y z x y z + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * + * y x z y x z + * 0 1 9 7 --> 1 0 3 9 + * 1 0 3 9 0 1 9 7 + */ + TS_ASSERT(res[x_mul_xx] == x1); + TS_ASSERT(res[y_mul_yy] == y1); + } + } + + void testGaussElimRewriteForUremNotInvalid1() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * 3x / 2z = 4 modulo 11 + * 2x % 5y = 2 + * y O z = 5 + * ------------------------------------------------------------------- */ + + Node n1 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, + d_nm->mkNode(kind::BITVECTOR_MULT, d_three, d_x), + d_nm->mkNode(kind::BITVECTOR_MULT, d_two, d_y)); + Node n2 = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, + d_nm->mkNode(kind::BITVECTOR_MULT, d_two, d_x), + d_nm->mkNode(kind::BITVECTOR_MULT, d_five, d_y)); + Node n3 = mkConcat( + d_zero, + mkExtract(d_nm->mkNode(kind::BITVECTOR_CONCAT, d_y, d_z), 15, 0)); + + Node eq1 = d_nm->mkNode( + kind::EQUAL, d_nm->mkNode(kind::BITVECTOR_UREM, n1, d_p), d_four); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, d_nm->mkNode(kind::BITVECTOR_UREM, n2, d_p), d_two); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, d_nm->mkNode(kind::BITVECTOR_UREM, n3, d_p), d_five); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::UNIQUE); + TS_ASSERT(res.size() == 3); + + TS_ASSERT(res[n1] == d_four32); + TS_ASSERT(res[n2] == d_two32); + TS_ASSERT(res[n3] == d_five32); + } + + void testGaussElimRewriteForUremNotInvalid2() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * x*y = 4 modulo 11 + * x*y*z = 2 + * 2*x*y + 2*z = 9 + * ------------------------------------------------------------------- */ + + Node zero32 = mkZero(32); + + Node x = mkConcat(zero32, d_nm->mkVar("x", d_nm->mkBitVectorType(16))); + Node y = mkConcat(zero32, d_nm->mkVar("y", d_nm->mkBitVectorType(16))); + Node z = mkConcat(zero32, d_nm->mkVar("z", d_nm->mkBitVectorType(16))); + + Node n1 = d_nm->mkNode(kind::BITVECTOR_MULT, x, y); + Node n2 = d_nm->mkNode( + kind::BITVECTOR_MULT, d_nm->mkNode(kind::BITVECTOR_MULT, x, y), z); + Node n3 = d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_MULT, + d_nm->mkNode(kind::BITVECTOR_MULT, x, y), + mkConcat(d_zero, d_two)), + d_nm->mkNode(kind::BITVECTOR_MULT, mkConcat(d_zero, d_two), z)); + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, n1, mkConcat(d_zero, d_p)), + mkConcat(d_zero, d_four)); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, n2, mkConcat(d_zero, d_p)), + mkConcat(d_zero, d_two)); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, n3, mkConcat(d_zero, d_p)), + mkConcat(d_zero, d_nine)); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::UNIQUE); + TS_ASSERT(res.size() == 3); + + n1 = Rewriter::rewrite(n1); + n2 = Rewriter::rewrite(n2); + z = Rewriter::rewrite(z); + + TS_ASSERT(res[n1] == mkConst(48, 4)); + TS_ASSERT(res[n2] == mkConst(48, 2)); + + Integer twoxy = (res[n1].getConst().getValue() * Integer(2)) + .euclidianDivideRemainder(Integer(48)); + Integer twoz = (res[z].getConst().getValue() * Integer(2)) + .euclidianDivideRemainder(Integer(48)); + Integer r = (twoxy + twoz).euclidianDivideRemainder(Integer(11)); + TS_ASSERT(r == Integer(9)); + } + + void testGaussElimRewriteForUremInvalid() + { + std::unordered_map res; + BVGaussElim::Result