mirror of https://github.com/YosysHQ/yosys.git
1262 lines
32 KiB
C++
1262 lines
32 KiB
C++
/*
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* ezSAT -- A simple and easy to use CNF generator for SAT solvers
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*
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* Copyright (C) 2013 Clifford Wolf <clifford@clifford.at>
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*
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* Permission to use, copy, modify, and/or distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*
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*/
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#include "ezsat.h"
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#include <algorithm>
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#include <stdlib.h>
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#include <assert.h>
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ezSAT::ezSAT()
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{
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literal("TRUE");
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literal("FALSE");
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assert(literal("TRUE") == TRUE);
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assert(literal("FALSE") == FALSE);
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cnfConsumed = false;
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cnfVariableCount = 0;
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cnfClausesCount = 0;
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}
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ezSAT::~ezSAT()
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{
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}
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int ezSAT::value(bool val)
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{
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return val ? TRUE : FALSE;
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}
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int ezSAT::literal()
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{
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literals.push_back(std::string());
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return literals.size();
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}
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int ezSAT::literal(const std::string &name)
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{
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if (literalsCache.count(name) == 0) {
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literals.push_back(name);
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literalsCache[name] = literals.size();
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}
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return literalsCache.at(name);
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}
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int ezSAT::expression(OpId op, int a, int b, int c, int d, int e, int f)
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{
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std::vector<int> args(6);
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args[0] = a, args[1] = b, args[2] = c;
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args[3] = d, args[4] = e, args[5] = f;
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return expression(op, args);
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}
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int ezSAT::expression(OpId op, const std::vector<int> &args)
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{
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std::vector<int> myArgs;
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myArgs.reserve(args.size());
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bool xorRemovedOddTrues = false;
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for (auto arg : args)
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{
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if (arg == 0)
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continue;
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if (op == OpAnd && arg == TRUE)
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continue;
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if ((op == OpOr || op == OpXor) && arg == FALSE)
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continue;
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if (op == OpXor && arg == TRUE) {
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xorRemovedOddTrues = !xorRemovedOddTrues;
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continue;
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}
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myArgs.push_back(arg);
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}
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if (myArgs.size() > 0 && (op == OpAnd || op == OpOr || op == OpXor || op == OpIFF)) {
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std::sort(myArgs.begin(), myArgs.end());
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int j = 0;
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for (int i = 1; i < int(myArgs.size()); i++)
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if (j < 0 || myArgs[j] != myArgs[i])
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myArgs[++j] = myArgs[i];
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else if (op == OpXor)
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j--;
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myArgs.resize(j+1);
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}
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switch (op)
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{
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case OpNot:
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assert(myArgs.size() == 1);
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if (myArgs[0] == TRUE)
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return FALSE;
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if (myArgs[0] == FALSE)
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return TRUE;
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break;
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case OpAnd:
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if (myArgs.size() == 0)
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return TRUE;
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if (myArgs.size() == 1)
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return myArgs[0];
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break;
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case OpOr:
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if (myArgs.size() == 0)
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return FALSE;
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if (myArgs.size() == 1)
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return myArgs[0];
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break;
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case OpXor:
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if (myArgs.size() == 0)
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return xorRemovedOddTrues ? TRUE : FALSE;
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if (myArgs.size() == 1)
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return xorRemovedOddTrues ? NOT(myArgs[0]) : myArgs[0];
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break;
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case OpIFF:
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assert(myArgs.size() >= 1);
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if (myArgs.size() == 1)
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return TRUE;
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// FIXME: Add proper const folding
