// Normalizes a MIN/MAX expression
private SimpleExpression normalizeMINMAX() {
// Literal/non-literal separation
TreeSet<Double> literals = new TreeSet<Double>();
TreeSet<SimpleExpression> exprs = new TreeSet<SimpleExpression>();
SimpleExpression ret = new SimpleExpression(sop);
for (SimpleExpression child : children) {
if (child.sop == LIT) literals.add(child.getValue());
else exprs.add(child);
}
if (sop == MIN) ret.add(getInt(literals.first().intValue()));
else ret.add(getInt(literals.last().intValue()));
ret.addAll(exprs);
// Quick return for single-entry min/max.
if (ret.children.size() == 1) return ret.getChild(0);
// Match min(a,max(a,b))=a or max(a,min(a,b))=a
if (ret.sop == MIN
&& ret.children.size() == 2
&& ret.getChild(1).sop == MAX
&& ret.getChild(1).children.size() == 2
&& ret.getChild(1).children.contains(ret.getChild(0))
|| ret.sop == MAX
&& ret.children.size() == 2
&& ret.getChild(1).sop == MIN
&& ret.getChild(1).children.size() == 2
&& ret.getChild(1).children.contains(ret.getChild(0))) return ret.getChild(0);
return ret;
}
// Normalizes a comparison operation
private SimpleExpression normalizeCompare() {
SimpleExpression lhs = getChild(0), rhs = getChild(1);
// Before normalization ( lhs <op> rhs )
if (lhs.sop == LIT && rhs.sop == LIT) {
double diff = lhs.getValue().doubleValue() - rhs.getValue().doubleValue();
switch (sop) {
case EQ:
return (diff == 0) ? sone : szero;
case NE:
return (diff != 0) ? sone : szero;
case LE:
return (diff <= 0) ? sone : szero;
case LT:
return (diff < 0) ? sone : szero;
case GE:
return (diff >= 0) ? sone : szero;
case GT:
return (diff > 0) ? sone : szero;
default:
Tools.exit("[SimpleExpression] unknown comparison expression");
}
} else if (lhs.equals(rhs)) return (sop == EQ || sop == LE || sop == GE) ? sone : szero;
// Normalization ( lhs-rhs <op> 0 )
SimpleExpression ret = new SimpleExpression(sop);
if (compare(lhs, rhs) < 0) {
ret.add(subtract(rhs, lhs));
ret.sop = exchangeOp(sop);
} else ret.add(subtract(lhs, rhs));
ret.add(szero);
return ret;
}
// Negates this simple expression
private SimpleExpression negate() {
SimpleExpression ret = null;
if (sop == NEG) ret = getChild(0);
else if (sop == LIT) ret = (equals(szero)) ? sone : szero;
else if (sop >= EQ && sop <= GT) {
ret = (SimpleExpression) clone();
ret.sop = negateOp(sop);
} else if (sop == AND || sop == OR) {
ret = new SimpleExpression((sop == AND) ? OR : AND);
for (SimpleExpression child : children) ret.add(child.negate());
} else {
ret = new SimpleExpression(NEG);
ret.add(this);
}
return ret;
}
// Distributes terms; a*(b+c) --> a*b+a*c
private SimpleExpression distribute() {
if (!allow(DISTRIBUTE) || sop != MUL || !containsChildOfType(ADD)) return this;
SimpleExpression ret = sone;
for (SimpleExpression child : children) {
SimpleExpression lhs = new SimpleExpression(szero, ADD, ret);
SimpleExpression rhs = new SimpleExpression(szero, ADD, child);
ret = new SimpleExpression(ADD);
for (SimpleExpression lhs_child : lhs.children)
for (SimpleExpression rhs_child : rhs.children) ret.add(multiply(lhs_child, rhs_child));
}
ret = ret.normalizeADD();
// Tools.printlnStatus("[DIST] "+this+" --> "+ret, 1);
return ret;
}
// Returns the non-literal term in the simple expression.
protected SimpleExpression getTerm() {
SimpleExpression ret = null;
if (sop == LIT) ret = sone;
else if (sop != MUL) ret = this;
else {
ret = new SimpleExpression(MUL);
for (SimpleExpression child : children) if (child.sop != LIT) ret.add(child);
if (ret.children.size() == 0) ret = sone;
else if (ret.children.size() == 1) ret = ret.getChild(0);
}
// Tools.printlnStatus("[TERM] "+this+" --> "+ret, 1);
return ret;
}
// Parses a binary expression
private void parse(BinaryExpression be) {
BinaryOperator bop = be.getOperator();
SimpleExpression lhs = new SimpleExpression(be.getLHS());
SimpleExpression rhs = new SimpleExpression(be.getRHS());
contains_side_effect |= (lhs.contains_side_effect || rhs.contains_side_effect);
if (bop == BinaryOperator.SUBTRACT) {
sop = ADD;
SimpleExpression new_rhs = new SimpleExpression(MUL);
new_rhs.add(getInt(-1));
new_rhs.add(rhs);
add(lhs);
add(new_rhs);
} else {
sop = cop.indexOf(bop);
if (sop == -1) {
sop = TREE;
expr = be;
}
add(lhs);
add(rhs);
}
}
// Removes division by replacing with modulus operations.
// The returned list contains the modified simple expression (get(0)) and
// the additionally multiplied value (get(1)).
// e.g., a*(b/c)*(d/e) returns {a*(b-b%c)*(d-d%e), c*e}.
// It is important to notice that the legality check of this transformation
// is up to the callers.
