From e505da6535074550ddb96ca0f5fccb9453ae1c3c Mon Sep 17 00:00:00 2001 From: Aina Niemetz Date: Mon, 22 Feb 2021 17:32:55 -0800 Subject: [PATCH] google test: preprocessing: Migrate pass_bv_gauss_white. (#5935) --- test/unit/preprocessing/CMakeLists.txt | 4 +- .../preprocessing/pass_bv_gauss_white.cpp | 3115 +++++++++++++++++ test/unit/preprocessing/pass_bv_gauss_white.h | 3031 ---------------- test/unit/test_node.h | 3 +- 4 files changed, 3118 insertions(+), 3035 deletions(-) create mode 100644 test/unit/preprocessing/pass_bv_gauss_white.cpp delete mode 100644 test/unit/preprocessing/pass_bv_gauss_white.h diff --git a/test/unit/preprocessing/CMakeLists.txt b/test/unit/preprocessing/CMakeLists.txt index ebb0a5189..71c658f4b 100644 --- a/test/unit/preprocessing/CMakeLists.txt +++ b/test/unit/preprocessing/CMakeLists.txt @@ -11,5 +11,5 @@ #-----------------------------------------------------------------------------# # Add unit tests -cvc4_add_cxx_unit_test_white(pass_bv_gauss_white preprocessing) -cvc4_add_unit_test_white(pass_foreign_theory_rewrite_white preprocessing) +cvc4_add_unit_test_white(pass_bv_gauss_white preprocessing) +cvc4_add_unit_test_white(pass_foreign_theory_rewrite_white preprocessing) \ No newline at end of file diff --git a/test/unit/preprocessing/pass_bv_gauss_white.cpp b/test/unit/preprocessing/pass_bv_gauss_white.cpp new file mode 100644 index 000000000..1a3412186 --- /dev/null +++ b/test/unit/preprocessing/pass_bv_gauss_white.cpp @@ -0,0 +1,3115 @@ +/********************* */ +/*! \file pass_bv_gauss_white.cpp + ** \verbatim + ** Top contributors (to current version): + ** Aina Niemetz, Mathias Preiner, Andres Noetzli + ** This file is part of the CVC4 project. + ** Copyright (c) 2009-2020 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 +#include + +#include "context/context.h" +#include "expr/node.h" +#include "expr/node_manager.h" +#include "preprocessing/passes/bv_gauss.h" +#include "smt/smt_engine.h" +#include "smt/smt_engine_scope.h" +#include "test_smt.h" +#include "theory/bv/theory_bv_utils.h" +#include "theory/rewriter.h" +#include "util/bitvector.h" + +namespace CVC4 { + +using namespace preprocessing; +using namespace preprocessing::passes; +using namespace theory; +using namespace smt; + +namespace test { + +class TestPPWhiteBVGauss : public TestSmt +{ + protected: + void SetUp() override + { + TestSmt::SetUp(); + + d_zero = bv::utils::mkZero(16); + + d_p = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 11u))); + d_x = bv::utils::mkConcat( + d_zero, d_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16))); + d_y = bv::utils::mkConcat( + d_zero, d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16))); + d_z = bv::utils::mkConcat( + d_zero, d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16))); + + d_one = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 1u))); + d_two = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 2u))); + d_three = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 3u))); + d_four = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 4u))); + d_five = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 5u))); + d_six = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 6u))); + d_seven = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 7u))); + d_eight = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 8u))); + d_nine = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 9u))); + d_ten = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 10u))); + d_twelve = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 12u))); + d_eighteen = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 18u))); + d_twentyfour = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 24u))); + d_thirty = bv::utils::mkConcat( + d_zero, d_nodeManager->mkConst(BitVector(16, 30u))); + + d_one32 = d_nodeManager->mkConst(BitVector(32, 1u)); + d_two32 = d_nodeManager->mkConst(BitVector(32, 2u)); + d_three32 = d_nodeManager->mkConst(BitVector(32, 3u)); + d_four32 = d_nodeManager->mkConst(BitVector(32, 4u)); + d_five32 = d_nodeManager->mkConst(BitVector(32, 5u)); + d_six32 = d_nodeManager->mkConst(BitVector(32, 6u)); + d_seven32 = d_nodeManager->mkConst(BitVector(32, 7u)); + d_eight32 = d_nodeManager->mkConst(BitVector(32, 8u)); + d_nine32 = d_nodeManager->mkConst(BitVector(32, 9u)); + d_ten32 = d_nodeManager->mkConst(BitVector(32, 10u)); + + d_x_mul_one = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_one); + d_x_mul_two = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_two); + d_x_mul_four = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four); + d_y_mul_three = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three); + d_y_mul_one = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_one); + d_y_mul_four = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_four); + d_y_mul_five = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_five); + d_y_mul_seven = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven); + d_z_mul_one = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_one); + d_z_mul_three = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_three); + d_z_mul_five = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_five); + d_z_mul_six = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_six); + d_z_mul_twelve = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_twelve); + d_z_mul_nine = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_nine); + } + + 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; + } + } + + void testGaussElimX(Integer prime, + std::vector rhs, + std::vector> lhs, + BVGauss::Result expected, + std::vector* rrhs = nullptr, + std::vector>* rlhs = nullptr) + { + size_t nrows = lhs.size(); + size_t ncols = lhs[0].size(); + BVGauss::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 = BVGauss::gaussElim(prime, resrhs, reslhs); + + std::cout << "BVGauss::Result: " + << (ret == BVGauss::Result::INVALID + ? "INVALID" + : (ret == BVGauss::Result::UNIQUE + ? "UNIQUE" + : (ret == BVGauss::Result::PARTIAL ? "PARTIAL" + : "NONE"))) + << std::endl; + print_matrix_dbg(resrhs, reslhs); + + ASSERT_EQ(expected, ret); + + if (expected == BVGauss::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 + ASSERT_EQ(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); + ASSERT_EQ(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) + { + ASSERT_EQ(reslhs[i][j], (*rlhs)[i][j]); + } + ASSERT_EQ(resrhs[i], (*rrhs)[i]); + } + } + } + + 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; +}; + +TEST_F(TestPPWhiteBVGauss, elim_mod) +{ + 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 + ASSERT_DEATH(BVGauss::gaussElim(Integer(0), rhs, lhs), "prime > 0"); + std::cout << "matrix 0, modulo 1" << std::endl; + testGaussElimX(Integer(1), rhs, lhs, BVGauss::Result::UNIQUE); + std::cout << "matrix 0, modulo 2" << std::endl; + testGaussElimX(Integer(2), rhs, lhs, BVGauss::Result::UNIQUE); + std::cout << "matrix 0, modulo 3" << std::endl; + testGaussElimX(Integer(3), rhs, lhs, BVGauss::Result::UNIQUE); + std::cout << "matrix 0, modulo 4" << std::endl; // no inverse + testGaussElimX(Integer(4), rhs, lhs, BVGauss::Result::INVALID); + std::cout << "matrix 0, modulo 5" << std::endl; + testGaussElimX(Integer(5), rhs, lhs, BVGauss::Result::UNIQUE); + std::cout << "matrix 0, modulo 6" << std::endl; // no inverse + testGaussElimX(Integer(6), rhs, lhs, BVGauss::Result::INVALID); + std::cout << "matrix 0, modulo 7" << std::endl; + testGaussElimX(Integer(7), rhs, lhs, BVGauss::Result::UNIQUE); + std::cout << "matrix 0, modulo 8" << std::endl; // no inverse + testGaussElimX(Integer(8), rhs, lhs, BVGauss::Result::INVALID); + std::cout << "matrix 0, modulo 9" << std::endl; + testGaussElimX(Integer(9), rhs, lhs, BVGauss::Result::UNIQUE); + std::cout << "matrix 0, modulo 10" << std::endl; // no inverse + testGaussElimX(Integer(10), rhs, lhs, BVGauss::Result::INVALID); + std::cout << "matrix 0, modulo 11" << std::endl; + testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE); +} + +TEST_F(TestPPWhiteBVGauss, elim_unique_done) +{ + 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, BVGauss::Result::UNIQUE); +} + +TEST_F(TestPPWhiteBVGauss, elim_unique) +{ + 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, BVGauss::Result::UNIQUE); + std::cout << "matrix 2, modulo 17" << std::endl; + testGaussElimX(Integer(17), rhs, lhs, BVGauss::Result::UNIQUE); + std::cout << "matrix 2, modulo 59" << std::endl; + testGaussElimX(Integer(59), rhs, lhs, BVGauss::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, BVGauss::Result::UNIQUE); +} + +TEST_F(TestPPWhiteBVGauss, elim_unique_zero1) +{ + 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, BVGauss::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, BVGauss::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, BVGauss::Result::UNIQUE); +} + +TEST_F(TestPPWhiteBVGauss, elim_unique_zero2) +{ + 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, BVGauss::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, BVGauss::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, BVGauss::Result::UNIQUE); +} + +TEST_F(TestPPWhiteBVGauss, elim_unique_zero3) +{ + 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, BVGauss::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, BVGauss::Result::UNIQUE); +} + +TEST_F(TestPPWhiteBVGauss, elim_unique_zero4) +{ + 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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::Result::UNIQUE, &resrhs, &reslhs); +} + +TEST_F(TestPPWhiteBVGauss, elim_unique_partial) +{ + 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, BVGauss::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, BVGauss::Result::UNIQUE); +} + +TEST_F(TestPPWhiteBVGauss, elim_none) +{ + 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, BVGauss::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, BVGauss::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, BVGauss::Result::INVALID); +} + +TEST_F(TestPPWhiteBVGauss, elim_none_zero) +{ + 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, BVGauss::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, BVGauss::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, BVGauss::Result::NONE); +} + +TEST_F(TestPPWhiteBVGauss, elim_partial1) +{ + 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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::Result::PARTIAL, &resrhs, &reslhs); +} + +TEST_F(TestPPWhiteBVGauss, elim_partial2) +{ + 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, BVGauss::Result::PARTIAL); +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_unique1) +{ + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 1 1 5 + * 2 3 5 8 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_one, d_y_mul_one), + d_z_mul_one), + d_p), + d_five); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_three), + d_z_mul_five), + d_p), + d_eight); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->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; + BVGauss::Result ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::UNIQUE); + ASSERT_EQ(res.size(), 3); + ASSERT_EQ(res[d_x], d_three32); + ASSERT_EQ(res[d_y], d_four32); + ASSERT_EQ(res[d_z], d_nine32); +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_unique2) +{ + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 1 1 5 + * 2 3 5 8 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + + Node zextop6 = + d_nodeManager->mkConst(BitVectorZeroExtend(6)); + + Node p = d_nodeManager->mkNode( + zextop6, + bv::utils::mkConcat(bv::utils::mkZero(6), + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, + bv::utils::mkConst(20, 7), + bv::utils::mkConst(20, 4)))); + + Node x_mul_one = d_nodeManager->mkNode( + kind::BITVECTOR_MULT, + d_nodeManager->mkNode(kind::BITVECTOR_SUB, d_five, d_four), + d_x); + Node y_mul_one = d_nodeManager->mkNode( + kind::BITVECTOR_MULT, + d_nodeManager->mkNode(kind::BITVECTOR_UREM_TOTAL, d_one, d_five), + d_y); + Node z_mul_one = + d_nodeManager->mkNode(kind::BITVECTOR_MULT, bv::utils::mkOne(32), d_z); + + Node x_mul_two = d_nodeManager->mkNode( + kind::BITVECTOR_MULT, + d_nodeManager->mkNode( + kind::BITVECTOR_SHL, bv::utils::mkOne(32), bv::utils::mkOne(32)), + d_x); + Node y_mul_three = + d_nodeManager->mkNode(kind::BITVECTOR_MULT, + d_nodeManager->mkNode(kind::BITVECTOR_LSHR, + bv::utils::mkOnes(32), + bv::utils::mkConst(32, 30)), + d_y); + Node z_mul_five = d_nodeManager->mkNode( + kind::BITVECTOR_MULT, + bv::utils::mkExtract( + d_nodeManager->mkNode( + zextop6, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, d_three, d_two)), + 31, + 0), + d_z); + + Node x_mul_four = d_nodeManager->mkNode( + kind::BITVECTOR_MULT, + d_nodeManager->mkNode( + kind::BITVECTOR_UDIV_TOTAL, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, + bv::utils::mkConst(32, 4), + bv::utils::mkConst(32, 5)), + bv::utils::mkConst(32, 4)), + bv::utils::mkConst(32, 6)), + d_x); + + Node eq1 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, x_mul_one, y_mul_one), + z_mul_one), + p), + d_five); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, x_mul_two, y_mul_three), + z_mul_five), + p), + d_eight); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, x_mul_four, z_mul_five), + d_p), + d_two); + + std::vector eqs = {eq1, eq2, eq3}; + std::unordered_map res; + BVGauss::Result ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::UNIQUE); + ASSERT_EQ(res.size(), 3); + ASSERT_EQ(res[d_x], d_three32); + ASSERT_EQ(res[d_y], d_four32); + ASSERT_EQ(res[d_z], d_nine32); +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial1a) +{ + std::unordered_map res; + BVGauss::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_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_one, d_z_mul_nine), + d_p), + d_seven); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_y_mul_one, d_z_mul_three), + d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::PARTIAL); + ASSERT_EQ(res.size(), 2); + + Node x1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_seven32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)), + d_p); + Node y1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nine32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)), + d_p); + + Node x2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)), + d_p); + Node z2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)), + d_p); + + Node y3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)), + d_p); + Node z3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->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 + */ + ASSERT_EQ(res[d_y], y3); + ASSERT_EQ(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 + */ + ASSERT_EQ(res[d_x], x2); + ASSERT_EQ(res[d_z], z2); + } + else + { + ASSERT_EQ(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 + */ + ASSERT_EQ(res[d_x], x1); + ASSERT_EQ(res[d_y], y1); + } +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial1b) +{ + std::unordered_map res; + BVGauss::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_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, d_x, d_z_mul_nine), + d_p), + d_seven); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, d_y, d_z_mul_three), + d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::PARTIAL); + ASSERT_EQ(res.size(), 2); + + Node x1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_seven32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)), + d_p); + Node y1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nine32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)), + d_p); + + Node x2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)), + d_p); + Node z2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)), + d_p); + + Node y3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)), + d_p); + Node z3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->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 + */ + ASSERT_EQ(res[d_y], y3); + ASSERT_EQ(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 + */ + ASSERT_EQ(res[d_x], x2); + ASSERT_EQ(res[d_z], z2); + } + else + { + ASSERT_EQ(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 + */ + ASSERT_EQ(res[d_x], x1); + ASSERT_EQ(res[d_y], y1); + } +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial2) +{ + std::unordered_map res; + BVGauss::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_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_one, d_y_mul_three), + d_p), + d_seven); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode(kind::BITVECTOR_UREM, d_z_mul_one, d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::PARTIAL); + ASSERT_EQ(res.size(), 2); + + Node x1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_seven32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_eight32)), + d_p); + Node y2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_six32, + d_nodeManager->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 + */ + ASSERT_EQ(res[d_y], y2); + ASSERT_EQ(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 + */ + ASSERT_EQ(res[d_x], x1); + ASSERT_EQ(res[d_z], d_nine32); + } + else + { + ASSERT_TRUE(false); + } +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial3) +{ + std::unordered_map res; + BVGauss::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_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, d_x_mul_one, d_y), + d_z_mul_one), + d_p), + d_five); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->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 = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::PARTIAL); + ASSERT_EQ(res.size(), 2); + + Node x1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_seven32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)), + d_p); + Node y1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nine32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)), + d_p); + Node x2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)), + d_p); + Node z2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)), + d_p); + Node y3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)), + d_p); + Node z3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->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 + */ + ASSERT_EQ(res[d_y], y3); + ASSERT_EQ(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 + */ + ASSERT_EQ(res[d_x], x2); + ASSERT_EQ(res[d_z], z2); + } + else + { + ASSERT_EQ(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 + */ + ASSERT_EQ(res[d_x], x1); + ASSERT_EQ(res[d_y], y1); + } +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial4) +{ + std::unordered_map res; + BVGauss::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_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_four), + d_z_mul_six), + d_p), + d_eighteen); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_four, d_y_mul_five), + d_z_mul_six), + d_p), + d_twentyfour); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->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 = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::PARTIAL); + ASSERT_EQ(res.size(), 2); + + Node x1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_one32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_one32)), + d_p); + Node y1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_four32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_nine32)), + d_p); + Node x2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_five32)), + d_p); + Node z2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_five32)), + d_p); + Node y3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_six32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_nine32)), + d_p); + Node z3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_ten32, + d_nodeManager->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 + * + */ + ASSERT_EQ(res[d_y], y3); + ASSERT_EQ(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 + * + */ + ASSERT_EQ(res[d_x], x2); + ASSERT_EQ(res[d_z], z2); + } + else + { + ASSERT_EQ(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 + */ + ASSERT_EQ(res[d_x], x1); + ASSERT_EQ(res[d_y], y1); + } +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial5) +{ + std::unordered_map res; + BVGauss::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_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_four), + d_z_mul_six), + d_three), + d_eighteen); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_four, d_y_mul_five), + d_z_mul_six), + d_three), + d_twentyfour); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->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 = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::PARTIAL); + ASSERT_EQ(res.size(), 1); + + Node x1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_one32), + d_three); + Node y2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->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 + * + */ + ASSERT_EQ(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 + * + */ + ASSERT_EQ(res[d_x], x1); + } + else + { + ASSERT_TRUE(false); + } +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial6) +{ + std::unordered_map res; + BVGauss::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_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_two); + Node z_mul_two = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two); + Node w = bv::utils::mkConcat( + d_zero, d_nodeManager->mkVar("w", d_nodeManager->mkBitVectorType(16))); + Node w_mul_six = d_nodeManager->mkNode(kind::BITVECTOR_MULT, w, d_six); + Node w_mul_two = d_nodeManager->mkNode(kind::BITVECTOR_MULT, w, d_two); + + Node eq1 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_one, y_mul_two), + w_mul_six), + d_p), + d_two); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, z_mul_two, w_mul_two), + d_p), + d_two); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, d_nodeManager->mkNode(kind::BITVECTOR_UREM, w, d_p), d_two); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::PARTIAL); + ASSERT_EQ(res.size(), 3); + + Node x1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_one32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_nine32)), + d_p); + Node z1 = d_ten32; + Node w1 = d_two32; + + Node y2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_six32, + d_nodeManager->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()) + { + ASSERT_EQ(res[d_y], y2); + ASSERT_EQ(res[d_z], z2); + ASSERT_EQ(res[w], w2); + } + else if (res.find(d_y) == res.end()) + { + ASSERT_EQ(res[d_x], x1); + ASSERT_EQ(res[d_z], z1); + ASSERT_EQ(res[w], w1); + } + else + { + ASSERT_TRUE(false); + } +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_with_expr_partial) +{ + std::unordered_map res; + BVGauss::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 = bv::utils::mkZero(8); + Node xx = d_nodeManager->mkVar("xx", d_nodeManager->mkBitVectorType(8)); + Node yy = d_nodeManager->mkVar("yy", d_nodeManager->mkBitVectorType(8)); + Node zz = d_nodeManager->mkVar("zz", d_nodeManager->mkBitVectorType(8)); + + Node x = bv::utils::mkConcat( + d_zero, + bv::utils::mkConcat( + zero, bv::utils::mkExtract(bv::utils::mkConcat(zero, xx), 7, 0))); + Node y = bv::utils::mkConcat( + d_zero, + bv::utils::mkConcat( + zero, bv::utils::mkExtract(bv::utils::mkConcat(zero, yy), 7, 0))); + Node z = bv::utils::mkConcat( + d_zero, + bv::utils::mkConcat( + zero, bv::utils::mkExtract(bv::utils::mkConcat(zero, zz), 7, 0))); + + Node x_mul_one = d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, d_one32); + Node nine_mul_z = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_nine32, z); + Node one_mul_y = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_one, y); + Node z_mul_three = d_nodeManager->mkNode(kind::BITVECTOR_MULT, z, d_three); + + Node eq1 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, x_mul_one, nine_mul_z), + d_p), + d_seven); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, one_mul_y, z_mul_three), + d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::PARTIAL); + ASSERT_EQ(res.size(), 2); + + x = Rewriter::rewrite(x); + y = Rewriter::rewrite(y); + z = Rewriter::rewrite(z); + + Node x1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_seven32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, z, d_two32)), + d_p); + Node y1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nine32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, z, d_eight32)), + d_p); + + Node x2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, y, d_three32)), + d_p); + Node z2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, y, d_seven32)), + d_p); + + Node y3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, d_four32)), + d_p); + Node z3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->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 + */ + ASSERT_EQ(res[Rewriter::rewrite(y)], y3); + ASSERT_EQ(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 + */ + ASSERT_EQ(res[x], x2); + ASSERT_EQ(res[z], z2); + } + else + { + ASSERT_EQ(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 + */ + ASSERT_EQ(res[x], x1); + ASSERT_EQ(res[y], y1); + } +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_nary_partial) +{ + std::unordered_map res; + BVGauss::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 = bv::utils::mkZero(8); + Node xx = d_nodeManager->mkVar("xx", d_nodeManager->mkBitVectorType(8)); + Node yy = d_nodeManager->mkVar("yy", d_nodeManager->mkBitVectorType(8)); + Node zz = d_nodeManager->mkVar("zz", d_nodeManager->mkBitVectorType(8)); + + Node x = bv::utils::mkConcat( + d_zero, + bv::utils::mkConcat( + zero, + bv::utils::mkExtract( + d_nodeManager->mkNode(kind::BITVECTOR_CONCAT, zero, xx), 7, 0))); + Node y = bv::utils::mkConcat( + d_zero, + bv::utils::mkConcat( + zero, + bv::utils::mkExtract( + d_nodeManager->mkNode(kind::BITVECTOR_CONCAT, zero, yy), 7, 0))); + Node z = bv::utils::mkConcat( + d_zero, + bv::utils::mkConcat( + zero, + bv::utils::mkExtract( + d_nodeManager->mkNode(kind::BITVECTOR_CONCAT, zero, zz), 7, 0))); + + NodeBuilder<> nbx(d_nodeManager.get(), kind::BITVECTOR_MULT); + nbx << d_x << d_one << x; + Node x_mul_one_mul_xx = nbx.constructNode(); + NodeBuilder<> nby(d_nodeManager.get(), kind::BITVECTOR_MULT); + nby << d_y << y << d_one; + Node y_mul_yy_mul_one = nby.constructNode(); + NodeBuilder<> nbz(d_nodeManager.get(), kind::BITVECTOR_MULT); + nbz << d_three << d_z << z; + Node three_mul_z_mul_zz = nbz.constructNode(); + NodeBuilder<> nbz2(d_nodeManager.get(), kind::BITVECTOR_MULT); + nbz2 << d_z << d_nine << z; + Node z_mul_nine_mul_zz = nbz2.constructNode(); + + Node x_mul_xx = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, x); + Node y_mul_yy = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, y); + Node z_mul_zz = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, z); + + Node eq1 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, x_mul_one_mul_xx, z_mul_nine_mul_zz), + d_p), + d_seven); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, y_mul_yy_mul_one, three_mul_z_mul_zz), + d_p), + d_nine); + + std::vector eqs = {eq1, eq2}; + ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::PARTIAL); + ASSERT_EQ(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_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_seven32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, z_mul_zz, d_two32)), + d_p); + Node y1 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nine32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, z_mul_zz, d_eight32)), + d_p); + + Node x2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, y_mul_yy, d_three32)), + d_p); + Node z2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, y_mul_yy, d_seven32)), + d_p); + + Node y3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, x_mul_xx, d_four32)), + d_p); + Node z3 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->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 + */ + ASSERT_EQ(res[y_mul_yy], y3); + ASSERT_EQ(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 + */ + ASSERT_EQ(res[x_mul_xx], x2); + ASSERT_EQ(res[z_mul_zz], z2); + } + else + { + ASSERT_EQ(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 + */ + ASSERT_EQ(res[x_mul_xx], x1); + ASSERT_EQ(res[y_mul_yy], y1); + } +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_not_invalid1) +{ + std::unordered_map res; + BVGauss::Result ret; + + /* ------------------------------------------------------------------- + * 3x / 2z = 4 modulo 11 + * 2x % 5y = 2 + * y O z = 5 + * ------------------------------------------------------------------- */ + + Node n1 = d_nodeManager->mkNode( + kind::BITVECTOR_UDIV_TOTAL, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_three, d_x), + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_two, d_y)); + Node n2 = d_nodeManager->mkNode( + kind::BITVECTOR_UREM_TOTAL, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_two, d_x), + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_five, d_y)); + + Node n3 = bv::utils::mkConcat( + d_zero, + bv::utils::mkExtract( + d_nodeManager->mkNode(kind::BITVECTOR_CONCAT, d_y, d_z), 15, 0)); + + Node eq1 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode(kind::BITVECTOR_UREM, n1, d_p), + d_four); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, d_nodeManager->mkNode(kind::BITVECTOR_UREM, n2, d_p), d_two); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode(kind::BITVECTOR_UREM, n3, d_p), + d_five); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::UNIQUE); + ASSERT_EQ(res.size(), 3); + + ASSERT_EQ(res[n1], d_four32); + ASSERT_EQ(res[n2], d_two32); + ASSERT_EQ(res[n3], d_five32); +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_not_invalid2) +{ + std::unordered_map res; + BVGauss::Result ret; + + /* ------------------------------------------------------------------- + * x*y = 4 modulo 11 + * x*y*z = 2 + * 2*x*y + 2*z = 9 + * ------------------------------------------------------------------- */ + + Node zero32 = bv::utils::mkZero(32); + + Node x = bv::utils::mkConcat( + zero32, d_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16))); + Node