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Diffstat (limited to 'bigint/BigUnsigned.hh')
| -rw-r--r-- | bigint/BigUnsigned.hh | 418 |
1 files changed, 0 insertions, 418 deletions
diff --git a/bigint/BigUnsigned.hh b/bigint/BigUnsigned.hh deleted file mode 100644 index 9228753c..00000000 --- a/bigint/BigUnsigned.hh +++ /dev/null @@ -1,418 +0,0 @@ -#ifndef BIGUNSIGNED_H -#define BIGUNSIGNED_H - -#include "NumberlikeArray.hh" - -/* A BigUnsigned object represents a nonnegative integer of size limited only by - * available memory. BigUnsigneds support most mathematical operators and can - * be converted to and from most primitive integer types. - * - * The number is stored as a NumberlikeArray of unsigned longs as if it were - * written in base 256^sizeof(unsigned long). The least significant block is - * first, and the length is such that the most significant block is nonzero. */ -class BigUnsigned : protected NumberlikeArray<unsigned long> { - -public: - // Enumeration for the result of a comparison. - enum CmpRes { less = -1, equal = 0, greater = 1 }; - - // BigUnsigneds are built with a Blk type of unsigned long. - typedef unsigned long Blk; - - typedef NumberlikeArray<Blk>::Index Index; - using NumberlikeArray<Blk>::N; - -protected: - // Creates a BigUnsigned with a capacity; for internal use. - BigUnsigned(int, Index c) : NumberlikeArray<Blk>(0, c) {} - - // Decreases len to eliminate any leading zero blocks. - void zapLeadingZeros() { - while (len > 0 && blk[len - 1] == 0) - len--; - } - -public: - // Constructs zero. - BigUnsigned() : NumberlikeArray<Blk>() {} - - // Copy constructor - BigUnsigned(const BigUnsigned &x) : NumberlikeArray<Blk>(x) {} - - // Assignment operator - void operator=(const BigUnsigned &x) { - NumberlikeArray<Blk>::operator =(x); - } - - // Constructor that copies from a given array of blocks. - BigUnsigned(const Blk *b, Index blen) : NumberlikeArray<Blk>(b, blen) { - // Eliminate any leading zeros we may have been passed. - zapLeadingZeros(); - } - - // Destructor. NumberlikeArray does the delete for us. - ~BigUnsigned() {} - - // Constructors from primitive integer types - BigUnsigned(unsigned long x); - BigUnsigned( long x); - BigUnsigned(unsigned int x); - BigUnsigned( int x); - BigUnsigned(unsigned short x); - BigUnsigned( short x); -protected: - // Helpers - template <class X> void initFromPrimitive (X x); - template <class X> void initFromSignedPrimitive(X x); -public: - - /* 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: - // Helpers - template <class X> X convertToSignedPrimitive() const; - template <class X> X convertToPrimitive () const; -public: - - // BIT/BLOCK ACCESSORS - - // Expose these from NumberlikeArray directly. - using NumberlikeArray<Blk>::getCapacity; - using NumberlikeArray<Blk>::getLength; - - /* Returns the requested block, or 0 if it is beyond the length (as if - * the number had 0s infinitely to the left). */ - Blk getBlock(Index i) const { return i >= len ? 0 : blk[i]; } - /* Sets the requested block. The number grows or shrinks as necessary. */ - void setBlock(Index i, Blk newBlock); - - // The number is zero if and only if the canonical length is zero. - bool isZero() const { return NumberlikeArray<Blk>::isEmpty(); } - - /* Returns the length of the number in bits, i.e., zero if the number - * is zero and otherwise one more than the largest value of bi for - * which getBit(bi) returns true. */ - Index bitLength() const; - /* Get the state of bit bi, which has value 2^bi. Bits beyond the - * number's length are considered to be 0. */ - bool getBit(Index bi) const { - return (getBlock(bi / N) & (Blk(1) << (bi % N))) != 0; - } - /* Sets the state of bit bi to newBit. The number grows or shrinks as - * necessary. */ - void setBit(Index bi, bool newBit); - - // COMPARISONS - - // Compares this to x like Perl's <=> - CmpRes compareTo(const BigUnsigned &x) const; - - // Ordinary comparison operators - 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. Most also take a second read-only operand. - * Example: - * BigInteger a(1), b(1); - * a += b; - * - * (3) Copy-less operations: `add', `subtract', etc. - * These named methods take operands as arguments and store the result - * in the receiver (*this), avoiding unnecessary copies and allocations. - * `divideWithRemainder' is special: it both takes the dividend from and - * stores the remainder into the receiver, and it takes a separate - * object in which to store the quotient. NOTE: If you are wondering - * why these don't return a value, you