BigInteger.cpp

#include "BigInteger.h"

void BigInteger::operator =(const BigInteger &x) {
	// Calls like a = a have no effect
	if (this == &x)
		return;
	// Copy sign
	sign = x.sign;
	// Copy the rest
	mag = x.mag;
}

BigInteger::BigInteger(const Blk *b, Index blen, Sign s) : mag(b, blen) {
	switch (s) {
	case zero:
		if (!mag.isZero())
			throw "BigInteger::BigInteger(const Blk *, Index, Sign): Cannot use a sign of zero with a nonzero magnitude";
		sign = zero;
		break;
	case positive:
	case negative:
		// If the magnitude is zero, force the sign to zero.
		sign = mag.isZero() ? zero : s;
		break;
	default:
		/* g++ seems to be optimizing out this case on the assumption
		 * that the sign is a valid member of the enumeration.  Oh well. */
		throw "BigInteger::BigInteger(const Blk *, Index, Sign): Invalid sign";
	}
}

BigInteger::BigInteger(const BigUnsigned &x, Sign s) : mag(x) {
	switch (s) {
	case zero:
		if (!mag.isZero())
			throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Cannot use a sign of zero with a nonzero magnitude";
		sign = zero;
		break;
	case positive:
	case negative:
		// If the magnitude is zero, force the sign to zero.
		sign = mag.isZero() ? zero : s;
		break;
	default:
		/* g++ seems to be optimizing out this case on the assumption
		 * that the sign is a valid member of the enumeration.  Oh well. */
		throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Invalid sign";
	}
}

/* CONSTRUCTION FROM PRIMITIVE INTEGERS
 * Same idea as in BigUnsigned.cc, except that negative input results in a
 * negative BigInteger instead of an exception. */

// Done longhand to let us use initialization.
BigInteger::BigInteger(unsigned long  x) : mag(x) { sign = mag.isZero() ? zero : positive; }
BigInteger::BigInteger(unsigned int   x) : mag(x) { sign = mag.isZero() ? zero : positive; }
BigInteger::BigInteger(unsigned short x) : mag(x) { sign = mag.isZero() ? zero : positive; }

// For signed input, determine the desired magnitude and sign separately.

namespace {
	template <class X, class UX>
	BigInteger::Blk magOf(X x) {
		/* UX(...) cast needed to stop short(-2^15), which negates to
		 * itself, from sign-extending in the conversion to Blk. */
		return BigInteger::Blk(x < 0 ? UX(-x) : x);
	}
	template <class X>
	BigInteger::Sign signOf(X x) {
		return (x == 0) ? BigInteger::zero
			: (x > 0) ? BigInteger::positive
			: BigInteger::negative;
	}
}

BigInteger::BigInteger(long  x) : sign(signOf(x)), mag(magOf<long , unsigned long >(x)) {}
BigInteger::BigInteger(int   x) : sign(signOf(x)), mag(magOf<int  , unsigned int  >(x)) {}
BigInteger::BigInteger(short x) : sign(signOf(x)), mag(magOf<short, unsigned short>(x)) {}

// CONVERSION TO PRIMITIVE INTEGERS

/* Reuse BigUnsigned's conversion to an unsigned primitive integer.
 * The friend is a separate function rather than
 * BigInteger::convertToUnsignedPrimitive to avoid requiring BigUnsigned to
 * declare BigInteger. */
template <class X>
inline X convertBigUnsignedToPrimitiveAccess(const BigUnsigned &a) {
	return a.convertToPrimitive<X>();
}

template <class X>
X BigInteger::convertToUnsignedPrimitive() const {
	if (sign == negative)
		throw "BigInteger::to<Primitive>: "
			"Cannot convert a negative integer to an unsigned type";
	else
		return convertBigUnsignedToPrimitiveAccess<X>(mag);
}

/* Similar to BigUnsigned::convertToPrimitive, but split into two cases for
 * nonnegative and negative numbers. */
template <class X, class UX>
X BigInteger::convertToSignedPrimitive() const {
	if (sign == zero)
		return 0;
	else if (mag.getLength() == 1) {
		// The single block might fit in an X.  Try the conversion.
		Blk b = mag.getBlock(0);
		if (sign == positive) {
			X x = X(b);
			if (x >= 0 && Blk(x) == b)
				return x;
		} else {
			X x = -X(b);
			/* UX(...) needed to avoid rejecting conversion of
			 * -2^15 to a short. */
			if (x < 0 && Blk(UX(-x)) == b)
				return x;
		}
		// Otherwise fall through.
	}
	throw "BigInteger::to<Primitive>: "
		"Value is too big to fit in the requested type";
}

