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Recipe 11.19. Performing Arithmetic on Bitsets
You want to perform basic arithmetic and comparison operations on a set of bits as if it were a binary
representation of an unsigned integer number.
The functions in Example 11-36
provide functions that allow arithmetic and comparison of bitset class
template from the <bitset> header as if it represents an unsigned integer.
Example 11-36. bitset_arithmetic.hpp
#include <stdexcept>
#include <bitset>
bool fullAdder(bool b1, bool b2, bool& carry) {
bool sum = (b1 ^ b2) ^ carry;
carry = (b1 && b2) || (b1 && carry) || (b2 && carry);
return sum;
bool fullSubtractor(bool b1, bool b2, bool& borrow) {
bool diff;
if (borrow) {
diff = !(b1 ^ b2);
borrow = !b1 || (b1 && b2);
else {
diff = b1 ^ b2;
borrow = !b1 && b2;
return diff;
template<unsigned int N>
bool bitsetLtEq(const std::bitset<N>& x, const std::bitset<N>& y)
for (int i=N-1; i >= 0; i--) {
if (x[i] && !y[i]) return false;
if (!x[i] && y[i]) return true;
return true;
template<unsigned int N>
bool bitsetLt(const std::bitset<N>& x, const std::bitset<N>& y)
for (int i=N-1; i >= 0; i--) {
if (x[i] && !y[i]) return false;
if (!x[i] && y[i]) return true;
return false;
template<unsigned int N>
bool bitsetGtEq(const std::bitset<N>& x, const std::bitset<N>& y)
for (int i=N-1; i >= 0; i--) {
if (x[i] && !y[i]) return true;
if (!x[i] && y[i]) return false;
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Recipe 11.20. Representing Large Fixed-Width Integers
You need to perform arithmetic of numbers larger than can be represented by a long int.
The BigInt template in Example 11-38
uses the bitset from the <bitset> header to allow you to represent
unsigned integers using a fixed number of bits specified as a template parameter.
Example 11-38. big_int.hpp
#ifndef BIG_INT_HPP
#define BIG_INT_HPP
#include <bitset>
#include "bitset_arithmetic.hpp" // Recipe 11.20
template<unsigned int N>
class BigInt
typedef BigInt self;
BigInt( ) : bits( ) { }
BigInt(const self& x) : bits(x.bits) { }
BigInt(unsigned long x) {
int n = 0;
while (x) {
bits[n++] = x & 0x1;
x >>= 1;
explicit BigInt(const std::bitset<N>& x) : bits(x) { }
// public functions
bool operator[](int n) const { return bits[n]; }
unsigned long toUlong( ) const { return bits.to_ulong( ); }
// operators
self& operator<<=(unsigned int n) {
bits <<= n;
return *this;
self& operator>>=(unsigned int n) {
bits >>= n;
return *this;
self operator++(int) {
self i = *this;
operator++( );
return i;
self operator--(int) {
self i = *this;
operator--( );
return i;
self& operator++( ) {
bool carry = false;
bits[0] = fullAdder(bits[0], 1, carry);
for (int i = 1; i < N; i++) {
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Recipe 11.21. Implementing Fixed-Point Numbers
You want to perform computations on real numbers using a fixed-point representation of a real number
rather than using a floating-point type.
Example 11-40
provides the implementation of a fixed-point real number, where the number of places to
the right of the binary point is a template parameter. For instance basic_fixed_real<10> has 10 binary
digits to the right of the binary point, allowing it to represent numbers up to a precision of 1/1,024.
Example 11-40. Representing real numbers using a fixed-point implementation
#include <iostream>
using namespace std;
template<int E>
struct BasicFixedReal
typedef BasicFixedReal self;
static const int factor = 1 << (E - 1);
BasicFixedReal( ) : m(0) { }
BasicFixedReal(double d) : m(static_cast<int>(d * factor)) { }
self& operator+=(const self& x) { m += x.m; return *this; }
self& operator-=(const self& x) { m -= x.m; return *this; }
self& operator*=(const self& x) { m *= x.m; m >>= E; return *this; }
self& operator/=(const self& x) { m /= x.m; m *= factor; return *this; }
self& operator*=(int x) { m *= x; return *this; }
self& operator/=(int x) { m /= x; return *this; }
self operator-( ) { return self(-m); }
double toDouble( ) const { return double(m) / factor;  }
// friend functions
friend self operator+(self x, const self& y) { return x += y; }
friend self operator-(self x, const self& y) { return x -= y; }
friend self operator*(self x, const self& y) { return x *= y; }
friend self operator/(self x, const self& y) { return x /= y; }
// comparison operators
friend bool operator==(const self& x, const self& y) { return x.m == y.m; }
friend bool operator!=(const self& x, const self& y) { return x.m != y.m; }
friend bool operator>(const self& x, const self& y) { return x.m > y.m; }
friend bool operator<(const self& x, const self& y) { return x.m < y.m; }
friend bool operator>=(const self& x, const self& y) { return x.m >= y.m; }
friend bool operator<=(const self& x, const self& y) { return x.m <= y.m; }
int m;
typedef BasicFixedReal<10> FixedReal;
int main( ) {
FixedReal x(0);
for (int i=0; i < 100; ++i) {
x += FixedReal(0.0625);
cout << x.toDouble( ) << endl;
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Chapter 12. Multithreading
Recipe 12.1.  Creating a Thread
Recipe 12.2.  Making a Resource Thread-Safe
Recipe 12.3.  Notifying One Thread from Another
Recipe 12.4.  Initializing Shared Resources Once
Recipe 12.5.  Passing an Argument to a Thread Function
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