X-Git-Url: https://mattmccutchen.net/bigint/bigint.git/blobdiff_plain/05780f4b578d6ae054be0b19b8498d32a4f16c60..6e1e0f2f3c2fee3e1e9df39c6d4816566c10aafb:/BigInteger.cc

diff --git a/BigInteger.cc b/BigInteger.cc
index 34a4e17..11ac841 100644
--- a/BigInteger.cc
+++ b/BigInteger.cc
@@ -1,7 +1,6 @@
 /*
-* Matt McCutchen's Big Integer Library
-* http://mysite.verizon.net/mccutchen/bigint/
-*/
+ * Matt McCutchen's Big Integer Library
+ */
 
 #include "BigInteger.hh"
 
@@ -45,32 +44,32 @@ BigInteger::BigInteger(const BigUnsigned &x, Sign s) : BigUnsigned(x) {
 }
 
 /*
-* 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.
-*/
+ * 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) {
-		cap = 0;
-		blk = new Blk[0];
-		sign = zero;
-		len = 0;
-	} else {
+	if (x == 0)
+		sign = zero; // NumberlikeArray did the rest
+	else {
 		cap = 1;
 		blk = new Blk[1];
 		sign = positive;
 		len = 1;
-		*blk = Blk(x);
+		blk[0] = Blk(x);
 	}
 }
 
@@ -80,33 +79,26 @@ BigInteger::BigInteger(long x) {
 		blk = new Blk[1];
 		sign = positive;
 		len = 1;
-		*blk = Blk(x);
+		blk[0] = Blk(x);
 	} else if (x < 0) {
 		cap = 1;
 		blk = new Blk[1];
 		sign = negative;
 		len = 1;
-		*blk = Blk(-x);
-	} else {
-		cap = 0;
-		blk = new Blk[0];
-		sign = zero;
-		len = 0;
-	}
+		blk[0] = Blk(-x);
+	} else
+	sign = zero;
 }
 
 BigInteger::BigInteger(unsigned int x) {
-	if (x == 0) {
-		cap = 0;
-		blk = new Blk[0];
+	if (x == 0)
 		sign = zero;
-		len = 0;
-	} else {
+	else {
 		cap = 1;
 		blk = new Blk[1];
 		sign = positive;
 		len = 1;
-		*blk = Blk(x);
+		blk[0] = Blk(x);
 	}
 }
 
@@ -116,33 +108,26 @@ BigInteger::BigInteger(int x) {
 		blk = new Blk[1];
 		sign = positive;
 		len = 1;
-		*blk = Blk(x);
+		blk[0] = Blk(x);
 	} else if (x < 0) {
 		cap = 1;
 		blk = new Blk[1];
 		sign = negative;
 		len = 1;
-		*blk = Blk(-x);
-	} else {
-		cap = 0;
-		blk = new Blk[0];
-		sign = zero;
-		len = 0;
-	}
+		blk[0] = Blk(-x);
+	} else
+	sign = zero;
 }
 
 BigInteger::BigInteger(unsigned short x) {
-	if (x == 0) {
-		cap = 0;
-		blk = new Blk[0];
+	if (x == 0)
 		sign = zero;
-		len = 0;
-	} else {
+	else {
 		cap = 1;
 		blk = new Blk[1];
 		sign = positive;
 		len = 1;
-		*blk = Blk(x);
+		blk[0] = Blk(x);
 	}
 }
 
@@ -152,40 +137,36 @@ BigInteger::BigInteger(short x) {
 		blk = new Blk[1];
 		sign = positive;
 		len = 1;
-		*blk = Blk(x);
+		blk[0] = Blk(x);
 	} else if (x < 0) {
 		cap = 1;
 		blk = new Blk[1];
 		sign = negative;
 		len = 1;
-		*blk = Blk(-x);
-	} else {
-		cap = 0;
-		blk = new Blk[0];
-		sign = zero;
-		len = 0;
-	}
+		blk[0] = Blk(-x);
+	} else
+	sign = zero;
 }
 