ret; + + /* ------------------------------------------------------------------- + * x*y = 4 modulo 11 + * x*y*z = 2 + * 2*x*y = 9 + * ------------------------------------------------------------------- */ + + Node zero32 = mkZero(32); + + Node x = mkConcat(zero32, d_nm->mkVar("x", d_nm->mkBitVectorType(16))); + Node y = mkConcat(zero32, d_nm->mkVar("y", d_nm->mkBitVectorType(16))); + Node z = mkConcat(zero32, d_nm->mkVar("z", d_nm->mkBitVectorType(16))); + + Node n1 = d_nm->mkNode(kind::BITVECTOR_MULT, x, y); + Node n2 = d_nm->mkNode( + kind::BITVECTOR_MULT, d_nm->mkNode(kind::BITVECTOR_MULT, x, y), z); + Node n3 = d_nm->mkNode(kind::BITVECTOR_MULT, + d_nm->mkNode(kind::BITVECTOR_MULT, x, y), + mkConcat(d_zero, d_two)); + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, n1, mkConcat(d_zero, d_p)), + mkConcat(d_zero, d_four)); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, n2, mkConcat(d_zero, d_p)), + mkConcat(d_zero, d_two)); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, n3, mkConcat(d_zero, d_p)), + mkConcat(d_zero, d_nine)); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGaussElim::gaussElimRewriteForUrem(eqs, res); + TS_ASSERT(ret == BVGaussElim::Result::INVALID); + } + + void testGaussElimRewriteUnique1() + { + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 1 1 5 + * 2 3 5 8 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_one, d_y_mul_one), + d_z_mul_one), + d_p), + d_five); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_three), + d_z_mul_five), + d_p), + d_eight); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_four, d_z_mul_five), + d_p), + d_two); + + Node a = d_nm->mkNode(kind::AND, d_nm->mkNode(kind::AND, eq1, eq2), eq3); + + std::vector ass = {a}; + std::unordered_map res; + BVGaussElim::gaussElimRewrite(ass); + Node resx = d_nm->mkNode( + kind::EQUAL, d_x, d_nm->mkConst(BitVector(32, 3u))); + Node resy = d_nm->mkNode( + kind::EQUAL, d_y, d_nm->mkConst(BitVector(32, 4u))); + Node resz = d_nm->mkNode( + kind::EQUAL, d_z, d_nm->mkConst(BitVector(32, 9u))); + TS_ASSERT(ass.size() == 4); + TS_ASSERT(std::find(ass.begin(), ass.end(), resx) != ass.end()); + TS_ASSERT(std::find(ass.begin(), ass.end(), resy) != ass.end()); + TS_ASSERT(std::find(ass.begin(), ass.end(), resz) != ass.end()); + } + + void testGaussElimRewriteUnique2() + { + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 1 1 5 1 0 0 3 + * 2 3 5 8 0 1 0 4 + * 4 0 5 2 0 0 1 9 + * + * lhs rhs lhs rhs modulo 7 + * --^-- ^ --^-- ^ + * 2 6 0 4 1 0 0 3 + * 4 6 0 3 0 1 0 2 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_one, d_y_mul_one), + d_z_mul_one), + d_p), + d_five); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode( + kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_three), + d_z_mul_five), + d_p), + d_eight); + + Node eq3 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_four, d_z_mul_five), + d_p), + d_two); + + Node y_mul_six = d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_six); + + Node eq4 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode(kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, y_mul_six), + d_seven), + d_four); + + Node eq5 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_four, y_mul_six), + d_seven), + d_three); + + Node