/** 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(); }