ezsat.cc

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/*
 *  ezSAT -- A simple and easy to use CNF generator for SAT solvers
 *
 *  Copyright (C) 2013  Clifford Wolf <clifford@clifford.at>
 *  
 *  Permission to use, copy, modify, and/or distribute this software for any
 *  purpose with or without fee is hereby granted, provided that the above
 *  copyright notice and this permission notice appear in all copies.
 *  
 *  THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 *  WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 *  MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 *  ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 *  WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 *  ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 *  OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 *
 */

#include "ezsat.h"

#include <cmath>
#include <algorithm>
#include <cassert>
#include <string>

#include <stdlib.h>

const int ezSAT::CONST_TRUE = 1;
const int ezSAT::CONST_FALSE = 2;

static std::string my_int_to_string(int i)
{
#ifdef __MINGW32__
    char buffer[64];
    snprintf(buffer, 64, "%d", i);
    return buffer;
#else
    return std::to_string(i);
#endif
}

ezSAT::ezSAT()
{
    flag_keep_cnf = false;
    flag_non_incremental = false;

    non_incremental_solve_used_up = false;

    cnfConsumed = false;
    cnfVariableCount = 0;
    cnfClausesCount = 0;

    solverTimeout = 0;
    solverTimoutStatus = false;

    literal("CONST_TRUE");
    literal("CONST_FALSE");

    assert(literal("CONST_TRUE") == CONST_TRUE);
    assert(literal("CONST_FALSE") == CONST_FALSE);
}

ezSAT::~ezSAT()
{
}

int ezSAT::value(bool val)
{
    return val ? CONST_TRUE : CONST_FALSE;
}

int ezSAT::literal()
{
    literals.push_back(std::string());
    return literals.size();
}

int ezSAT::literal(const std::string &name)
{
    if (literalsCache.count(name) == 0) {
        literals.push_back(name);
        literalsCache[name] = literals.size();
    }
    return literalsCache.at(name);
}

int ezSAT::frozen_literal()
{
    int id = literal();
    freeze(id);
    return id;
}

int ezSAT::frozen_literal(const std::string &name)
{
    int id = literal(name);
    freeze(id);
    return id;
}

int ezSAT::expression(OpId op, int a, int b, int c, int d, int e, int f)
{
    std::vector<int> args(6);
    args[0] = a, args[1] = b, args[2] = c;
    args[3] = d, args[4] = e, args[5] = f;
    return expression(op, args);
}

int ezSAT::expression(OpId op, const std::vector<int> &args)
{
    std::vector<int> myArgs;
    myArgs.reserve(args.size());
    bool xorRemovedOddTrues = false;

    for (auto arg : args)
    {
        if (arg == 0)
            continue;
        if (op == OpAnd && arg == CONST_TRUE)
            continue;
        if ((op == OpOr || op == OpXor) && arg == CONST_FALSE)
            continue;
        if (op == OpXor && arg == CONST_TRUE) {
            xorRemovedOddTrues = !xorRemovedOddTrues;
            continue;
        }
        myArgs.push_back(arg);
    }

    if (myArgs.size() > 0 && (op == OpAnd || op == OpOr || op == OpXor || op == OpIFF)) {
        std::sort(myArgs.begin(), myArgs.end());
        int j = 0;
        for (int i = 1; i < int(myArgs.size()); i++)
            if (j < 0 || myArgs[j] != myArgs[i])
                myArgs[++j] = myArgs[i];
            else if (op == OpXor)
                j--;
        myArgs.resize(j+1);
    }

    switch (op)
    {
    case OpNot:
        assert(myArgs.size() == 1);
        if (myArgs[0] == CONST_TRUE)
            return CONST_FALSE;
        if (myArgs[0] == CONST_FALSE)
            return CONST_TRUE;
        break;

    case OpAnd:
        if (myArgs.size() == 0)
            return CONST_TRUE;
        if (myArgs.size() == 1)
            return myArgs[0];
        break;

    case OpOr:
        if (myArgs.size() == 0)
            return CONST_FALSE;
        if (myArgs.size() == 1)
            return myArgs[0];
        break;

    case OpXor:
        if (myArgs.size() == 0)
            return xorRemovedOddTrues ? CONST_TRUE : CONST_FALSE;
        if (myArgs.size() == 1)
            return xorRemovedOddTrues ? NOT(myArgs[0]) : myArgs[0];
        break;

    case OpIFF:
        assert(myArgs.size() >= 1);
        if (myArgs.size() == 1)
            return CONST_TRUE;
        // FIXME: Add proper const folding
        break;

    case OpITE:
        assert(myArgs.size() == 3);
        if (myArgs[0] == CONST_TRUE)
            return myArgs[1];
        if (myArgs[0] == CONST_FALSE)
            return myArgs[2];
        break;

    default:
        abort();
    }

    std::pair<OpId, std::vector<int>> myExpr(op, myArgs);
    int id = 0;

    if (expressionsCache.count(myExpr) > 0) {
        id = expressionsCache.at(myExpr);
    } else {
        id = -(int(expressions.size()) + 1);
        expressionsCache[myExpr] = id;
        expressions.push_back(myExpr);
    }

    return xorRemovedOddTrues ? NOT(id) : id;
}

void ezSAT::lookup_literal(int id, std::string &name) const
{
    assert(0 < id && id <= int(literals.size()));
    name = literals[id - 1];
}

const std::string &ezSAT::lookup_literal(int id) const
{
    assert(0 < id && id <= int(literals.size()));
    return literals[id - 1];
}

void ezSAT::lookup_expression(int id, OpId &op, std::vector<int> &args) const
{
    assert(0 < -id && -id <= int(expressions.size()));
    op = expressions[-id - 1].first;
    args = expressions[-id - 1].second;
}