unsigned long  BigInteger::toUnsignedLong () const { return convertToUnsignedPrimitive<unsigned long >       (); }
unsigned int   BigInteger::toUnsignedInt  () const { return convertToUnsignedPrimitive<unsigned int  >       (); }
unsigned short BigInteger::toUnsignedShort() const { return convertToUnsignedPrimitive<unsigned short>       (); }
long           BigInteger::toLong         () const { return convertToSignedPrimitive  <long , unsigned long> (); }
int            BigInteger::toInt          () const { return convertToSignedPrimitive  <int  , unsigned int>  (); }
short          BigInteger::toShort        () const { return convertToSignedPrimitive  <short, unsigned short>(); }

// COMPARISON
BigInteger::CmpRes BigInteger::compareTo(const BigInteger &x) const {
	// A greater sign implies a greater number
	if (sign < x.sign)
		return less;
	else if (sign > x.sign)
		return greater;
	else switch (sign) {
		// If the signs are the same...
	case zero:
		return equal; // Two zeros are equal
	case positive:
		// Compare the magnitudes
		return mag.compareTo(x.mag);
	case negative:
		// Compare the magnitudes, but return the opposite result
		return CmpRes(-mag.compareTo(x.mag));
	default:
		throw "BigInteger internal error";
	}
}

/* COPY-LESS OPERATIONS
 * These do some messing around to determine the sign of the result,
 * then call one of BigUnsigned's copy-less operations. */

// See remarks about aliased calls in BigUnsigned.cc .
#define DTRT_ALIASED(cond, op) \
	if (cond) { \
		BigInteger tmpThis; \
		tmpThis.op; \
		*this = tmpThis; \
		return; \
	}

void BigInteger::add(const BigInteger &a, const BigInteger &b) {
	DTRT_ALIASED(this == &a || this == &b, add(a, b));
	// If one argument is zero, copy the other.
	if (a.sign == zero)
		operator =(b);
	else if (b.sign == zero)
		operator =(a);
	// If the arguments have the same sign, take the
	// common sign and add their magnitudes.
	else if (a.sign == b.sign) {
		sign = a.sign;
		mag.add(a.mag, b.mag);
	} else {
		// Otherwise, their magnitudes must be compared.
		switch (a.mag.compareTo(b.mag)) {
		case equal:
			// If their magnitudes are the same, copy zero.
			mag = 0;
			sign = zero;
			break;
			// Otherwise, take the sign of the greater, and subtract
			// the lesser magnitude from the greater magnitude.
		case greater:
			sign = a.sign;
			mag.subtract(a.mag, b.mag);
			break;
		case less:
			sign = b.sign;
			mag.subtract(b.mag, a.mag);
			break;
		}
	}
}

void BigInteger::subtract(const BigInteger &a, const BigInteger &b) {
	// Notice that this routine is identical to BigInteger::add,
	// if one replaces b.sign by its opposite.
	DTRT_ALIASED(this == &a || this == &b, subtract(a, b));
	// If a is zero, copy b and flip its sign.  If b is zero, copy a.
	if (a.sign == zero) {
		mag = b.mag;
		// Take the negative of _b_'s, sign, not ours.
		// Bug pointed out by Sam Larkin on 2005.03.30.
		sign = Sign(-b.sign);
	} else if (b.sign == zero)
		operator =(a);
	// If their signs differ, take a.sign and add the magnitudes.
	else if (a.sign != b.sign) {
		sign = a.sign;
		mag.add(a.mag, b.mag);
	} else {
		// Otherwise, their magnitudes must be compared.
		switch (a.mag.compareTo(b.mag)) {
			// If their magnitudes are the same, copy zero.
		case equal:
			mag = 0;
			sign = zero;
			break;
			// If a's magnitude is greater, take a.sign and
			// subtract a from b.
		case greater:
			sign = a.sign;
			mag.subtract(a.mag, b.mag);
			break;
			// If b's magnitude is greater, take the opposite
			// of b.sign and subtract b from a.
		case less:
			sign = Sign(-b.sign);
			mag.subtract(b.mag, a.mag);
			break;
		}
	}
}

void BigInteger::multiply(const BigInteger &a, const BigInteger &b) {
	DTRT_ALIASED(this == &a || this == &b, multiply(a, b));
	// If one object is zero, copy zero and return.
	if (a.sign == zero || b.sign == zero) {
		sign = zero;
		mag = 0;
		return;
	}
	// If the signs of the arguments are the same, the result
	// is positive, otherwise it is negative.
	sign = (a.sign == b.sign) ? positive : negative;
	// Multiply the magnitudes.
	mag.multiply(a.mag, b.mag);
}

