Initial check in of big integer library

third_party/bigint/BigUnsigned.hh

Index: third_party/bigint/BigUnsigned.hh
diff --git a/third_party/bigint/BigUnsigned.hh b/third_party/bigint/BigUnsigned.hh
new file mode 100644
index 0000000000000000000000000000000000000000..adf1c00bc3d741edb596886ce48effd234e040eb
--- /dev/null
+++ b/third_party/bigint/BigUnsigned.hh
@@ -0,0 +1,418 @@
+#ifndef BIGUNSIGNED_H
+#define BIGUNSIGNED_H
+
+#include "NumberlikeArray.hh"
+
+/* A BigUnsigned object represents a nonnegative integer of size limited only by
+ * available memory.  BigUnsigneds support most mathematical operators and can
+ * be converted to and from most primitive integer types.
+ *
+ * The number is stored as a NumberlikeArray of unsigned longs as if it were
+ * written in base 256^sizeof(unsigned long).  The least significant block is
+ * first, and the length is such that the most significant block is nonzero. */
+class BigUnsigned : protected NumberlikeArray<unsigned long> {
+
+public:
+	// Enumeration for the result of a comparison.
+	enum CmpRes { less = -1, equal = 0, greater = 1 };
+
+	// BigUnsigneds are built with a Blk type of unsigned long.
+	typedef unsigned long Blk;
+
+	typedef NumberlikeArray<Blk>::Index Index;
+	NumberlikeArray<Blk>::N;
+
+protected:
+	// Creates a BigUnsigned with a capacity; for internal use.
+	BigUnsigned(int, Index c) : NumberlikeArray<Blk>(0, c) {}
+
+	// Decreases len to eliminate any leading zero blocks.
+	void zapLeadingZeros() { 
+		while (len > 0 && blk[len - 1] == 0)
+			len--;
+	}
+
+public:
+	// Constructs zero.
+	BigUnsigned() : NumberlikeArray<Blk>() {}
+
+	// Copy constructor
+	BigUnsigned(const BigUnsigned &x) : NumberlikeArray<Blk>(x) {}
+
+	// Assignment operator
+	void operator=(const BigUnsigned &x) {
+		NumberlikeArray<Blk>::operator =(x);
+	}
+
+	// Constructor that copies from a given array of blocks.
+	BigUnsigned(const Blk *b, Index blen) : NumberlikeArray<Blk>(b, blen) {
+		// Eliminate any leading zeros we may have been passed.
+		zapLeadingZeros();
+	}
+
+	// Destructor.  NumberlikeArray does the delete for us.
+	~BigUnsigned() {}
+	
+	// Constructors from primitive integer types
+	BigUnsigned(unsigned long  x);
+	BigUnsigned(         long  x);
+	BigUnsigned(unsigned int   x);
+	BigUnsigned(         int   x);
+	BigUnsigned(unsigned short x);
+	BigUnsigned(         short x);
+protected:
+	// Helpers
+	template <class X> void initFromPrimitive      (X x);
+	template <class X> void initFromSignedPrimitive(X x);
+public:
+
+	/* 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:
+	// Helpers
+	template <class X> X convertToSignedPrimitive() const;
+	template <class X> X convertToPrimitive      () const;
+public:
+
+	// BIT/BLOCK ACCESSORS
+
+	// Expose these from NumberlikeArray directly.
+	NumberlikeArray<Blk>::getCapacity;
+	NumberlikeArray<Blk>::getLength;
+
+	/* Returns the requested block, or 0 if it is beyond the length (as if
+	 * the number had 0s infinitely to the left). */
+	Blk getBlock(Index i) const { return i >= len ? 0 : blk[i]; }
+	/* Sets the requested block.  The number grows or shrinks as necessary. */
+	void setBlock(Index i, Blk newBlock);
+
+	// The number is zero if and only if the canonical length is zero.
