BigUnsigned.hh

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#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;
    using 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.
    using NumberlikeArray<Blk>::getCapacity;
    using 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