const std::vector<int> &ezSAT::lookup_expression(int id, OpId &op) const
{
    assert(0 < -id && -id <= int(expressions.size()));
    op = expressions[-id - 1].first;
    return expressions[-id - 1].second;
}

int ezSAT::parse_string(const std::string &)
{
    abort();
}

std::string ezSAT::to_string(int id) const
{
    std::string text;

    if (id > 0)
    {
        lookup_literal(id, text);
    }
    else
    {
        OpId op;
        std::vector<int> args;
        lookup_expression(id, op, args);

        switch (op)
        {
        case OpNot:
            text = "not(";
            break;

        case OpAnd:
            text = "and(";
            break;

        case OpOr:
            text = "or(";
            break;

        case OpXor:
            text = "xor(";
            break;

        case OpIFF:
            text = "iff(";
            break;

        case OpITE:
            text = "ite(";
            break;

        default:
            abort();
        }

        for (int i = 0; i < int(args.size()); i++) {
            if (i > 0)
                text += ", ";
            text += to_string(args[i]);
        }

        text += ")";
    }

    return text;
}

int ezSAT::eval(int id, const std::vector<int> &values) const
{
    if (id > 0) {
        if (id <= int(values.size()) && (values[id-1] == CONST_TRUE || values[id-1] == CONST_FALSE || values[id-1] == 0))
            return values[id-1];
        return 0;
    }

    OpId op;
    const std::vector<int> &args = lookup_expression(id, op);
    int a, b;

    switch (op)
    {
    case OpNot:
        assert(args.size() == 1);
        a = eval(args[0], values);
        if (a == CONST_TRUE)
            return CONST_FALSE;
        if (a == CONST_FALSE)
            return CONST_TRUE;
        return 0;
    case OpAnd:
        a = CONST_TRUE;
        for (auto arg : args) {
            b = eval(arg, values);
            if (b != CONST_TRUE && b != CONST_FALSE)
                a = 0;
            if (b == CONST_FALSE)
                return CONST_FALSE;
        }
        return a;
    case OpOr:
        a = CONST_FALSE;
        for (auto arg : args) {
            b = eval(arg, values);
            if (b != CONST_TRUE && b != CONST_FALSE)
                a = 0;
            if (b == CONST_TRUE)
                return CONST_TRUE;
        }
        return a;
    case OpXor:
        a = CONST_FALSE;
        for (auto arg : args) {
            b = eval(arg, values);
            if (b != CONST_TRUE && b != CONST_FALSE)
                return 0;
            if (b == CONST_TRUE)
                a = a == CONST_TRUE ? CONST_FALSE : CONST_TRUE;
        }
        return a;
    case OpIFF:
        assert(args.size() > 0);
        a = eval(args[0], values);
        for (auto arg : args) {
            b = eval(arg, values);
            if (b != CONST_TRUE && b != CONST_FALSE)
                return 0;
            if (b != a)
                return CONST_FALSE;
        }
        return CONST_TRUE;
    case OpITE:
        assert(args.size() == 3);
        a = eval(args[0], values);
        if (a == CONST_TRUE)
            return eval(args[1], values);
        if (a == CONST_FALSE)
            return eval(args[2], values);
        return 0;
    default:
        abort();
    }
}

void ezSAT::clear()
{
    cnfConsumed = false;
    cnfVariableCount = 0;
    cnfClausesCount = 0;
    cnfLiteralVariables.clear();
    cnfExpressionVariables.clear();
    cnfClauses.clear();
}

void ezSAT::freeze(int)
{
}

bool ezSAT::eliminated(int)
{
    return false;
}

void ezSAT::assume(int id)
{
    if (id < 0)
    {
        assert(0 < -id && -id <= int(expressions.size()));
        cnfExpressionVariables.resize(expressions.size());

        if (cnfExpressionVariables[-id-1] == 0)
        {
            OpId op;
            std::vector<int> args;
            lookup_expression(id, op, args);

            if (op == OpNot) {
                int idx = bind(args[0]);
                cnfClauses.push_back(std::vector<int>(1, -idx));
                cnfClausesCount++;
                return;
            }
            if (op == OpOr) {
                std::vector<int> clause;
                for (int arg : args)
                    clause.push_back(bind(arg));
                cnfClauses.push_back(clause);
                cnfClausesCount++;
                return;
            }
            if (op == OpAnd) {
                for (int arg : args) {
                    cnfClauses.push_back(std::vector<int>(1, bind(arg)));
                    cnfClausesCount++;
                }
                return;
            }
        }
    }

    int idx = bind(id);
    cnfClauses.push_back(std::vector<int>(1, idx));
    cnfClausesCount++;
}

void ezSAT::add_clause(const std::vector<int> &args)
{
    cnfClauses.push_back(args);
    cnfClausesCount++;
}

void ezSAT::add_clause(const std::vector<int> &args, bool argsPolarity, int a, int b, int c)
{
    std::vector<int> clause;
    for (auto arg : args)
        clause.push_back(argsPolarity ? +arg : -arg);
    if (a != 0)
        clause.push_back(a);
    if (b != 0)
        clause.push_back(b);
    if (c != 0)
        clause.push_back(c);
    add_clause(clause);
}

void ezSAT::add_clause(int a, int b, int c)
{
    std::vector<int> clause;
    if (a != 0)
        clause.push_back(a);
    if (b != 0)
        clause.push_back(b);
    if (c != 0)
        clause.push_back(c);
    add_clause(clause);
}

