X-Git-Url: https://mattmccutchen.net/bigint/bigint.git/blobdiff_plain/2301f99c6175d543626d61c0bda90e80f85e7eac..HEAD:/BigInteger.hh diff --git a/BigInteger.hh b/BigInteger.hh index bfe3190..cf6e910 100644 --- a/BigInteger.hh +++ b/BigInteger.hh @@ -3,81 +3,99 @@ #include "BigUnsigned.hh" -/* - * A BigInteger object represents a signed integer of size - * limited only by available memory. A BigInteger can be - * created from and converted back to most integral types, - * and many math operations are defined on BigIntegers. - * - * The number is stored as a series of blocks in a - * 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.** +/* A BigInteger object represents a signed integer of size limited only by + * available memory. BigUnsigneds support most mathematical operators and can + * be converted to and from most primitive integer types. * - * This class is derived from BigUnsigned, which represents - * a large nonnegative integer. BigUnsigned should be studied - * first, as only new or different things are declared here. - * Some things are redeclared so that they use the BigInteger - * versions of methods, rather than the BigUnsigned versions. - */ - -class BigInteger : public BigUnsigned { + * A BigInteger is just an aggregate of a BigUnsigned and a sign. (It is no + * longer derived from BigUnsigned because that led to harmful implicit + * conversions.) */ +class BigInteger { - // TYPES & CONSTANTS public: - enum Sign { negative = -1, zero = 0, positive = 1 }; // Enumeration for the sign of a BigInteger + typedef BigUnsigned::Blk Blk; + typedef BigUnsigned::Index Index; + typedef BigUnsigned::CmpRes CmpRes; + static const CmpRes + less = BigUnsigned::less , + equal = BigUnsigned::equal , + greater = BigUnsigned::greater; + // Enumeration for the sign of a BigInteger. + enum Sign { negative = -1, zero = 0, positive = 1 }; - // FIELDS protected: - Sign sign; // The sign of this BigInteger + Sign sign; + BigUnsigned mag; - // MANAGEMENT -protected: - BigInteger(Sign s, Index c) : BigUnsigned(0, c), sign(s) {}; // Creates a BigInteger with a sign and capacity public: + // Constructs zero. + BigInteger() : sign(zero), mag() {} + + // Copy constructor + BigInteger(const BigInteger &x) : sign(x.sign), mag(x.mag) {}; + + // Assignment operator + void operator=(const BigInteger &x); + + // Constructor that copies from a given array of blocks with a sign. + BigInteger(const Blk *b, Index blen, Sign s); - BigInteger() : BigUnsigned(), sign(zero) {} // Default constructor (value is 0) - BigInteger(const BigInteger &x) : BigUnsigned(x), sign(x.sign) {}; // Copy constructor - void operator=(const BigInteger &x); // Assignment operator - BigInteger(const Blk *b, Index l) : BigUnsigned(b, l) { // Constructor from an array of blocks - sign = (len == 0) ? zero : positive; + // Nonnegative constructor that copies from a given array of blocks. + BigInteger(const Blk *b, Index blen) : mag(b, blen) { + sign = mag.isZero() ? zero : positive; } - BigInteger(const Blk *b, Index l, Sign s); // Constructor from an array of blocks and a sign - BigInteger(const BigUnsigned &x) : BigUnsigned(x) { // Constructor from a BigUnsigned - sign = (len == 0) ? zero : positive; + + // Constructor from a BigUnsigned and a sign + BigInteger(const BigUnsigned &x, Sign s); + + // Nonnegative constructor from a BigUnsigned + BigInteger(const BigUnsigned &x) : mag(x) { + sign = mag.isZero() ? zero : positive; } - BigInteger(const BigUnsigned &x, Sign s); // Constructor from a BigUnsigned and a sign - // Constructors from integral types + + // Constructors from primitive integer types BigInteger(unsigned long x); BigInteger( long x); BigInteger(unsigned int x); BigInteger( int x); BigInteger(unsigned short x); BigInteger( short x); - // Note that a BigInteger can be converted to a BigUnsigned - // automatically; this takes its absolute value. - // 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 + /* 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: + // Helper + template X convertToUnsignedPrimitive() const; + template X convertToSignedPrimitive() const; public: - Sign getSign() const; + + // ACCESSORS + Sign getSign() const { return sign; } + /* The client can't do any harm by holding a read-only reference to the + * magnitude. */ + const BigUnsigned &getMagnitude() const { return mag; } + + // Some accessors that go through to the magnitude + Index getLength() const { return mag.getLength(); } + Index getCapacity() const { return mag.getCapacity(); } + Blk getBlock(Index i) const { return mag.getBlock(i); } + bool isZero() const { return sign == zero; } // A bit special // COMPARISONS -public: + // Compares this to x like Perl's <=> CmpRes compareTo(const BigInteger &x) const; - // Normal comparison operators + + // Ordinary comparison operators bool operator ==(const BigInteger &x) const { - return sign == x.sign && BigUnsigned::operator ==(x); + return sign == x.sign && mag == x.mag; } bool operator !