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yosys/libs/ezsat/ezsat.cc
Clifford Wolf ccf36cb7d8 Added SAT support for $div and $mod cells
2013-08-11 16:27:15 +02:00

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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>
const int ezSAT::TRUE = 1;
const int ezSAT::FALSE = 2;
ezSAT::ezSAT()
{
literal("TRUE");
literal("FALSE");
assert(literal("TRUE") == TRUE);
assert(literal("FALSE") == FALSE);
cnfConsumed = false;
cnfVariableCount = 0;
cnfClausesCount = 0;
solverTimeout = 0;
solverTimoutStatus = false;
}
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 xorRemovedOddTrues ? NOT(myArgs[0]) : 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 ? NOT(id) : id;
}
void ezSAT::lookup_literal(int id, std::string &name) const
{
assert(0 < id && id <= int(literals.size()));
name = literals[id - 1];
}
const std::string &ezSAT::lookup_literal(int id) const
{
assert(0 < id && id <= int(literals.size()));
return literals[id - 1];
}
void ezSAT::lookup_expression(int id, OpId &op, std::vector<int> &args) const
{
assert(0 < -id && -id <= int(expressions.size()));
op = expressions[-id - 1].first;
args = expressions[-id - 1].second;
}
const std::vector<int> &ezSAT::lookup_expression(int id, OpId &op) const
{
assert(0 < -id && -id <= int(expressions.size()));
op = expressions[-id - 1].first;
return expressions[-id - 1].second;
}
int ezSAT::parse_string(const std::string &)
{
abort();
}
std::string ezSAT::to_string(int id) const
{
std::string text;
if (id > 0)
{
lookup_literal(id, text);
}
else
{
OpId op;
std::vector<int> args;
lookup_expression(id, op, args);
switch (op)
{
case OpNot:
text = "not(";
break;
case OpAnd:
text = "and(";
break;
case OpOr:
text = "or(";
break;
case OpXor:
text = "xor(";
break;
case OpIFF:
text = "iff(";
break;
case OpITE:
text = "ite(";
break;
default:
abort();
}
for (int i = 0; i < int(args.size()); i++) {
if (i > 0)
text += ", ";
text += to_string(args[i]);
}
text += ")";
}
return text;
}
int ezSAT::eval(int id, const std::vector<int> &values) const
{
if (id > 0) {
if (id <= int(values.size()) && (values[id-1] == 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;
cnfClausesCount = 0;
cnfLiteralVariables.clear();
cnfExpressionVariables.clear();
cnfClauses.clear();
cnfAssumptions.clear();
}
void ezSAT::assume(int id)
{
cnfAssumptions.insert(id);
if (id < 0)
{
assert(0 < -id && -id <= int(expressions.size()));
cnfExpressionVariables.resize(expressions.size());
if (cnfExpressionVariables[-id-1] == 0)
{
OpId op;
std::vector<int> args;
lookup_expression(id, op, args);
if (op == OpNot) {
int idx = bind(args[0]);
cnfClauses.push_back(std::vector<int>(1, -idx));
cnfClausesCount++;
return;
}
if (op == OpOr) {
std::vector<int> clause;
for (int arg : args)
clause.push_back(bind(arg));
cnfClauses.push_back(clause);
cnfClausesCount++;
return;
}
if (op == OpAnd) {
for (int arg : args) {
cnfClauses.push_back(std::vector<int>(1, bind(arg)));
cnfClausesCount++;
}
return;
}
}
}
int idx = bind(id);
cnfClauses.push_back(std::vector<int>(1, idx));
cnfClausesCount++;
}
void ezSAT::add_clause(const std::vector<int> &args)
{
cnfClauses.push_back(args);
cnfClausesCount++;
}
void ezSAT::add_clause(const std::vector<int> &args, bool argsPolarity, int a, int b, int c)
{
std::vector<int> clause;
for (auto arg : args)
clause.push_back(argsPolarity ? +arg : -arg);
if (a != 0)
clause.push_back(a);
if (b != 0)
clause.push_back(b);
if (c != 0)
clause.push_back(c);
add_clause(clause);
}
void ezSAT::add_clause(int a, int b, int c)
{
std::vector<int> clause;
if (a != 0)
clause.push_back(a);
if (b != 0)
clause.push_back(b);
if (c != 0)
clause.push_back(c);
add_clause(clause);
}
int ezSAT::bind_cnf_not(const std::vector<int> &args)
{
assert(args.size() == 1);
return -args[0];
}
int ezSAT::bind_cnf_and(const std::vector<int> &args)
{
assert(args.size() >= 2);
int idx = ++cnfVariableCount;
add_clause(args, false, idx);
for (auto arg : args)
add_clause(-idx, arg);
return idx;
}
int ezSAT::bind_cnf_or(const std::vector<int> &args)
{
assert(args.size() >= 2);
int idx = ++cnfVariableCount;
add_clause(args, true, -idx);
for (auto arg : args)
add_clause(idx, -arg);
return idx;
}
int ezSAT::bound(int id) const
{
if (id > 0 && id <= int(cnfLiteralVariables.size()))
return cnfLiteralVariables[id-1];
if (-id > 0 && -id <= int(cnfExpressionVariables.size()))
return cnfExpressionVariables[-id-1];
return 0;
}
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;
}
std::vector<int> ezSAT::vec_neg(const std::vector<int> &vec)
{
std::vector<int> zero(vec.size(), FALSE);
return vec_sub(zero, vec);
}
void ezSAT::vec_cmp(const std::vector<int> &vec1, const std::vector<int> &vec2, int &carry, int &overflow, int &sign, int &zero)
{
assert(vec1.size() == vec2.size());
carry = 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);
}
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