+	bool isZero() const { return NumberlikeArray<Blk>::isEmpty(); }
+
+	/* Returns the length of the number in bits, i.e., zero if the number
+	 * is zero and otherwise one more than the largest value of bi for
+	 * which getBit(bi) returns true. */
+	Index bitLength() const;
+	/* Get the state of bit bi, which has value 2^bi.  Bits beyond the
+	 * number's length are considered to be 0. */
+	bool getBit(Index bi) const {
+		return (getBlock(bi / N) & (Blk(1) << (bi % N))) != 0;
+	}
+	/* Sets the state of bit bi to newBit.  The number grows or shrinks as
+	 * necessary. */
+	void setBit(Index bi, bool newBit);
+
+	// COMPARISONS
+
+	// Compares this to x like Perl's <=>
+	CmpRes compareTo(const BigUnsigned &x) const;
+
+	// Ordinary comparison operators
+	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.  Most also take a second read-only operand.
+	 * Example:
+	 *     BigInteger a(1), b(1);
+	 *     a += b;
+	 *
+	 * (3) Copy-less operations: `add', `subtract', etc.
+	 * These named methods take operands as arguments and store the result
+	 * in the receiver (*this), avoiding unnecessary copies and allocations.
+	 * `divideWithRemainder' is special: it both takes the dividend from and
+	 * stores the remainder into the receiver, and it takes a separate
+	 * object in which to store the quotient.  NOTE: If you are wondering
+	 * why these don't return a value, you probably mean to use the
+	 * overloaded return-by-value operators instead.
+	 * 
+	 * Examples:
+	 *     BigInteger a(43), b(7), c, d;
+	 *
+	 *     c = a + b;   // Now c == 50.
+	 *     c.add(a, b); // Same effect but without the two copies.
+	 *
+	 *     c.divideWithRemainder(b, d);
+	 *     // 50 / 7; now d == 7 (quotient) and c == 1 (remainder).
+	 *
+	 *     // ``Aliased'' calls now do the right thing using a temporary
+	 *     // copy, but see note on `divideWithRemainder'.
+	 *     a.add(a, b); 
+	 */
+
+	// COPY-LESS OPERATIONS
+
+	// These 8: Arguments are read-only operands, result is saved in *this.
+	void add(const BigUnsigned &a, const BigUnsigned &b);
+	void subtract(const BigUnsigned &a, const BigUnsigned &b);
+	void multiply(const BigUnsigned &a, const BigUnsigned &b);
+	void bitAnd(const BigUnsigned &a, const BigUnsigned &b);
+	void bitOr(const BigUnsigned &a, const BigUnsigned &b);
+	void bitXor(const BigUnsigned &a, const BigUnsigned &b);
+	/* Negative shift amounts translate to opposite-direction shifts,
+	 * except for -2^(8*sizeof(int)-1) which is unimplemented. */
+	void bitShiftLeft(const BigUnsigned &a, int b);
+	void bitShiftRight(const BigUnsigned &a, int b);
+
+	/* `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'.
+	 * / and % use semantics similar to Knuth's, which differ from the
+	 * primitive integer semantics under division by zero.  See the
+	 * implementation in BigUnsigned.cc for details.
+	 * `a.divideWithRemainder(b, a)' throws an exception: it doesn't make
+	 * sense to write quotient and remainder into the same variable. */
+	void divideWithRemainder(const BigUnsigned &b, BigUnsigned &q);
+
+	/* `divide' and `modulo' are no longer offered.  Use
+	 * `divideWithRemainder' instead. */
+
+	// OVERLOADED RETURN-BY-VALUE OPERATORS
+	BigUnsigned operator +(const BigUnsigned &x) const;
+	BigUnsigned operator -(const BigUnsigned &x) const;
+	BigUnsigned operator *(const BigUnsigned &x) const;
+	BigUnsigned operator /(const BigUnsigned &x) const;
+	BigUnsigned operator %(const BigUnsigned &x) const;
+	/* OK, maybe unary minus could succeed in one case, but it really
+	 * shouldn't be used, so it isn't provided. */
+	BigUnsigned operator &(const BigUnsigned &x) const;
+	BigUnsigned operator |(const BigUnsigned &x) const;
+	BigUnsigned operator ^(const BigUnsigned &x) const;
+	BigUnsigned operator <<(int b) const;
+	BigUnsigned operator >>(int b) const;
+
+	// OVERLOADED ASSIGNMENT OPERATORS
+	void operator +=(const BigUnsigned &x);
+	void operator -=(const BigUnsigned &x);
+	void operator *=(const BigUnsigned &x);
+	void operator /=(const BigUnsigned &x);
+	void operator %=(const BigUnsigned &x);
+	void operator &=(const BigUnsigned &x);
+	void operator |=(const BigUnsigned &x);
+	void operator ^=(const BigUnsigned &x);
+	void operator <<=(int b);
+	void operator >>=(int b);
+
+	/* INCREMENT/DECREMENT OPERATORS
+	 * To discourage messy coding, these do not return *this, so prefix
+	 * and postfix behave the same. */
+	void operator ++(   );
+	void operator ++(int);
+	void operator --(   );
+	void operator --(int);
+
+	// Helper function that needs access to BigUnsigned internals
+	friend Blk getShiftedBlock(const BigUnsigned &num, Index x,
+			unsigned int y);
+
+	// See BigInteger.cc.
