extendedlinearization.cpp

/*****************************************************************************
Copyright (C) 2018  Davin Choo, Kian Ming A. Chai, DSO National Laboratories

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#include <iomanip>
#include "extendedlinearization.hpp"
#include "anfutils.hpp"
#include "gaussjordan.hpp"

using std::vector;

using namespace BLib;

bool BLib::extendedLinearization(const ConfigData& config,
                           const vector<BoolePolynomial>& eqs,
                           vector<BoolePolynomial>& loop_learnt)
{
    if (eqs.empty()) {
        if (config.verbosity >= 3) {
            cout << "c System is empty. Skip XL\n";
        }
        return true;
    }

    double myTime = cpuTime();
    if (config.verbosity) {
        cout << "c [XL] Running XL... ring size: "
             << eqs.front().ring().nVariables() << endl;
    }

    const size_t loop_learnt_size_orig = loop_learnt.size();
    const polybori::BoolePolyRing& ring(eqs.front().ring());

    vector<BoolePolynomial> equations;
    map<uint32_t, vector<BoolePolynomial> > deg_buckets;
    unordered_set<uint32_t> unique_poly_degrees;
    vector<uint32_t> sorted_poly_degrees;

    // Get a copy;
    const size_t XLsample =
        config.XLsample + config.XLsampleX; // amount of expansion allowed
    double numUnique =
        sample_and_clone(config.verbosity, eqs, equations,
                         config.XLsample); // give some leeway for expansion

    // Put them into degree buckets
    for (const BoolePolynomial& poly : equations) {
        uint32_t poly_deg = poly.deg();
        unique_poly_degrees.insert(poly_deg);
        deg_buckets[poly_deg].push_back(poly);
    }
    sorted_poly_degrees.assign(unique_poly_degrees.begin(),
                               unique_poly_degrees.end());
    sort(sorted_poly_degrees.begin(), sorted_poly_degrees.end());

    // Expansion step
    bool done_expansion = false;
    unsigned long nVars = ring.nVariables();
    for (uint32_t deg = 1; deg <= config.xlDeg && !done_expansion; deg++) {
        for (uint32_t poly_deg : sorted_poly_degrees) {
            const vector<BoolePolynomial>& to_expand = deg_buckets[poly_deg];
            if (config.verbosity >= 3) {
                cout << "c  There are " << to_expand.size()
                     << " polynomials of degree " << poly_deg << endl;
            }
            for (const BoolePolynomial& poly : to_expand) {
                const double log2eqsz = log2(equations.size());
                if (log2eqsz + numUnique > XLsample) {
                    done_expansion = true;
                    break;
                } else {
                    // Ugly hack
                    // To do: Efficient implementation of "nVars choose xlDeg"
                    //        e.g. http://howardhinnant.github.io/combinations.html?
                    if (deg >= 1) {
                        //how many variables to be multiplied with
                        const size_t num_variables_allowed = std::min(
                            nVars,
                            static_cast<size_t>(ceil(exp(
                                log(2) * (XLsample - log2eqsz - numUnique)))));

                        if (config.verbosity >= 3 &&
                            num_variables_allowed < nVars
                        ) {
                            cout << "c  Allowing " << num_variables_allowed
                                 << " variables in degree one expansion\n";
                        }

                        if (num_variables_allowed == nVars) {
                            for (unsigned long i = 0; i < nVars; ++i) {
                                BooleVariable v = ring.variable(i);
                                equations.push_back(BoolePolynomial(v * poly));
                            }
                        } else {
                            if (config.verbosity >= 4) {
                                cout << "c   Adding variables [";
                            }

                            unsigned long i = 0;
                            for (size_t n = 0; n < num_variables_allowed; ++n) {
                                double p = (double)(num_variables_allowed - n) / (double)(nVars - i);
                                if (p == 0) {
                                    p = 0.01;
                                }
                                i += std::floor(
                                    std::log(((double)rand()/(double)RAND_MAX)) / std::log(1.0 - p)
                                );

                                if (i >= nVars) {
                                    i = nVars - 1;
                                }

                                if (config.verbosity >= 4) {
                                    cout << i << ' ';
                                }

                                BooleVariable v = ring.variable(i);
                                equations.push_back(BoolePolynomial(v * poly));
                            }
                            if (config.verbosity >= 4)
                                cout << "] in degree one expansion\n";
                        }
                        numUnique += log2(num_variables_allowed);
                    }

                    //When degree 2 expansion is allowed
                    if (deg >= 2) {
                        for (unsigned long i = 0; i < nVars; ++i) {
                            for (unsigned long j = i + 1; j < nVars; ++j) {
                                BooleVariable v1 = ring.variable(i);
                                BooleVariable v2 = ring.variable(j);
                                equations.push_back(
                                    BoolePolynomial(v1 * v2 * poly));
                            }
                        }
                        numUnique += 2 * log2(nVars) - 1;
                    }
                    if (deg >= 3) {
                        for (unsigned long i = 0; i < nVars; ++i) {
                            for (unsigned long j = i + 1; j < nVars; ++j) {
                                for (unsigned long k = j + 1; k < nVars; ++k) {
                                    BooleVariable v1 = ring.variable(i);
                                    BooleVariable v2 = ring.variable(j);
                                    BooleVariable v3 = ring.variable(k);
                                    equations.push_back(
                                        BoolePolynomial(v1 * v2 * v3 * poly));
                                }
                            }
                        }
                        numUnique += 3 * log2(nVars) - 2;
                    }
                }
            } //for poly
            if (done_expansion) {
                break;
            }
        } //for poly_deg
        if (done_expansion) {
            break;
        }
    } // for deg
    // Run GJE after expansion

    GaussJordan gj(equations, ring, config.verbosity);
    long num = gj.run(NULL, &loop_learnt);

    if (config.verbosity) {
        cout << "c [XL] Done. Learnt: "
             << (loop_learnt.size() - loop_learnt_size_orig)
             << " T: " << std::fixed << std::setprecision(2)
             << (cpuTime() - myTime) << endl;
    }

    return num != GaussJordan::BAD;
}