int ezSAT::bind_cnf_not(const std::vector<int> &args)
{
    assert(args.size() == 1);
    return -args[0];
}

int ezSAT::bind_cnf_and(const std::vector<int> &args)
{
    assert(args.size() >= 2);

    int idx = ++cnfVariableCount;
    add_clause(args, false, idx);

    for (auto arg : args)
        add_clause(-idx, arg);

    return idx;
}

int ezSAT::bind_cnf_or(const std::vector<int> &args)
{
    assert(args.size() >= 2);

    int idx = ++cnfVariableCount;
    add_clause(args, true, -idx);

    for (auto arg : args)
        add_clause(idx, -arg);

    return idx;
}

int ezSAT::bound(int id) const
{
    if (id > 0 && id <= int(cnfLiteralVariables.size()))
        return cnfLiteralVariables[id-1];
    if (-id > 0 && -id <= int(cnfExpressionVariables.size()))
        return cnfExpressionVariables[-id-1];
    return 0;
}

std::string ezSAT::cnfLiteralInfo(int idx) const
{
    for (int i = 0; i < int(cnfLiteralVariables.size()); i++) {
        if (cnfLiteralVariables[i] == idx)
            return to_string(i+1);
        if (cnfLiteralVariables[i] == -idx)
            return "NOT " + to_string(i+1);
    }
    for (int i = 0; i < int(cnfExpressionVariables.size()); i++) {
        if (cnfExpressionVariables[i] == idx)
            return to_string(-i-1);
        if (cnfExpressionVariables[i] == -idx)
            return "NOT " + to_string(-i-1);
    }
    return "<unnamed>";
}

int ezSAT::bind(int id, bool auto_freeze)
{
    if (id >= 0) {
        assert(0 < id && id <= int(literals.size()));
        cnfLiteralVariables.resize(literals.size());
        if (eliminated(cnfLiteralVariables[id-1])) {
            fprintf(stderr, "ezSAT: Missing freeze on literal `%s'.\n", to_string(id).c_str());
            abort();
        }
        if (cnfLiteralVariables[id-1] == 0) {
            cnfLiteralVariables[id-1] = ++cnfVariableCount;
            if (id == CONST_TRUE)
                add_clause(+cnfLiteralVariables[id-1]);
            if (id == CONST_FALSE)
                add_clause(-cnfLiteralVariables[id-1]);
        }
        return cnfLiteralVariables[id-1];
    }

    assert(0 < -id && -id <= int(expressions.size()));
    cnfExpressionVariables.resize(expressions.size());

    if (eliminated(cnfExpressionVariables[-id-1]))
    {
        cnfExpressionVariables[-id-1] = 0;

        // this will recursively call bind(id). within the recursion
        // the cnf is pre-set to 0. an idx is allocated there, then it
        // is frozen, then it returns here with the new idx already set.
        if (auto_freeze)
            freeze(id);
    }

    if (cnfExpressionVariables[-id-1] == 0)
    {
        OpId op;
        std::vector<int> args;
        lookup_expression(id, op, args);
        int idx = 0;

        if (op == OpXor) {
            while (args.size() > 1) {
                std::vector<int> newArgs;
                for (int i = 0; i < int(args.size()); i += 2)
                    if (i+1 == int(args.size()))
                        newArgs.push_back(args[i]);
                    else
                        newArgs.push_back(OR(AND(args[i], NOT(args[i+1])), AND(NOT(args[i]), args[i+1])));
                args.swap(newArgs);
            }
            idx = bind(args.at(0), false);
            goto assign_idx;
        }

        if (op == OpIFF) {
            std::vector<int> invArgs;
            for (auto arg : args)
                invArgs.push_back(NOT(arg));
            idx = bind(OR(expression(OpAnd, args), expression(OpAnd, invArgs)), false);
            goto assign_idx;
        }

        if (op == OpITE) {
            idx = bind(OR(AND(args[0], args[1]), AND(NOT(args[0]), args[2])), false);
            goto assign_idx;
        }

        for (int i = 0; i < int(args.size()); i++)
            args[i] = bind(args[i], false);

        switch (op)
        {
            case OpNot: idx = bind_cnf_not(args); break;
            case OpAnd: idx = bind_cnf_and(args); break;
            case OpOr:  idx = bind_cnf_or(args);  break;
            default: abort();
        }

    assign_idx:
        assert(idx != 0);
        cnfExpressionVariables[-id-1] = idx;
    }

    return cnfExpressionVariables[-id-1];
}

void ezSAT::consumeCnf()
{
    if (mode_keep_cnf())
        cnfClausesBackup.insert(cnfClausesBackup.end(), cnfClauses.begin(), cnfClauses.end());
    else
        cnfConsumed = true;
    cnfClauses.clear();
}

void ezSAT::consumeCnf(std::vector<std::vector<int>> &cnf)
{
    if (mode_keep_cnf())
        cnfClausesBackup.insert(cnfClausesBackup.end(), cnfClauses.begin(), cnfClauses.end());
    else
        cnfConsumed = true;
    cnf.swap(cnfClauses);
    cnfClauses.clear();
}

void ezSAT::getFullCnf(std::vector<std::vector<int>> &full_cnf) const
{
    assert(full_cnf.empty());
    full_cnf.insert(full_cnf.end(), cnfClausesBackup.begin(), cnfClausesBackup.end());
    full_cnf.insert(full_cnf.end(), cnfClauses.begin(), cnfClauses.end());
}

void ezSAT::preSolverCallback()
{
    assert(!non_incremental_solve_used_up);
    if (mode_non_incremental())
        non_incremental_solve_used_up = true;
}

