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-rw-r--r--libs/ezsat/ezsat.cc1221
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diff --git a/libs/ezsat/ezsat.cc b/libs/ezsat/ezsat.cc
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+/*
+ * ezSAT -- A simple and easy to use CNF generator for SAT solvers
+ *
+ * Copyright (C) 2013 Clifford Wolf <clifford@clifford.at>
+ *
+ * Permission to use, copy, modify, and/or distribute this software for any
+ * purpose with or without fee is hereby granted, provided that the above
+ * copyright notice and this permission notice appear in all copies.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
+ * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
+ * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+ * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
+ * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
+ * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ */
+
+#include "ezsat.h"
+
+#include <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);
+}
+
generated by cgit v1.2.3 (git 2.25.1) at 2024-04-25 02:07:21 +0000