| // Copyright 2014 PDFium Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| // Original code by Matt McCutchen, see the LICENSE file. |
| |
| #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 |
| BigUnsigned& operator=(const BigUnsigned &x) { |
| NumberlikeArray<Blk>::operator =(x); |
| return *this; |
| } |
| |
| // 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 |
| BigUnsigned& operator +=(const BigUnsigned &x); |
| BigUnsigned& operator -=(const BigUnsigned &x); |
| BigUnsigned& operator *=(const BigUnsigned &x); |
| BigUnsigned& operator /=(const BigUnsigned &x); |
| BigUnsigned& operator %=(const BigUnsigned &x); |
| BigUnsigned& operator &=(const BigUnsigned &x); |
| BigUnsigned& operator |=(const BigUnsigned &x); |
| BigUnsigned& operator ^=(const BigUnsigned &x); |
| BigUnsigned& operator <<=(int b); |
| BigUnsigned& operator >>=(int b); |
| |
| /* INCREMENT/DECREMENT OPERATORS |
| * To discourage messy coding, these do not return *this, so prefix |
| * and postfix behave the same. */ |
| BigUnsigned& operator ++( ); |
| BigUnsigned operator ++(int); |
| BigUnsigned& operator --( ); |
| BigUnsigned 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()) |
| abort(); |
| BigUnsigned q, r; |
| r = *this; |
| r.divideWithRemainder(x, q); |
| return q; |
| } |
| inline BigUnsigned BigUnsigned::operator %(const BigUnsigned &x) const { |
| if (x.isZero()) |
| abort(); |
| 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 BigUnsigned& BigUnsigned::operator +=(const BigUnsigned &x) { |
| add(*this, x); |
| return *this; |
| } |
| inline BigUnsigned& BigUnsigned::operator -=(const BigUnsigned &x) { |
| subtract(*this, x); |
| return *this; |
| } |
| inline BigUnsigned& BigUnsigned::operator *=(const BigUnsigned &x) { |
| multiply(*this, x); |
| return *this; |
| } |
| inline BigUnsigned& BigUnsigned::operator /=(const BigUnsigned &x) { |
| if (x.isZero()) |
| abort(); |
| /* 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; |
| return *this; |
| } |
| inline BigUnsigned& BigUnsigned::operator %=(const BigUnsigned &x) { |
| if (x.isZero()) |
| abort(); |
| BigUnsigned q; |
| // Mods *this by x. Don't care about quotient left in q. |
| divideWithRemainder(x, q); |
| return *this; |
| } |
| inline BigUnsigned& BigUnsigned::operator &=(const BigUnsigned &x) { |
| bitAnd(*this, x); |
| return *this; |
| } |
| inline BigUnsigned& BigUnsigned::operator |=(const BigUnsigned &x) { |
| bitOr(*this, x); |
| return *this; |
| } |
| inline BigUnsigned& BigUnsigned::operator ^=(const BigUnsigned &x) { |
| bitXor(*this, x); |
| return *this; |
| } |
| inline BigUnsigned& BigUnsigned::operator <<=(int b) { |
| bitShiftLeft(*this, b); |
| return *this; |
| } |
| inline BigUnsigned& BigUnsigned::operator >>=(int b) { |
| bitShiftRight(*this, b); |
| return *this; |
| } |
| |
| /* 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) |
| abort(); |
| 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. |
| } |
| abort(); |
| } |
| |
| /* 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 |
| abort(); |
| } |
| |
| #endif |