bool ezSAT::solver(const std::vector<int>&, std::vector<bool>&, const std::vector<int>&)
{
    preSolverCallback();
    fprintf(stderr, "************************************************************************\n");
    fprintf(stderr, "ERROR: You are trying to use the solve() method of the ezSAT base class!\n");
    fprintf(stderr, "Use a dervied class like ezMiniSAT instead.\n");
    fprintf(stderr, "************************************************************************\n");
    abort();
}

std::vector<int> ezSAT::vec_const(const std::vector<bool> &bits)
{
    std::vector<int> vec;
    for (auto bit : bits)
        vec.push_back(bit ? CONST_TRUE : CONST_FALSE);
    return vec;
}

std::vector<int> ezSAT::vec_const_signed(int64_t value, int numBits)
{
    std::vector<int> vec;
    for (int i = 0; i < numBits; i++)
        vec.push_back(((value >> i) & 1) != 0 ? CONST_TRUE : CONST_FALSE);
    return vec;
}

std::vector<int> ezSAT::vec_const_unsigned(uint64_t value, int numBits)
{
    std::vector<int> vec;
    for (int i = 0; i < numBits; i++)
        vec.push_back(((value >> i) & 1) != 0 ? CONST_TRUE : CONST_FALSE);
    return vec;
}

std::vector<int> ezSAT::vec_var(int numBits)
{
    std::vector<int> vec;
    for (int i = 0; i < numBits; i++)
        vec.push_back(literal());
    return vec;
}

std::vector<int> ezSAT::vec_var(std::string name, int numBits)
{
    std::vector<int> vec;
    for (int i = 0; i < numBits; i++) {
        vec.push_back(VAR(name + my_int_to_string(i)));
    }
    return vec;
}

std::vector<int> ezSAT::vec_cast(const std::vector<int> &vec1, int toBits, bool signExtend)
{
    std::vector<int> vec;
    for (int i = 0; i < toBits; i++)
        if (i >= int(vec1.size()))
            vec.push_back(signExtend ? vec1.back() : CONST_FALSE);
        else
            vec.push_back(vec1[i]);
    return vec;
}

std::vector<int> ezSAT::vec_not(const std::vector<int> &vec1)
{
    std::vector<int> vec;
    for (auto bit : vec1)
        vec.push_back(NOT(bit));
    return vec;
}

std::vector<int> ezSAT::vec_and(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    assert(vec1.size() == vec2.size());
    std::vector<int> vec(vec1.size());
    for (int i = 0; i < int(vec1.size()); i++)
        vec[i] = AND(vec1[i], vec2[i]);
    return vec;
}

std::vector<int> ezSAT::vec_or(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    assert(vec1.size() == vec2.size());
    std::vector<int> vec(vec1.size());
    for (int i = 0; i < int(vec1.size()); i++)
        vec[i] = OR(vec1[i], vec2[i]);
    return vec;
}

std::vector<int> ezSAT::vec_xor(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    assert(vec1.size() == vec2.size());
    std::vector<int> vec(vec1.size());
    for (int i = 0; i < int(vec1.size()); i++)
        vec[i] = XOR(vec1[i], vec2[i]);
    return vec;
}

std::vector<int> ezSAT::vec_iff(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    assert(vec1.size() == vec2.size());
    std::vector<int> vec(vec1.size());
    for (int i = 0; i < int(vec1.size()); i++)
        vec[i] = IFF(vec1[i], vec2[i]);
    return vec;
}

std::vector<int> ezSAT::vec_ite(const std::vector<int> &vec1, const std::vector<int> &vec2, const std::vector<int> &vec3)
{
    assert(vec1.size() == vec2.size() && vec2.size() == vec3.size());
    std::vector<int> vec(vec1.size());
    for (int i = 0; i < int(vec1.size()); i++)
        vec[i] = ITE(vec1[i], vec2[i], vec3[i]);
    return vec;
}


std::vector<int> ezSAT::vec_ite(int sel, const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    assert(vec1.size() == vec2.size());
    std::vector<int> vec(vec1.size());
    for (int i = 0; i < int(vec1.size()); i++)
        vec[i] = ITE(sel, vec1[i], vec2[i]);
    return vec;
}

// 'y' is the MSB (carry) and x the LSB (sum) output
static void fulladder(ezSAT *that, int a, int b, int c, int &y, int &x)
{
    int tmp = that->XOR(a, b);
    int new_x = that->XOR(tmp, c);
    int new_y = that->OR(that->AND(a, b), that->AND(c, tmp));
#if 0
    printf("FULLADD> a=%s, b=%s, c=%s, carry=%s, sum=%s\n", that->to_string(a).c_str(), that->to_string(b).c_str(),
            that->to_string(c).c_str(), that->to_string(new_y).c_str(), that->to_string(new_x).c_str());
#endif
    x = new_x, y = new_y;
}

// 'y' is the MSB (carry) and x the LSB (sum) output
static void halfadder(ezSAT *that, int a, int b, int &y, int &x)
{
    int new_x = that->XOR(a, b);
    int new_y = that->AND(a, b);
#if 0
    printf("HALFADD> a=%s, b=%s, carry=%s, sum=%s\n", that->to_string(a).c_str(), that->to_string(b).c_str(),
            that->to_string(new_y).c_str(), that->to_string(new_x).c_str());
#endif
    x = new_x, y = new_y;
}

std::vector<int> ezSAT::vec_count(const std::vector<int> &vec, int numBits, bool clip)
{
    std::vector<int> sum = vec_const_unsigned(0, numBits);
    std::vector<int> carry_vector;

    for (auto bit : vec) {
        int carry = bit;
        for (int i = 0; i < numBits; i++)
            halfadder(this, carry, sum[i], carry, sum[i]);
        carry_vector.push_back(carry);
    }

    if (clip) {
        int overflow = vec_reduce_or(carry_vector);
        sum = vec_ite(overflow, vec_const_unsigned(~0, numBits), sum);
    }

