X-Git-Url: https://mattmccutchen.net/bigint/bigint.git/blobdiff_plain/b1f5f69ee6a55e326f1336a3967513fd22f57d7f..cb2f0c288d4b7acfa37d7a9c8bc1024c3f332b5f:/BigInteger.cc

diff --git a/BigInteger.cc b/BigInteger.cc
index 0ad7fc1..3b23aa1 100644
--- a/BigInteger.cc
+++ b/BigInteger.cc
@@ -1,13 +1,5 @@
-/*
-* Matt McCutchen's Big Integer Library
-* http://hashproduct.metaesthetics.net/bigint/
-*/
-
 #include "BigInteger.hh"
 
-// MANAGEMENT
-
-// Assignment operator
 void BigInteger::operator =(const BigInteger &x) {
 	// Calls like a = a have no effect
 	if (this == &x)
@@ -15,276 +7,130 @@ void BigInteger::operator =(const BigInteger &x) {
 	// Copy sign
 	sign = x.sign;
 	// Copy the rest
-	BigUnsigned::operator =(x);
+	mag = x.mag;
 }
 
-// Constructor from an array of blocks and a sign
-BigInteger::BigInteger(const Blk *b, Index l, Sign s) : BigUnsigned(b, l) {
+BigInteger::BigInteger(const Blk *b, Index blen, Sign s) : mag(b, blen) {
 	switch (s) {
-		case zero:
-		case positive:
-		case negative:
-		sign = (len == 0) ? zero : 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;
-		default:
-		throw "BigInteger::BigInteger(Blk *, Index, Sign): Invalid sign";
-	}
-}
-
-// Constructor from a BigUnsigned and a sign
-BigInteger::BigInteger(const BigUnsigned &x, Sign s) : BigUnsigned(x) {
-	switch (s) {
-		case zero:
-		case positive:
-		case negative:
-		sign = (len == 0) ? zero : s;
+	case positive:
+	case negative:
+		// If the magnitude is zero, force the sign to zero.
+		sign = mag.isZero() ? zero : s;
 		break;
-		default:
-		throw "BigInteger::BigInteger(Blk *, Index, Sign): Invalid sign";
+	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";
 	}
 }
 
-/*
-* The steps for construction of a BigInteger
-* from an integral value x are as follows:
-* 1. If x is zero, create an empty BigInteger and stop.
-* 2. Allocate a one-block number array.
-* 3. If x is positive (or of an unsigned type), set the
-*    sign of the BigInteger to positive.
-* 4. If x is of a signed type and is negative, set the
-*    sign of the BigInteger to negative.
-* 5. If x is of a signed type, convert x (or -x if x < 0)
-*    to the unsigned type of the same length.
-* 6. Expand x (or the result of step 5) to a Blk,
-*    and store it in the number array.
-*
-* See remarks in `BigUnsigned.cc' and `NumberlikeArray.hh'
-* about new handling of zero-length arrays.
-*/
-
-BigInteger::BigInteger(unsigned long x) {
-	if (x == 0)
-		sign = zero; // NumberlikeArray did the rest
-	else {
-		cap = 1;
-		blk = new Blk[1];
-		sign = positive;
-		len = 1;
-		blk[0] = Blk(x);
-	}
-}
-
-BigInteger::BigInteger(long x) {
-	if (x > 0) {
-		cap = 1;
-		blk = new Blk[1];
-		sign = positive;
-		len = 1;
-		blk[0] = Blk(x);
-	} else if (x < 0) {
-		cap = 1;
-		blk = new Blk[1];
-		sign = negative;
-		len = 1;
-		blk[0] = Blk(-x);
-	} else
-	sign = zero;
-}
-
-BigInteger::BigInteger(unsigned int x) {
-	if (x == 0)
+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;
-	else {
-		cap = 1;
-		blk = new Blk[1];
-		sign = positive;
-		len = 1;
-		blk[0] = Blk(x);
+		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";
 	}
 }
 