y = bv::utils::mkConcat( + zero32, d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16))); + Node z = bv::utils::mkConcat( + zero32, d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16))); + + Node n1 = d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y); + Node n2 = + d_nodeManager->mkNode(kind::BITVECTOR_MULT, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y), + z); + Node n3 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y), + bv::utils::mkConcat(d_zero, d_two)), + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConcat(d_zero, d_two), z)); + + Node eq1 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, n1, bv::utils::mkConcat(d_zero, d_p)), + bv::utils::mkConcat(d_zero, d_four)); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, n2, bv::utils::mkConcat(d_zero, d_p)), + bv::utils::mkConcat(d_zero, d_two)); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, n3, bv::utils::mkConcat(d_zero, d_p)), + bv::utils::mkConcat(d_zero, d_nine)); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::UNIQUE); + ASSERT_EQ(res.size(), 3); + + n1 = Rewriter::rewrite(n1); + n2 = Rewriter::rewrite(n2); + z = Rewriter::rewrite(z); + + ASSERT_EQ(res[n1], bv::utils::mkConst(48, 4)); + ASSERT_EQ(res[n2], bv::utils::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)); + ASSERT_EQ(r, Integer(9)); +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_invalid) +{ + std::unordered_map res; + BVGauss::Result ret; + + /* ------------------------------------------------------------------- + * x*y = 4 modulo 11 + * x*y*z = 2 + * 2*x*y = 9 + * ------------------------------------------------------------------- */ + + Node zero32 = bv::utils::mkZero(32); + + Node x = bv::utils::mkConcat( + zero32, d_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16))); + Node y = bv::utils::mkConcat( + zero32, d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16))); + Node z = bv::utils::mkConcat( + zero32, d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16))); + + Node n1 = d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y); + Node n2 = + d_nodeManager->mkNode(kind::BITVECTOR_MULT, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y), + z); + Node n3 = + d_nodeManager->mkNode(kind::BITVECTOR_MULT, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y), + bv::utils::mkConcat(d_zero, d_two)); + + Node eq1 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, n1, bv::utils::mkConcat(d_zero, d_p)), + bv::utils::mkConcat(d_zero, d_four)); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, n2, bv::utils::mkConcat(d_zero, d_p)), + bv::utils::mkConcat(d_zero, d_two)); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, n3, bv::utils::mkConcat(d_zero, d_p)), + bv::utils::mkConcat(d_zero, d_nine)); + + std::vector eqs = {eq1, eq2, eq3}; + ret = BVGauss::gaussElimRewriteForUrem(eqs, res); + ASSERT_EQ(ret, BVGauss::Result::INVALID); +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_unique1) +{ + /* ------------------------------------------------------------------- + * lhs rhs modulo 11 + * --^-- ^ + * 1 1 1 5 + * 2 3 5 8 + * 4 0 5 2 + * ------------------------------------------------------------------- */ + + Node eq1 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_one, d_y_mul_one), + d_z_mul_one), + d_p), + d_five); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_three), + d_z_mul_five), + d_p), + d_eight); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_four, d_z_mul_five), + d_p), + d_two); + + Node a = d_nodeManager->mkNode( + kind::AND, d_nodeManager->mkNode(kind::AND, eq1, eq2), eq3); + + AssertionPipeline apipe; + apipe.push_back(a); + passes::BVGauss bgauss(nullptr, "bv-gauss-unit"); + std::unordered_map res; + PreprocessingPassResult pres = bgauss.applyInternal(&apipe); + ASSERT_EQ(pres, PreprocessingPassResult::NO_CONFLICT); + Node resx = d_nodeManager->mkNode( + kind::EQUAL, d_x, d_nodeManager->mkConst(BitVector(32, 3u))); + Node resy = d_nodeManager->mkNode( + kind::EQUAL, d_y, d_nodeManager->mkConst(BitVector(32, 4u))); + Node resz = d_nodeManager->mkNode( + kind::EQUAL, d_z, d_nodeManager->mkConst(BitVector(32, 9u))); + ASSERT_EQ(apipe.size(), 4); + ASSERT_NE(std::find(apipe.begin(), apipe.end(), resx), apipe.end()); + ASSERT_NE(std::find(apipe.begin(), apipe.end(), resy), apipe.end()); + ASSERT_NE(std::find(apipe.begin(), apipe.end(), resz), apipe.end()); +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_unique2) +{ + /* ------------------------------------------------------------------- + * 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_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_one, d_y_mul_one), + d_z_mul_one), + d_p), + d_five); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_two, d_y_mul_three), + d_z_mul_five), + d_p), + d_eight); + + Node eq3 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_four, d_z_mul_five), + d_p), + d_two); + + Node y_mul_six = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_six); + + Node eq4 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, d_x_mul_two, y_mul_six), + d_seven), + d_four); + + Node eq5 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode(kind::BITVECTOR_PLUS, d_x_mul_four, y_mul_six), + d_seven), + d_three); + + Node a = d_nodeManager->mkNode( + kind::AND, d_nodeManager->mkNode(kind::AND, eq1, eq2), eq3); + + AssertionPipeline apipe; + apipe.push_back(a); + apipe.push_back(eq4); + apipe.push_back(eq5); + passes::BVGauss bgauss(nullptr, "bv-gauss-unit"); + std::unordered_map res; + PreprocessingPassResult pres = bgauss.applyInternal(&apipe); + ASSERT_EQ(pres, PreprocessingPassResult::NO_CONFLICT); + Node resx1 = d_nodeManager->mkNode( + kind::EQUAL, d_x, d_nodeManager->mkConst(BitVector(32, 3u))); + Node resx2 = d_nodeManager->mkNode( + kind::EQUAL, d_x, d_nodeManager->mkConst(BitVector(32, 3u))); + Node resy1 = d_nodeManager->mkNode( + kind::EQUAL, d_y, d_nodeManager->mkConst(BitVector(32, 4u))); + Node resy2 = d_nodeManager->mkNode( + kind::EQUAL, d_y, d_nodeManager->mkConst(BitVector(32, 2u))); + Node resz = d_nodeManager->mkNode( + kind::EQUAL, d_z, d_nodeManager->mkConst(BitVector(32, 9u))); + ASSERT_EQ(apipe.size(), 8); + ASSERT_NE(std::find(apipe.begin(), apipe.end(), resx1), apipe.end()); + ASSERT_NE(std::find(apipe.begin(), apipe.end(), resx2), apipe.end()); + ASSERT_NE(std::find(apipe.begin(), apipe.end(), resy1), apipe.end()); + ASSERT_NE(std::find(apipe.begin(), apipe.end(), resy2), apipe.end()); + ASSERT_NE(std::find(apipe.begin(), apipe.end(), resz), apipe.end()); +} + +TEST_F(TestPPWhiteBVGauss, elim_rewrite_partial) +{ + /* ------------------------------------------------------------------- + * 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_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_x_mul_one, d_z_mul_nine), + d_p), + d_seven); + + Node eq2 = d_nodeManager->mkNode( + kind::EQUAL, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, d_y_mul_one, d_z_mul_three), + d_p), + d_nine); + + AssertionPipeline apipe; + apipe.push_back(eq1); + apipe.push_back(eq2); + passes::BVGauss bgauss(nullptr, "bv-gauss-unit"); + std::unordered_map res; + PreprocessingPassResult pres = bgauss.applyInternal(&apipe); + ASSERT_EQ(pres, PreprocessingPassResult::NO_CONFLICT); + ASSERT_EQ(apipe.size(), 4); + + Node resx1 = d_nodeManager->mkNode( + kind::EQUAL, + d_x, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_seven32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)), + d_p)); + Node resy1 = d_nodeManager->mkNode( + kind::EQUAL, + d_y, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nine32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)), + d_p)); + + Node resx2 = d_nodeManager->mkNode( + kind::EQUAL, + d_x, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)), + d_p)); + Node resz2 = d_nodeManager->mkNode( + kind::EQUAL, + d_z, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)), + d_p)); + + Node resy3 = d_nodeManager->mkNode( + kind::EQUAL, + d_y, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_three32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)), + d_p)); + Node resz3 = d_nodeManager->mkNode( + kind::EQUAL, + d_z, + d_nodeManager->mkNode( + kind::BITVECTOR_UREM, + d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_two32, + d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_six32)), + d_p)); + + bool fx1 = std::find(apipe.begin(), apipe.end(), resx1) != apipe.end(); + bool fy1 = std::find(apipe.begin(), apipe.end(), resy1) != apipe.end(); + bool fx2 = std::find(apipe.begin(), apipe.end(), resx2) != apipe.end(); + bool fz2 = std::find(apipe.begin(), apipe.end(), resz2) != apipe.end(); + bool fy3 = std::find(apipe.begin(), apipe.end(), resy3) != apipe.end(); + bool fz3 = std::find(apipe.begin(), apipe.end(), resz3) != apipe.end(); + + /* result depends on order of variables in matrix */ + ASSERT_TRUE((fx1 && fy1) || (fx2 && fz2) || (fy3 && fz3)); +} + +TEST_F(TestPPWhiteBVGauss, get_min_bw1) +{ + ASSERT_EQ(BVGauss::getMinBwExpr(bv::utils::mkConst(32, 11)), 4); + + ASSERT_EQ(BVGauss::getMinBwExpr(d_p), 4); + ASSERT_EQ(BVGauss::getMinBwExpr(d_x), 16); + + Node extp = bv::utils::mkExtract(d_p, 4, 0); + ASSERT_EQ(BVGauss::getMinBwExpr(extp), 4); + Node extx = bv::utils::mkExtract(d_x, 4, 0); + ASSERT_EQ(BVGauss::getMinBwExpr(extx), 5); + + Node zextop8 = + d_nodeManager->mkConst(BitVectorZeroExtend(8)); + Node zextop16 = + d_nodeManager->mkConst(BitVectorZeroExtend(16)); + Node zextop32 = + d_nodeManager->mkConst(BitVectorZeroExtend(32)); + Node zextop40 = + d_nodeManager->mkConst(BitVectorZeroExtend(40)); + + Node zext40p = d_nodeManager->mkNode(zextop8, d_p); + ASSERT_EQ(BVGauss::getMinBwExpr(zext40p), 4); + Node zext40x = d_nodeManager->mkNode(zextop8, d_x); + ASSERT_EQ(BVGauss::getMinBwExpr(zext40x), 16); + + Node zext48p = d_nodeManager->mkNode(zextop16, d_p); + ASSERT_EQ(BVGauss::getMinBwExpr(zext48p), 4); + Node zext48x = d_nodeManager->mkNode(zextop16, d_x); + ASSERT_EQ(BVGauss::getMinBwExpr(zext48x), 