-/*
-* 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 number
-* were written digit by digit in base 2 ^ N, **where N is the
-* number of bits in an 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. 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 number
+ * were written digit by digit in base 2 ^ N, **where N is the
+ * number of bits in an 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.
+ */
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
NumberlikeArray<Blk>::N; // Number of bits in a Blk
-
+
/*
// FIELDS
protected:
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
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
NumberlikeArray<Blk>::operator =(x);
}
-
+
BigUnsigned(const Blk *b, Index l) : NumberlikeArray<Blk>(b, l) { // Constructor from an array of blocks
zapLeadingZeros();
}
-
+
// Constructors from integral types
BigUnsigned(unsigned long x);
BigUnsigned( long x);
BigUnsigned(unsigned short x);
BigUnsigned( short x);
~BigUnsigned() {} // Destructor
-
+
// CONVERTERS to integral types
public:
operator unsigned long () 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:
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
-
+
// 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.
+ // Bug fixed 2006.04.24: Only we, not the user, can pass a BigUnsigned off as a
+ // NumberlikeArray, so we have to wrap == and !=.
+ 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. The first eight also take
- * a second read-only operand. Example:
- * BigInteger a(1), b(1);
- * a += b;
- *
- * (3) ``Put-here'' operations: `add', `subtract', etc.
- * Using a return-by-value or assignment operator generally involves
- * copy constructions and/or assignments. The ``put-here'' operations
- * require none, but they are more of a hassle to use. Most take two
- * read-only operands and save the result in the calling object `*this',
- * whose previous value is ignored. `divideWithRemainder' is an exception.
- * <<< NOTE >>>: Put-here operations do not return a value: they don't need to!!
- * Examples:
- * BigInteger a(43), b(7), c, d;
- * c = a + b; // Now c == 50.
- * c.add(a, b); // Same effect but without the two bulk-copies.
- * c.divideWithRemainder(b, d); // 50 / 7; now d == 7 (quotient) and c == 1 (remainder).
- * a.add(a, b); // Unsafe ``aliased'' call; causes a runtime error.
- */
-
+ * 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. The first eight also take
+ * a second read-only operand. Example:
+ * BigInteger a(1), b(1);
+ * a += b;
+ *
+ * (3) ``Put-here'' operations: `add', `subtract', etc.
+ * Using a return-by-value or assignment operator generally involves
+ * copy constructions and/or assignments. The ``put-here'' operations
+ * require none, but they are more of a hassle to use. Most take two
+ * read-only operands and save the result in the calling object `*this',
+ * whose previous value is ignored. `divideWithRemainder' is an exception.
+ * <<< NOTE >>>: Put-here operations do not return a value: they don't need to!!
+ * Examples:
+ * BigInteger a(43), b(7), c, d;
+ * c = a + b; // Now c == 50.
+ * c.add(a, b); // Same effect but without the two bulk-copies.
+ * c.divideWithRemainder(b, d); // 50 / 7; now d == 7 (quotient) and c == 1 (remainder).
+ * a.add(a, b); // ``Aliased'' calls now do the right thing using a
+ * // temporary copy, but see note on divideWithRemainder.
+ */
+
// PUT-HERE OPERATIONS
public:
/* These 3: Two read-only operands as arguments. Result left in *this. */
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.
- */
+ * `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.
+ * `a.divideWithRemainder(b, a)' causes 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 backward 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 backward compatibility
*this = a;
BigUnsigned q;
divideWithRemainder(b, q);
// remainder now in *this
// don't care about quotient left in q
}
- // Bitwise operations. Two read-only operands as arguments. Result left in *this.
+ // Bitwise operations. Result left in *this.
// These are not provided for BigIntegers; I think that using them on BigIntegers
// will discard the sign first.
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.
BigUnsigned operator &(const BigUnsigned &x) const; // Bitwise AND
BigUnsigned operator |(const BigUnsigned &x) const; // Bitwise OR
BigUnsigned operator ^(const BigUnsigned &x) const; // Bitwise XOR
-
+ BigUnsigned operator <<(unsigned int b) const; // Bitwise left shift
+ BigUnsigned operator >>(unsigned int b) const; // Bitwise right shift
+ // Additional operators in an attempt to avoid overloading tangles.
+ BigUnsigned operator <<(int b) const;
+ BigUnsigned operator >>(int b) const;
+
// ASSIGNMENT OPERATORS
// These perform the operation on this and x, storing the result into this.
public:
void operator &=(const BigUnsigned &x); // Bitwise AND
void operator |=(const BigUnsigned &x); // Bitwise OR
void operator ^=(const BigUnsigned &x); // Bitwise XOR
-
+ void operator <<=(unsigned int b); // Bitwise left shift
+ void operator >>=(unsigned int b); // Bitwise right shift
+ // Additional operators in an attempt to avoid overloading tangles.
+ void operator <<=(int b);
+ void operator >>=(int b);
+
// 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.
void operator ++(int); // Postfix decrement
void operator --( ); // Prefix increment
void operator --(int); // Postfix decrement
-
+
// Helper function that needs access to BigUnsigned internals
friend Blk getShiftedBlock(const BigUnsigned &num, Index x, unsigned int y);
};
// 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. */
+ * the appropriate put-here operation on it, passing
+ * this and x. The new object is then returned. */
inline BigUnsigned BigUnsigned::operator +(const BigUnsigned &x) const {
BigUnsigned ans;
ans.add(*this, x);
ans.bitXor(*this, x);
return ans;
}
+inline BigUnsigned BigUnsigned::operator <<(unsigned int b) const {
+ BigUnsigned ans;
+ ans.bitShiftLeft(*this, b);
+ return ans;
+}
+inline BigUnsigned BigUnsigned::operator >>(unsigned int b) const {
+ BigUnsigned ans;
+ ans.bitShiftRight(*this, b);
+ return ans;
+}
+inline BigUnsigned BigUnsigned::operator <<(int b) const {
+ if (b < 0)
+ throw "BigUnsigned::operator <<(int): Negative shift amounts are not supported";
+ return *this << (unsigned int)(b);
+}
+inline BigUnsigned BigUnsigned::operator >>(int b) const {
+ if (b < 0)
+ throw "BigUnsigned::operator >>(int): Negative shift amounts are not supported";
+ return *this >> (unsigned int)(b);
+}
-// 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.
+/*
+ * ASSIGNMENT OPERATORS
+ *
+ * Now the responsibility for making a temporary copy if necessary
+ * belongs to the put-here operations. I made this change on 2007.02.13 after
+ * Boris Dessy pointed out that the old implementation handled calls like
+ * "a *= a" badly: it translated them to essentially "a.multiply(aCopy, a)",
+ * which threw an exception.
+ */
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
// 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 <<=(unsigned int b) {
+ bitShiftLeft(*this, b);
+}
+inline void BigUnsigned::operator >>=(unsigned int b) {
+ bitShiftRight(*this, b);
+}
+inline void BigUnsigned::operator <<=(int b) {
+ if (b < 0)
+ throw "BigUnsigned::operator <<=(int): Negative shift amounts are not supported";
+ *this <<= (unsigned int)(b);
+}
+inline void BigUnsigned::operator >>=(int b) {
+ if (b < 0)
+ throw "BigUnsigned::operator >>=(int): Negative shift amounts are not supported";
+ *this >>= (unsigned int)(b);
}
#endif
Matt McCutchen's Web Site / bigint / bigint.git / blobdiff