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break;
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case OpITE:
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assert(myArgs.size() == 3);
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if (myArgs[0] == TRUE)
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return myArgs[1];
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if (myArgs[0] == FALSE)
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return myArgs[2];
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break;
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default:
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abort();
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}
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std::pair<OpId, std::vector<int>> myExpr(op, myArgs);
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int id = 0;
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if (expressionsCache.count(myExpr) > 0) {
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id = expressionsCache.at(myExpr);
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} else {
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id = -(expressions.size() + 1);
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expressionsCache[myExpr] = id;
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expressions.push_back(myExpr);
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}
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return xorRemovedOddTrues ? NOT(id) : id;
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}
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void ezSAT::lookup_literal(int id, std::string &name) const
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{
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assert(0 < id && id <= int(literals.size()));
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name = literals[id - 1];
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}
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const std::string &ezSAT::lookup_literal(int id) const
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{
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assert(0 < id && id <= int(literals.size()));
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return literals[id - 1];
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}
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void ezSAT::lookup_expression(int id, OpId &op, std::vector<int> &args) const
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{
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assert(0 < -id && -id <= int(expressions.size()));
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op = expressions[-id - 1].first;
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args = expressions[-id - 1].second;
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}
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const std::vector<int> &ezSAT::lookup_expression(int id, OpId &op) const
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{
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assert(0 < -id && -id <= int(expressions.size()));
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op = expressions[-id - 1].first;
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return expressions[-id - 1].second;
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}
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int ezSAT::parse_string(const std::string &)
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{
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abort();
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}
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std::string ezSAT::to_string(int id) const
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{
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std::string text;
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if (id > 0)
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{
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lookup_literal(id, text);
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}
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else
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{
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OpId op;
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std::vector<int> args;
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lookup_expression(id, op, args);
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switch (op)
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{
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case OpNot:
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text = "not(";
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break;
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case OpAnd:
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text = "and(";
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break;
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case OpOr:
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text = "or(";
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break;
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case OpXor:
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text = "xor(";
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break;
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case OpIFF:
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text = "iff(";
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break;
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case OpITE:
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text = "ite(";
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break;
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default:
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abort();
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}
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for (int i = 0; i < int(args.size()); i++) {
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if (i > 0)
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text += ", ";
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text += to_string(args[i]);
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}
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text += ")";
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}
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return text;
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}
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int ezSAT::eval(int id, const std::vector<int> &values) const
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{
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if (id > 0) {
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if (id <= int(values.size()) && (values[id-1] == TRUE || values[id-1] == FALSE || values[id-1] == 0))
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return values[id-1];
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return 0;
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}
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OpId op;
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const std::vector<int> &args = lookup_expression(id, op);
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int a, b;
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switch (op)
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{
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case OpNot:
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assert(args.size() == 1);
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a = eval(args[0], values);
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if (a == TRUE)
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return FALSE;
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if (a == FALSE)
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return TRUE;
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return 0;
