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#ifndef BIGINTEGER_H
#define BIGINTEGER_H
#include "BigUnsigned.hh"
/* A BigInteger object represents a signed integer of size limited only by
* available memory. BigUnsigneds support most mathematical operators and can
* be converted to and from most primitive integer types.
*
* A BigInteger is just an aggregate of a BigUnsigned and a sign. (It is no
* longer derived from BigUnsigned because that led to harmful implicit
* conversions.) */
class BigInteger {
public:
typedef BigUnsigned::Blk Blk;
typedef BigUnsigned::Index Index;
typedef BigUnsigned::CmpRes CmpRes;
static const CmpRes
less = BigUnsigned::less ,
equal = BigUnsigned::equal ,
greater = BigUnsigned::greater;
// Enumeration for the sign of a BigInteger.
enum Sign { negative = -1, zero = 0, positive = 1 };
protected:
Sign sign;
BigUnsigned mag;
public:
// Constructs zero.
BigInteger() : sign(zero), mag() {}
// Copy constructor
BigInteger(const BigInteger &x) : sign(x.sign), mag(x.mag) {};
// Assignment operator
void operator=(const BigInteger &x);
// Constructor that copies from a given array of blocks with a sign.
BigInteger(const Blk *b, Index blen, Sign s);
// Nonnegative constructor that copies from a given array of blocks.
BigInteger(const Blk *b, Index blen) : mag(b, blen) {
sign = mag.isZero() ? zero : positive;
}
// Constructor from a BigUnsigned and a sign
BigInteger(const BigUnsigned &x, Sign s);
// Nonnegative constructor from a BigUnsigned
BigInteger(const BigUnsigned &x) : mag(x) {
sign = mag.isZero() ? zero : positive;
}
// Constructors from primitive integer types
BigInteger(unsigned long x);
BigInteger( long x);
BigInteger(unsigned int x);
BigInteger( int x);
BigInteger(unsigned short x);
BigInteger( short x);
/* Converters to primitive integer types
* The implicit conversion operators caused trouble, so these are now
* named. */
unsigned long toUnsignedLong () const;
long toLong () const;
unsigned int toUnsignedInt () const;
int toInt () const;
unsigned short toUnsignedShort() const;
short toShort () const;
protected:
// Helper
template <class X> X convertToUnsignedPrimitive() const;
template <class X, class UX> X convertToSignedPrimitive() const;
public:
// ACCESSORS
Sign getSign() const { return sign; }
/* The client can't do any harm by holding a read-only reference to the
* magnitude. */
const BigUnsigned &getMagnitude() const { return mag; }
// Some accessors that go through to the magnitude
Index getLength() const { return mag.getLength(); }
Index getCapacity() const { return mag.getCapacity(); }
Blk getBlock(Index i) const { return mag.getBlock(i); }
bool isZero() const { return sign == zero; } // A bit special
// COMPARISONS
// Compares this to x like Perl's <=>
CmpRes compareTo(const BigInteger &x) const;
// Ordinary comparison operators
bool operator ==(const BigInteger &x) const {
return sign == x.sign && mag == x.mag;
}
bool operator !=(const BigInteger &x) const { return !operator ==(x); };
bool operator < (const BigInteger &x) const { return compareTo(x) == less ; }
bool operator <=(const BigInteger &x) const { return compareTo(x) != greater; }
bool operator >=(const BigInteger &x) const { return compareTo(x) != less ; }
bool operator > (const BigInteger &x) const { return compareTo(x) == greater; }
// OPERATORS -- See the discussion in BigUnsigned.hh.
void add (const BigInteger &a, const BigInteger &b);
void subtract(const BigInteger &a, const BigInteger &b);
void multiply(const BigInteger &a, const BigInteger &b);
/* See the comment on BigUnsigned::divideWithRemainder. Semantics
* differ from those of primitive integers when negatives and/or zeros
* are involved. */
void divideWithRemainder(const BigInteger &b, BigInteger &q);
void negate(const BigInteger &a);
/* Bitwise operators are not provided for BigIntegers. Use
* getMagnitude to get the magnitude and operate on that instead. */
BigInteger operator +(const BigInteger &x) const;
BigInteger operator -(const BigInteger &x) const;
BigInteger operator *(const BigInteger &x) const;
BigInteger operator /(const BigInteger &x) const;
BigInteger operator %(const BigInteger &x) const;
BigInteger operator -() const;
void operator +=(const BigInteger &x);
void operator -=(const BigInteger &x);
void operator *=(const BigInteger &x);
void operator /=(const BigInteger &x);
void operator %=(const BigInteger &x);
void flipSign();
// INCREMENT/DECREMENT OPERATORS
void operator ++( );
void operator ++(int);
void operator --( );
void operator --(int);
};
// NORMAL OPERATORS
/* These create an object to hold the result and invoke
* the appropriate put-here operation on it, passing
* this and x. The new object is then returned. */
inline BigInteger BigInteger::operator +(const BigInteger &x) const {
BigInteger ans;
ans.add(*this, x);
return ans;
}
inline BigInteger BigInteger::operator -(const BigInteger &x) const {
BigInteger ans;
ans.subtract(*this, x);
return ans;
}
inline BigInteger BigInteger::operator *(const BigInteger &x) const {
BigInteger ans;
ans.multiply(*this, x);
return ans;
}
inline BigInteger BigInteger::operator /(const BigInteger &x) const {
if (x.isZero()) throw "BigInteger::operator /: division by zero";
BigInteger q, r;
r = *this;
r.divideWithRemainder(x, q);
return q;
}
inline BigInteger BigInteger::operator %(const BigInteger &x) const {
if (x.isZero()) throw "BigInteger::operator %: division by zero";
BigInteger q, r;
r = *this;
r.divideWithRemainder(x, q);
return r;
}
inline BigInteger BigInteger::operator -() const {
BigInteger ans;
ans.negate(*this);
return ans;
}
/*
* ASSIGNMENT OPERATORS
*
* Now the responsibility for making a temporary copy if necessary
* belongs to the put-here operations. See Assignment Operators in
* BigUnsigned.hh.
*/
inline void BigInteger::operator +=(const BigInteger &x) {
add(*this, x);
}
inline void BigInteger::operator -=(const BigInteger &x) {
subtract(*this, x);
}
inline void BigInteger::operator *=(const BigInteger &x) {
multiply(*this, x);
}
inline void BigInteger::operator /=(const BigInteger &x) {
if (x.isZero()) throw "BigInteger::operator /=: division by zero";
/* The following technique is slightly faster than copying *this first
* when x is large. */
BigInteger q;
divideWithRemainder(x, q);
// *this contains the remainder, but we overwrite it with the quotient.
*this = q;
}
inline void BigInteger::operator %=(const BigInteger &x) {
if (x.isZero()) throw "BigInteger::operator %=: division by zero";
BigInteger q;
// Mods *this by x. Don't care about quotient left in q.
divideWithRemainder(x, q);
}
// This one is trivial
inline void BigInteger::flipSign() {
sign = Sign(-sign);
}
#endif
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