/*
 * DIVISION WITH REMAINDER
 * Please read the comments before the definition of
 * `BigUnsigned::divideWithRemainder' in `BigUnsigned.cc' for lots of
 * information you should know before reading this function.
 *
 * Following Knuth, I decree that x / y is to be
 * 0 if y==0 and floor(real-number x / y) if y!=0.
 * Then x % y shall be x - y*(integer x / y).
 *
 * Note that x = y * (x / y) + (x % y) always holds.
 * In addition, (x % y) is from 0 to y - 1 if y > 0,
 * and from -(|y| - 1) to 0 if y < 0.  (x % y) = x if y = 0.
 *
 * Examples: (q = a / b, r = a % b)
 *	a	b	q	r
 *	===	===	===	===
 *	4	3	1	1
 *	-4	3	-2	2
 *	4	-3	-2	-2
 *	-4	-3	1	-1
 */
void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) {
	// Defend against aliased calls;
	// same idea as in BigUnsigned::divideWithRemainder .
	if (this == &q)
		throw "BigInteger::divideWithRemainder: Cannot write quotient and remainder into the same variable";
	if (this == &b || &q == &b) {
		BigInteger tmpB(b);
		divideWithRemainder(tmpB, q);
		return;
	}

	// Division by zero gives quotient 0 and remainder *this
	if (b.sign == zero) {
		q.mag = 0;
		q.sign = zero;
		return;
	}
	// 0 / b gives quotient 0 and remainder 0
	if (sign == zero) {
		q.mag = 0;
		q.sign = zero;
		return;
	}

	// Here *this != 0, b != 0.

	// Do the operands have the same sign?
	if (sign == b.sign) {
		// Yes: easy case.  Quotient is zero or positive.
		q.sign = positive;
	} else {
		// No: harder case.  Quotient is negative.
		q.sign = negative;
		// Decrease the magnitude of the dividend by one.
		mag--;
		/*
		 * We tinker with the dividend before and with the
		 * quotient and remainder after so that the result
		 * comes out right.  To see why it works, consider the following
		 * list of examples, where A is the magnitude-decreased
		 * a, Q and R are the results of BigUnsigned division
		 * with remainder on A and |b|, and q and r are the
		 * final results we want:
		 *
		 *	a	A	b	Q	R	q	r
		 *	-3	-2	3	0	2	-1	0
		 *	-4	-3	3	1	0	-2	2
		 *	-5	-4	3	1	1	-2	1
		 *	-6	-5	3	1	2	-2	0
		 *
		 * It appears that we need a total of 3 corrections:
		 * Decrease the magnitude of a to get A.  Increase the
		 * magnitude of Q to get q (and make it negative).
		 * Find r = (b - 1) - R and give it the desired sign.
		 */
	}

	// Divide the magnitudes.
	mag.divideWithRemainder(b.mag, q.mag);

	if (sign != b.sign) {
		// More for the harder case (as described):
		// Increase the magnitude of the quotient by one.
		q.mag++;
		// Modify the remainder.
		mag.subtract(b.mag, mag);
		mag--;
	}

	// Sign of the remainder is always the sign of the divisor b.
	sign = b.sign;

	// Set signs to zero as necessary.  (Thanks David Allen!)
	if (mag.isZero())
		sign = zero;
	if (q.mag.isZero())
		q.sign = zero;

	// WHEW!!!
}

// Negation
void BigInteger::negate(const BigInteger &a) {
	DTRT_ALIASED(this == &a, negate(a));
	// Copy a's magnitude
	mag = a.mag;
	// Copy the opposite of a.sign
	sign = Sign(-a.sign);
}

// INCREMENT/DECREMENT OPERATORS

// Prefix increment
void BigInteger::operator ++() {
	if (sign == negative) {
		mag--;
		if (mag == 0)
			sign = zero;
	} else {
		mag++;
		sign = positive; // if not already
	}
}

// Postfix increment: same as prefix
void BigInteger::operator ++(int) {
	operator ++();
}

// Prefix decrement
void BigInteger::operator --() {
	if (sign == positive) {
		mag--;
		if (mag == 0)
			sign = zero;
	} else {
		mag++;
		sign = negative;
	}
}

// Postfix decrement: same as prefix
void BigInteger::operator --(int) {
	operator --();
}