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case OpAnd:
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a = TRUE;
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for (auto arg : args) {
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b = eval(arg, values);
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if (b != TRUE && b != FALSE)
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a = 0;
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if (b == FALSE)
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return FALSE;
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}
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return a;
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case OpOr:
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a = FALSE;
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for (auto arg : args) {
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b = eval(arg, values);
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if (b != TRUE && b != FALSE)
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a = 0;
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if (b == TRUE)
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return TRUE;
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}
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return a;
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case OpXor:
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a = FALSE;
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for (auto arg : args) {
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b = eval(arg, values);
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if (b != TRUE && b != FALSE)
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return 0;
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if (b == TRUE)
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a = a == TRUE ? FALSE : TRUE;
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}
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return a;
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case OpIFF:
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assert(args.size() > 0);
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a = eval(args[0], values);
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for (auto arg : args) {
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b = eval(arg, values);
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if (b != TRUE && b != FALSE)
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return 0;
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if (b != a)
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return FALSE;
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}
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return TRUE;
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case OpITE:
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assert(args.size() == 3);
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a = eval(args[0], values);
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if (a == TRUE)
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return eval(args[1], values);
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if (a == FALSE)
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return eval(args[2], values);
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return 0;
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default:
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abort();
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}
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}
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void ezSAT::clear()
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{
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cnfConsumed = false;
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cnfVariableCount = 0;
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cnfClausesCount = 0;
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cnfLiteralVariables.clear();
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cnfExpressionVariables.clear();
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cnfClauses.clear();
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cnfAssumptions.clear();
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}
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void ezSAT::assume(int id)
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{
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cnfAssumptions.insert(id);
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if (id < 0)
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{
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assert(0 < -id && -id <= int(expressions.size()));
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cnfExpressionVariables.resize(expressions.size());
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if (cnfExpressionVariables[-id-1] == 0)
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{
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OpId op;
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std::vector<int> args;
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lookup_expression(id, op, args);
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if (op == OpNot) {
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int idx = bind(args[0]);
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cnfClauses.push_back(std::vector<int>(1, -idx));
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cnfClausesCount++;
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return;
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}
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if (op == OpOr) {
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std::vector<int> clause;
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for (int arg : args)
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clause.push_back(bind(arg));
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cnfClauses.push_back(clause);
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cnfClausesCount++;
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return;
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}
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if (op == OpAnd) {
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for (int arg : args) {
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cnfClauses.push_back(std::vector<int>(1, bind(arg)));
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cnfClausesCount++;
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}
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return;
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}
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}
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}
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int idx = bind(id);
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cnfClauses.push_back(std::vector<int>(1, idx));
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cnfClausesCount++;
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}
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void ezSAT::add_clause(const std::vector<int> &args)
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{
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cnfClauses.push_back(args);
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cnfClausesCount++;
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}
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void ezSAT::add_clause(const std::vector<int> &args, bool argsPolarity, int a, int b, int c)
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{
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std::vector<int> clause;
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for (auto arg : args)
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clause.push_back(argsPolarity ? +arg : -arg);
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if (a != 0)
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clause.push_back(a);