16); + + Node p8 = d_nodeManager->mkConst(BitVector(8, 11u)); + Node x8 = d_nodeManager->mkVar("x8", d_nodeManager->mkBitVectorType(8)); + + Node zext48p8 = d_nodeManager->mkNode(zextop40, p8); + ASSERT_EQ(BVGauss::getMinBwExpr(zext48p8), 4); + Node zext48x8 = d_nodeManager->mkNode(zextop40, x8); + ASSERT_EQ(BVGauss::getMinBwExpr(zext48x8), 8); + + Node mult1p = d_nodeManager->mkNode(kind::BITVECTOR_MULT, extp, extp); + ASSERT_EQ(BVGauss::getMinBwExpr(mult1p), 5); + Node mult1x = d_nodeManager->mkNode(kind::BITVECTOR_MULT, extx, extx); + ASSERT_EQ(BVGauss::getMinBwExpr(mult1x), 0); + + Node mult2p = d_nodeManager->mkNode(kind::BITVECTOR_MULT, zext40p, zext40p); + ASSERT_EQ(BVGauss::getMinBwExpr(mult2p), 7); + Node mult2x = d_nodeManager->mkNode(kind::BITVECTOR_MULT, zext40x, zext40x); + ASSERT_EQ(BVGauss::getMinBwExpr(mult2x), 32); + + NodeBuilder<> nbmult3p(kind::BITVECTOR_MULT); + nbmult3p << zext48p << zext48p << zext48p; + Node mult3p = nbmult3p; + ASSERT_EQ(BVGauss::getMinBwExpr(mult3p), 11); + NodeBuilder<> nbmult3x(kind::BITVECTOR_MULT); + nbmult3x << zext48x << zext48x << zext48x; + Node mult3x = nbmult3x; + ASSERT_EQ(BVGauss::getMinBwExpr(mult3x), 48); + + NodeBuilder<> nbmult4p(kind::BITVECTOR_MULT); + nbmult4p << zext48p << zext48p8 << zext48p; + Node mult4p = nbmult4p; + ASSERT_EQ(BVGauss::getMinBwExpr(mult4p), 11); + NodeBuilder<> nbmult4x(kind::BITVECTOR_MULT); + nbmult4x << zext48x << zext48x8 << zext48x; + Node mult4x = nbmult4x; + ASSERT_EQ(BVGauss::getMinBwExpr(mult4x), 40); + + Node concat1p = bv::utils::mkConcat(d_p, zext48p); + ASSERT_EQ(BVGauss::getMinBwExpr(concat1p), 52); + Node concat1x = bv::utils::mkConcat(d_x, zext48x); + ASSERT_EQ(BVGauss::getMinBwExpr(concat1x), 64); + + Node concat2p = bv::utils::mkConcat(bv::utils::mkZero(16), zext48p); + ASSERT_EQ(BVGauss::getMinBwExpr(concat2p), 4); + Node concat2x = bv::utils::mkConcat(bv::utils::mkZero(16), zext48x); + ASSERT_EQ(BVGauss::getMinBwExpr(concat2x), 16); + + Node udiv1p = + d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48p, zext48p); + ASSERT_EQ(BVGauss::getMinBwExpr(udiv1p), 1); + Node udiv1x = + d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48x, zext48x); + ASSERT_EQ(BVGauss::getMinBwExpr(udiv1x), 48); + + Node udiv2p = + d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48p, zext48p8); + ASSERT_EQ(BVGauss::getMinBwExpr(udiv2p), 1); + Node udiv2x = + d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48x, zext48x8); + ASSERT_EQ(BVGauss::getMinBwExpr(udiv2x), 48); + + Node urem1p = + d_nodeManager->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48p, zext48p); + ASSERT_EQ(BVGauss::getMinBwExpr(urem1p), 1); + Node urem1x = + d_nodeManager->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48x, zext48x); + ASSERT_EQ(BVGauss::getMinBwExpr(urem1x), 1); + + Node urem2p = + d_nodeManager->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48p, zext48p8); + ASSERT_EQ(BVGauss::getMinBwExpr(urem2p), 1); + Node urem2x = + d_nodeManager->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48x, zext48x8); + ASSERT_EQ(BVGauss::getMinBwExpr(urem2x), 16); + + Node urem3p = + d_nodeManager->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48p8, zext48p); + ASSERT_EQ(BVGauss::getMinBwExpr(urem3p), 1); + Node urem3x = + d_nodeManager->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48x8, zext48x); + ASSERT_EQ(BVGauss::getMinBwExpr(urem3x), 8); + + Node add1p = d_nodeManager->mkNode(kind::BITVECTOR_PLUS, extp, extp); + ASSERT_EQ(BVGauss::getMinBwExpr(add1p), 5); + Node add1x = d_nodeManager->mkNode(kind::BITVECTOR_PLUS, extx, extx); + ASSERT_EQ(BVGauss::getMinBwExpr(add1x), 0); + + Node add2p = d_nodeManager->mkNode(kind::BITVECTOR_PLUS, zext40p, zext40p); + ASSERT_EQ(BVGauss::getMinBwExpr(add2p), 5); + Node add2x = d_nodeManager->mkNode(kind::BITVECTOR_PLUS, zext40x, zext40x); + ASSERT_EQ(BVGauss::getMinBwExpr(add2x), 17); + + Node add3p = d_nodeManager->mkNode(kind::BITVECTOR_PLUS, zext48p8, zext48p); + ASSERT_EQ(BVGauss::getMinBwExpr(add3p), 5); + Node add3x = d_nodeManager->mkNode(kind::BITVECTOR_PLUS, zext48x8, zext48x); + ASSERT_EQ(BVGauss::getMinBwExpr(add3x), 17); + + NodeBuilder<> nbadd4p(kind::BITVECTOR_PLUS); + nbadd4p << zext48p << zext48p << zext48p; + Node add4p = nbadd4p; + ASSERT_EQ(BVGauss::getMinBwExpr(add4p), 6); + NodeBuilder<> nbadd4x(kind::BITVECTOR_PLUS); + nbadd4x << zext48x << zext48x << zext48x; + Node add4x = nbadd4x; + ASSERT_EQ(BVGauss::getMinBwExpr(add4x), 18); + + NodeBuilder<> nbadd5p(kind::BITVECTOR_PLUS); + nbadd5p << zext48p << zext48p8 << zext48p; + Node add5p = nbadd5p; + ASSERT_EQ(BVGauss::getMinBwExpr(add5p), 6); + NodeBuilder<> nbadd5x(kind::BITVECTOR_PLUS); + nbadd5x << zext48x << zext48x8 << zext48x; + Node add5x = nbadd5x; + ASSERT_EQ(BVGauss::getMinBwExpr(add5x), 18); + + NodeBuilder<> nbadd6p(kind::BITVECTOR_PLUS); + nbadd6p << zext48p << zext48p << zext48p << zext48p; + Node add6p = nbadd6p; + ASSERT_EQ(BVGauss::getMinBwExpr(add6p), 6); + NodeBuilder<> nbadd6x(kind::BITVECTOR_PLUS); + nbadd6x << zext48x << zext48x << zext48x << zext48x; + Node add6x = nbadd6x; + ASSERT_EQ(BVGauss::getMinBwExpr(add6x), 18); + + Node not1p = d_nodeManager->mkNode(kind::BITVECTOR_NOT, zext40p); + ASSERT_EQ(BVGauss::getMinBwExpr(not1p), 40); + Node not1x = d_nodeManager->mkNode(kind::BITVECTOR_NOT, zext40x); + ASSERT_EQ(BVGauss::getMinBwExpr(not1x), 40); +} + +TEST_F(TestPPWhiteBVGauss, get_min_bw2) +{ + /* ((_ zero_extend 5) + * ((_ extract 7 0) ((_ zero_extend 15) d_p))) */ + Node zextop5 = + d_nodeManager->mkConst(BitVectorZeroExtend(5)); + Node zextop15 = + d_nodeManager->mkConst(BitVectorZeroExtend(15)); + Node zext1 = d_nodeManager->mkNode(zextop15, d_p); + Node ext = bv::utils::mkExtract(zext1, 7, 0); + Node zext2 = d_nodeManager->mkNode(zextop5, ext); + ASSERT_EQ(BVGauss::getMinBwExpr(zext2), 4); +} + +TEST_F(TestPPWhiteBVGauss, get_min_bw3a) +{ + /* ((_ zero_extend 5) + * (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x z))) + * ((_ extract 4 0) z))) */ + Node x = d_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16)); + Node y = d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16)); + Node z = d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16)); + Node zextop5 = + d_nodeManager->mkConst(BitVectorZeroExtend(5)); + Node udiv1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, x, y); + Node zext1 = d_nodeManager->mkNode(zextop5, udiv1); + Node ext1 = bv::utils::mkExtract(zext1, 4, 0); + Node ext2 = bv::utils::mkExtract(z, 4, 0); + Node udiv2 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1, ext2); + Node zext2 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2); + ASSERT_EQ(BVGauss::getMinBwExpr(zext2), 5); +} + +TEST_F(TestPPWhiteBVGauss, get_min_bw3b) +{ + /* ((_ zero_extend 5) + * (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x z))) + * ((_ extract 4 0) z))) */ + Node zextop5 = + d_nodeManager->mkConst(BitVectorZeroExtend(5)); + Node udiv1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, d_x, d_y); + Node zext1 = d_nodeManager->mkNode(zextop5, udiv1); + Node ext1 = bv::utils::mkExtract(zext1, 4, 0); + Node ext2 = bv::utils::mkExtract(d_z, 4, 0); + Node udiv2 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1, ext2); + Node zext2 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2); + ASSERT_EQ(BVGauss::getMinBwExpr(zext2), 5); +} + +TEST_F(TestPPWhiteBVGauss, get_min_bw4a) +{ + /* (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_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16)); + Node y = d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16)); + Node z = d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16)); + Node zextop5 = + d_nodeManager->mkConst(BitVectorZeroExtend(5)); + Node zextop7 = + d_nodeManager->mkConst(BitVectorZeroExtend(7)); + + Node udiv1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, x, y); + Node zext1 = d_nodeManager->mkNode(zextop5, udiv1); + + Node ext1_1 = bv::utils::mkExtract(zext1, 4, 0); + Node ext2_1 = bv::utils::mkExtract(z, 4, 0); + Node udiv2_1 = + d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_1, ext2_1); + Node zext2_1 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2_1); + + Node ext1_2 = bv::utils::mkExtract(zext1, 2, 0); + Node ext2_2 = bv::utils::mkExtract(z, 2, 0); + Node udiv2_2 = + d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_2, ext2_2); + Node zext2_2 = d_nodeManager->mkNode(zextop7, udiv2_2); + + Node plus = d_nodeManager->mkNode(kind::BITVECTOR_PLUS, zext2_1, zext2_2); + + ASSERT_EQ(BVGauss::getMinBwExpr(plus), 6); +} + +TEST_F(TestPPWhiteBVGauss, get_min_bw4b) +{ + /* (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_nodeManager->mkConst(BitVectorZeroExtend(5)); + Node zextop7 = + d_nodeManager->mkConst(BitVectorZeroExtend(7)); + + Node udiv1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, d_x, d_y); + Node zext1 = d_nodeManager->mkNode(zextop5, udiv1); + + Node ext1_1 = bv::utils::mkExtract(zext1, 4, 0); + Node ext2_1 = bv::utils::mkExtract(d_z, 4, 0); + Node udiv2_1 = + d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_1, ext2_1); + Node zext2_1 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2_1); + + Node ext1_2 = bv::utils::mkExtract(zext1, 2, 0); + Node ext2_2 = bv::utils::mkExtract(d_z, 2, 0); + Node udiv2_2 = + d_nodeManager->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_2, ext2_2); + Node zext2_2 = d_nodeManager->mkNode(zextop7, udiv2_2); + + Node plus = d_nodeManager->mkNode(kind::BITVECTOR_PLUS, zext2_1, zext2_2); + + ASSERT_EQ(BVGauss::getMinBwExpr(plus), 6); +} + +TEST_F(TestPPWhiteBVGauss, get_min_bw5a) +{ + /* (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 = bv::utils::mkVar(1); + Node y = bv::utils::mkVar(1); + Node z = bv::utils::mkVar(1); + Node u = bv::utils::mkVar(1); + Node v = bv::utils::mkVar(1); + Node w = bv::utils::mkVar(1); + Node s = bv::utils::mkVar(16); + + Node zextop5 = + d_nodeManager->mkConst(BitVectorZeroExtend(5)); + Node zextop15 = + d_nodeManager->mkConst(BitVectorZeroExtend(15)); + + Node