a = d_nm->mkNode(kind::AND, d_nm->mkNode(kind::AND, eq1, eq2), eq3); + + std::vector ass = {a, eq4, eq5}; + std::unordered_map res; + BVGaussElim::gaussElimRewrite(ass); + Node resx1 = d_nm->mkNode( + kind::EQUAL, d_x, d_nm->mkConst(BitVector(32, 3u))); + Node resx2 = d_nm->mkNode( + kind::EQUAL, d_x, d_nm->mkConst(BitVector(32, 3u))); + Node resy1 = d_nm->mkNode( + kind::EQUAL, d_y, d_nm->mkConst(BitVector(32, 4u))); + Node resy2 = d_nm->mkNode( + kind::EQUAL, d_y, d_nm->mkConst(BitVector(32, 2u))); + Node resz = d_nm->mkNode( + kind::EQUAL, d_z, d_nm->mkConst(BitVector(32, 9u))); + TS_ASSERT(ass.size() == 8); + TS_ASSERT(std::find(ass.begin(), ass.end(), resx1) != ass.end()); + TS_ASSERT(std::find(ass.begin(), ass.end(), resx2) != ass.end()); + TS_ASSERT(std::find(ass.begin(), ass.end(), resy1) != ass.end()); + TS_ASSERT(std::find(ass.begin(), ass.end(), resy2) != ass.end()); + TS_ASSERT(std::find(ass.begin(), ass.end(), resz) != ass.end()); + } + + void testGaussElimRewritePartial() + { + /* ------------------------------------------------------------------- + * lhs rhs lhs rhs modulo 11 + * --^-- ^ --^-- ^ + * 1 0 9 7 --> 1 0 9 7 + * 0 1 3 9 0 1 3 9 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_x_mul_one, d_z_mul_nine), + d_p), + d_seven); + + Node eq2 = d_nm->mkNode( + kind::EQUAL, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, d_y_mul_one, d_z_mul_three), + d_p), + d_nine); + + std::vector ass = {eq1, eq2}; + BVGaussElim::gaussElimRewrite(ass); + TS_ASSERT(ass.size() == 4); + + Node resx1 = d_nm->mkNode( + kind::EQUAL, + d_x, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_seven32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)), + d_p)); + Node resy1 = d_nm->mkNode( + kind::EQUAL, + d_y, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nine32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)), + d_p)); + + Node resx2 = d_nm->mkNode( + kind::EQUAL, + d_x, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)), + d_p)); + Node resz2 = d_nm->mkNode( + kind::EQUAL, + d_z, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)), + d_p)); + + Node resy3 = d_nm->mkNode( + kind::EQUAL, + d_y, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_three32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)), + d_p)); + Node resz3 = d_nm->mkNode( + kind::EQUAL, + d_z, + d_nm->mkNode( + kind::BITVECTOR_UREM, + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_two32, + d_nm->mkNode(kind::BITVECTOR_MULT, d_x, d_six32)), + d_p)); + + bool fx1 = std::find(ass.begin(), ass.end(), resx1) != ass.end(); + bool fy1 = std::find(ass.begin(), ass.end(), resy1) != ass.end(); + bool fx2 = std::find(ass.begin(), ass.end(), resx2) != ass.end(); + bool fz2 = std::find(ass.begin(), ass.end(), resz2) != ass.end(); + bool fy3 = std::find(ass.begin(), ass.end(), resy3) != ass.end(); + bool fz3 = std::find(ass.begin(), ass.end(), resz3) != ass.end(); + + /* result depends on order of variables in matrix */ + TS_ASSERT((fx1 && fy1) || (fx2 && fz2) || (fy3 && fz3)); + } + + void testGetMinBw1() + { + TS_ASSERT(BVGaussElim::getMinBwExpr(utils::mkConst(32, 11)) == 4); + + TS_ASSERT(BVGaussElim::getMinBwExpr(d_p) == 