Added ezSAT library

1 files changed, 1221 insertions, 0 deletions

diff --git a/libs/ezsat/ezsat.cc b/libs/ezsat/ezsat.cc
new file mode 100644
index 000000000..d6ebd678b
--- /dev/null
+++ b/libs/ezsat/ezsat.cc
@@ -0,0 +1,1221 @@
+/*
+ *  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 <algorithm>
+
+#include <stdlib.h>
+#include <assert.h>
+
+ezSAT::ezSAT()
+{
+	literal("TRUE");
+	literal("FALSE");
+
+	assert(literal("TRUE") == TRUE);
+	assert(literal("FALSE") == FALSE);
+
+	cnfConsumed = false;
+	cnfVariableCount = 0;
+}
+
+ezSAT::~ezSAT()
+{
+}
+
+int ezSAT::value(bool val)
+{
+	return val ? TRUE : 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::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 == TRUE)
+			continue;
+		if ((op == OpOr || op == OpXor) && arg == FALSE)
+			continue;
+		if (op == OpXor && arg == 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] == TRUE)
+			return FALSE;
+		if (myArgs[0] == FALSE)
+			return TRUE;
+		break;
+
+	case OpAnd:
+		if (myArgs.size() == 0)
+			return TRUE;
+		if (myArgs.size() == 1)
+			return myArgs[0];
+		break;
+
+	case OpOr:
+		if (myArgs.size() == 0)
+			return FALSE;
+		if (myArgs.size() == 1)
+			return myArgs[0];
+		break;
+
+	case OpXor:
+		if (myArgs.size() == 0)
+			return xorRemovedOddTrues ? TRUE : FALSE;
+		if (myArgs.size() == 1)
+			return myArgs[0];
+		break;
+
+	case OpIFF:
+		assert(myArgs.size() >= 1);
+		if (myArgs.size() == 1)
+			return TRUE;
+		// FIXME: Add proper const folding
+		break;
+
+	case OpITE:
+		assert(myArgs.size() == 3);
+		if (myArgs[0] == TRUE)
+			return myArgs[1];
+		if (myArgs[0] == 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 = -(expressions.size() + 1);
+		expressionsCache[myExpr] = id;
+		expressions.push_back(myExpr);
+	}
+
+	return xorRemovedOddTrues ? expression(OpNot, 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] == TRUE || values[id-1] == 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 == TRUE)
+			return FALSE;
+		if (a == FALSE)
+			return TRUE;
+		return 0;
+	case OpAnd:
+		a = TRUE;
+		for (auto arg : args) {
+			b = eval(arg, values);
+			if (b != TRUE && b != FALSE)
+				a = 0;
+			if (b == FALSE)
+				return FALSE;
+		}
+		return a;
+	case OpOr:
+		a = FALSE;
+		for (auto arg : args) {
+			b = eval(arg, values);
+			if (b != TRUE && b != FALSE)
+				a = 0;
+			if (b == TRUE)
+				return TRUE;
+		}
+		return a;
+	case OpXor:
+		a = FALSE;
+		for (auto arg : args) {
+			b = eval(arg, values);
+			if (b != TRUE && b != FALSE)
+				return 0;
+			if (b == TRUE)
+				a = a == TRUE ? FALSE : TRUE;
+		}
+		return a;
+	case OpIFF:
+		assert(args.size() > 0);
+		a = eval(args[0], values);
+		for (auto arg : args) {
+			b = eval(arg, values);
+			if (b != TRUE && b != FALSE)
+				return 0;
+			if (b != a)
+				return FALSE;
+		}
+		return TRUE;
+	case OpITE:
+		assert(args.size() == 3);
+		a = eval(args[0], values);
+		if (a == TRUE)
+			return eval(args[1], values);
+		if (a == FALSE)
+			return eval(args[2], values);
+		return 0;
+	default:
+		abort();
+	}
+}
+
+void ezSAT::clear()
+{
+	cnfConsumed = false;
+	cnfVariableCount = 0;
+	cnfLiteralVariables.clear();
+	cnfExpressionVariables.clear();
+	cnfClauses.clear();
+	cnfAssumptions.clear();
+}
+
+void ezSAT::assume(int id)
+{
+	int idx = bind(id);
+	cnfClauses.push_back(std::vector<int>(1, idx));
+	cnfAssumptions.insert(id);
+}
+
+void ezSAT::add_clause(const std::vector<int> &args)
+{
+	cnfClauses.push_back(args);
+}
+
+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;
+}
+
+int ezSAT::bind(int id)
+{
+	if (id >= 0) {
+		assert(0 < id && id <= int(literals.size()));
+		cnfLiteralVariables.resize(literals.size());
+		if (cnfLiteralVariables[id-1] == 0) {
+			cnfLiteralVariables[id-1] = ++cnfVariableCount;
+			if (id == TRUE)
+				add_clause(+cnfLiteralVariables[id-1]);
+			if (id == FALSE)
+				add_clause(-cnfLiteralVariables[id-1]);
+		}
+		return cnfLiteralVariables[id-1];
+	}
+
+	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);
+		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));
+			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)));
+			goto assign_idx;
+		}
+
+		if (op == OpITE) {
+			idx = bind(OR(AND(args[0], args[1]), AND(NOT(args[0]), args[2])));
+			goto assign_idx;
+		}
+
+		for (int i = 0; i < int(args.size()); i++)
+			args[i] = bind(args[i]);
+
+		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()
+{
+	cnfConsumed = true;
+	cnfClauses.clear();
+}
+
+void ezSAT::consumeCnf(std::vector<std::vector<int>> &cnf)
+{
+	cnfConsumed = true;
+	cnf.swap(cnfClauses);
+	cnfClauses.clear();
+}
+
+static bool test_bit(uint32_t bitmask, int idx)
+{
+	if (idx > 0)
+		return (bitmask & (1 << (+idx-1))) != 0;
+	else
+		return (bitmask & (1 << (-idx-1))) == 0;
+}
+
+bool ezSAT::solver(const std::vector<int> &modelExpressions, std::vector<bool> &modelValues, const std::vector<int> &assumptions)
+{
+	std::vector<int> extraClauses, modelIdx;
+	std::vector<int> values(numLiterals());
+
+	for (auto id : assumptions)
+		extraClauses.push_back(bind(id));
+	for (auto id : modelExpressions)
+		modelIdx.push_back(bind(id));
+
+	if (cnfVariableCount > 20) {
+		fprintf(stderr, "*************************************************************************************\n");
+		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");
+		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);
+}
+