X-Git-Url: https://mattmccutchen.net/bigint/bigint.git/blobdiff_plain/05780f4b578d6ae054be0b19b8498d32a4f16c60..2406559a7644b4b9dd2bb19b99591c5ef6fc1cc4:/BigUnsigned.hh

diff --git a/BigUnsigned.hh b/BigUnsigned.hh
index 101f697..1eb056f 100644
--- a/BigUnsigned.hh
+++ b/BigUnsigned.hh
@@ -1,6 +1,5 @@
 /*
 * Matt McCutchen's Big Integer Library
-* http://mysite.verizon.net/mccutchen/bigint/
 */
 
 #ifndef BIGUNSIGNED
@@ -15,8 +14,9 @@
 * and many math operations are defined on BigUnsigneds.
 *
 * The number is stored as a series of blocks in a
-* dynamically allocated array.  It is as if the numbers
-* were written digit by digit in base 256 ^ sizeof(unsigned long).
+* dynamically allocated array.  It is as if the number
+* were written digit by digit in base 2 ^ N, **where N is the
+* number of bits in an unsigned long.**
 *
 * The memory-management details that used to be in here have
 * been moved into NumberlikeArray, which BigUnsigned now derives from.
@@ -32,6 +32,7 @@ class BigUnsigned : protected NumberlikeArray<unsigned long> {
 	enum CmpRes { less = -1, equal = 0, greater = 1 }; // Enumeration for the result of a comparison
 	typedef unsigned long Blk; // The number block type that BigUnsigneds are built from
 	typedef NumberlikeArray<Blk>::Index Index; // (NlA) Type for the index of a block in the array
+	NumberlikeArray<Blk>::N; // Number of bits in a Blk
 	
 	/*
 	// FIELDS
@@ -102,54 +103,97 @@ class BigUnsigned : protected NumberlikeArray<unsigned long> {
 	// Compares this to x like Perl's <=>
 	CmpRes compareTo(const BigUnsigned &x) const;
 	// Normal comparison operators
-	NumberlikeArray<Blk>::operator ==; // (NlA) The body used to be `{ return compareTo(x) == equal; }'.  For performance reasons we use NumberlikeArray code that only worries about (in)equality and doesn't waste time determining which is bigger
-	NumberlikeArray<Blk>::operator !=; // (NlA) Ditto.
+	// Bug fixed 2006.04.24: Only we, not the user, can pass a BigUnsigned off as a
+	// NumberlikeArray, so we have to wrap == and !=.
+	bool operator ==(const BigUnsigned &x) const {
+		return NumberlikeArray<Blk>::operator ==(x);
+	}
+	bool operator !=(const BigUnsigned &x) const {
+		return NumberlikeArray<Blk>::operator !=(x);
+	}
 	bool operator < (const BigUnsigned &x) const { return compareTo(x) == less   ; }
 	bool operator <=(const BigUnsigned &x) const { return compareTo(x) != greater; }
 	bool operator >=(const BigUnsigned &x) const { return compareTo(x) != less   ; }
 	bool operator > (const BigUnsigned &x) const { return compareTo(x) == greater; }
+
+	/*
+	* BigUnsigned and BigInteger both provide three kinds of operators.
+	* Here ``big-integer'' refers to BigInteger or BigUnsigned.
+	*
+	* (1) Overloaded ``return-by-value'' operators:
+	*     +, -, *, /, %, unary -.
+	* Big-integer code using these operators looks identical to
+	* code using the primitive integer types.  These operators take
+	* one or two big-integer inputs and return a big-integer result,
+	* which can then be assigned to a BigInteger variable or used
+	* in an expression.  Example:
+	*     BigInteger a(1), b = 1;
+	*     BigInteger c = a + b;
+	*
+	* (2) Overloaded assignment operators:
+	*     +=, -=, *=, /=, %=, &=, |=, ^=, ++, --, flipSign.
+	* Again, these are used on big integers just like on ints.
+	* They take one writable big integer that both provides an
+	* operand and receives a result.  The first eight also take
+	* a second read-only operand.  Example:
+	*     BigInteger a(1), b(1);
+	*     a += b;
+	*
+	* (3) ``Put-here'' operations: `add', `subtract', etc.
+	* Using a return-by-value or assignment operator generally involves
+	* copy constructions and/or assignments.  The ``put-here'' operations
+	* require none, but they are more of a hassle to use.  Most take two
+	* read-only operands and save the result in the calling object `*this',
+	* whose previous value is ignored.  `divideWithRemainder' is an exception.
+	* <<< NOTE >>>: Put-here operations do not return a value: they don't need to!!
+	* Examples:
+	*     BigInteger a(43), b(7), c, d;
+	*     c = a + b;   // Now c == 50.
+	*     c.add(a, b); // Same effect but without the two bulk-copies.
+	*     c.divideWithRemainder(b, d); // 50 / 7; now d == 7 (quotient) and c == 1 (remainder).
+	*     a.add(a, b); // ``Aliased'' calls now do the right thing using a
+	*              // temporary copy, but see note on divideWithRemainder.
+	*/
 	