+	template <class X>
+	friend X convertBigUnsignedToPrimitiveAccess(const BigUnsigned &a);
+};
+
+/* Implementing the return-by-value and assignment operators in terms of the
+ * copy-less operations.  The copy-less operations are responsible for making
+ * any necessary temporary copies to work around aliasing. */
+
+inline BigUnsigned BigUnsigned::operator +(const BigUnsigned &x) const {
+	BigUnsigned ans;
+	ans.add(*this, x);
+	return ans;
+}
+inline BigUnsigned BigUnsigned::operator -(const BigUnsigned &x) const {
+	BigUnsigned ans;
+	ans.subtract(*this, x);
+	return ans;
+}
+inline BigUnsigned BigUnsigned::operator *(const BigUnsigned &x) const {
+	BigUnsigned ans;
+	ans.multiply(*this, x);
+	return ans;
+}
+inline BigUnsigned BigUnsigned::operator /(const BigUnsigned &x) const {
+	if (x.isZero()) throw "BigUnsigned::operator /: division by zero";
+	BigUnsigned q, r;
+	r = *this;
+	r.divideWithRemainder(x, q);
+	return q;
+}
+inline BigUnsigned BigUnsigned::operator %(const BigUnsigned &x) const {
+	if (x.isZero()) throw "BigUnsigned::operator %: division by zero";
+	BigUnsigned q, r;
+	r = *this;
+	r.divideWithRemainder(x, q);
+	return r;
+}
+inline BigUnsigned BigUnsigned::operator &(const BigUnsigned &x) const {
+	BigUnsigned ans;
+	ans.bitAnd(*this, x);
+	return ans;
+}
+inline BigUnsigned BigUnsigned::operator |(const BigUnsigned &x) const {
+	BigUnsigned ans;
+	ans.bitOr(*this, x);
+	return ans;
+}
+inline BigUnsigned BigUnsigned::operator ^(const BigUnsigned &x) const {
+	BigUnsigned ans;
+	ans.bitXor(*this, x);
+	return ans;
+}
+inline BigUnsigned BigUnsigned::operator <<(int b) const {
+	BigUnsigned ans;
+	ans.bitShiftLeft(*this, b);
+	return ans;
+}
+inline BigUnsigned BigUnsigned::operator >>(int b) const {
+	BigUnsigned ans;
+	ans.bitShiftRight(*this, b);
+	return ans;
+}
+
+inline void BigUnsigned::operator +=(const BigUnsigned &x) {
+	add(*this, x);
+}
+inline void BigUnsigned::operator -=(const BigUnsigned &x) {
+	subtract(*this, x);
+}
+inline void BigUnsigned::operator *=(const BigUnsigned &x) {
+	multiply(*this, x);
+}
+inline void BigUnsigned::operator /=(const BigUnsigned &x) {
+	if (x.isZero()) throw "BigUnsigned::operator /=: division by zero";
+	/* The following technique is slightly faster than copying *this first
+	 * when x is large. */
+	BigUnsigned q;
+	divideWithRemainder(x, q);
+	// *this contains the remainder, but we overwrite it with the quotient.