4); + TS_ASSERT(BVGaussElim::getMinBwExpr(d_x) == 16); + + Node extp = mkExtract(d_p, 4, 0); + TS_ASSERT(BVGaussElim::getMinBwExpr(extp) == 4); + Node extx = mkExtract(d_x, 4, 0); + TS_ASSERT(BVGaussElim::getMinBwExpr(extx) == 5); + + Node zextop8 = d_nm->mkConst(BitVectorZeroExtend(8)); + Node zextop16 = d_nm->mkConst(BitVectorZeroExtend(16)); + Node zextop32 = d_nm->mkConst(BitVectorZeroExtend(32)); + Node zextop40 = d_nm->mkConst(BitVectorZeroExtend(40)); + + Node zext40p = d_nm->mkNode(zextop8, d_p); + TS_ASSERT(BVGaussElim::getMinBwExpr(zext40p) == 4); + Node zext40x = d_nm->mkNode(zextop8, d_x); + TS_ASSERT(BVGaussElim::getMinBwExpr(zext40x) == 16); + + Node zext48p = d_nm->mkNode(zextop16, d_p); + TS_ASSERT(BVGaussElim::getMinBwExpr(zext48p) == 4); + Node zext48x = d_nm->mkNode(zextop16, d_x); + TS_ASSERT(BVGaussElim::getMinBwExpr(zext48x) == 16); + + Node p8 = d_nm->mkConst(BitVector(8, 11u)); + Node x8 = d_nm->mkVar("x8", d_nm->mkBitVectorType(8)); + + Node zext48p8 = d_nm->mkNode(zextop40, p8); + TS_ASSERT(BVGaussElim::getMinBwExpr(zext48p8) == 4); + Node zext48x8 = d_nm->mkNode(zextop40, x8); + TS_ASSERT(BVGaussElim::getMinBwExpr(zext48x8) == 8); + + Node mult1p = d_nm->mkNode(kind::BITVECTOR_MULT, extp, extp); + TS_ASSERT(BVGaussElim::getMinBwExpr(mult1p) == 5); + Node mult1x = d_nm->mkNode(kind::BITVECTOR_MULT, extx, extx); + TS_ASSERT(BVGaussElim::getMinBwExpr(mult1x) == 0); + + Node mult2p = d_nm->mkNode(kind::BITVECTOR_MULT, zext40p, zext40p); + TS_ASSERT(BVGaussElim::getMinBwExpr(mult2p) == 7); + Node mult2x = d_nm->mkNode(kind::BITVECTOR_MULT, zext40x, zext40x); + TS_ASSERT(BVGaussElim::getMinBwExpr(mult2x) == 32); + + NodeBuilder<> nbmult3p(kind::BITVECTOR_MULT); + nbmult3p << zext48p << zext48p << zext48p; + Node mult3p = nbmult3p; + TS_ASSERT(BVGaussElim::getMinBwExpr(mult3p) == 11); + NodeBuilder<> nbmult3x(kind::BITVECTOR_MULT); + nbmult3x << zext48x << zext48x << zext48x; + Node mult3x = nbmult3x; + TS_ASSERT(BVGaussElim::getMinBwExpr(mult3x) == 48); + + NodeBuilder<> nbmult4p(kind::BITVECTOR_MULT); + nbmult4p << zext48p << zext48p8 << zext48p; + Node mult4p = nbmult4p; + TS_ASSERT(BVGaussElim::getMinBwExpr(mult4p) == 11); + NodeBuilder<> nbmult4x(kind::BITVECTOR_MULT); + nbmult4x << zext48x << zext48x8 << zext48x; + Node mult4x = nbmult4x; + TS_ASSERT(BVGaussElim::getMinBwExpr(mult4x) == 40); + + Node concat1p = mkConcat(d_p, zext48p); + TS_ASSERT(BVGaussElim::getMinBwExpr(concat1p) == 52); + Node concat1x = mkConcat(d_x, zext48x); + TS_ASSERT(BVGaussElim::getMinBwExpr(concat1x) == 64); + + Node concat2p = mkConcat(mkZero(16), zext48p); + TS_ASSERT(BVGaussElim::getMinBwExpr(concat2p) == 4); + Node concat2x = mkConcat(mkZero(16), zext48x); + TS_ASSERT(BVGaussElim::getMinBwExpr(concat2x) == 16); + + Node udiv1p = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48p, zext48p); + TS_ASSERT(BVGaussElim::getMinBwExpr(udiv1p) == 1); + Node udiv1x = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48x, zext48x); + TS_ASSERT(BVGaussElim::getMinBwExpr(udiv1x) == 48); + + Node udiv2p = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48p, zext48p8); + TS_ASSERT(BVGaussElim::getMinBwExpr(udiv2p) == 1); + Node udiv2x = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48x, zext48x8); + TS_ASSERT(BVGaussElim::getMinBwExpr(udiv2x) == 