#if 0
    printf("COUNT> vec=[");
    for (int i = int(vec.size())-1; i >= 0; i--)
        printf("%s%s", to_string(vec[i]).c_str(), i ? ", " : "");
    printf("], result=[");
    for (int i = int(sum.size())-1; i >= 0; i--)
        printf("%s%s", to_string(sum[i]).c_str(), i ? ", " : "");
    printf("]\n");
#endif

    return sum;
}

std::vector<int> ezSAT::vec_add(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    assert(vec1.size() == vec2.size());
    std::vector<int> vec(vec1.size());
    int carry = CONST_FALSE;
    for (int i = 0; i < int(vec1.size()); i++)
        fulladder(this, vec1[i], vec2[i], carry, carry, vec[i]);

#if 0
    printf("ADD> vec1=[");
    for (int i = int(vec1.size())-1; i >= 0; i--)
        printf("%s%s", to_string(vec1[i]).c_str(), i ? ", " : "");
    printf("], vec2=[");
    for (int i = int(vec2.size())-1; i >= 0; i--)
        printf("%s%s", to_string(vec2[i]).c_str(), i ? ", " : "");
    printf("], result=[");
    for (int i = int(vec.size())-1; i >= 0; i--)
        printf("%s%s", to_string(vec[i]).c_str(), i ? ", " : "");
    printf("]\n");
#endif

    return vec;
}

std::vector<int> ezSAT::vec_sub(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    assert(vec1.size() == vec2.size());
    std::vector<int> vec(vec1.size());
    int carry = CONST_TRUE;
    for (int i = 0; i < int(vec1.size()); i++)
        fulladder(this, vec1[i], NOT(vec2[i]), carry, carry, vec[i]);

#if 0
    printf("SUB> vec1=[");
    for (int i = int(vec1.size())-1; i >= 0; i--)
        printf("%s%s", to_string(vec1[i]).c_str(), i ? ", " : "");
    printf("], vec2=[");
    for (int i = int(vec2.size())-1; i >= 0; i--)
        printf("%s%s", to_string(vec2[i]).c_str(), i ? ", " : "");
    printf("], result=[");
    for (int i = int(vec.size())-1; i >= 0; i--)
        printf("%s%s", to_string(vec[i]).c_str(), i ? ", " : "");
    printf("]\n");
#endif

    return vec;
}

std::vector<int> ezSAT::vec_neg(const std::vector<int> &vec)
{
    std::vector<int> zero(vec.size(), CONST_FALSE);
    return vec_sub(zero, vec);
}

void ezSAT::vec_cmp(const std::vector<int> &vec1, const std::vector<int> &vec2, int &carry, int &overflow, int &sign, int &zero)
{
    assert(vec1.size() == vec2.size());
    carry = CONST_TRUE;
    zero = CONST_FALSE;
    for (int i = 0; i < int(vec1.size()); i++) {
        overflow = carry;
        fulladder(this, vec1[i], NOT(vec2[i]), carry, carry, sign);
        zero = OR(zero, sign);
    }
    overflow = XOR(overflow, carry);
    carry = NOT(carry);
    zero = NOT(zero);

#if 0
    printf("CMP> vec1=[");
    for (int i = int(vec1.size())-1; i >= 0; i--)
        printf("%s%s", to_string(vec1[i]).c_str(), i ? ", " : "");
    printf("], vec2=[");
    for (int i = int(vec2.size())-1; i >= 0; i--)
        printf("%s%s", to_string(vec2[i]).c_str(), i ? ", " : "");
    printf("], carry=%s, overflow=%s, sign=%s, zero=%s\n", to_string(carry).c_str(), to_string(overflow).c_str(), to_string(sign).c_str(), to_string(zero).c_str());
#endif
}

int ezSAT::vec_lt_signed(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    int carry, overflow, sign, zero;
    vec_cmp(vec1, vec2, carry, overflow, sign, zero);
    return OR(AND(NOT(overflow), sign), AND(overflow, NOT(sign)));
}

int ezSAT::vec_le_signed(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    int carry, overflow, sign, zero;
    vec_cmp(vec1, vec2, carry, overflow, sign, zero);
    return OR(AND(NOT(overflow), sign), AND(overflow, NOT(sign)), zero);
}

int ezSAT::vec_ge_signed(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    int carry, overflow, sign, zero;
    vec_cmp(vec1, vec2, carry, overflow, sign, zero);
    return OR(AND(NOT(overflow), NOT(sign)), AND(overflow, sign));
}

int ezSAT::vec_gt_signed(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    int carry, overflow, sign, zero;
    vec_cmp(vec1, vec2, carry, overflow, sign, zero);
    return AND(OR(AND(NOT(overflow), NOT(sign)), AND(overflow, sign)), NOT(zero));
}

int ezSAT::vec_lt_unsigned(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    int carry, overflow, sign, zero;
    vec_cmp(vec1, vec2, carry, overflow, sign, zero);
    return carry;
}

int ezSAT::vec_le_unsigned(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    int carry, overflow, sign, zero;
    vec_cmp(vec1, vec2, carry, overflow, sign, zero);
    return OR(carry, zero);
}

int ezSAT::vec_ge_unsigned(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    int carry, overflow, sign, zero;
    vec_cmp(vec1, vec2, carry, overflow, sign, zero);
    return NOT(carry);
}

