X-Git-Url: https://mattmccutchen.net/bigint/bigint.git/blobdiff_plain/ef2b7c5922c36f93923dd3482c5bfd41b14d82ce..b9e459aab5aff20564efc14602d214fd4f6a233a:/BigUnsigned.hh diff --git a/BigUnsigned.hh b/BigUnsigned.hh index 61fcb90..360c341 100644 --- a/BigUnsigned.hh +++ b/BigUnsigned.hh @@ -1,39 +1,35 @@ -/* -* Matt McCutchen's Big Integer Library -*/ - #ifndef BIGUNSIGNED #define BIGUNSIGNED #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 { - + // 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::Index Index; // (NlA) Type for the index of a block in the array NumberlikeArray::N; // Number of bits in a Blk - + /* // FIELDS protected: @@ -41,34 +37,34 @@ class BigUnsigned : protected NumberlikeArray { 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(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() {} // Default constructor (value is 0) BigUnsigned(const BigUnsigned &x) : NumberlikeArray(x) {} // Copy constructor - + void operator=(const BigUnsigned &x) { // Assignment operator NumberlikeArray::operator =(x); } - + BigUnsigned(const Blk *b, Index l) : NumberlikeArray(b, l) { // Constructor from an array of blocks zapLeadingZeros(); } - + // Constructors from integral types BigUnsigned(unsigned long x); BigUnsigned( long x); @@ -77,7 +73,7 @@ class BigUnsigned : protected NumberlikeArray { BigUnsigned(unsigned short x); BigUnsigned( short x); ~BigUnsigned() {} // Destructor - + // CONVERTERS to integral types public: operator unsigned long () const; @@ -86,7 +82,7 @@ class BigUnsigned : protected NumberlikeArray { 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: @@ -97,7 +93,7 @@ class BigUnsigned : protected NumberlikeArray { 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::isEmpty(); } // Often convenient for loops - + // COMPARISONS public: // Compares this to x like Perl's <=> @@ -117,44 +113,44 @@ class BigUnsigned : protected NumberlikeArray { 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. - */ - + * 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. */ @@ -162,14 +158,14 @@ class BigUnsigned : protected NumberlikeArray { 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. - */ + * `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) { BigUnsigned a2(a); @@ -192,7 +188,7 @@ class BigUnsigned : protected NumberlikeArray { void bitXor(const BigUnsigned &a, const BigUnsigned &b); // Bitwise XOR 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. @@ -210,7 +206,7 @@ class BigUnsigned : protected NumberlikeArray { // 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: @@ -227,7 +223,7 @@ class BigUnsigned : protected NumberlikeArray { // 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. @@ -236,15 +232,15 @@ class BigUnsigned : protected NumberlikeArray { 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);