// 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
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())
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 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())
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;
}
inline void 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);
}
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)
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