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if (b != 0)
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clause.push_back(b);
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if (c != 0)
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clause.push_back(c);
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add_clause(clause);
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}
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void ezSAT::add_clause(int a, int b, int c)
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{
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std::vector<int> clause;
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if (a != 0)
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clause.push_back(a);
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if (b != 0)
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clause.push_back(b);
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if (c != 0)
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clause.push_back(c);
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add_clause(clause);
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}
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int ezSAT::bind_cnf_not(const std::vector<int> &args)
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{
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assert(args.size() == 1);
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return -args[0];
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}
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int ezSAT::bind_cnf_and(const std::vector<int> &args)
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{
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assert(args.size() >= 2);
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int idx = ++cnfVariableCount;
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add_clause(args, false, idx);
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for (auto arg : args)
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add_clause(-idx, arg);
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return idx;
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}
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int ezSAT::bind_cnf_or(const std::vector<int> &args)
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{
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assert(args.size() >= 2);
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int idx = ++cnfVariableCount;
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add_clause(args, true, -idx);
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for (auto arg : args)
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add_clause(idx, -arg);
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return idx;
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}
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int ezSAT::bound(int id) const
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{
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if (id > 0 && id <= int(cnfLiteralVariables.size()))
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return cnfLiteralVariables[id-1];
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if (-id > 0 && -id <= int(cnfExpressionVariables.size()))
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return cnfExpressionVariables[-id-1];
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return 0;
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}
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int ezSAT::bind(int id)
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{
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if (id >= 0) {
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assert(0 < id && id <= int(literals.size()));
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cnfLiteralVariables.resize(literals.size());
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if (cnfLiteralVariables[id-1] == 0) {
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cnfLiteralVariables[id-1] = ++cnfVariableCount;
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if (id == TRUE)
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add_clause(+cnfLiteralVariables[id-1]);
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if (id == FALSE)
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add_clause(-cnfLiteralVariables[id-1]);
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}
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return cnfLiteralVariables[id-1];
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}
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assert(0 < -id && -id <= int(expressions.size()));
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cnfExpressionVariables.resize(expressions.size());
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if (cnfExpressionVariables[-id-1] == 0)
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{
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OpId op;
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std::vector<int> args;
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lookup_expression(id, op, args);
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int idx = 0;
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if (op == OpXor) {
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while (args.size() > 1) {
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std::vector<int> newArgs;
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for (int i = 0; i < int(args.size()); i += 2)
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if (i+1 == int(args.size()))
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newArgs.push_back(args[i]);
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else
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newArgs.push_back(OR(AND(args[i], NOT(args[i+1])), AND(NOT(args[i]), args[i+1])));
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args.swap(newArgs);
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}
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idx = bind(args.at(0));
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goto assign_idx;
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}
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if (op == OpIFF) {
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std::vector<int> invArgs;
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for (auto arg : args)
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invArgs.push_back(NOT(arg));
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idx = bind(OR(expression(OpAnd, args), expression(OpAnd, invArgs)));
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goto assign_idx;
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}
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if (op == OpITE) {
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idx = bind(OR(AND(args[0], args[1]), AND(NOT(args[0]), args[2])));
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goto assign_idx;
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}
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for (int i = 0; i < int(args.size()); i++)
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args[i] = bind(args[i]);
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switch (op)
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{
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case OpNot: idx = bind_cnf_not(args); break;
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case OpAnd: idx = bind_cnf_and(args); break;
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case OpOr: idx = bind_cnf_or(args); break;
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default: abort();
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}
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assign_idx:
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assert(idx != 0);
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cnfExpressionVariables[-id-1] = idx;