// It is assumed that the original simple expressions has been normalized.
protected List<SimpleExpression> multiplyByLCM() {
List<SimpleExpression> ret = new ArrayList<SimpleExpression>(2);
if (sop == DIV) {
ret.add(subtract(getChild(0), mod(getChild(0), getChild(1))));
ret.add(getChild(1));
} else if (sop == ADD) {
List<SimpleExpression> terms = new LinkedList<SimpleExpression>();
List<SimpleExpression> factors = new LinkedList<SimpleExpression>();
SimpleExpression lcm = sone;
for (SimpleExpression child : children) {
List<SimpleExpression> ret0 = child.multiplyByLCM();
terms.add(ret0.get(0));
factors.add(ret0.get(1));
lcm = computeLCM(lcm, ret0.get(1));
}
SimpleExpression ret1 = new SimpleExpression(ADD);
for (int i = 0; i < terms.size(); i++)
ret1.add(multiply(divide(lcm, factors.get(i)), terms.get(i)));
ret.add(ret1.normalize());
ret.add(lcm);
} else if (sop == MUL) {
SimpleExpression terms = new SimpleExpression(MUL);
SimpleExpression factors = sone;
for (SimpleExpression child : children) {
List<SimpleExpression> ret0 = child.multiplyByLCM();
terms.add(ret0.get(0));
factors = multiply(factors, ret0.get(1));
}
ret.add(terms.normalize());
ret.add(factors);
} else {
ret.add(this);
ret.add(sone);
}
return ret;
}
// Normalizes an AND|OR operation
private SimpleExpression normalizeLogic() {
if (!allow(LOGIC)) return this;
TreeSet<SimpleExpression> set = new TreeSet<SimpleExpression>(children);
TreeSet<SimpleExpression> neg = new TreeSet<SimpleExpression>();
SimpleExpression ret = new SimpleExpression(sop);
for (SimpleExpression child : set) {
if (sop == AND) {
if (child.equals(szero) || neg.contains(child)) return szero;
else if (child.sop != LIT) // ==LIT means non-zero literal.
ret.add(child);
} else // sop == OR
{
if ((child.sop == LIT && !child.equals(szero)) || neg.contains(child)) return sone;
else if (child.sop != LIT) // ==LIT means zero literal.
ret.add(child);
}
neg.add(child.negate());
}
if (ret.children.size() == 0) // skipped literals.
ret = (ret.sop == AND) ? sone : szero;
else if (ret.children.size() == 1) ret = ret.getChild(0);
// Tools.printlnStatus("[LOGIC] "+this+" --> "+ret, 1);
return ret;
}
// Normalizes a MUL expression
private SimpleExpression normalizeMUL() {
SimpleExpression ret = this;
if (allow(FOLD)) {
SimpleExpression coef = sone;
LinkedList<SimpleExpression> terms = new LinkedList<SimpleExpression>();
for (SimpleExpression child : children) {
if (child.sop == LIT) coef = multiply(coef, child);
else terms.add(child);
}
ret = new SimpleExpression(MUL);
if (coef.equals(szero)) ret = szero;
else {
if (!coef.equals(sone) || terms.size() == 0) ret.add(coef);
ret.addAll(terms);
if (ret.children.size() == 1) ret = ret.getChild(0);
}
}
ret = ret.distribute();
// Tools.printlnStatus("[MUL] "+this+" --> "+ret, 1);
return ret;
}
// Normalizes an ADD expression
private SimpleExpression normalizeADD() {
if (!allow(FOLD)) return this;
TreeMap<SimpleExpression, SimpleExpression> terms =
new TreeMap<SimpleExpression, SimpleExpression>();
for (SimpleExpression child : children) {
SimpleExpression term = child.getTerm(), coef = child.getCoef();
if (terms.containsKey(term)) terms.put(term, add(terms.get(term), coef));
else terms.put(term, coef);
}
SimpleExpression ret = new SimpleExpression(ADD);
for (SimpleExpression term : terms.keySet()) {
SimpleExpression coef = terms.get(term);
if (!coef.equals(szero)) ret.add((coef.equals(sone)) ? term : multiply(coef, term));
}
if (ret.children.size() == 0) ret = szero;
else if (ret.children.size() == 1) ret = ret.getChild(0);
// Tools.printlnStatus("[ADD] "+this+" --> "+ret, 1);
return ret;
}
// Normalizes this simple expression recursively.
protected SimpleExpression normalize() {
SimpleExpression ret = new SimpleExpression(this);
for (SimpleExpression child : children) ret.add(child.normalize());
if (contains_side_effect) return ret;
switch (ret.sop) {
case ID:
case LIT:
case LEAF:
ret = this;
break;
case ADD:
ret = ret.normalizeADD();
break;
case MUL:
ret = ret.normalizeMUL();
break;
case DIV:
ret = ret.normalizeDIV();
break;
case MOD:
ret = ret.normalizeMOD();
break;
case SFTL:
case SFTR:
case BAND:
case BOR:
case BXOR:
ret = ret.normalizeBitOperation();
break;
case BCMP:
ret = ret.normalizeBCMP();
break;
case AND:
case OR:
ret = ret.normalizeLogic();
break;
case EQ:
case NE:
case LE:
case LT:
case GE:
case GT:
ret = ret.normalizeCompare();
break;
case NEG:
ret = ret.normalizeNEG();
break;
case MIN:
case MAX:
ret = ret.normalizeMINMAX();
break;
default:
}
if (ret.isCommAssoc()) ret.sort();
// Tools.printlnStatus("[NORM] "+this+" --> "+ret, 1);
return ret;
}