/** Assigning multiplication of this cardinality with another. */
Cardinality& Cardinality::operator*=(const Cardinality& c) {
if (isUnknown()) {
return *this;
} else if (c.isUnknown()) {
d_card = s_unknownCard;
return *this;
}
if (c.isFinite() && isLargeFinite()) {
return *this;
} else if (isFinite() && c.isLargeFinite()) {
d_card = s_largeFiniteCard;
return *this;
}
if (compare(0) == EQUAL || c.compare(0) == EQUAL) {
return *this = 0;
} else if (!isFinite() || !c.isFinite()) {
if (compare(c) == LESS) {
return *this = c;
} else {
return *this;
}
} else {
d_card -= 1;
d_card *= c.d_card - 1;
d_card += 1;
return *this;
}
Unreachable();
}
Cardinality& Cardinality::operator+=(const Cardinality& c) {
if (isUnknown()) {
return *this;
} else if (c.isUnknown()) {
d_card = s_unknownCard;
return *this;
}
if (c.isFinite() && isLargeFinite()) {
return *this;
} else if (isFinite() && c.isLargeFinite()) {
d_card = s_largeFiniteCard;
return *this;
}
if (isFinite() && c.isFinite()) {
d_card += c.d_card - 1;
return *this;
}
if (compare(c) == LESS) {
return *this = c;
} else {
return *this;
}
Unreachable();
}
Integer Cardinality::getFiniteCardinality() const {
PrettyCheckArgument(isFinite(), *this, "This cardinality is not finite.");
PrettyCheckArgument(
!isLargeFinite(), *this,
"This cardinality is finite, but too large to represent.");
return d_card - 1;
}
Cardinality::CardinalityComparison Cardinality::compare(const Cardinality& c) const throw() {
if(isUnknown() || c.isUnknown()) {
return UNKNOWN;
} else if(isLargeFinite()) {
if(c.isLargeFinite()) {
return UNKNOWN;
} else if(c.isFinite()) {
return GREATER;
} else {
Assert(c.isInfinite());
return LESS;
}
} else if(c.isLargeFinite()) {
if(isLargeFinite()) {
return UNKNOWN;
} else if(isFinite()) {
return LESS;
} else {
Assert(isInfinite());
return GREATER;
}
} else if(isInfinite()) {
if(c.isFinite()) {
return GREATER;
} else {
return d_card < c.d_card ? GREATER :
(d_card == c.d_card ? EQUAL : LESS);
}
} else if(c.isInfinite()) {
Assert(isFinite());
return LESS;
} else {
Assert(isFinite() && !isLargeFinite());
Assert(c.isFinite() && !c.isLargeFinite());
return d_card < c.d_card ? LESS :
(d_card == c.d_card ? EQUAL : GREATER);
}
Unreachable();
}
/** Assigning exponentiation of this cardinality with another. */
Cardinality& Cardinality::operator^=(const Cardinality& c) {
if (isUnknown()) {
return *this;
} else if (c.isUnknown()) {
d_card = s_unknownCard;
return *this;
}
if (c.isFinite() && isLargeFinite()) {
return *this;
} else if (isFinite() && c.isLargeFinite()) {
d_card = s_largeFiniteCard;
return *this;
}
if (c.compare(0) == EQUAL) {
// (anything) ^ 0 == 1
d_card = 2; // remember, +1 for finite cardinalities
return *this;
} else if (compare(0) == EQUAL) {
// 0 ^ (>= 1) == 0
return *this;
} else if (compare(1) == EQUAL) {
// 1 ^ (>= 1) == 1
return *this;
} else if (c.compare(1) == EQUAL) {
// (anything) ^ 1 == (that thing)
return *this;
} else if (isFinite() && c.isFinite()) {
// finite ^ finite == finite
try {
// Note: can throw an assertion if c is too big for
// exponentiation
if (d_card - 1 >= 2 && c.d_card - 1 >= 64) {
// don't bother, it's too large anyways
d_card = s_largeFiniteCard;
} else {
d_card = (d_card - 1).pow(c.d_card.getUnsignedLong() - 1) + 1;
}
} catch (IllegalArgumentException&) {
d_card = s_largeFiniteCard;
}
return *this;
} else if (!isFinite() && c.isFinite()) {
// inf ^ finite == inf
return *this;
} else {
Assert(compare(2) != LESS && !c.isFinite(),
"fall-through case not as expected:\n%s\n%s",
this->toString().c_str(), c.toString().c_str());
// (>= 2) ^ beth_k == beth_(k+1)
// unless the base is already > the exponent
if (compare(c) == GREATER) {
return *this;
}
d_card = c.d_card - 1;
return *this;
}
Unreachable();
}