int ezSAT::vec_gt_unsigned(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    int carry, overflow, sign, zero;
    vec_cmp(vec1, vec2, carry, overflow, sign, zero);
    return AND(NOT(carry), NOT(zero));
}

int ezSAT::vec_eq(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    return vec_reduce_and(vec_iff(vec1, vec2));
}

int ezSAT::vec_ne(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    return NOT(vec_reduce_and(vec_iff(vec1, vec2)));
}

std::vector<int> ezSAT::vec_shl(const std::vector<int> &vec1, int shift, bool signExtend)
{
    std::vector<int> vec;
    for (int i = 0; i < int(vec1.size()); i++) {
        int j = i-shift;
        if (int(vec1.size()) <= j)
            vec.push_back(signExtend ? vec1.back() : CONST_FALSE);
        else if (0 <= j)
            vec.push_back(vec1[j]);
        else
            vec.push_back(CONST_FALSE);
    }
    return vec;
}

std::vector<int> ezSAT::vec_srl(const std::vector<int> &vec1, int shift)
{
    std::vector<int> vec;
    for (int i = 0; i < int(vec1.size()); i++) {
        int j = i-shift;
        while (j < 0)
            j += vec1.size();
        while (j >= int(vec1.size()))
            j -= vec1.size();
        vec.push_back(vec1[j]);
    }
    return vec;
}

std::vector<int> ezSAT::vec_shift(const std::vector<int> &vec1, int shift, int extend_left, int extend_right)
{
    std::vector<int> vec;
    for (int i = 0; i < int(vec1.size()); i++) {
        int j = i+shift;
        if (j < 0)
            vec.push_back(extend_right);
        else if (j >= int(vec1.size()))
            vec.push_back(extend_left);
        else
            vec.push_back(vec1[j]);
    }
    return vec;
}

static int my_clog2(int x)
{
    int result = 0;
    for (x--; x > 0; result++)
        x >>= 1;
    return result;
}

std::vector<int> ezSAT::vec_shift_right(const std::vector<int> &vec1, const std::vector<int> &vec2, bool vec2_signed, int extend_left, int extend_right)
{
    int vec2_bits = std::min(my_clog2(vec1.size()) + (vec2_signed ? 1 : 0), int(vec2.size()));

    std::vector<int> overflow_bits(vec2.begin() + vec2_bits, vec2.end());
    int overflow_left = CONST_FALSE, overflow_right = CONST_FALSE;

    if (vec2_signed) {
        int overflow = CONST_FALSE;
        for (auto bit : overflow_bits)
            overflow = OR(overflow, XOR(bit, vec2[vec2_bits-1]));
        overflow_left = AND(overflow, NOT(vec2.back()));
        overflow_right = AND(overflow, vec2.back());
    } else
        overflow_left = vec_reduce_or(overflow_bits);

    std::vector<int> buffer = vec1;

    if (vec2_signed)
        while (buffer.size() < vec1.size() + (1 << vec2_bits))
            buffer.push_back(extend_left);

    std::vector<int> overflow_pattern_left(buffer.size(), extend_left);
    std::vector<int> overflow_pattern_right(buffer.size(), extend_right);

    buffer = vec_ite(overflow_left, overflow_pattern_left, buffer);

    if (vec2_signed)
        buffer = vec_ite(overflow_right, overflow_pattern_left, buffer);

    for (int i = vec2_bits-1; i >= 0; i--) {
        std::vector<int> shifted_buffer;
        if (vec2_signed && i == vec2_bits-1)
            shifted_buffer = vec_shift(buffer, -(1 << i), extend_left, extend_right);
        else
            shifted_buffer = vec_shift(buffer, 1 << i, extend_left, extend_right);
        buffer = vec_ite(vec2[i], shifted_buffer, buffer);
    }

    buffer.resize(vec1.size());
    return buffer;
}

std::vector<int> ezSAT::vec_shift_left(const std::vector<int> &vec1, const std::vector<int> &vec2, bool vec2_signed, int extend_left, int extend_right)
{
    // vec2_signed is not implemented in vec_shift_left() yet
    assert(vec2_signed == false);

    int vec2_bits = std::min(my_clog2(vec1.size()), int(vec2.size()));

    std::vector<int> overflow_bits(vec2.begin() + vec2_bits, vec2.end());
    int overflow = vec_reduce_or(overflow_bits);

    std::vector<int> buffer = vec1;
    std::vector<int> overflow_pattern_right(buffer.size(), extend_right);
    buffer = vec_ite(overflow, overflow_pattern_right, buffer);

    for (int i = 0; i < vec2_bits; i++) {
        std::vector<int> shifted_buffer;
        shifted_buffer = vec_shift(buffer, -(1 << i), extend_left, extend_right);
        buffer = vec_ite(vec2[i], shifted_buffer, buffer);
    }

    buffer.resize(vec1.size());
    return buffer;
}

void ezSAT::vec_append(std::vector<int> &vec, const std::vector<int> &vec1) const
{
    for (auto bit : vec1)
        vec.push_back(bit);
}

void ezSAT::vec_append_signed(std::vector<int> &vec, const std::vector<int> &vec1, int64_t value)
{
    assert(int(vec1.size()) <= 64);
    for (int i = 0; i < int(vec1.size()); i++) {
        if (((value >> i) & 1) != 0)
            vec.push_back(vec1[i]);
        else
            vec.push_back(NOT(vec1[i]));
    }
}

void ezSAT::vec_append_unsigned(std::vector<int> &vec, const std::vector<int> &vec1, uint64_t value)
{
    assert(int(vec1.size()) <= 64);
    for (int i = 0; i < int(vec1.size()); i++) {
        if (((value >> i) & 1) != 0)
            vec.push_back(vec1[i]);
        else
            vec.push_back(NOT(vec1[i]));
    }
}