zext15x = d_nodeManager->mkNode(zextop15, x); + Node zext15y = d_nodeManager->mkNode(zextop15, y); + Node zext15z = d_nodeManager->mkNode(zextop15, z); + Node zext15u = d_nodeManager->mkNode(zextop15, u); + Node zext15v = d_nodeManager->mkNode(zextop15, v); + Node zext15w = d_nodeManager->mkNode(zextop15, w); + + Node ext7x = bv::utils::mkExtract(zext15x, 7, 0); + Node ext7y = bv::utils::mkExtract(zext15y, 7, 0); + Node ext7z = bv::utils::mkExtract(zext15z, 7, 0); + Node ext7u = bv::utils::mkExtract(zext15u, 7, 0); + Node ext7v = bv::utils::mkExtract(zext15v, 7, 0); + Node ext7w = bv::utils::mkExtract(zext15w, 7, 0); + Node ext7s = bv::utils::mkExtract(s, 7, 0); + Node ext15s = bv::utils::mkExtract(s, 15, 8); + + Node xx = bv::utils::mkConcat(bv::utils::mkZero(5), ext7x); + Node yy = bv::utils::mkConcat(bv::utils::mkZero(5), ext7y); + Node zz = bv::utils::mkConcat(bv::utils::mkZero(5), ext7z); + Node uu = bv::utils::mkConcat(bv::utils::mkZero(5), ext7u); + Node vv = bv::utils::mkConcat(bv::utils::mkZero(5), ext7v); + Node ww = bv::utils::mkConcat(bv::utils::mkZero(5), ext7w); + Node s7 = bv::utils::mkConcat(bv::utils::mkZero(5), ext7s); + Node s15 = bv::utils::mkConcat(bv::utils::mkZero(5), ext15s); + + Node plus1 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(13, 86), xx), + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(13, 41), yy)); + Node plus2 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus1, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(13, 37), zz)); + Node plus3 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus2, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(13, 170), uu)); + Node plus4 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus3, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(13, 112), uu)); + Node plus5 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus4, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(13, 195), s15)); + Node plus6 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus5, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(13, 124), s7)); + Node plus7 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus6, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(13, 83), ww)); + + ASSERT_EQ(BVGauss::getMinBwExpr(plus7), 0); +} + +TEST_F(TestPPWhiteBVGauss, get_min_bw5b) +{ + /* (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 = bv::utils::mkVar(1); + Node y = bv::utils::mkVar(1); + Node z = bv::utils::mkVar(1); + Node u = bv::utils::mkVar(1); + Node v = bv::utils::mkVar(1); + Node w = bv::utils::mkVar(1); + Node s = bv::utils::mkVar(16); + + Node zextop15 = + d_nodeManager->mkConst(BitVectorZeroExtend(15)); + + Node zext15x = d_nodeManager->mkNode(zextop15, x); + Node zext15y = d_nodeManager->mkNode(zextop15, y); + Node zext15z = d_nodeManager->mkNode(zextop15, z); + Node zext15u = d_nodeManager->mkNode(zextop15, u); + Node zext15v = d_nodeManager->mkNode(zextop15, v); + Node zext15w = d_nodeManager->mkNode(zextop15, w); + + Node ext7x = bv::utils::mkExtract(zext15x, 7, 0); + Node ext7y = bv::utils::mkExtract(zext15y, 7, 0); + Node ext7z = bv::utils::mkExtract(zext15z, 7, 0); + Node ext7u = bv::utils::mkExtract(zext15u, 7, 0); + Node ext7v = bv::utils::mkExtract(zext15v, 7, 0); + Node ext7w = bv::utils::mkExtract(zext15w, 7, 0); + Node ext7s = bv::utils::mkExtract(s, 7, 0); + Node ext15s = bv::utils::mkExtract(s, 15, 8); + + Node xx = bv::utils::mkConcat(bv::utils::mkZero(12), ext7x); + Node yy = bv::utils::mkConcat(bv::utils::mkZero(12), ext7y); + Node zz = bv::utils::mkConcat(bv::utils::mkZero(12), ext7z); + Node uu = bv::utils::mkConcat(bv::utils::mkZero(12), ext7u); + Node vv = bv::utils::mkConcat(bv::utils::mkZero(12), ext7v); + Node ww = bv::utils::mkConcat(bv::utils::mkZero(12), ext7w); + Node s7 = bv::utils::mkConcat(bv::utils::mkZero(12), ext7s); + Node s15 = bv::utils::mkConcat(bv::utils::mkZero(12), ext15s); + + Node plus1 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(20, 86), xx), + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(20, 41), yy)); + Node plus2 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus1, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(20, 37), zz)); + Node plus3 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus2, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(20, 170), uu)); + Node plus4 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus3, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(20, 112), uu)); + Node plus5 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus4, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(20, 195), s15)); + Node plus6 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus5, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(20, 124), s7)); + Node plus7 = d_nodeManager->mkNode( + kind::BITVECTOR_PLUS, + plus6, + d_nodeManager->mkNode( + kind::BITVECTOR_MULT, bv::utils::mkConst(20, 83), ww)); + + ASSERT_EQ(BVGauss::getMinBwExpr(plus7), 19); + ASSERT_EQ(BVGauss::getMinBwExpr(Rewriter::rewrite(plus7)), 17); +} +} // namespace test +} // namespace CVC4 diff --git a/test/unit/preprocessing/pass_bv_gauss_white.h b/test/unit/preprocessing/pass_bv_gauss_white.h deleted file mode 100644 index a0a708c5b..000000000 --- a/test/unit/preprocessing/pass_bv_gauss_white.h +++ /dev/null @@ -1,3031 +0,0 @@ -/********************* */ -/*! \file pass_bv_gauss_white.h - ** \verbatim - ** Top contributors (to current version): - ** Aina Niemetz, Mathias Preiner, Andres Noetzli - ** This file is part of the CVC4 project. - ** Copyright (c) 2009-2020 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 "context/context.h" -#include "expr/node.h" -#include "expr/node_manager.h" -#include "preprocessing/passes/bv_gauss.h" -#include "smt/smt_engine.h" -#include "smt/smt_engine_scope.h" -#include "test_utils.h" -#include "theory/bv/theory_bv_utils.h" -#include "theory/rewriter.h" -#include "util/bitvector.h" - -#include -#include -#include - -using namespace CVC4; -using namespace CVC4::preprocessing; -using namespace CVC4::preprocessing::passes; -using namespace CVC4::theory; -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, - BVGauss::Result expected, - std::vector* rrhs = nullptr, - std::vector>* rlhs = nullptr) -{ - size_t nrows = lhs.size(); - size_t ncols = lhs[0].size(); - BVGauss::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 = BVGauss::gaussElim(prime, resrhs, reslhs); - - std::cout << "BVGauss::Result: " - << (ret == BVGauss::Result::INVALID - ? "INVALID" - : (ret == BVGauss::Result::UNIQUE - ? "UNIQUE" - : (ret == BVGauss::Result::PARTIAL ? "PARTIAL" - : "NONE"))) - << std::endl; - print_matrix_dbg(resrhs, reslhs); - - TS_ASSERT_EQUALS(expected, ret); - - if (expected == BVGauss::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]); - } - } -} - -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() override - { - d_em = new ExprManager(); - d_nm = NodeManager::fromExprManager(d_em); - d_smt = new SmtEngine(d_nm); - d_scope = new SmtScope(d_smt); - d_smt->finishInit(); - - d_zero = bv::utils::mkZero(16); - - d_p = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 11u))); - d_x = bv::utils::mkConcat( - d_zero, d_nm->mkVar("x", d_nm->mkBitVectorType(16))); - d_y = bv::utils::mkConcat( - d_zero, d_nm->mkVar("y", d_nm->mkBitVectorType(16))); - d_z = bv::utils::mkConcat( - d_zero, d_nm->mkVar("z", d_nm->mkBitVectorType(16))); - - d_one = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 1u))); - d_two = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 2u))); - d_three = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 3u))); - d_four = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 4u))); - d_five = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 5u))); - d_six = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 6u))); - d_seven = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 7u))); - d_eight = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 8u))); - d_nine = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 9u))); - d_ten = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 10u))); - d_twelve = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 12u))); - d_eighteen = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 18u))); - d_twentyfour = bv::utils::mkConcat( - d_zero, d_nm->mkConst(BitVector(16, 24u))); - d_thirty = bv::utils::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() override - { - (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 - TS_UTILS_EXPECT_ABORT(BVGauss::gaussElim(Integer(0), rhs, lhs)); - std::cout << "matrix 0, modulo 1" << std::endl; - testGaussElimX(Integer(1), rhs, lhs, BVGauss::Result::UNIQUE); - std::cout << "matrix 0, modulo 2" << std::endl; - testGaussElimX(Integer(2), rhs, lhs, BVGauss::Result::UNIQUE); - std::cout << "matrix 0, modulo 3" << std::endl; - testGaussElimX(Integer(3), rhs, lhs, BVGauss::Result::UNIQUE); - std::cout << "matrix 0, modulo 4" << std::endl; // no inverse - testGaussElimX(Integer(4), rhs, lhs, BVGauss::Result::INVALID); - std::cout << "matrix 0, modulo 5" << std::endl; - testGaussElimX(Integer(5), rhs, lhs, BVGauss::Result::UNIQUE); - std::cout << "matrix 0, modulo 6" << std::endl; // no inverse - testGaussElimX(Integer(6), rhs, lhs, BVGauss::Result::INVALID); - std::cout << "matrix 0, modulo 7" << std::endl; - testGaussElimX(Integer(7), rhs, lhs, BVGauss::Result::UNIQUE); - std::cout << "matrix 0, modulo 8" << std::endl; // no inverse - testGaussElimX(Integer(8), rhs, lhs, BVGauss::Result::INVALID); - std::cout << "matrix 0, modulo 9" << std::endl; - testGaussElimX(Integer(9), rhs, lhs, BVGauss::Result::UNIQUE); - std::cout << "matrix 0, modulo 10" << std::endl; // no inverse - testGaussElimX(Integer(10), rhs, lhs, BVGauss::Result::INVALID); - std::cout << "matrix 0, modulo 11" << std::endl; - testGaussElimX(Integer(11), rhs, lhs, BVGauss::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, BVGauss::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, BVGauss::Result::UNIQUE); - std::cout << "matrix 