-BigInteger::BigInteger(int x) {
-	if (x > 0) {
-		cap = 1;
-		blk = new Blk[1];
-		sign = positive;
-		len = 1;
-		blk[0] = Blk(x);
-	} else if (x < 0) {
-		cap = 1;
-		blk = new Blk[1];
-		sign = negative;
-		len = 1;
-		blk[0] = Blk(-x);
-	} else
-	sign = zero;
-}
-
-BigInteger::BigInteger(unsigned short x) {
-	if (x == 0)
-		sign = zero;
-	else {
-		cap = 1;
-		blk = new Blk[1];
-		sign = positive;
-		len = 1;
-		blk[0] = Blk(x);
-	}
-}
+/* CONSTRUCTION FROM PRIMITIVE INTEGERS
+ * Same idea as in BigUnsigned.cc, except that negative input results in a
+ * negative BigInteger instead of an exception. */
 
-BigInteger::BigInteger(short x) {
-	if (x > 0) {
-		cap = 1;
-		blk = new Blk[1];
-		sign = positive;
-		len = 1;
-		blk[0] = Blk(x);
-	} else if (x < 0) {
-		cap = 1;
-		blk = new Blk[1];
-		sign = negative;
-		len = 1;
-		blk[0] = Blk(-x);
-	} else
-	sign = zero;
-}
+// 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; }
 
-// CONVERTERS
-/*
-* The steps for conversion of a BigInteger to an
-* integral type are as follows:
-* 1. If the BigInteger is zero, return zero.
-* 2. If the BigInteger is positive:
-*    3. If it is more than one block long or its lowest
-*       block has bits set out of the range of the target
-*       type, throw an exception.
-*    4. Otherwise, convert the lowest block to the
-*       target type and return it.
-* 5. If the BigInteger is negative:
-*    6. If the target type is unsigned, throw an exception.
-*    7. If it is more than one block long or its lowest
-*       block has bits set out of the range of the target
-*       type, throw an exception.
-*    8. Otherwise, convert the lowest block to the
-*       target type, negate it, and return it.
-*/
+// For signed input, determine the desired magnitude and sign separately.
 
 namespace {
-	// These masks are used to test whether a Blk has bits
-	// set out of the range of a smaller integral type.  Note
-	// that this range is not considered to include the sign bit.
-	const BigUnsigned::Blk  lMask = ~0 >> 1;
-	const BigUnsigned::Blk uiMask = (unsigned int)(~0);
-	const BigUnsigned::Blk  iMask = uiMask >> 1;
-	const BigUnsigned::Blk usMask = (unsigned short)(~0);
-	const BigUnsigned::Blk  sMask = usMask >> 1;
-}
-
-BigInteger::operator unsigned long() const {
-	switch (sign) {
-		case zero:
-		return 0;
-		case positive:
-		if (len == 1)
-			return blk[0];
-		else
-			throw "BigInteger operator unsigned long() const: Value is too big for an unsigned long";
-		case negative:
-		throw "BigInteger operator unsigned long() const: Cannot convert a negative integer to an unsigned type";
-		default:
-		throw "BigInteger: Internal error";
+	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);
 	}
-}
-
-BigInteger::operator long() const {
-	switch (sign) {
-		case zero:
-		return 0;
-		case positive:
-		if (len == 1 && (blk[0] & ~lMask) == 0)
-			return long(blk[0]);
-		else
-			throw "BigInteger operator long() const: Value is too big for a long";
-		case negative:
-		if (len == 1 && (blk[0] & ~lMask) == 0)
-			return -long(blk[0]);
-		else
-			throw "BigInteger operator long() const: Value is too big for a long";
-		default:
-		throw "BigInteger: Internal error";
+	template <class X>
+	BigInteger::Sign signOf(X x) {
+		return (x == 0) ? BigInteger::zero
+			: (x > 0) ? BigInteger::positive
+			: BigInteger::negative;
 	}
 }
 
-BigInteger::operator unsigned int() const {
-	switch (sign) {
-		case zero:
-		return 0;
-		case positive:
-		if (len == 1 && (blk[0] & ~uiMask) == 0)
-			return (unsigned int)(blk[0]);
-		else
-			throw "BigInteger operator unsigned int() const: Value is too big for an unsigned int";
-		case negative:
-		throw "BigInteger operator unsigned int() const: Cannot convert a negative integer to an unsigned type";
-		default:
-		throw "BigInteger: Internal error";
-	}
-}
+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)) {}
 