+	*this = q;
+}
+inline void BigUnsigned::operator %=(const BigUnsigned &x) {
+	if (x.isZero()) throw "BigUnsigned::operator %=: division by zero";
+	BigUnsigned q;
+	// Mods *this by x.  Don't care about quotient left in q.
+	divideWithRemainder(x, q);
+}
+inline void BigUnsigned::operator &=(const BigUnsigned &x) {
+	bitAnd(*this, x);
+}
+inline void BigUnsigned::operator |=(const BigUnsigned &x) {
+	bitOr(*this, x);
+}
+inline void BigUnsigned::operator ^=(const BigUnsigned &x) {
+	bitXor(*this, x);
+}
+inline void BigUnsigned::operator <<=(int b) {
+	bitShiftLeft(*this, b);
+}
+inline void BigUnsigned::operator >>=(int b) {
+	bitShiftRight(*this, b);
+}
+
+/* Templates for conversions of BigUnsigned to and from primitive integers.
+ * BigInteger.cc needs to instantiate convertToPrimitive, and the uses in
+ * BigUnsigned.cc didn't do the trick; I think g++ inlined convertToPrimitive
+ * instead of generating linkable instantiations.  So for consistency, I put
+ * all the templates here. */
+
+// CONSTRUCTION FROM PRIMITIVE INTEGERS
+
+/* Initialize this BigUnsigned from the given primitive integer.  The same
+ * pattern works for all primitive integer types, so I put it into a template to
+ * reduce code duplication.  (Don't worry: this is protected and we instantiate
+ * it only with primitive integer types.)  Type X could be signed, but x is
+ * known to be nonnegative. */
+template <class X>
+void BigUnsigned::initFromPrimitive(X x) {
+	if (x == 0)
+		; // NumberlikeArray already initialized us to zero.
+	else {
+		// Create a single block.  blk is NULL; no need to delete it.
+		cap = 1;
+		blk = new Blk[1];
+		len = 1;
+		blk[0] = Blk(x);
+	}
+}
+
+/* Ditto, but first check that x is nonnegative.  I could have put the check in
+ * initFromPrimitive and let the compiler optimize it out for unsigned-type
+ * instantiations, but I wanted to avoid the warning stupidly issued by g++ for
+ * a condition that is constant in *any* instantiation, even if not in all. */
+template <class X>
+void BigUnsigned::initFromSignedPrimitive(X x) {
+	if (x < 0)
+		throw "BigUnsigned constructor: "
+			"Cannot construct a BigUnsigned from a negative number";
+	else
+		initFromPrimitive(x);
+}
+
+// CONVERSION TO PRIMITIVE INTEGERS
+
+/* Template with the same idea as initFromPrimitive.  This might be slightly
+ * slower than the previous version with the masks, but it's much shorter and
+ * clearer, which is the library's stated goal. */
+template <class X>
+X BigUnsigned::convertToPrimitive() const {
+	if (len == 0)
+		// The number is zero; return zero.
+		return 0;
+	else if (len == 1) {
+		// The single block might fit in an X.  Try the conversion.
+		X x = X(blk[0]);
+		// Make sure the result accurately represents the block.
+		if (Blk(x) == blk[0])
+			// Successful conversion.
+			return x;
+		// Otherwise fall through.
+	}
+	throw "BigUnsigned::to<Primitive>: "
+		"Value is too big to fit in the requested type";
+}
+
+/* Wrap the above in an x >= 0 test to make sure we got a nonnegative result,
+ * not a negative one that happened to convert back into the correct nonnegative
+ * one.  (E.g., catch incorrect conversion of 2^31 to the long -2^31.)  Again,
+ * separated to avoid a g++ warning. */
+template <class X>
+X BigUnsigned::convertToSignedPrimitive() const {
+	X x = convertToPrimitive<X>();
+	if (x >= 0)
+		return x;
+	else
+		throw "BigUnsigned::to(Primitive): "
+			"Value is too big to fit in the requested type";
+}
+
+#endif