2, modulo 17" << std::endl; - testGaussElimX(Integer(17), rhs, lhs, BVGauss::Result::UNIQUE); - std::cout << "matrix 2, modulo 59" << std::endl; - testGaussElimX(Integer(59), rhs, lhs, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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, BVGauss::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; - BVGauss::Result ret = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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, - bv::utils::mkConcat(bv::utils::mkZero(6), - d_nm->mkNode(kind::BITVECTOR_PLUS, - bv::utils::mkConst(20, 7), - bv::utils::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, bv::utils::mkOne(32), d_z); - - Node x_mul_two = d_nm->mkNode( - kind::BITVECTOR_MULT, - d_nm->mkNode( - kind::BITVECTOR_SHL, bv::utils::mkOne(32), bv::utils::mkOne(32)), - d_x); - Node y_mul_three = d_nm->mkNode(kind::BITVECTOR_MULT, - d_nm->mkNode(kind::BITVECTOR_LSHR, - bv::utils::mkOnes(32), - bv::utils::mkConst(32, 30)), - d_y); - Node z_mul_five = d_nm->mkNode(kind::BITVECTOR_MULT, - bv::utils::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, - bv::utils::mkConst(32, 4), - bv::utils::mkConst(32, 5)), - bv::utils::mkConst(32, 4)), - bv::utils::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; - BVGauss::Result ret = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = bv::utils::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = bv::utils::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 = bv::utils::mkConcat( - d_zero, - bv::utils::mkConcat( - zero, bv::utils::mkExtract(bv::utils::mkConcat(zero, xx), 7, 0))); - Node y = bv::utils::mkConcat( - d_zero, - bv::utils::mkConcat( - zero, bv::utils::mkExtract(bv::utils::mkConcat(zero, yy), 7, 0))); - Node z = bv::utils::mkConcat( - d_zero, - bv::utils::mkConcat( - zero, bv::utils::mkExtract(bv::utils::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = bv::utils::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 = bv::utils::mkConcat( - d_zero, - bv::utils::mkConcat( - zero, - bv::utils::mkExtract( - d_nm->mkNode(kind::BITVECTOR_CONCAT, zero, xx), 7, 0))); - Node y = bv::utils::mkConcat( - d_zero, - bv::utils::mkConcat( - zero, - bv::utils::mkExtract( - d_nm->mkNode(kind::BITVECTOR_CONCAT, zero, yy), 7, 0))); - Node z = bv::utils::mkConcat( - d_zero, - bv::utils::mkConcat( - zero, - bv::utils::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::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 = bv::utils::mkConcat( - d_zero, - bv::utils::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 = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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; - BVGauss::Result ret; - - /* ------------------------------------------------------------------- - * x*y = 4 modulo 11 - * x*y*z = 2 - * 2*x*y + 2*z = 9 - * ------------------------------------------------------------------- */ - - Node zero32 = bv::utils::mkZero(32); - - Node x = bv::utils::mkConcat(zero32, - d_nm->mkVar("x", d_nm->mkBitVectorType(16))); - Node y = bv::utils::mkConcat(zero32, - d_nm->mkVar("y", d_nm->mkBitVectorType(16))); - Node z = bv::utils::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), - bv::utils::mkConcat(d_zero, d_two)), - d_nm->mkNode( - kind::BITVECTOR_MULT, bv::utils::mkConcat(d_zero, d_two), z)); - - Node eq1 = d_nm->mkNode( - kind::EQUAL, - d_nm->mkNode( - kind::BITVECTOR_UREM, n1, bv::utils::mkConcat(d_zero, d_p)), - bv::utils::mkConcat(d_zero, d_four)); - - Node eq2 = d_nm->mkNode( - kind::EQUAL, - d_nm->mkNode( - kind::BITVECTOR_UREM, n2, bv::utils::mkConcat(d_zero, d_p)), - bv::utils::mkConcat(d_zero, d_two)); - - Node eq3 = d_nm->mkNode( - kind::EQUAL, - d_nm->mkNode( - kind::BITVECTOR_UREM, n3, bv::utils::mkConcat(d_zero, d_p)), - bv::utils::mkConcat(d_zero, d_nine)); - - std::vector eqs = {eq1, eq2, eq3}; - ret = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::Result::UNIQUE); - TS_ASSERT(res.size() == 3); - - n1 = Rewriter::rewrite(n1); - n2 = Rewriter::rewrite(n2); - z = Rewriter::rewrite(z); - - TS_ASSERT(res[n1] ==bv::utils::mkConst(48, 4)); - TS_ASSERT(res[n2] ==bv::utils::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; - BVGauss::Result ret; - - /* ------------------------------------------------------------------- - * x*y = 4 modulo 11 - * x*y*z = 2 - * 2*x*y = 9 - * ------------------------------------------------------------------- */ - - Node zero32 = bv::utils::mkZero(32); - - Node x = bv::utils::mkConcat(zero32, - d_nm->mkVar("x", d_nm->mkBitVectorType(16))); - Node y = bv::utils::mkConcat(zero32, - d_nm->mkVar("y", d_nm->mkBitVectorType(16))); - Node z = bv::utils::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), - bv::utils::mkConcat(d_zero, d_two)); - - Node eq1 = d_nm->mkNode( - kind::EQUAL, - d_nm->mkNode( - kind::BITVECTOR_UREM, n1, bv::utils::mkConcat(d_zero, d_p)), - bv::utils::mkConcat(d_zero, d_four)); - - Node eq2 = d_nm->mkNode( - kind::EQUAL, - d_nm->mkNode( - kind::BITVECTOR_UREM, n2, bv::utils::mkConcat(d_zero, d_p)), - bv::utils::mkConcat(d_zero, d_two)); - - Node eq3 = d_nm->mkNode( - kind::EQUAL, - d_nm->mkNode( - kind::BITVECTOR_UREM, n3, bv::utils::mkConcat(d_zero, d_p)), - bv::utils::mkConcat(d_zero, d_nine)); - - std::vector eqs = {eq1, eq2, eq3}; - ret = BVGauss::gaussElimRewriteForUrem(eqs, res); - TS_ASSERT(ret == BVGauss::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); - - AssertionPipeline apipe; - apipe.push_back(a); - passes::BVGauss bgauss(nullptr, "bv-gauss-unit"); - std::unordered_map res; - PreprocessingPassResult pres = bgauss.applyInternal(&apipe); - TS_ASSERT (pres == PreprocessingPassResult::NO_CONFLICT); - 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(apipe.size() == 4); - TS_ASSERT(std::find(apipe.begin(), apipe.end(), resx) != apipe.end()); - TS_ASSERT(std::find(apipe.begin(), apipe.end(), resy) != apipe.end()); - TS_ASSERT(std::find(apipe.begin(), apipe.end(), resz) != apipe.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); - - AssertionPipeline apipe; - apipe.push_back(a); - apipe.push_back(eq4); - apipe.push_back(eq5); - passes::BVGauss bgauss(nullptr, "bv-gauss-unit"); - std::unordered_map res; - PreprocessingPassResult pres = bgauss.applyInternal(&apipe); - TS_ASSERT (pres == PreprocessingPassResult::NO_CONFLICT); - 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(apipe.size() == 8); - TS_ASSERT(std::find(apipe.begin(), apipe.end(), resx1) != apipe.end()); - TS_ASSERT(std::find(apipe.begin(), apipe.end(), resx2) != apipe.end()); - TS_ASSERT(std::find(apipe.begin(), apipe.end(), resy1) != apipe.end()); - TS_ASSERT(std::find(apipe.begin(), apipe.end(), resy2) != apipe.end()); - TS_ASSERT(std::find(apipe.begin(), apipe.end(), resz) != apipe.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); - - AssertionPipeline apipe; - apipe.push_back(eq1); - apipe.push_back(eq2); - passes::BVGauss bgauss(nullptr, "bv-gauss-unit"); - std::unordered_map res; - PreprocessingPassResult pres = bgauss.applyInternal(&apipe); - TS_ASSERT (pres == PreprocessingPassResult::NO_CONFLICT); - TS_ASSERT(apipe.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(apipe.begin(), apipe.end(), resx1) != apipe.end(); - bool fy1 = std::find(apipe.begin(), apipe.end(), resy1) != apipe.end(); - bool fx2 = std::find(apipe.begin(), apipe.end(), resx2) != apipe.end(); - bool fz2 = std::find(apipe.begin(), apipe.end(), resz2) != apipe.end(); - bool fy3 = std::find(apipe.begin(), apipe.end(), resy3) != apipe.end(); - bool fz3 = std::find(apipe.begin(), apipe.end(), resz3) != apipe.end(); - - /* result depends on order of variables in matrix */ - TS_ASSERT((fx1 && fy1) || (fx2 && fz2) || (fy3 && fz3)); - } - - void testGetMinBw1() - { - TS_ASSERT(BVGauss::getMinBwExpr(bv::utils::mkConst(32, 11)) == 4); - - TS_ASSERT(BVGauss::getMinBwExpr(d_p) == 4); - TS_ASSERT(BVGauss::getMinBwExpr(d_x) == 16); - - Node extp = bv::utils::mkExtract(d_p, 4, 0); - TS_ASSERT(BVGauss::getMinBwExpr(extp) == 4); - Node extx = bv::utils::mkExtract(d_x, 4, 0); - TS_ASSERT(BVGauss::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(BVGauss::getMinBwExpr(zext40p) == 4); - Node zext40x = d_nm->mkNode(zextop8, d_x); - TS_ASSERT(BVGauss::getMinBwExpr(zext40x) == 16); - - Node zext48p = d_nm->mkNode(zextop16, d_p); - TS_ASSERT(BVGauss::getMinBwExpr(zext48p) == 4); - Node zext48x = d_nm->mkNode(zextop16, d_x); - TS_ASSERT(BVGauss::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(BVGauss::getMinBwExpr(zext48p8) == 4); - Node zext48x8 = d_nm->mkNode(zextop40, x8); - TS_ASSERT(BVGauss::getMinBwExpr(zext48x8) == 8); - - Node mult1p = d_nm->mkNode(kind::BITVECTOR_MULT, extp, extp); - TS_ASSERT(BVGauss::getMinBwExpr(mult1p) == 5); - Node mult1x = d_nm->mkNode(kind::BITVECTOR_MULT, extx, extx); - TS_ASSERT(BVGauss::getMinBwExpr(mult1x) == 0); - - Node mult2p = d_nm->mkNode(kind::BITVECTOR_MULT, zext40p, zext40p); - TS_ASSERT(BVGauss::getMinBwExpr(mult2p) == 7); - Node mult2x = d_nm->mkNode(kind::BITVECTOR_MULT, zext40x, zext40x); - TS_ASSERT(BVGauss::getMinBwExpr(mult2x) == 32); - - NodeBuilder<> nbmult3p(kind::BITVECTOR_MULT); - nbmult3p << zext48p << zext48p << zext48p; - Node mult3p = nbmult3p; - TS_ASSERT(BVGauss::getMinBwExpr(mult3p) == 11); - NodeBuilder<> nbmult3x(kind::BITVECTOR_MULT); - nbmult3x << zext48x << zext48x << zext48x; - Node mult3x = nbmult3x; - TS_ASSERT(BVGauss::getMinBwExpr(mult3x) == 48); - - NodeBuilder<> nbmult4p(kind::BITVECTOR_MULT); - nbmult4p << zext48p << zext48p8 << zext48p; - Node mult4p = nbmult4p; - TS_ASSERT(BVGauss::getMinBwExpr(mult4p) == 11); - NodeBuilder<> nbmult4x(kind::BITVECTOR_MULT); - nbmult4x << zext48x << zext48x8 << zext48x; - Node mult4x = nbmult4x; - TS_ASSERT(BVGauss::getMinBwExpr(mult4x) == 40); - - Node concat1p = bv::utils::mkConcat(d_p, zext48p); - TS_ASSERT(BVGauss::getMinBwExpr(concat1p) == 52); - Node concat1x = bv::utils::mkConcat(d_x, zext48x); - TS_ASSERT(BVGauss::getMinBwExpr(concat1x) == 64); - - Node concat2p = bv::utils::mkConcat(bv::utils::mkZero(16), zext48p); - TS_ASSERT(BVGauss::getMinBwExpr(concat2p) == 