// Returns the number of descendants with the specified type.
private int countsOperations(int op) {
int ret = 0;
if (children == null) return ret;
for (SimpleExpression child : children) ret += child.countsOperations(op);
if (sop == op) ret += children.size() - 1;
return ret;
}
// Returns se1<op>se2 with constant evaluation.
private static SimpleExpression compute(SimpleExpression se1, int op, SimpleExpression se2) {
SimpleExpression ret = null;
if (se1.sop == LIT && se2.sop == LIT) {
Double result = null, v1 = se1.getValue(), v2 = se2.getValue();
switch (op) {
case ADD:
result = v1 + v2;
break;
case MUL:
result = v1 * v2;
break;
case DIV:
result = v1 / v2;
break;
case MOD:
result = v1 % v2;
break;
default:
Tools.exit("[SimpleExpression] unknown operation in normalization");
}
if (se1.expr instanceof IntegerLiteral && se2.expr instanceof IntegerLiteral)
ret = getInt(result.intValue());
else ret = getDouble(result.doubleValue());
} else {
ret = new SimpleExpression(se1, op, se2);
ret = ret.normalize();
}
// Tools.printlnStatus("[COM] "+se1+" "+cop.get(op)+" "+se2+" --> "+ret, 1);
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;
}
/**
* Returns a clone of this simple expression.
*
* @return a clone object.
*/
public Object clone() {
SimpleExpression ret = new SimpleExpression(sop);
ret.order = order;
ret.expr = expr;
ret.contains_side_effect = contains_side_effect;
ret.children.addAll(children);
return ret;
}
// Computes the least common multiple of the two simple expression.
// Assumes se1 and se2 have been normalized.
private static SimpleExpression computeLCM(SimpleExpression se1, SimpleExpression se2) {
se1 = se1.factorize();
se2 = se2.factorize();
List<SimpleExpression> gcd = computeGCD(se1, se2);
SimpleExpression ret = multiply(gcd.get(0), gcd.get(1));
ret = multiply(ret, gcd.get(2));
return ret;
}
/**
* Returns if a simple expression is greater than, less than, or equal to the other.
*
* @param se1 the first simple expression.
* @param se2 the second simple expression.
* @return the comparison result (-1, 0, 1).
*/
public int compare(SimpleExpression se1, SimpleExpression se2) {
if (se1.order < se2.order) return -1;
else if (se1.order > se2.order) return 1;
se1 = se1.getTerm();
se2 = se2.getTerm();
if (se1.children.size() < se2.children.size()) return -1;
else if (se1.children.size() > se2.children.size()) return 1;
else return se1.compareTo(se2);
}
// 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;
}
// 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;
}
// 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;
}
// 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 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 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 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 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;
}
// Assumes se1 and se2 have been normalized.
// Returns a triplet (gcd, dividend1, dividend2).
private static List<SimpleExpression> computeGCD(SimpleExpression se1, SimpleExpression se2) {
// Compute symbolic parts.
List<SimpleExpression> terms1 = new LinkedList<SimpleExpression>();
List<SimpleExpression> terms2 = new LinkedList<SimpleExpression>();
SimpleExpression term1 = se1.getTerm(), term2 = se2.getTerm();
if (term1.sop == MUL) terms1.addAll(term1.children);
else terms1.add(term1);
if (term2.sop == MUL) terms2.addAll(term2.children);
else terms2.add(term2);
TreeSet<SimpleExpression> gcd_terms = new TreeSet<SimpleExpression>(terms1);
gcd_terms.retainAll(terms2);
for (SimpleExpression gcd_term : gcd_terms) {
terms1.remove(gcd_term); // removes the first occurrence
terms2.remove(gcd_term); // of the gcd term
}
// Compute numeric parts.
SimpleExpression s1 = se1.getCoef(), s2 = se2.getCoef(), sgcd = null;
if (s1.expr instanceof IntegerLiteral && s2.expr instanceof IntegerLiteral) {
int n1 = s1.getValue().intValue(), n2 = s2.getValue().intValue();
int gcd = cetus.analysis.GCD.compute(n1, n2);
s1 = getInt(n1 / gcd);
s2 = getInt(n2 / gcd);
sgcd = getInt(gcd);
} else sgcd = sone;
// Combine two parts.
for (SimpleExpression child : gcd_terms) sgcd = multiply(sgcd, child);
for (SimpleExpression child : terms1) s1 = multiply(s1, child);
for (SimpleExpression child : terms2) s2 = multiply(s2, child);
List<SimpleExpression> ret = new LinkedList<SimpleExpression>();
ret.add(sgcd);
ret.add(s1);
ret.add(s2);
// Tools.printlnStatus("[GCD] "+se1+" and "+se2+" --> "+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;
}
// 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;
}
// Computes the least common denominator of the two simple expression.
private static SimpleExpression computeLCD(SimpleExpression se1, SimpleExpression se2) {
SimpleExpression divider1 = sone, divider2 = sone;
if (se1.sop == DIV) divider1 = se1.getChild(1);
if (se2.sop == DIV) divider2 = se2.getChild(1);
return computeLCM(divider1, divider2);
}
/**
* Compares this simple expression with the given simple expression.
*
* @param the given simple expression.
* @return the result of Expression.compareTo(Expression).
*/
public int compareTo(SimpleExpression se) {
return getExpression().compareTo(se.getExpression());
}
// Sorts the child terms if they are commutative and associative
protected void sort() {
for (SimpleExpression child : children) child.sort();
if (isCommAssoc()) Collections.sort(children, this);
}
// 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;
}
// 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;
}
// 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;
}