48); + + Node urem1p = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48p, zext48p); + TS_ASSERT(BVGaussElim::getMinBwExpr(urem1p) == 1); + Node urem1x = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48x, zext48x); + TS_ASSERT(BVGaussElim::getMinBwExpr(urem1x) == 1); + + Node urem2p = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48p, zext48p8); + TS_ASSERT(BVGaussElim::getMinBwExpr(urem2p) == 1); + Node urem2x = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48x, zext48x8); + TS_ASSERT(BVGaussElim::getMinBwExpr(urem2x) == 16); + + Node urem3p = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48p8, zext48p); + TS_ASSERT(BVGaussElim::getMinBwExpr(urem3p) == 1); + Node urem3x = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48x8, zext48x); + TS_ASSERT(BVGaussElim::getMinBwExpr(urem3x) == 8); + + Node add1p = d_nm->mkNode(kind::BITVECTOR_PLUS, extp, extp); + TS_ASSERT(BVGaussElim::getMinBwExpr(add1p) == 5); + Node add1x = d_nm->mkNode(kind::BITVECTOR_PLUS, extx, extx); + TS_ASSERT(BVGaussElim::getMinBwExpr(add1x) == 0); + + Node add2p = d_nm->mkNode(kind::BITVECTOR_PLUS, zext40p, zext40p); + TS_ASSERT(BVGaussElim::getMinBwExpr(add2p) == 5); + Node add2x = d_nm->mkNode(kind::BITVECTOR_PLUS, zext40x, zext40x); + TS_ASSERT(BVGaussElim::getMinBwExpr(add2x) == 17); + + Node add3p = d_nm->mkNode(kind::BITVECTOR_PLUS, zext48p8, zext48p); + TS_ASSERT(BVGaussElim::getMinBwExpr(add3p) == 5); + Node add3x = d_nm->mkNode(kind::BITVECTOR_PLUS, zext48x8, zext48x); + TS_ASSERT(BVGaussElim::getMinBwExpr(add3x) == 17); + + NodeBuilder<> nbadd4p(kind::BITVECTOR_PLUS); + nbadd4p << zext48p << zext48p << zext48p; + Node add4p = nbadd4p; + TS_ASSERT(BVGaussElim::getMinBwExpr(add4p) == 6); + NodeBuilder<> nbadd4x(kind::BITVECTOR_PLUS); + nbadd4x << zext48x << zext48x << zext48x; + Node add4x = nbadd4x; + TS_ASSERT(BVGaussElim::getMinBwExpr(add4x) == 18); + + NodeBuilder<> nbadd5p(kind::BITVECTOR_PLUS); + nbadd5p << zext48p << zext48p8 << zext48p; + Node add5p = nbadd5p; + TS_ASSERT(BVGaussElim::getMinBwExpr(add5p) == 6); + NodeBuilder<> nbadd5x(kind::BITVECTOR_PLUS); + nbadd5x << zext48x << zext48x8 << zext48x; + Node add5x = nbadd5x; + TS_ASSERT(BVGaussElim::getMinBwExpr(add5x) == 18); + + NodeBuilder<> nbadd6p(kind::BITVECTOR_PLUS); + nbadd6p << zext48p << zext48p << zext48p << zext48p; + Node add6p = nbadd6p; + TS_ASSERT(BVGaussElim::getMinBwExpr(add6p) == 6); + NodeBuilder<> nbadd6x(kind::BITVECTOR_PLUS); + nbadd6x << zext48x << zext48x << zext48x << zext48x; + Node add6x = nbadd6x; + TS_ASSERT(BVGaussElim::getMinBwExpr(add6x) == 18); + + Node not1p = d_nm->mkNode(kind::BITVECTOR_NOT, zext40p); + TS_ASSERT(BVGaussElim::getMinBwExpr(not1p) == 40); + Node not1x = d_nm->mkNode(kind::BITVECTOR_NOT, zext40x); + TS_ASSERT(BVGaussElim::getMinBwExpr(not1x) == 40); + } + + void testGetMinBw2() + { + /* ((_ zero_extend 5) + * ((_ extract 7 0) ((_ zero_extend 15) d_p))) */ + Node zextop5 = d_nm->mkConst(BitVectorZeroExtend(5)); + Node zextop15 = d_nm->mkConst(BitVectorZeroExtend(15)); + Node zext1 = d_nm->mkNode(zextop15, d_p); + Node ext = mkExtract(zext1, 7, 0); + Node zext2 = d_nm->mkNode(zextop5, ext); + TS_ASSERT(BVGaussElim::getMinBwExpr(zext2) == 