int64_t ezSAT::vec_model_get_signed(const std::vector<int> &modelExpressions, const std::vector<bool> &modelValues, const std::vector<int> &vec1) const
{
    int64_t value = 0;
    std::map<int, bool> modelMap;
    assert(modelExpressions.size() == modelValues.size());
    for (int i = 0; i < int(modelExpressions.size()); i++)
        modelMap[modelExpressions[i]] = modelValues[i];
    for (int i = 0; i < 64; i++) {
        int j = i < int(vec1.size()) ? i : vec1.size()-1;
        if (modelMap.at(vec1[j]))
            value |= int64_t(1) << i;
    }
    return value;
}

uint64_t ezSAT::vec_model_get_unsigned(const std::vector<int> &modelExpressions, const std::vector<bool> &modelValues, const std::vector<int> &vec1) const
{
    uint64_t value = 0;
    std::map<int, bool> modelMap;
    assert(modelExpressions.size() == modelValues.size());
    for (int i = 0; i < int(modelExpressions.size()); i++)
        modelMap[modelExpressions[i]] = modelValues[i];
    for (int i = 0; i < int(vec1.size()); i++)
        if (modelMap.at(vec1[i]))
            value |= uint64_t(1) << i;
    return value;
}

int ezSAT::vec_reduce_and(const std::vector<int> &vec1)
{
    return expression(OpAnd, vec1);
}

int ezSAT::vec_reduce_or(const std::vector<int> &vec1)
{
    return expression(OpOr, vec1);
}

void ezSAT::vec_set(const std::vector<int> &vec1, const std::vector<int> &vec2)
{
    assert(vec1.size() == vec2.size());
    for (int i = 0; i < int(vec1.size()); i++)
        SET(vec1[i], vec2[i]);
}

void ezSAT::vec_set_signed(const std::vector<int> &vec1, int64_t value)
{
    assert(int(vec1.size()) <= 64);
    for (int i = 0; i < int(vec1.size()); i++) {
        if (((value >> i) & 1) != 0)
            assume(vec1[i]);
        else
            assume(NOT(vec1[i]));
    }
}

void ezSAT::vec_set_unsigned(const std::vector<int> &vec1, uint64_t value)
{
    assert(int(vec1.size()) <= 64);
    for (int i = 0; i < int(vec1.size()); i++) {
        if (((value >> i) & 1) != 0)
            assume(vec1[i]);
        else
            assume(NOT(vec1[i]));
    }
}

ezSATbit ezSAT::bit(_V a)
{
    return ezSATbit(*this, a);
}

ezSATvec ezSAT::vec(const std::vector<int> &vec)
{
    return ezSATvec(*this, vec);
}

void ezSAT::printDIMACS(FILE *f, bool verbose) const
{
    if (cnfConsumed) {
        fprintf(stderr, "Usage error: printDIMACS() must not be called after cnfConsumed()!");
        abort();
    }

    int digits = ceil(log10f(cnfVariableCount)) + 2;

    fprintf(f, "c generated by ezSAT\n");

    if (verbose)
    {
        fprintf(f, "c\n");
        fprintf(f, "c mapping of variables to literals:\n");
        for (int i = 0; i < int(cnfLiteralVariables.size()); i++)
            if (cnfLiteralVariables[i] != 0)
                fprintf(f, "c %*d: %s\n", digits, cnfLiteralVariables[i], literals[i].c_str());

        fprintf(f, "c\n");
        fprintf(f, "c mapping of variables to expressions:\n");
        for (int i = 0; i < int(cnfExpressionVariables.size()); i++)
            if (cnfExpressionVariables[i] != 0)
                fprintf(f, "c %*d: %d\n", digits, cnfExpressionVariables[i], -i-1);

        if (mode_keep_cnf()) {
            fprintf(f, "c\n");
            fprintf(f, "c %d clauses from backup, %d from current buffer\n",
                    int(cnfClausesBackup.size()), int(cnfClauses.size()));
        }

        fprintf(f, "c\n");
    }

    std::vector<std::vector<int>> all_clauses;
    getFullCnf(all_clauses);
    assert(cnfClausesCount == int(all_clauses.size()));

    fprintf(f, "p cnf %d %d\n", cnfVariableCount, cnfClausesCount);
    int maxClauseLen = 0;
    for (auto &clause : all_clauses)
        maxClauseLen = std::max(int(clause.size()), maxClauseLen);
    if (!verbose)
        maxClauseLen = std::min(maxClauseLen, 3);
    for (auto &clause : all_clauses) {
        for (auto idx : clause)
            fprintf(f, " %*d", digits, idx);
        if (maxClauseLen >= int(clause.size()))
            fprintf(f, " %*d\n", (digits + 1)*int(maxClauseLen - clause.size()) + digits, 0);
        else
            fprintf(f, " %*d\n", digits, 0);
    }
}

static std::string expression2str(const std::pair<ezSAT::OpId, std::vector<int>> &data)
{
    std::string text;
    switch (data.first) {
#define X(op) case ezSAT::op: text += #op; break;
        X(OpNot)
        X(OpAnd)
        X(OpOr)
        X(OpXor)
        X(OpIFF)
        X(OpITE)
    default:
        abort();
#undef X
    }
    text += ":";
    for (auto it : data.second)
        text += " " + my_int_to_string(it);
    return text;
}

void ezSAT::printInternalState(FILE *f) const
{
    fprintf(f, "--8<-- snip --8<--\n");

    fprintf(f, "literalsCache:\n");
    for (auto &it : literalsCache)
        fprintf(f, "    `%s' -> %d\n", it.first.c_str(), it.second);