 	// PUT-HERE OPERATIONS
-	/* These store the result of the operation on the arguments into this.
-	* a.add(b, c) is equivalent to, but faster than, a = b + c.
-	* Calls like a.operation(a, b) are unsafe and not allowed. */
 	public:
-	// Easy 3
-	void add          (const BigUnsigned &a, const BigUnsigned &b); // Addition
-	void subtract     (const BigUnsigned &a, const BigUnsigned &b); // Subtraction
-	void multiply     (const BigUnsigned &a, const BigUnsigned &b); // Multiplication
+	/* These 3: Two read-only operands as arguments.  Result left in *this. */
+	void add(const BigUnsigned &a, const BigUnsigned &b); // Addition
+	void subtract(const BigUnsigned &a, const BigUnsigned &b); // Subtraction
+	void multiply(const BigUnsigned &a, const BigUnsigned &b); // Multiplication
 	/* Divisive stuff
 	* `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'.
 	* Semantics similar to Donald E. Knuth's are used for / and %,
 	* and these differ from the semantics of primitive-type
 	* / and % under division by zero.
 	* Look in `BigUnsigned.cc' for details.
+	* `a.divideWithRemainder(b, a)' causes an exception: it doesn't make
+	* sense to write quotient and remainder into the same variable.
 	*/
 	void divideWithRemainder(const BigUnsigned &b, BigUnsigned &q);
 	void divide(const BigUnsigned &a, const BigUnsigned &b) {
-		// Division, deprecated and provided for compatibility
 		BigUnsigned a2(a);
 		a2.divideWithRemainder(b, *this);
 		// quotient now in *this
 		// don't care about remainder left in a2
 	}
 	void modulo(const BigUnsigned &a, const BigUnsigned &b) {
-		// Modular reduction, deprecated and provided for compatibility
 		*this = a;
 		BigUnsigned q;
 		divideWithRemainder(b, q);
 		// remainder now in *this
 		// don't care about quotient left in q
 	}
-	// Bitwise
-	void bitAnd       (const BigUnsigned &a, const BigUnsigned &b); // Bitwise AND
-	void bitOr        (const BigUnsigned &a, const BigUnsigned &b); // Bitwise OR
-	void bitXor       (const BigUnsigned &a, const BigUnsigned &b); // Bitwise XOR
+	// Bitwise operations.  Two read-only operands as arguments.  Result left in *this.
+	// These are not provided for BigIntegers; I think that using them on BigIntegers
+	// will discard the sign first.
+	void bitAnd(const BigUnsigned &a, const BigUnsigned &b); // Bitwise AND
+	void bitOr(const BigUnsigned &a, const BigUnsigned &b); // Bitwise OR
+	void bitXor(const BigUnsigned &a, const BigUnsigned &b); // Bitwise XOR
 	
-	// These functions are declared but not defined.  (Sorry.)
-	// Trying to call either will result in a link-time error.
-	void bitShiftLeft (const BigUnsigned &a, unsigned int b); // Bitwise left shift
-	void bitShiftRight(const BigUnsigned &a, unsigned int b); // Bitwise right shift
+	// These functions might exist someday.
+	//void bitShiftLeft(const BigUnsigned &a, unsigned int b); // Bitwise left shift
+	//void bitShiftRight(const BigUnsigned &a, unsigned int b); // Bitwise right shift
 	
 	// NORMAL OPERATORS
 	// These perform the operation on this (to the left of the operator)
@@ -185,6 +229,8 @@ class BigUnsigned : protected NumberlikeArray<unsigned long> {
 	void operator --(   ); // Prefix  increment
 	void operator --(int); // Postfix decrement
 	
+	// Helper function that needs access to BigUnsigned internals
+	friend Blk getShiftedBlock(const BigUnsigned &num, Index x, unsigned int y);
 };
 
 // NORMAL OPERATORS
@@ -232,21 +278,23 @@ inline BigUnsigned BigUnsigned::operator ^(const BigUnsigned &x) const {
 	return ans;
 }
 
-// ASSIGNMENT OPERATORS
-// These create a copy of this, then invoke the appropriate
-// put-here operation on this, passing the copy and x.
-// Exception: those updated for divideWithRemainder.
+/*
+ * ASSIGNMENT OPERATORS
+ * 
+ * Now the responsibility for making a temporary copy if necessary
+ * belongs to the put-here operations.  I made this change on 2007.02.13 after
+ * Boris Dessy pointed out that the old implementation handled calls like
+ * "a *= a" badly: it translated them to essentially "a.multiply(aCopy, a)",
+ * which threw an exception.
+ */
 inline void BigUnsigned::operator +=(const BigUnsigned &x) {
-	BigUnsigned thisCopy(*this);
-	add(thisCopy, x);
+	add(*this, x);
 }
 inline void BigUnsigned::operator -=(const BigUnsigned &x) {
-	BigUnsigned thisCopy(*this);
-	subtract(thisCopy, x);
+	subtract(*this, x);
 }
 inline void BigUnsigned::operator *=(const BigUnsigned &x) {
-	BigUnsigned thisCopy(*this);
-	multiply(thisCopy, x);
+	multiply(*this, x);
 }
 inline void BigUnsigned::operator /=(const BigUnsigned &x) {
 	// Updated for divideWithRemainder
@@ -263,16 +311,13 @@ inline void BigUnsigned::operator %=(const BigUnsigned &x) {
 	// don't care about quotient left in q
 }
 inline void BigUnsigned::operator &=(const BigUnsigned &x) {
-	BigUnsigned thisCopy(*this);
-	bitAnd(thisCopy, x);
+	bitAnd(*this, x);
 }
 inline void BigUnsigned::operator |=(const BigUnsigned &x) {
-	BigUnsigned thisCopy(*this);
-	bitOr(thisCopy, x);
+	bitOr(*this, x);
 }
 inline void BigUnsigned::operator ^=(const BigUnsigned &x) {
-	BigUnsigned thisCopy(*this);
-	bitXor(thisCopy, x);
+	bitXor(*this, x);
 }
 
 #endif