4); + } + + void testGetMinBw3a() + { + /* ((_ zero_extend 5) + * (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x z))) + * ((_ extract 4 0) z))) */ + Node x = d_nm->mkVar("x", d_nm->mkBitVectorType(16)); + Node y = d_nm->mkVar("y", d_nm->mkBitVectorType(16)); + Node z = d_nm->mkVar("z", d_nm->mkBitVectorType(16)); + Node zextop5 = d_nm->mkConst(BitVectorZeroExtend(5)); + Node udiv1 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, x, y); + Node zext1 = d_nm->mkNode(zextop5, udiv1); + Node ext1 = mkExtract(zext1, 4, 0); + Node ext2 = mkExtract(z, 4, 0); + Node udiv2 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1, ext2); + Node zext2 = mkConcat(mkZero(5), udiv2); + TS_ASSERT(BVGaussElim::getMinBwExpr(zext2) == 5); + } + + void testGetMinBw3b() + { + /* ((_ zero_extend 5) + * (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x z))) + * ((_ extract 4 0) z))) */ + Node zextop5 = d_nm->mkConst(BitVectorZeroExtend(5)); + Node udiv1 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, d_x, d_y); + Node zext1 = d_nm->mkNode(zextop5, udiv1); + Node ext1 = mkExtract(zext1, 4, 0); + Node ext2 = mkExtract(d_z, 4, 0); + Node udiv2 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1, ext2); + Node zext2 = mkConcat(mkZero(5), udiv2); + TS_ASSERT(BVGaussElim::getMinBwExpr(zext2) == 5); + } + + void testGetMinBw4a() + { + /* (bvadd + * ((_ zero_extend 5) + * (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x y))) + * ((_ extract 4 0) z))) + * ((_ zero_extend 7) + * (bvudiv ((_ extract 2 0) ((_ zero_extend 5) (bvudiv x y))) + * ((_ extract 2 0) z))) */ + Node x = d_nm->mkVar("x", d_nm->mkBitVectorType(16)); + Node y = d_nm->mkVar("y", d_nm->mkBitVectorType(16)); + Node z = d_nm->mkVar("z", d_nm->mkBitVectorType(16)); + Node zextop5 = d_nm->mkConst(BitVectorZeroExtend(5)); + Node zextop7 = d_nm->mkConst(BitVectorZeroExtend(7)); + + Node udiv1 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, x, y); + Node zext1 = d_nm->mkNode(zextop5, udiv1); + + Node ext1_1 = mkExtract(zext1, 4, 0); + Node ext2_1 = mkExtract(z, 4, 0); + Node udiv2_1 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_1, ext2_1); + Node zext2_1 = mkConcat(mkZero(5), udiv2_1); + + Node ext1_2 = mkExtract(zext1, 2, 0); + Node ext2_2 = mkExtract(z, 2, 0); + Node udiv2_2 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_2, ext2_2); + Node zext2_2 = d_nm->mkNode(zextop7, udiv2_2); + + Node plus = d_nm->mkNode(kind::BITVECTOR_PLUS, zext2_1, zext2_2); + + TS_ASSERT(BVGaussElim::getMinBwExpr(plus) == 6); + } + + void testGetMinBw4b() + { + /* (bvadd + * ((_ zero_extend 5) + * (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x y))) + * ((_ extract 4 0) z))) + * ((_ zero_extend 7) + * (bvudiv ((_ extract 2 0) ((_ zero_extend 5) (bvudiv x y))) + * ((_ extract 2 0) z))) */ + Node zextop5 = d_nm->mkConst(BitVectorZeroExtend(5)); + Node zextop7 = d_nm->mkConst(BitVectorZeroExtend(7)); + + Node udiv1 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, d_x, d_y); + Node zext1 = d_nm->mkNode(zextop5, udiv1); + + Node ext1_1 = mkExtract(zext1, 4, 0); + Node ext2_1 = mkExtract(d_z, 4, 0); + Node udiv2_1 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_1, ext2_1); + Node