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}
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return cnfExpressionVariables[-id-1];
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}
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void ezSAT::consumeCnf()
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{
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cnfConsumed = true;
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cnfClauses.clear();
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}
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void ezSAT::consumeCnf(std::vector<std::vector<int>> &cnf)
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{
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cnfConsumed = true;
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cnf.swap(cnfClauses);
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cnfClauses.clear();
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}
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|
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static bool test_bit(uint32_t bitmask, int idx)
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{
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if (idx > 0)
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return (bitmask & (1 << (+idx-1))) != 0;
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else
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return (bitmask & (1 << (-idx-1))) == 0;
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}
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|
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bool ezSAT::solver(const std::vector<int> &modelExpressions, std::vector<bool> &modelValues, const std::vector<int> &assumptions)
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{
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std::vector<int> extraClauses, modelIdx;
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std::vector<int> values(numLiterals());
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for (auto id : assumptions)
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extraClauses.push_back(bind(id));
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for (auto id : modelExpressions)
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modelIdx.push_back(bind(id));
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|
|
if (cnfVariableCount > 20) {
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fprintf(stderr, "*************************************************************************************\n");
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fprintf(stderr, "ERROR: You are trying to use the builtin solver of ezSAT with more than 20 variables!\n");
|
|
fprintf(stderr, "The builtin solver is a dumb brute force solver and only ment for testing and demo\n");
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|
fprintf(stderr, "purposes. Use a real SAT solve like MiniSAT (e.g. using the ezMiniSAT class) instead.\n");
|
|
fprintf(stderr, "*************************************************************************************\n");
|
|
abort();
|
|
}
|
|
|
|
for (uint32_t bitmask = 0; bitmask < (1 << numCnfVariables()); bitmask++)
|
|
{
|
|
// printf("%07o:", int(bitmask));
|
|
// for (int i = 2; i < numLiterals(); i++)
|
|
// if (bound(i+1))
|
|
// printf(" %s=%d", to_string(i+1).c_str(), test_bit(bitmask, bound(i+1)));
|
|
// printf(" |");
|
|
// for (int idx = 1; idx <= numCnfVariables(); idx++)
|
|
// printf(" %3d", test_bit(bitmask, idx) ? idx : -idx);
|
|
// printf("\n");
|
|
|
|
for (auto idx : extraClauses)
|
|
if (!test_bit(bitmask, idx))
|
|
goto next;
|
|
|
|
for (auto &clause : cnfClauses) {
|
|
for (auto idx : clause)
|
|
if (test_bit(bitmask, idx))
|
|
goto next_clause;
|
|
// printf("failed clause:");
|
|
// for (auto idx2 : clause)
|
|
// printf(" %3d", idx2);
|
|
// printf("\n");
|
|
goto next;
|
|
next_clause:;
|
|
// printf("passed clause:");
|
|
// for (auto idx2 : clause)
|
|
// printf(" %3d", idx2);
|
|
// printf("\n");
|
|
}
|
|
|
|
modelValues.resize(modelIdx.size());
|
|
for (int i = 0; i < int(modelIdx.size()); i++)
|
|
modelValues[i] = test_bit(bitmask, modelIdx[i]);
|
|
|
|
// validate result using eval()
|
|
|
|
values[0] = TRUE, values[1] = FALSE;
|
|
for (int i = 2; i < numLiterals(); i++) {
|
|
int idx = bound(i+1);
|
|
values[i] = idx != 0 ? (test_bit(bitmask, idx) ? TRUE : FALSE) : 0;
|
|
}
|
|
|
|
for (auto id : cnfAssumptions) {
|
|
int result = eval(id, values);
|
|
if (result != TRUE) {
|
|
printInternalState(stderr);
|
|
fprintf(stderr, "Variables:");
|
|
for (int i = 0; i < numLiterals(); i++)
|
|
fprintf(stderr, " %s=%s", lookup_literal(i+1).c_str(), values[i] == TRUE ? "TRUE" : values[i] == FALSE ? "FALSE" : "UNDEF");
|
|
fprintf(stderr, "\nValidation of solver results failed: got `%d' (%s) for assumption '%d': %s\n",
|
|
result, result == FALSE ? "FALSE" : "UNDEF", id, to_string(id).c_str());
|
|
abort();
|
|
}
|
|
// printf("OK: %d -> %d\n", id, result);
|
|
}
|
|
|
|
for (auto id : assumptions) {
|
|
int result = eval(id, values);
|
|
if (result != TRUE) {
|
|
printInternalState(stderr);
|
|
fprintf(stderr, "Variables:");
|
|
for (int i = 0; i < numLiterals(); i++)
|
|
fprintf(stderr, " %s=%s", lookup_literal(i+1).c_str(), values[i] == TRUE ? "TRUE" : values[i] == FALSE ? "FALSE" : "UNDEF");
|
|
fprintf(stderr, "\nValidation of solver results failed: got `%d' (%s) for assumption '%d': %s\n",
|
|
result, result == FALSE ? "FALSE" : "UNDEF", id, to_string(id).c_str());
|
|
abort();
|
|
}
|
|
// printf("OK: %d -> %d\n", id, result);
|
|
}
|
|
|
|
return true;
|
|
next:;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
std::vector<int> ezSAT::vec_const_signed(int64_t value, int bits)
|
|
{
|
|
std::vector<int> vec;
|
|
for (int i = 0; i < bits; i++)
|
|
vec.push_back(((value >> i) & 1) != 0 ? TRUE : FALSE);
|
|
return vec;
|
|
}
|
|
|
|
std::vector<int> ezSAT::vec_const_unsigned(uint64_t value, int bits)
|
|
{
|
|
std::vector<int> vec;
|
|
for (int i = 0; i < bits; i++)
|
|
vec.push_back(((value >> i) & 1) != 0 ? TRUE : FALSE);
|
|
return vec;
|
|
}
|
|
|
|
std::vector<int> ezSAT::vec_var(std::string name, int bits)
|
|
{
|
|
std::vector<int> vec;
|
|
for (int i = 0; i < bits; i++)
|
|
vec.push_back(VAR(name + "[" + std::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() : 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 bits, bool clip)
|
|
{
|
|
std::vector<int> sum = vec_const_unsigned(0, bits);
|
|
std::vector<int> carry_vector;
|
|
|
|
for (auto bit : vec) {
|
|
int carry = bit;
|
|
for (int i = 0; i < bits; 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, bits), 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 = 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 = 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;
|
|
}
|
|
|
|
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 = TRUE;
|
|
zero = 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() : FALSE);
|
|
else if (0 <= j)
|
|
vec.push_back(vec1[j]);
|
|
else
|
|
vec.push_back(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;
|
|
}
|
|
|
|
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 |= 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 |= 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: %s\n", digits, cnfExpressionVariables[i], to_string(-i-1).c_str());
|
|
|
|
fprintf(f, "c\n");
|
|
}
|
|
|
|
fprintf(f, "p cnf %d %d\n", cnfVariableCount, int(cnfClauses.size()));
|
|
int maxClauseLen = 0;
|
|
for (auto &clause : cnfClauses)
|
|
maxClauseLen = std::max(int(clause.size()), maxClauseLen);
|
|
for (auto &clause : cnfClauses) {
|
|
for (auto idx : clause)
|
|
fprintf(f, " %*d", digits, idx);
|
|
fprintf(f, " %*d\n", (digits + 1)*int(maxClauseLen - clause.size()) + 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 += " " + std::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 ? TRUE : i < 0 ? 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 = 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 ? FALSE : 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);
|
|
}
|
|
|