=(const BigInteger &x) const { return !operator ==(x); }; bool operator < (const BigInteger &x) const { return compareTo(x) == less ; } @@ -85,78 +103,40 @@ public: bool operator >=(const BigInteger &x) const { return compareTo(x) != less ; } bool operator > (const BigInteger &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. - * See explanation of "put-here operations" in BigUnsigned.cc . */ -public: - void add (const BigInteger &a, const BigInteger &b); // Addition - void subtract(const BigInteger &a, const BigInteger &b); // Subtraction - void multiply(const BigInteger &a, const BigInteger &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 usually differ from the semantics of primitive-type - * / and % when negatives and/or zeroes are involved. - * Look in `BigInteger.cc' for details. - * `a.divideWithRemainder(b, a)' causes an exception: it doesn't make - * sense to write quotient and remainder into the same variable. - */ + // OPERATORS -- See the discussion in BigUnsigned.hh. + void add (const BigInteger &a, const BigInteger &b); + void subtract(const BigInteger &a, const BigInteger &b); + void multiply(const BigInteger &a, const BigInteger &b); + /* See the comment on BigUnsigned::divideWithRemainder. Semantics + * differ from those of primitive integers when negatives and/or zeros + * are involved. */ void divideWithRemainder(const BigInteger &b, BigInteger &q); - void divide(const BigInteger &a, const BigInteger &b) { - BigInteger a2(a); - a2.divideWithRemainder(b, *this); - // quotient now in *this - // don't care about remainder left in a2 - } - void modulo(const BigInteger &a, const BigInteger &b) { - *this = a; - BigInteger q; - divideWithRemainder(b, q); - // remainder now in *this - // don't care about quotient left in q - } - void negate(const BigInteger &a); // Negative - // Some operations are inherently unsigned and are not - // redefined for BigIntegers. Calling one of these on - // a BigInteger will convert it to a BigUnsigned, - // which takes its absolute value. - - // 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 BigInteger with the result. -public: - BigInteger operator +(const BigInteger &x) const; // Addition - BigInteger operator -(const BigInteger &x) const; // Subtraction - BigInteger operator *(const BigInteger &x) const; // Multiplication - BigInteger operator /(const BigInteger &x) const; // Division - BigInteger operator %(const BigInteger &x) const; // Modular reduction - BigInteger operator -( ) const; // Negative - - // ASSIGNMENT OPERATORS - // These perform the operation on this and x, storing the result into this. -public: - void operator +=(const BigInteger &x); // Addition - void operator -=(const BigInteger &x); // Subtraction - void operator *=(const BigInteger &x); // Multiplication - void operator /=(const BigInteger &x); // Division - void operator %=(const BigInteger &x); // Modular reduction - void flipSign(); // Negative + void negate(const BigInteger &a); + + /* Bitwise operators are not provided for BigIntegers. Use + * getMagnitude to get the magnitude and operate on that instead. */ + + BigInteger operator +(const BigInteger &x) const; + BigInteger operator -(const BigInteger &x) const; + BigInteger operator *(const BigInteger &x) const; + BigInteger operator /(const BigInteger &x) const; + BigInteger operator %(const BigInteger &x) const; + BigInteger operator -() const; + + void operator +=(const BigInteger &x); + void operator -=(const BigInteger &x); + void operator *=(const BigInteger &x); + void operator /=(const BigInteger &x); + void operator %=(const BigInteger &x); + void flipSign(); // 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 - + void operator ++( ); + void operator ++(int); + void operator --( ); + void operator --(int); }; -// PICKING APART -inline BigInteger::Sign BigInteger::getSign() const { return sign; } - // NORMAL OPERATORS /* These create an object to hold the result and invoke * the appropriate put-here operation on it, passing @@ -177,14 +157,18 @@ inline BigInteger BigInteger::operator *(const BigInteger &x) const { return ans; } inline BigInteger BigInteger::operator /(const BigInteger &x) const { - BigInteger ans; - ans.divide(*this, x); - return ans; + if (x.isZero()) throw "BigInteger::operator /: division by zero"; + BigInteger q, r; + r = *this; + r.divideWithRemainder(x, q); + return q; } inline BigInteger BigInteger::operator %(const BigInteger &x) const { - BigInteger ans; - ans.modulo(*this, x); - return ans; + if (x.isZero()) throw "BigInteger::operator %: division by zero"; + BigInteger q, r; + r = *this; + r.divideWithRemainder(x, q); + return r; } inline BigInteger BigInteger::operator -() const { BigInteger ans; @@ -209,18 +193,19 @@ inline void BigInteger::operator *=(const BigInteger &x) { multiply(*this, x); } inline void BigInteger::operator /=(const BigInteger &x) { - // Updated for divideWithRemainder - BigInteger thisCopy(*this); - thisCopy.divideWithRemainder(x, *this); - // quotient left in *this - // don't care about remainder left in thisCopy + if (x.isZero()) throw "BigInteger::operator /=: division by zero"; + /* The following technique is slightly faster than copying *this first + * when x is large. */ + BigInteger q; + divideWithRemainder(x, q); + // *this contains the remainder, but we overwrite it with the quotient. + *this = q; } inline void BigInteger::operator %=(const BigInteger &x) { - // Shortcut (woohoo!) + if (x.isZero()) throw "BigInteger::operator %=: division by zero"; BigInteger 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 } // This one is trivial inline void BigInteger::flipSign() {