/*
* Matt McCutchen's Big Integer Library
-* http://mysite.verizon.net/mccutchen/bigint/
*/
#ifndef BIGUNSIGNED
* 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).
+* 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.
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
// 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); // ``Aliased'' calls now do the right thing using a
+ * // temporary copy, but see note on divideWithRemainder.
+ */
// 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
+ /* These 3: Two read-only operands as arguments. Result left in *this. */
+ 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.
+ * `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 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
+ // Bitwise operations. Two read-only operands as arguments. 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
+ // These functions might exist someday.
+ //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)
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
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.
+/*
+ * 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);
}
#endif
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