 // 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.
-*/
+ * 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.
+ */
 
 namespace {
 	// These masks are used to test whether a Blk has bits
@@ -204,7 +185,7 @@ BigInteger::operator unsigned long() const {
 		return 0;
 		case positive:
 		if (len == 1)
-			return *blk;
+			return blk[0];
 		else
 			throw "BigInteger operator unsigned long() const: Value is too big for an unsigned long";
 		case negative:
@@ -219,13 +200,13 @@ BigInteger::operator long() const {
 		case zero:
 		return 0;
 		case positive:
-		if (len == 1 && (*blk & ~lMask) == 0)
-			return long(*blk);
+		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 & ~lMask) == 0)
-			return -long(*blk);
+		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:
@@ -238,8 +219,8 @@ BigInteger::operator unsigned int() const {
 		case zero:
 		return 0;
 		case positive:
-		if (len == 1 && (*blk & ~uiMask) == 0)
-			return (unsigned int)(*blk);
+		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:
@@ -254,13 +235,13 @@ BigInteger::operator int() const {
 		case zero:
 		return 0;
 		case positive:
-		if (len == 1 && (*blk & ~iMask) == 0)
-			return int(*blk);
+		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 & ~iMask) == 0)
-			return -int(*blk);
+		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:
@@ -273,8 +254,8 @@ BigInteger::operator unsigned short() const {
 		case zero:
 		return 0;
 		case positive:
-		if (len == 1 && (*blk & ~usMask) == 0)
-			return (unsigned short)(*blk);
+		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:
@@ -289,13 +270,13 @@ BigInteger::operator short() const {
 		case zero:
 		return 0;
 		case positive:
-		if (len == 1 && (*blk & ~sMask) == 0)
-			return short(*blk);
+		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 & ~sMask) == 0)
-			return -short(*blk);
+		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:
@@ -329,11 +310,18 @@ BigInteger::CmpRes BigInteger::compareTo(const BigInteger &x) const {
 // These do some messing around to determine the sign of the result,
 // then call one of BigUnsigned's put-heres.
 
+// 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);
@@ -370,15 +358,15 @@ void BigInteger::add(const BigInteger &a, const BigInteger &b) {
 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);
-		sign = Sign(-sign);
+		// 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);
+		operator =(a);
 	// If their signs differ, take a.sign and add the magnitudes.
 	else if (a.sign != b.sign) {
 		sign = a.sign;
@@ -409,9 +397,7 @@ void BigInteger::subtract(const BigInteger &a, const BigInteger &b) {
 
 // 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;
@@ -426,31 +412,38 @@ void BigInteger::multiply(const BigInteger &a, const BigInteger &b) {
 }
 
 /*
-* 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;
@@ -463,9 +456,9 @@ void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) {
 		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.
@@ -476,30 +469,30 @@ void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) {
 		// Decrease the magnitude of the dividend by one.
 		BigUnsigned::operator --();
 		/*
-		* 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);
-	
+
 	if (sign != b.sign) {
 		// More for the harder case (as described):
 		// Increase the magnitude of the quotient by one.
@@ -509,24 +502,22 @@ void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) {
 		BigUnsigned::subtract(b, temp);
 		BigUnsigned::operator --();
 	}
-	
+
 	// 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)
 		sign = zero;
 	if (q.len == 0)
 		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);
 	// Copy the opposite of a.sign
@@ -542,7 +533,7 @@ void BigInteger::operator ++() {
 		allocate(1);
 		sign = positive;
 		len = 1;
-		*blk = 1;
+		blk[0] = 1;
 		break;
 		case positive:
 		BigUnsigned::operator ++();
@@ -567,7 +558,7 @@ void BigInteger::operator --() {
 		allocate(1);
 		sign = negative;
 		len = 1;
-		*blk = 1;
+		blk[0] = 1;
 		break;
 		case negative:
 		BigUnsigned::operator ++();