BigUnsignedInABase.hh

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#ifndef BIGUNSIGNEDINABASE_H
#define BIGUNSIGNEDINABASE_H

#include "NumberlikeArray.hh"
#include "BigUnsigned.hh"
#include <string>

/*
 * A BigUnsignedInABase object represents a nonnegative integer of size limited
 * only by available memory, represented in a user-specified base that can fit
 * in an `unsigned short' (most can, and this saves memory).
 *
 * BigUnsignedInABase is intended as an intermediary class with little
 * functionality of its own.  BigUnsignedInABase objects can be constructed
 * from, and converted to, BigUnsigneds (requiring multiplication, mods, etc.)
 * and `std::string's (by switching digit values for appropriate characters).
 *
 * BigUnsignedInABase is similar to BigUnsigned.  Note the following:
 *
 * (1) They represent the number in exactly the same way, except that
 * BigUnsignedInABase uses ``digits'' (or Digit) where BigUnsigned uses
 * ``blocks'' (or Blk).
 *
 * (2) Both use the management features of NumberlikeArray.  (In fact, my desire
 * to add a BigUnsignedInABase class without duplicating a lot of code led me to
 * introduce NumberlikeArray.)
 *
 * (3) The only arithmetic operation supported by BigUnsignedInABase is an
 * equality test.  Use BigUnsigned for arithmetic.
 */

class BigUnsignedInABase : protected NumberlikeArray<unsigned short> {

public:
    // The digits of a BigUnsignedInABase are unsigned shorts.
    typedef unsigned short Digit;
    // That's also the type of a base.
    typedef Digit Base;

protected:
    // The base in which this BigUnsignedInABase is expressed
    Base base;

    // Creates a BigUnsignedInABase with a capacity; for internal use.
    BigUnsignedInABase(int, Index c) : NumberlikeArray<Digit>(0, c) {}

    // Decreases len to eliminate any leading zero digits.
    void zapLeadingZeros() { 
        while (len > 0 && blk[len - 1] == 0)
            len--;
    }

public:
    // Constructs zero in base 2.
    BigUnsignedInABase() : NumberlikeArray<Digit>(), base(2) {}

    // Copy constructor
    BigUnsignedInABase(const BigUnsignedInABase &x) : NumberlikeArray<Digit>(x), base(x.base) {}

    // Assignment operator
    void operator =(const BigUnsignedInABase &x) {
        NumberlikeArray<Digit>::operator =(x);
        base = x.base;
    }

    // Constructor that copies from a given array of digits.
    BigUnsignedInABase(const Digit *d, Index l, Base base);

    // Destructor.  NumberlikeArray does the delete for us.
    ~BigUnsignedInABase() {}

    // LINKS TO BIGUNSIGNED
    BigUnsignedInABase(const BigUnsigned &x, Base base);
    operator BigUnsigned() const;

    /* LINKS TO STRINGS
     *
     * These use the symbols ``0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'' to
     * represent digits of 0 through 35.  When parsing strings, lowercase is
     * also accepted.
     *
     * All string representations are big-endian (big-place-value digits
     * first).  (Computer scientists have adopted zero-based counting; why
     * can't they tolerate little-endian numbers?)
     *
     * No string representation has a ``base indicator'' like ``0x''.
     *
     * An exception is made for zero: it is converted to ``0'' and not the
     * empty string.
     *
     * If you want different conventions, write your own routines to go
     * between BigUnsignedInABase and strings.  It's not hard.
     */
    operator std::string() const;
    BigUnsignedInABase(const std::string &s, Base base);

public:

    // ACCESSORS
    Base getBase() const { return base; }

    // Expose these from NumberlikeArray directly.
    using NumberlikeArray<Digit>::getCapacity;
    using NumberlikeArray<Digit>::getLength;

    /* Returns the requested digit, or 0 if it is beyond the length (as if
     * the number had 0s infinitely to the left). */
    Digit getDigit(Index i) const { return i >= len ? 0 : blk[i]; }

    // The number is zero if and only if the canonical length is zero.
    bool isZero() const { return NumberlikeArray<Digit>::isEmpty(); }

    /* Equality test.  For the purposes of this test, two BigUnsignedInABase
     * values must have the same base to be equal. */ 
    bool operator ==(const BigUnsignedInABase &x) const {
        return base == x.base && NumberlikeArray<Digit>::operator ==(x);
    }
    bool operator !=(const BigUnsignedInABase &x) const { return !operator ==(x); }

};

#endif