zext2_1 = mkConcat(mkZero(5), udiv2_1); + + Node ext1_2 = mkExtract(zext1, 2, 0); + Node ext2_2 = mkExtract(d_z, 2, 0); + Node udiv2_2 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_2, ext2_2); + Node zext2_2 = d_nm->mkNode(zextop7, udiv2_2); + + Node plus = d_nm->mkNode(kind::BITVECTOR_PLUS, zext2_1, zext2_2); + + TS_ASSERT(BVGaussElim::getMinBwExpr(plus) == 6); + } + + void testGetMinBw5a() + { + /* (bvadd + * (bvadd + * (bvadd + * (bvadd + * (bvadd + * (bvadd + * (bvadd (bvmul (_ bv86 13) + * ((_ zero_extend 5) + * ((_ extract 7 0) ((_ zero_extend 15) x)))) + * (bvmul (_ bv41 13) + * ((_ zero_extend 5) + * ((_ extract 7 0) ((_ zero_extend 15) y))))) + * (bvmul (_ bv37 13) + * ((_ zero_extend 5) + * ((_ extract 7 0) ((_ zero_extend 15) z))))) + * (bvmul (_ bv170 13) + * ((_ zero_extend 5) + * ((_ extract 7 0) ((_ zero_extend 15) u))))) + * (bvmul (_ bv112 13) + * ((_ zero_extend 5) + * ((_ extract 7 0) ((_ zero_extend 15) v))))) + * (bvmul (_ bv195 13) ((_ zero_extend 5) ((_ extract 15 8) s)))) + * (bvmul (_ bv124 13) ((_ zero_extend 5) ((_ extract 7 0) s)))) + * (bvmul (_ bv83 13) + * ((_ zero_extend 5) ((_ extract 7 0) ((_ zero_extend 15) w))))) + */ + Node x = mkVar(1); + Node y = mkVar(1); + Node z = mkVar(1); + Node u = mkVar(1); + Node v = mkVar(1); + Node w = mkVar(1); + Node s = mkVar(16); + + Node zextop5 = d_nm->mkConst(BitVectorZeroExtend(5)); + Node zextop15 = d_nm->mkConst(BitVectorZeroExtend(15)); + + Node zext15x = d_nm->mkNode(zextop15, x); + Node zext15y = d_nm->mkNode(zextop15, y); + Node zext15z = d_nm->mkNode(zextop15, z); + Node zext15u = d_nm->mkNode(zextop15, u); + Node zext15v = d_nm->mkNode(zextop15, v); + Node zext15w = d_nm->mkNode(zextop15, w); + + Node ext7x = mkExtract(zext15x, 7, 0); + Node ext7y = mkExtract(zext15y, 7, 0); + Node ext7z = mkExtract(zext15z, 7, 0); + Node ext7u = mkExtract(zext15u, 7, 0); + Node ext7v = mkExtract(zext15v, 7, 0); + Node ext7w = mkExtract(zext15w, 7, 0); + Node ext7s = mkExtract(s, 7, 0); + Node ext15s = mkExtract(s, 15, 8); + + Node xx = mkConcat(mkZero(5), ext7x); + Node yy = mkConcat(mkZero(5), ext7y); + Node zz = mkConcat(mkZero(5), ext7z); + Node uu = mkConcat(mkZero(5), ext7u); + Node vv = mkConcat(mkZero(5), ext7v); + Node ww = mkConcat(mkZero(5), ext7w); + Node s7 = mkConcat(mkZero(5), ext7s); + Node s15 = mkConcat(mkZero(5), ext15s); + + Node plus1 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(13, 86), xx), + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(13, 41), yy)); + Node plus2 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus1, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(13, 37), zz)); + Node plus3 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus2, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(13, 170), uu)); + Node plus4 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus3, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(13, 112), uu)); + Node plus5 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus4, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(13, 195), s15)); + Node plus6 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus5, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(13, 124), s7)); + Node plus7 