// Converts ADD and MUL to division. e.g., a/2+1 --> (a+2)/2
// This is called only when the expression is divisible.
protected SimpleExpression toDivision() {
SimpleExpression ret;
if (sop == ADD) {
List<SimpleExpression> converted = new LinkedList<SimpleExpression>();
for (SimpleExpression child : children) converted.add(child.toDivision());
SimpleExpression lcd = getLCD(converted);
if (lcd.equals(sone)) ret = this;
else {
SimpleExpression dividend = szero;
for (SimpleExpression child : converted) {
if (child.sop == DIV)
dividend = add(dividend, multiply(child.getChild(0), divide(lcd, child.getChild(1))));
else dividend = add(dividend, multiply(child, lcd));
}
ret = divide(dividend, lcd);
}
} else if (sop == MUL) {
SimpleExpression dividend = sone, divider = sone;
for (SimpleExpression child : children) {
if (child.sop == DIV) {
dividend = multiply(dividend, child.getChild(0));
divider = multiply(divider, child.getChild(1));
} else dividend = multiply(dividend, child);
}
if (divider.equals(sone)) ret = this;
else ret = divide(dividend, divider);
} else ret = this;
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;
}
// Aggressively normalize divisible expressions to minimize ADD operations.
// This method is called only by induction variable substitution where
// the divisibility of an expression is defined well.
protected SimpleExpression normalizeDivisible() {
SimpleExpression ret = this;
if (sop == DIV) {
if (getChild(0).sop == DIV)
ret = divide(getChild(0).getChild(0), multiply(getChild(0).getChild(1), getChild(1)));
} else if (sop == MUL) {
ret = toDivision().normalize();
} else if (sop == ADD) {
ret = toDivision();
if (ret.sop == DIV && ret.getChild(0).sop == ADD) {
SimpleExpression non_div = szero, dividend = szero;
SimpleExpression divider = ret.getChild(1);
for (SimpleExpression child : ret.getChild(0).children) {
SimpleExpression divided = divide(child, divider);
if (divided.sop == DIV) dividend = add(dividend, child);
else non_div = add(non_div, divided);
}
if (non_div.equals(szero) && ret.countsOperations(ADD) >= countsOperations(ADD))
ret = this; // heuristics: no benefit from the simplification.
else ret = add(non_div, divide(dividend, divider));
}
}
return ret;
}
// Normalizes a MOD expression
private SimpleExpression normalizeMOD() {
if (!allow(DIVIDE)) return this;
SimpleExpression lhs = getChild(0), rhs = getChild(1), ret = null;
if (rhs.equals(szero)) ret = this;
else if (lhs.sop == LIT && rhs.sop == LIT) ret = mod(lhs, rhs);
else if (rhs.equals(sone) || rhs.equals(getInt(-1))) ret = szero;
if (ret == null) {
lhs = lhs.factorize();
rhs = rhs.factorize();
List<SimpleExpression> gcd = computeGCD(lhs, rhs);
if (gcd.get(0).equals(sone)) ret = this;
else // (a*x)%(b*x) = (a%b)*x
ret = multiply(gcd.get(0), new SimpleExpression(gcd.get(1), MOD, gcd.get(2)));
}
// Tools.printlnStatus("[MOD] "+this+" --> "+ret, 1);
return ret;
}
// Normalizes a DIV expression
private SimpleExpression normalizeDIV() {
if (!allow(DIVIDE)) return this;
SimpleExpression lhs = getChild(0), rhs = getChild(1), ret = null;
if (rhs.equals(szero)) ret = this; // Don't do anything with division by zero
else if (lhs.equals(szero)) ret = szero; // 0/<expr>: expr=0 is an exception anyhow
else if (lhs.sop == LIT && rhs.sop == LIT) ret = divide(lhs, rhs); // Call compute method
else if (rhs.equals(sone) || rhs.equals(getInt(-1)))
ret = multiply(rhs, lhs); // Division by one -> multiplication by one
if (ret == null) {
lhs = lhs.factorize();
rhs = rhs.factorize();
List<SimpleExpression> gcd = computeGCD(lhs, rhs);
if (gcd.get(0).equals(sone)) ret = this;
else ret = divide(gcd.get(1), gcd.get(2));
}
// Tools.printlnStatus("[DIV] "+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 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;
}
// Factorizes terms; a*b+a*c --> a*(b+c)
private SimpleExpression factorize() {
if (!allow(FACTORIZE) || sop != ADD) return this;
SimpleExpression ret = null, gcd = getChild(0); // for normalized form.
for (SimpleExpression child : children) {
gcd = computeGCD(gcd, child).get(0);
if (gcd.equals(sone)) {
ret = this;
break;
}
}
if (ret == null) {
SimpleExpression rhs = szero;
for (SimpleExpression child : children) rhs = add(rhs, computeGCD(gcd, child).get(2));
ret = new SimpleExpression(gcd, MUL, rhs);
ret.sort();
}
// Tools.printlnStatus("[FACT] "+this+" --> "+ret, 1);
return ret;
}
