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Diffstat (limited to 'third_party/bigint/BigUnsigned.hh')
| -rw-r--r-- | third_party/bigint/BigUnsigned.hh | 418 |
1 files changed, 418 insertions, 0 deletions
diff --git a/third_party/bigint/BigUnsigned.hh b/third_party/bigint/BigUnsigned.hh new file mode 100644 index 0000000000..adf1c00bc3 --- /dev/null +++ b/third_party/bigint/BigUnsigned.hh @@ -0,0 +1,418 @@ +#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; + 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. + NumberlikeArray<Blk>::getCapacity; + 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 |