    fprintf(f, "literals:\n");
    for (int i = 0; i < int(literals.size()); i++)
        fprintf(f, "    %d: `%s'\n", i+1, literals[i].c_str());

    fprintf(f, "expressionsCache:\n");
    for (auto &it : expressionsCache)
        fprintf(f, "    `%s' -> %d\n", expression2str(it.first).c_str(), it.second);

    fprintf(f, "expressions:\n");
    for (int i = 0; i < int(expressions.size()); i++)
        fprintf(f, "    %d: `%s'\n", -i-1, expression2str(expressions[i]).c_str());

    fprintf(f, "cnfVariables (count=%d):\n", cnfVariableCount);
    for (int i = 0; i < int(cnfLiteralVariables.size()); i++)
        if (cnfLiteralVariables[i] != 0)
            fprintf(f, "    literal %d -> %d (%s)\n", i+1, cnfLiteralVariables[i], to_string(i+1).c_str());
    for (int i = 0; i < int(cnfExpressionVariables.size()); i++)
        if (cnfExpressionVariables[i] != 0)
            fprintf(f, "    expression %d -> %d (%s)\n", -i-1, cnfExpressionVariables[i], to_string(-i-1).c_str());

    fprintf(f, "cnfClauses:\n");
    for (auto &i1 : cnfClauses) {
        for (auto &i2 : i1)
            fprintf(f, " %4d", i2);
        fprintf(f, "\n");
    }
    if (cnfConsumed)
        fprintf(f, " *** more clauses consumed via cnfConsume() ***\n");

    fprintf(f, "--8<-- snap --8<--\n");
}

int ezSAT::onehot(const std::vector<int> &vec, bool max_only)
{
    // Mixed one-hot/binary encoding as described by Claessen in Sec. 4.2 of
    // "Successful SAT Encoding Techniques. Magnus Bjiirk. 25th July 2009".
    // http://jsat.ewi.tudelft.nl/addendum/Bjork_encoding.pdf

    std::vector<int> formula;

    // add at-leat-one constraint
    if (max_only == false)
        formula.push_back(expression(OpOr, vec));

    // create binary vector
    int num_bits = ceil(log2(vec.size()));
    std::vector<int> bits;
    for (int k = 0; k < num_bits; k++)
        bits.push_back(literal());

    // add at-most-one clauses using binary encoding
    for (size_t i = 0; i < vec.size(); i++)
        for (int k = 0; k < num_bits; k++) {
            std::vector<int> clause;
            clause.push_back(NOT(vec[i]));
            clause.push_back((i & (1 << k)) != 0 ? bits[k] : NOT(bits[k]));
            formula.push_back(expression(OpOr, clause));
        }

    return expression(OpAnd, formula);
}

int ezSAT::manyhot(const std::vector<int> &vec, int min_hot, int max_hot)
{
    // many-hot encoding using a simple sorting network

    if (max_hot < 0)
        max_hot = min_hot;
    
    std::vector<int> formula;
    int M = max_hot+1, N = vec.size();
    std::map<std::pair<int,int>, int> x;

    for (int i = -1; i < N; i++)
    for (int j = -1; j < M; j++)
        x[std::pair<int,int>(i,j)] = j < 0 ? CONST_TRUE : i < 0 ? CONST_FALSE : literal();

    for (int i = 0; i < N; i++)
    for (int j = 0; j < M; j++) {
        formula.push_back(OR(NOT(vec[i]), x[std::pair<int,int>(i-1,j-1)], NOT(x[std::pair<int,int>(i,j)])));
        formula.push_back(OR(NOT(vec[i]), NOT(x[std::pair<int,int>(i-1,j-1)]), x[std::pair<int,int>(i,j)]));
        formula.push_back(OR(vec[i], x[std::pair<int,int>(i-1,j)], NOT(x[std::pair<int,int>(i,j)])));
        formula.push_back(OR(vec[i], NOT(x[std::pair<int,int>(i-1,j)]), x[std::pair<int,int>(i,j)]));
#if 0
        // explicit resolution clauses -- in tests it was better to let the sat solver figure those out
        formula.push_back(OR(NOT(x[std::pair<int,int>(i-1,j-1)]), NOT(x[std::pair<int,int>(i-1,j)]), x[std::pair<int,int>(i,j)]));
        formula.push_back(OR(x[std::pair<int,int>(i-1,j-1)], x[std::pair<int,int>(i-1,j)], NOT(x[std::pair<int,int>(i,j)])));
#endif
    }

    for (int j = 0; j < M; j++) {
        if (j+1 <= min_hot)
            formula.push_back(x[std::pair<int,int>(N-1,j)]);
        else if (j+1 > max_hot)
            formula.push_back(NOT(x[std::pair<int,int>(N-1,j)]));
    }

    return expression(OpAnd, formula);
}

int ezSAT::ordered(const std::vector<int> &vec1, const std::vector<int> &vec2, bool allow_equal)
{
    std::vector<int> formula;
    int last_x = CONST_FALSE;

    assert(vec1.size() == vec2.size());
    for (size_t i = 0; i < vec1.size(); i++)
    {
        int a = vec1[i], b = vec2[i];
        formula.push_back(OR(NOT(a), b, last_x));

        int next_x = i+1 < vec1.size() ? literal() : allow_equal ? CONST_FALSE : CONST_TRUE;
        formula.push_back(OR(a, b, last_x, NOT(next_x)));
        formula.push_back(OR(NOT(a), NOT(b), last_x, NOT(next_x)));
        last_x = next_x;
    }

    return expression(OpAnd, formula);
}