-/*
-* Matt McCutchen's Big Integer Library
-* http://mysite.verizon.net/mccutchen/bigint/
-*/
-
-#ifndef BIGUNSIGNED
-#define BIGUNSIGNED
+#ifndef BIGUNSIGNED_H
+#define BIGUNSIGNED_H
#include "NumberlikeArray.hh"
-/*
-* A BigUnsigned object represents a nonnegative integer of size
-* limited only by available memory. A BigUnsigned can be
-* created from and converted back to most integral types,
-* 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).
-*
-* The memory-management details that used to be in here have
-* been moved into NumberlikeArray, which BigUnsigned now derives from.
-* `(NlA)' means that member(s) are declared identically in NumberlikeArray.
-* Such members are either redeclared here to make them public or are
-* here, commented out, for reference.
-*/
-
+/* 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> {
-
- // TYPES & CONSTANTS
- public:
- 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
-
- /*
- // FIELDS
- protected:
- Index cap; // (NlA) The current allocated capacity of this BigUnsigned (in blocks)
- Index len; // (NlA) The actual length of the number stored in this BigUnsigned (in blocks)
- Blk *blk; // (NlA) Dynamically allocated array of the number blocks
- */
-
- // MANAGEMENT
- protected:
- // These members generally defer to those in NumberlikeArray, possibly with slight changes.
- // It might be nice if one could request that constructors be inherited in C++.
-
- BigUnsigned(int, Index c) : NumberlikeArray<Blk>(0, c) {} // Creates a BigUnsigned with a capacity
-
- void zapLeadingZeros() { // Decreases len to eliminate leading zeros
+
+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--;
}
-
- //void allocate(Index c); // (NlA) Ensures the number array has at least the indicated capacity, maybe discarding contents
- //void allocateAndCopy(Index c); // (NlA) Ensures the number array has at least the indicated capacity, preserving its contents
-
- public:
- BigUnsigned() : NumberlikeArray<Blk>() {} // Default constructor (value is 0)
- BigUnsigned(const BigUnsigned &x) : NumberlikeArray<Blk>(x) {} // Copy constructor
-
- void operator=(const BigUnsigned &x) { // Assignment operator
+
+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);
}
-
- BigUnsigned(const Blk *b, Index l) : NumberlikeArray<Blk>(b, l) { // Constructor from an array of blocks
+
+ // 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 integral types
+ // 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);
- ~BigUnsigned() {} // Destructor
-
- // CONVERTERS to integral types
- public:
- operator unsigned long () const;
- operator long () const;
- operator unsigned int () const;
- operator int () const;
- operator unsigned short() const;
- operator short() const;
-
- // PICKING APART
- // These accessors can be used to get the pieces of the number
- public:
+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;
- // Note that getBlock returns 0 if the block index is beyond the length of the number.
- // A routine that uses this accessor can safely assume a BigUnsigned has 0s infinitely to the left.
+
+ /* 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]; }
- // Note how we replace one level of abstraction with another. Isn't that neat?
- bool isZero() const { return NumberlikeArray<Blk>::isEmpty(); } // Often convenient for loops
-
+ /* 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) & (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
- public:
+
// 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.
+
+ // 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; }
-
- // 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
- /* 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.
- */
+
+ /*
+ * 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);
- 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
-
- // 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
-
- // NORMAL OPERATORS
- // These perform the operation on this (to the left of the operator)
- // and x (to the right of the operator) and return a new BigUnsigned with the result.
- public:
- BigUnsigned operator +(const BigUnsigned &x) const; // Addition
- BigUnsigned operator -(const BigUnsigned &x) const; // Subtraction
- BigUnsigned operator *(const BigUnsigned &x) const; // Multiplication
- BigUnsigned operator /(const BigUnsigned &x) const; // Division
- BigUnsigned operator %(const BigUnsigned &x) const; // Modular reduction
- BigUnsigned operator &(const BigUnsigned &x) const; // Bitwise AND
- BigUnsigned operator |(const BigUnsigned &x) const; // Bitwise OR
- BigUnsigned operator ^(const BigUnsigned &x) const; // Bitwise XOR
-
- // ASSIGNMENT OPERATORS
- // These perform the operation on this and x, storing the result into this.
- public:
- void operator +=(const BigUnsigned &x); // Addition
- void operator -=(const BigUnsigned &x); // Subtraction
- void operator *=(const BigUnsigned &x); // Multiplication
- void operator /=(const BigUnsigned &x); // Division
- void operator %=(const BigUnsigned &x); // Modular reduction
- void operator &=(const BigUnsigned &x); // Bitwise AND
- void operator |=(const BigUnsigned &x); // Bitwise OR
- void operator ^=(const BigUnsigned &x); // Bitwise XOR
-
- // INCREMENT/DECREMENT OPERATORS
- // These increase or decrease the number by 1. To discourage side effects,
- // these do not return *this, so prefix and postfix behave the same.
- public:
- void operator ++( ); // Prefix increment
- void operator ++(int); // Postfix decrement
- void operator --( ); // Prefix increment
- void operator --(int); // Postfix decrement
-
+
+ /* `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);
};
-// NORMAL OPERATORS
-/* These create an object to hold the result and invoke
-* the appropriate put-here operation on it, passing
-* this and x. The new object is then returned. */
+/* 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.divide(*this, x);
- return ans;
+ 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 {
- BigUnsigned ans;
- ans.modulo(*this, x);
- return ans;
+ 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.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;
+}
-// 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.
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
- BigUnsigned thisCopy(*this);
- thisCopy.divideWithRemainder(x, *this);
- // quotient left in *this
- // don't care about remainder left in thisCopy
+ 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) {
- // Shortcut (woohoo!)
+ 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);
- // remainder left in *this
- // 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);
+}
+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
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