4); - Node concat2x = bv::utils::mkConcat(bv::utils::mkZero(16), zext48x); - TS_ASSERT(BVGauss::getMinBwExpr(concat2x) == 16); - - Node udiv1p = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48p, zext48p); - TS_ASSERT(BVGauss::getMinBwExpr(udiv1p) == 1); - Node udiv1x = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48x, zext48x); - TS_ASSERT(BVGauss::getMinBwExpr(udiv1x) == 48); - - Node udiv2p = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48p, zext48p8); - TS_ASSERT(BVGauss::getMinBwExpr(udiv2p) == 1); - Node udiv2x = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, zext48x, zext48x8); - TS_ASSERT(BVGauss::getMinBwExpr(udiv2x) == 48); - - Node urem1p = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48p, zext48p); - TS_ASSERT(BVGauss::getMinBwExpr(urem1p) == 1); - Node urem1x = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48x, zext48x); - TS_ASSERT(BVGauss::getMinBwExpr(urem1x) == 1); - - Node urem2p = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48p, zext48p8); - TS_ASSERT(BVGauss::getMinBwExpr(urem2p) == 1); - Node urem2x = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48x, zext48x8); - TS_ASSERT(BVGauss::getMinBwExpr(urem2x) == 16); - - Node urem3p = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48p8, zext48p); - TS_ASSERT(BVGauss::getMinBwExpr(urem3p) == 1); - Node urem3x = d_nm->mkNode(kind::BITVECTOR_UREM_TOTAL, zext48x8, zext48x); - TS_ASSERT(BVGauss::getMinBwExpr(urem3x) == 8); - - Node add1p = d_nm->mkNode(kind::BITVECTOR_PLUS, extp, extp); - TS_ASSERT(BVGauss::getMinBwExpr(add1p) == 5); - Node add1x = d_nm->mkNode(kind::BITVECTOR_PLUS, extx, extx); - TS_ASSERT(BVGauss::getMinBwExpr(add1x) == 0); - - Node add2p = d_nm->mkNode(kind::BITVECTOR_PLUS, zext40p, zext40p); - TS_ASSERT(BVGauss::getMinBwExpr(add2p) == 5); - Node add2x = d_nm->mkNode(kind::BITVECTOR_PLUS, zext40x, zext40x); - TS_ASSERT(BVGauss::getMinBwExpr(add2x) == 17); - - Node add3p = d_nm->mkNode(kind::BITVECTOR_PLUS, zext48p8, zext48p); - TS_ASSERT(BVGauss::getMinBwExpr(add3p) == 5); - Node add3x = d_nm->mkNode(kind::BITVECTOR_PLUS, zext48x8, zext48x); - TS_ASSERT(BVGauss::getMinBwExpr(add3x) == 17); - - NodeBuilder<> nbadd4p(kind::BITVECTOR_PLUS); - nbadd4p << zext48p << zext48p << zext48p; - Node add4p = nbadd4p; - TS_ASSERT(BVGauss::getMinBwExpr(add4p) == 6); - NodeBuilder<> nbadd4x(kind::BITVECTOR_PLUS); - nbadd4x << zext48x << zext48x << zext48x; - Node add4x = nbadd4x; - TS_ASSERT(BVGauss::getMinBwExpr(add4x) == 18); - - NodeBuilder<> nbadd5p(kind::BITVECTOR_PLUS); - nbadd5p << zext48p << zext48p8 << zext48p; - Node add5p = nbadd5p; - TS_ASSERT(BVGauss::getMinBwExpr(add5p) == 6); - NodeBuilder<> nbadd5x(kind::BITVECTOR_PLUS); - nbadd5x << zext48x << zext48x8 << zext48x; - Node add5x = nbadd5x; - TS_ASSERT(BVGauss::getMinBwExpr(add5x) == 18); - - NodeBuilder<> nbadd6p(kind::BITVECTOR_PLUS); - nbadd6p << zext48p << zext48p << zext48p << zext48p; - Node add6p = nbadd6p; - TS_ASSERT(BVGauss::getMinBwExpr(add6p) == 6); - NodeBuilder<> nbadd6x(kind::BITVECTOR_PLUS); - nbadd6x << zext48x << zext48x << zext48x << zext48x; - Node add6x = nbadd6x; - TS_ASSERT(BVGauss::getMinBwExpr(add6x) == 18); - - Node not1p = d_nm->mkNode(kind::BITVECTOR_NOT, zext40p); - TS_ASSERT(BVGauss::getMinBwExpr(not1p) == 40); - Node not1x = d_nm->mkNode(kind::BITVECTOR_NOT, zext40x); - TS_ASSERT(BVGauss::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 = bv::utils::mkExtract(zext1, 7, 0); - Node zext2 = d_nm->mkNode(zextop5, ext); - TS_ASSERT(BVGauss::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 = bv::utils::mkExtract(zext1, 4, 0); - Node ext2 = bv::utils::mkExtract(z, 4, 0); - Node udiv2 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1, ext2); - Node zext2 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2); - TS_ASSERT(BVGauss::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 = bv::utils::mkExtract(zext1, 4, 0); - Node ext2 = bv::utils::mkExtract(d_z, 4, 0); - Node udiv2 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1, ext2); - Node zext2 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2); - TS_ASSERT(BVGauss::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 = bv::utils::mkExtract(zext1, 4, 0); - Node ext2_1 = bv::utils::mkExtract(z, 4, 0); - Node udiv2_1 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_1, ext2_1); - Node zext2_1 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2_1); - - Node ext1_2 = bv::utils::mkExtract(zext1, 2, 0); - Node ext2_2 = bv::utils::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(BVGauss::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 = bv::utils::mkExtract(zext1, 4, 0); - Node ext2_1 = bv::utils::mkExtract(d_z, 4, 0); - Node udiv2_1 = d_nm->mkNode(kind::BITVECTOR_UDIV_TOTAL, ext1_1, ext2_1); - Node zext2_1 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2_1); - - Node ext1_2 = bv::utils::mkExtract(zext1, 2, 0); - Node ext2_2 = bv::utils::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(BVGauss::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 =bv::utils::mkVar(1); - Node y =bv::utils::mkVar(1); - Node z =bv::utils::mkVar(1); - Node u =bv::utils::mkVar(1); - Node v =bv::utils::mkVar(1); - Node w =bv::utils::mkVar(1); - Node s =bv::utils::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 = bv::utils::mkExtract(zext15x, 7, 0); - Node ext7y = bv::utils::mkExtract(zext15y, 7, 0); - Node ext7z = bv::utils::mkExtract(zext15z, 7, 0); - Node ext7u = bv::utils::mkExtract(zext15u, 7, 0); - Node ext7v = bv::utils::mkExtract(zext15v, 7, 0); - Node ext7w = bv::utils::mkExtract(zext15w, 7, 0); - Node ext7s = bv::utils::mkExtract(s, 7, 0); - Node ext15s = bv::utils::mkExtract(s, 15, 8); - - Node xx = bv::utils::mkConcat(bv::utils::mkZero(5), ext7x); - Node yy = bv::utils::mkConcat(bv::utils::mkZero(5), ext7y); - Node zz = bv::utils::mkConcat(bv::utils::mkZero(5), ext7z); - Node uu = bv::utils::mkConcat(bv::utils::mkZero(5), ext7u); - Node vv = bv::utils::mkConcat(bv::utils::mkZero(5), ext7v); - Node ww = bv::utils::mkConcat(bv::utils::mkZero(5), ext7w); - Node s7 = bv::utils::mkConcat(bv::utils::mkZero(5), ext7s); - Node s15 = bv::utils::mkConcat(bv::utils::mkZero(5), ext15s); - - Node plus1 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(13, 86), xx), - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(13, 41), yy)); - Node plus2 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus1, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(13, 37), zz)); - Node plus3 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus2, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(13, 170), uu)); - Node plus4 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus3, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(13, 112), uu)); - Node plus5 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus4, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(13, 195), s15)); - Node plus6 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus5, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(13, 124), s7)); - Node plus7 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus6, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(13, 83), ww)); - - TS_ASSERT(BVGauss::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 =bv::utils::mkVar(1); - Node y =bv::utils::mkVar(1); - Node z =bv::utils::mkVar(1); - Node u =bv::utils::mkVar(1); - Node v =bv::utils::mkVar(1); - Node w =bv::utils::mkVar(1); - Node s =bv::utils::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 = bv::utils::mkExtract(zext15x, 7, 0); - Node ext7y = bv::utils::mkExtract(zext15y, 7, 0); - Node ext7z = bv::utils::mkExtract(zext15z, 7, 0); - Node ext7u = bv::utils::mkExtract(zext15u, 7, 0); - Node ext7v = bv::utils::mkExtract(zext15v, 7, 0); - Node ext7w = bv::utils::mkExtract(zext15w, 7, 0); - Node ext7s = bv::utils::mkExtract(s, 7, 0); - Node ext15s = bv::utils::mkExtract(s, 15, 8); - - Node xx = bv::utils::mkConcat(bv::utils::mkZero(12), ext7x); - Node yy = bv::utils::mkConcat(bv::utils::mkZero(12), ext7y); - Node zz = bv::utils::mkConcat(bv::utils::mkZero(12), ext7z); - Node uu = bv::utils::mkConcat(bv::utils::mkZero(12), ext7u); - Node vv = bv::utils::mkConcat(bv::utils::mkZero(12), ext7v); - Node ww = bv::utils::mkConcat(bv::utils::mkZero(12), ext7w); - Node s7 = bv::utils::mkConcat(bv::utils::mkZero(12), ext7s); - Node s15 = bv::utils::mkConcat(bv::utils::mkZero(12), ext15s); - - Node plus1 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(20, 86), xx), - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(20, 41), yy)); - Node plus2 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus1, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(20, 37), zz)); - Node plus3 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus2, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(20, 170), uu)); - Node plus4 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus3, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(20, 112), uu)); - Node plus5 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus4, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(20, 195), s15)); - Node plus6 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus5, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(20, 124), s7)); - Node plus7 = d_nm->mkNode( - kind::BITVECTOR_PLUS, - plus6, - d_nm->mkNode(kind::BITVECTOR_MULT, bv::utils::mkConst(20, 83), ww)); - - TS_ASSERT(BVGauss::getMinBwExpr(plus7) == 19); - TS_ASSERT(BVGauss::getMinBwExpr(Rewriter::rewrite(plus7)) == 17); - } - -}; diff --git a/test/unit/test_node.h b/test/unit/test_node.h index 82064c67a..81d3e250a 100644 --- a/test/unit/test_node.h +++ b/test/unit/test_node.h @@ -1,5 +1,5 @@ /********************* */ -/*! \file test_expr.h +/*! \file test_node.h ** \verbatim ** Top contributors (to current version): ** Aina Niemetz @@ -19,7 +19,6 @@ #include "smt/smt_engine.h" #include "smt/smt_engine_scope.h" #include "test.h" -#include "test_api.h" namespace CVC4 { namespace test { -- 2.30.2