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus6, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(13, 83), ww)); + + TS_ASSERT(BVGaussElim::getMinBwExpr(plus7) == 0); + } + + void testGetMinBw5b() + { + /* (bvadd + * (bvadd + * (bvadd + * (bvadd + * (bvadd + * (bvadd + * (bvadd (bvmul (_ bv86 20) + * ((_ zero_extend 12) + * ((_ extract 7 0) ((_ zero_extend 15) x)))) + * (bvmul (_ bv41 20) + * ((_ zero_extend 12) + * ((_ extract 7 0) ((_ zero_extend 15) y))))) + * (bvmul (_ bv37 20) + * ((_ zero_extend 12) + * ((_ extract 7 0) ((_ zero_extend 15) z))))) + * (bvmul (_ bv170 20) + * ((_ zero_extend 12) + * ((_ extract 7 0) ((_ zero_extend 15) u))))) + * (bvmul (_ bv112 20) + * ((_ zero_extend 12) + * ((_ extract 7 0) ((_ zero_extend 15) v))))) + * (bvmul (_ bv195 20) ((_ zero_extend 12) ((_ extract 15 8) s)))) + * (bvmul (_ bv124 20) ((_ zero_extend 12) ((_ extract 7 0) s)))) + * (bvmul (_ bv83 20) + * ((_ zero_extend 12) ((_ extract 7 0) ((_ zero_extend 15) w))))) + */ + Node x = mkVar(1); + Node y = mkVar(1); + Node z = mkVar(1); + Node u = mkVar(1); + Node v = mkVar(1); + Node w = mkVar(1); + Node s = mkVar(16); + + Node zextop15 = d_nm->mkConst(BitVectorZeroExtend(15)); + + Node zext15x = d_nm->mkNode(zextop15, x); + Node zext15y = d_nm->mkNode(zextop15, y); + Node zext15z = d_nm->mkNode(zextop15, z); + Node zext15u = d_nm->mkNode(zextop15, u); + Node zext15v = d_nm->mkNode(zextop15, v); + Node zext15w = d_nm->mkNode(zextop15, w); + + Node ext7x = mkExtract(zext15x, 7, 0); + Node ext7y = mkExtract(zext15y, 7, 0); + Node ext7z = mkExtract(zext15z, 7, 0); + Node ext7u = mkExtract(zext15u, 7, 0); + Node ext7v = mkExtract(zext15v, 7, 0); + Node ext7w = mkExtract(zext15w, 7, 0); + Node ext7s = mkExtract(s, 7, 0); + Node ext15s = mkExtract(s, 15, 8); + + Node xx = mkConcat(mkZero(12), ext7x); + Node yy = mkConcat(mkZero(12), ext7y); + Node zz = mkConcat(mkZero(12), ext7z); + Node uu = mkConcat(mkZero(12), ext7u); + Node vv = mkConcat(mkZero(12), ext7v); + Node ww = mkConcat(mkZero(12), ext7w); + Node s7 = mkConcat(mkZero(12), ext7s); + Node s15 = mkConcat(mkZero(12), ext15s); + + Node plus1 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(20, 86), xx), + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(20, 41), yy)); + Node plus2 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus1, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(20, 37), zz)); + Node plus3 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus2, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(20, 170), uu)); + Node plus4 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus3, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(20, 112), uu)); + Node plus5 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus4, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(20, 195), s15)); + Node plus6 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus5, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(20, 124), s7)); + Node plus7 = + d_nm->mkNode(kind::BITVECTOR_PLUS, + plus6, + d_nm->mkNode(kind::BITVECTOR_MULT, mkConst(20, 83), ww)); + + TS_ASSERT(BVGaussElim::getMinBwExpr(plus7) == 19); + TS_ASSERT(BVGaussElim::getMinBwExpr(Rewriter::rewrite(plus7)) == 17); + } + +}; -- 2.30.2