probably mean to use the - * overloaded return-by-value operators instead. - * - * Examples: - * BigInteger a(43), b(7), c, d; - * - * c = a + b; // Now c == 50. - * c.add(a, b); // Same effect but without the two copies. - * - * c.divideWithRemainder(b, d); - * // 50 / 7; now d == 7 (quotient) and c == 1 (remainder). - * - * // ``Aliased'' calls now do the right thing using a temporary - * // copy, but see note on `divideWithRemainder'. - * a.add(a, b); - */ - - // COPY-LESS OPERATIONS - - // These 8: Arguments are read-only operands, result is saved in *this. - void add(const BigUnsigned &a, const BigUnsigned &b); - void subtract(const BigUnsigned &a, const BigUnsigned &b); - void multiply(const BigUnsigned &a, const BigUnsigned &b); - void bitAnd(const BigUnsigned &a, const BigUnsigned &b); - void bitOr(const BigUnsigned &a, const BigUnsigned &b); - void bitXor(const BigUnsigned &a, const BigUnsigned &b); - /* Negative shift amounts translate to opposite-direction shifts, - * except for -2^(8*sizeof(int)-1) which is unimplemented. */ - void bitShiftLeft(const BigUnsigned &a, int b); - void bitShiftRight(const BigUnsigned &a, int b); - - /* `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'. - * / and % use semantics similar to Knuth's, which differ from the - * primitive integer semantics under division by zero. See the - * implementation in BigUnsigned.cc for details. - * `a.divideWithRemainder(b, a)' throws an exception: it doesn't make - * sense to write quotient and remainder into the same variable. */ - void divideWithRemainder(const BigUnsigned &b, BigUnsigned &q); - - /* `divide' and `modulo' are no longer offered. Use - * `divideWithRemainder' instead. */ - - // OVERLOADED RETURN-BY-VALUE OPERATORS - BigUnsigned operator +(const BigUnsigned &x) const; - BigUnsigned operator -(const BigUnsigned &x) const; - BigUnsigned operator *(const BigUnsigned &x) const; - BigUnsigned operator /(const BigUnsigned &x) const; - BigUnsigned operator %(const BigUnsigned &x) const; - /* OK, maybe unary minus could succeed in one case, but it really - * shouldn't be used, so it isn't provided. */ - BigUnsigned operator &(const BigUnsigned &x) const; - BigUnsigned operator |(const BigUnsigned &x) const; - BigUnsigned operator ^(const BigUnsigned &x) const; - BigUnsigned operator <<(int b) const; - BigUnsigned operator >>(int b) const; - - // OVERLOADED ASSIGNMENT OPERATORS - void operator +=(const BigUnsigned &x); - void operator -=(const BigUnsigned &x); - void operator *=(const BigUnsigned &x); - void operator /=(const BigUnsigned &x); - void operator %=(const BigUnsigned &x); - void operator &=(const BigUnsigned &x); - void operator |=(const BigUnsigned &x); - void operator ^=(const BigUnsigned &x); - void operator <<=(int b); - void operator >>=(int b); - - /* INCREMENT/DECREMENT OPERATORS - * To discourage messy coding, these do not return *this, so prefix - * and postfix behave the same. */ - void operator ++( ); - void operator ++(int); - void operator --( ); - void operator --(int); - - // Helper function that needs access to BigUnsigned internals - friend Blk getShiftedBlock(const BigUnsigned &num, Index x, - unsigned int y); - - // See BigInteger.cc. - template <class X> - friend X convertBigUnsignedToPrimitiveAccess(const BigUnsigned &a); -}; - -/* Implementing the return-by-value and assignment operators in terms of the - * copy-less operations. The copy-less operations are responsible for making - * any necessary temporary copies to work around aliasing. */ - -inline BigUnsigned BigUnsigned::operator +(const BigUnsigned &x) const { - BigUnsigned ans; - ans.add(*this, x); - return ans; -} -inline BigUnsigned BigUnsigned::operator -(const BigUnsigned &x) const { - BigUnsigned ans; - ans.subtract(*this, x); - return ans; -} -inline BigUnsigned BigUnsigned::operator *(const BigUnsigned &x) const { - BigUnsigned ans; - ans.multiply(*this, x); - return ans; -} -inline BigUnsigned BigUnsigned::operator /(const BigUnsigned &x) const { - if (x.isZero()) throw "BigUnsigned::operator /: division by zero"; - BigUnsigned q, r; - r = *this; - r.divideWithRemainder(x, q); - return q; -} -inline BigUnsigned BigUnsigned::operator %(const BigUnsigned &x) const { - if (x.isZero()) throw "BigUnsigned::operator %: division by zero"; - BigUnsigned q, r; - r = *this; - r.divideWithRemainder(x, q); - return r; -} -inline BigUnsigned BigUnsigned::operator &(const BigUnsigned &x) const { - BigUnsigned ans; - ans.bitAnd(*this, x); - return ans; -} -inline BigUnsigned BigUnsigned::operator |(const BigUnsigned &x) const { - BigUnsigned ans; - ans.bitOr(*this, x); - return ans; -} -inline BigUnsigned BigUnsigned::operator ^(const BigUnsigned &x) const { - BigUnsigned ans; - ans.bitXor(*this, x); - return ans; -} -inline BigUnsigned BigUnsigned::operator <<(int b) const { - BigUnsigned ans; - ans.bitShiftLeft(*this, b); - return ans; -} -inline BigUnsigned BigUnsigned::operator >>(int b) const { - BigUnsigned ans; - ans.bitShiftRight(*this, b); - return ans; -} - -inline void BigUnsigned::operator +=(const BigUnsigned &x) { - add(*this, x); -} -inline void BigUnsigned::operator -=(const BigUnsigned &x) { - subtract(*this, x); -} -inline void BigUnsigned::operator *=(const BigUnsigned &x) { - multiply(*this, x); -} -inline void BigUnsigned::operator /=(const BigUnsigned &x) { - if (x.isZero()) throw "BigUnsigned::operator /=: division by zero"; - /* The following technique is slightly faster than copying *this first - * when x is large. */ - BigUnsigned q; - divideWithRemainder(x, q); - // *this contains the remainder, but we overwrite it with the quotient. - *this = q; -} -inline void BigUnsigned::operator %=(const BigUnsigned &x) { - if (x.isZero()) throw "BigUnsigned::operator %=: division by zero"; - BigUnsigned q; - // Mods *this by x. Don't care about quotient left in q. - divideWithRemainder(x, q); -} -inline void BigUnsigned::operator &=(const BigUnsigned &x) { - bitAnd(*this, x); -} -inline void BigUnsigned::operator |=(const BigUnsigned &x) { - bitOr(*this, x); -} -inline void BigUnsigned::operator ^=(const BigUnsigned &x) { - bitXor(*this, x); -} -inline void BigUnsigned::operator <<=(int b) { - bitShiftLeft(*this, b); -} -inline void BigUnsigned::operator >>=(int b) { - bitShiftRight(*this, b); -} - -/* Templates for conversions of BigUnsigned to and from primitive integers. - * BigInteger.cc needs to instantiate convertToPrimitive, and the uses in - * BigUnsigned.cc didn't do the trick; I think g++ inlined convertToPrimitive - * instead of generating linkable instantiations. So for consistency, I put - * all the templates here. */ - -// CONSTRUCTION FROM PRIMITIVE INTEGERS - -/* Initialize this BigUnsigned from the given primitive integer. The same - * pattern works for all primitive integer types, so I put it into a template to - * reduce code duplication. (Don't worry: this is protected and we instantiate - * it only with primitive integer types.) Type X could be signed, but x is - * known to be nonnegative. */ -template <class X> -void BigUnsigned::initFromPrimitive(X x) { - if (x == 0) - ; // NumberlikeArray already initialized us to zero. - else { - // Create a single block. blk is NULL; no need to delete it. - cap = 1; - blk = new Blk[1]; - len = 1; - blk[0] = Blk(x); - } -} - -/* Ditto, but first check that x is nonnegative. I could have put the check in - * initFromPrimitive and let the compiler optimize it out for unsigned-type - * instantiations, but I wanted to avoid the warning stupidly issued by g++ for - * a condition that is constant in *any* instantiation, even if not in all. */ -template <class X> -void BigUnsigned::initFromSignedPrimitive(X x) { - if (x < 0) - throw "BigUnsigned constructor: " - "Cannot construct a BigUnsigned from a negative number"; - else - initFromPrimitive(x); -} - -// CONVERSION TO PRIMITIVE INTEGERS - -/* Template with the same idea as initFromPrimitive. This might be slightly - * slower than the previous version with the masks, but it's much shorter and - * clearer, which is the library's stated goal. */ -template <class X> -X BigUnsigned::convertToPrimitive() const { - if (len == 0) - // The number is zero; return zero. - return 0; - else if (len == 1) { - // The single block might fit in an X. Try the conversion. - X x = X(blk[0]); - // Make sure the result accurately represents the block. - if (Blk(x) == blk[0]) - // Successful conversion. - return x; - // Otherwise fall through. - } - throw "BigUnsigned::to<Primitive>: " - "Value is too big to fit in the requested type"; -} - -/* Wrap the above in an x >= 0 test to make sure we got a nonnegative result, - * not a negative one that happened to convert back into the correct nonnegative - * one. (E.g., catch incorrect conversion of 2^31 to the long -2^31.) Again, - * separated to avoid a g++ warning. */ -template <class X> -X BigUnsigned::convertToSignedPrimitive() const { - X x = convertToPrimitive<X>(); - if (x >= 0) - return x; - else - throw "BigUnsigned::to(Primitive): " - "Value is too big to fit in the requested type"; -} - -#endif |