-BigInteger::operator int() const {
-	switch (sign) {
-		case zero:
-		return 0;
-		case positive:
-		if (len == 1 && (blk[0] & ~iMask) == 0)
-			return int(blk[0]);
-		else
-			throw "BigInteger operator int() const: Value is too big for an int";
-		case negative:
-		if (len == 1 && (blk[0] & ~iMask) == 0)
-			return -int(blk[0]);
-		else
-			throw "BigInteger operator int() const: Value is too big for an int";
-		default:
-		throw "BigInteger: Internal error";
-	}
+// 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>();
 }
 
-BigInteger::operator unsigned short() const {
-	switch (sign) {
-		case zero:
-		return 0;
-		case positive:
-		if (len == 1 && (blk[0] & ~usMask) == 0)
-			return (unsigned short)(blk[0]);
-		else
-			throw "BigInteger operator unsigned short() const: Value is too big for an unsigned short";
-		case negative:
-		throw "BigInteger operator unsigned short() const: Cannot convert a negative integer to an unsigned type";
-		default:
-		throw "BigInteger: Internal error";
-	}
+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);
 }
 
-BigInteger::operator short() const {
-	switch (sign) {
-		case zero:
+/* 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;
-		case positive:
-		if (len == 1 && (blk[0] & ~sMask) == 0)
-			return short(blk[0]);
-		else
-			throw "BigInteger operator short() const: Value is too big for a short";
-		case negative:
-		if (len == 1 && (blk[0] & ~sMask) == 0)
-			return -short(blk[0]);
-		else
-			throw "BigInteger operator short() const: Value is too big for a short";
-		default:
-		throw "BigInteger: Internal error";
+	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
@@ -294,28 +140,34 @@ BigInteger::CmpRes BigInteger::compareTo(const BigInteger &x) const {
 		return greater;
 	else switch (sign) {
 		// If the signs are the same...
-		case zero:
+	case zero:
 		return equal; // Two zeros are equal
-		case positive:
+	case positive:
 		// Compare the magnitudes
-		return BigUnsigned::compareTo(x);
-		case negative:
+		return mag.compareTo(x.mag);
+	case negative:
 		// Compare the magnitudes, but return the opposite result
-		return CmpRes(-BigUnsigned::compareTo(x));
-		default:
-		throw "BigInteger: Internal error";
+		return CmpRes(-mag.compareTo(x.mag));
+	default:
+		throw "BigInteger internal error";
 	}
 }
 
-// PUT-HERE OPERATIONS
-// These do some messing around to determine the sign of the result,
-// then call one of BigUnsigned's put-heres.
+/* 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; \
+	}
 
-// Addition
 void BigInteger::add(const BigInteger &a, const BigInteger &b) {
-	// Block unsafe calls
-	if (this == &a || this == &b)
-		throw "BigInteger::add: One of the arguments is the invoked object";
+	DTRT_ALIASED(this == &a || this == &b, add(a, b));
 	// If one argument is zero, copy the other.
 	if (a.sign == zero)
 		operator =(b);
@@ -325,39 +177,36 @@ void BigInteger::add(const BigInteger &a, const BigInteger &b) {
 	// common sign and add their magnitudes.
 	else if (a.sign == b.sign) {
 		sign = a.sign;
-		BigUnsigned::add(a, b);
+		mag.add(a.mag, b.mag);
 	} else {
 		// Otherwise, their magnitudes must be compared.
-		switch (a.BigUnsigned::compareTo(b)) {
+		switch (a.mag.compareTo(b.mag)) {
+		case equal:
 			// If their magnitudes are the same, copy zero.
-			case equal:
-			len = 0;
+			mag = 0;
 			sign = zero;
 			break;
 			// Otherwise, take the sign of the greater, and subtract
 			// the lesser magnitude from the greater magnitude.
-			case greater:
+		case greater:
 			sign = a.sign;
-			BigUnsigned::subtract(a, b);
+			mag.subtract(a.mag, b.mag);
 			break;
-			case less:
+		case less:
 			sign = b.sign;
-			BigUnsigned::subtract(b, a);
+			mag.subtract(b.mag, a.mag);
 			break;
 		}
 	}
 }
 
-// Subtraction
 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.
-	// Block unsafe calls
-	if (this == &a || this == &b)
-		throw "BigInteger::subtract: One of the arguments is the invoked object";
+	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) {
-		BigUnsigned::operator =(b);
+		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);
@@ -366,90 +215,94 @@ void BigInteger::subtract(const BigInteger &a, const BigInteger &b) {
 	// If their signs differ, take a.sign and add the magnitudes.
 	else if (a.sign != b.sign) {
 		sign = a.sign;
-		BigUnsigned::add(a, b);
+		mag.add(a.mag, b.mag);
 	} else {
 		// Otherwise, their magnitudes must be compared.
-		switch (a.BigUnsigned::compareTo(b)) {
+		switch (a.mag.compareTo(b.mag)) {
 			// If their magnitudes are the same, copy zero.
-			case equal:
-			len = 0;
+		case equal:
+			mag = 0;
 			sign = zero;
 			break;
 			// If a's magnitude is greater, take a.sign and
 			// subtract a from b.
-			case greater:
+		case greater:
 			sign = a.sign;
-			BigUnsigned::subtract(a, b);
+			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:
+		case less:
 			sign = Sign(-b.sign);
-			BigUnsigned::subtract(b, a);
+			mag.subtract(b.mag, a.mag);
 			break;
 		}
 	}
 }
 
-// Multiplication
 void BigInteger::multiply(const BigInteger &a, const BigInteger &b) {
-	// Block unsafe calls
-	if (this == &a || this == &b)
-		throw "BigInteger::multiply: One of the arguments is the invoked object";
+	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;
-		len = 0;
+		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.
-	BigUnsigned::multiply(a, b);
+	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
-*/
+ * 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) {
-	// Block unsafe calls
-	if (this == &b || this == &q || &b == &q)
-		throw "BigInteger::divideWithRemainder: One of the arguments is the invoked object";
+	// 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.len = 0;
+		q.mag = 0;
 		q.sign = zero;
 		return;
 	}
 	// 0 / b gives quotient 0 and remainder 0
 	if (sign == zero) {
-		q.len = 0;
+		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.
@@ -458,61 +311,58 @@ void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) {
 		// No: harder case.  Quotient is negative.
 		q.sign = negative;
 		// Decrease the magnitude of the dividend by one.
-		BigUnsigned::operator --();
+		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.
-		*/
+		 * 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.
-	BigUnsigned::divideWithRemainder(b, q);
-	
+	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.BigUnsigned::operator ++();
+		q.mag++;
 		// Modify the remainder.
-		BigUnsigned temp(*this);
-		BigUnsigned::subtract(b, temp);
-		BigUnsigned::operator --();
+		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 (len == 0)
+	if (mag.isZero())
 		sign = zero;
-	if (q.len == 0)
+	if (q.mag.isZero())
 		q.sign = zero;
-	
+
 	// WHEW!!!
 }
 
 // Negation
 void BigInteger::negate(const BigInteger &a) {
-	// Block unsafe calls
-	if (this == &a)
-		throw "BigInteger::negate: The argument is the invoked object";
+	DTRT_ALIASED(this == &a, negate(a));
 	// Copy a's magnitude
-	BigUnsigned::operator =(a);
+	mag = a.mag;
 	// Copy the opposite of a.sign
 	sign = Sign(-a.sign);
 }
@@ -521,21 +371,13 @@ void BigInteger::negate(const BigInteger &a) {
 
 // Prefix increment
 void BigInteger::operator ++() {
-	switch (sign) {
-		case zero:
-		allocate(1);
-		sign = positive;
-		len = 1;
-		blk[0] = 1;
-		break;
-		case positive:
-		BigUnsigned::operator ++();
-		break;
-		case negative:
-		BigUnsigned::operator --();
-		if (len == 0)
+	if (sign == negative) {
+		mag--;
+		if (mag == 0)
 			sign = zero;
-		break;
+	} else {
+		mag++;
+		sign = positive; // if not already
 	}
 }
 
@@ -546,21 +388,13 @@ void BigInteger::operator ++(int) {
 
 // Prefix decrement
 void BigInteger::operator --() {
-	switch (sign) {
-		case zero:
-		allocate(1);
-		sign = negative;
-		len = 1;
-		blk[0] = 1;
-		break;
-		case negative:
-		BigUnsigned::operator ++();
-		break;
-		case positive:
-		BigUnsigned::operator --();
-		if (len == 0)
+	if (sign == positive) {
+		mag--;
+		if (mag == 0)
 			sign = zero;
-		break;
+	} else {
+		mag++;
+		sign = negative;
 	}
 }