Is using a vector of boolean values slower than a dynamic bitset?

Question

Is using a vector of boolean values slower than a dynamic bitset?

I just heard about boost's dynamic bitset, and I was wondering is it worth the trouble. Can I just use vector of boolean values instead?

Answer 1

A great deal here depends on how many Boolean values you're working with.

Both bitset and vector<bool> normally use a packed representation where a Boolean is stored as only a single bit.

On one hand, that imposes some overhead in the form of bit manipulation to access a single value.

On the other hand, that also means many more of your Booleans will fit in your cache.

If you're using a lot of Booleans (e.g., implementing a sieve of Eratosthenes) fitting more of them in the cache will almost always end up a net gain. The reduction in memory use will gain you a lot more than the bit manipulation loses.

Most of the arguments against std::vector<bool> come back to the fact that it is not a standard container (i.e., it does not meet the requirements for a container). IMO, this is mostly a question of expectations -- since it says vector, many people expect it to be a container (other types of vectors are), and they often react negatively to the fact that vector<bool> isn't a container.

If you're using the vector in a way that really requires it to be a container, then you probably want to use some other combination -- either deque<bool> or vector<char> can work fine. Think before you do that though -- there's a lot of (lousy, IMO) advice that vector<bool> should be avoided in general, with little or no explanation of why it should be avoided at all, or under what circumstances it makes a real difference to you.

Yes, there are situations where something else will work better. If you're in one of those situations, using something else is clearly a good idea. But, be sure you're really in one of those situations first. Anybody who tells you (for example) that "Herb says you should use vector<char>" without a lot of explanation about the tradeoffs involved should not be trusted.

Let's give a real example. Since it was mentioned in the comments, let's consider the Sieve of Eratosthenes:

#include <vector>
#include <iostream>
#include <iterator>
#include <chrono>

unsigned long primes = 0;

template <class bool_t>
unsigned long sieve(unsigned max) {
    std::vector<bool_t> sieve(max, false);
    sieve[0] = sieve[1] = true;

    for (int i = 2; i < max; i++) {
        if (!sieve[i]) {
            ++primes;
            for (int temp = 2 * i; temp < max; temp += i)
                sieve[temp] = true;
        }
    }
    return primes;
}

// Warning: auto return type will fail with older compilers
// Fine with g++ 5.1 and VC++ 2015 though.
//
template <class F>
auto timer(F f, int max) {
    auto start = std::chrono::high_resolution_clock::now();
    primes += f(max);
    auto stop = std::chrono::high_resolution_clock::now();

    return stop - start;
}

int main() {
    using namespace std::chrono;

    unsigned number = 100000000;

    auto using_bool = timer(sieve<bool>, number);
    auto using_char = timer(sieve<char>, number);

    std::cout << "ignore: " << primes << "\n";
    std::cout << "Time using bool: " << duration_cast<milliseconds>(using_bool).count() << "\n";
    std::cout << "Time using char: " << duration_cast<milliseconds>(using_char).count() << "\n";
}

We've used a large enough array that we can expect a large portion of it to occupy main memory. I've also gone to a little pain to ensure that the only thing that changes between one invocation and the other is the use of a vector<char> vs. vector<bool>. Here are some results. First with VC++ 2015:

ignore: 34568730
Time using bool: 2623
Time using char: 3108

...then the time using g++ 5.1:

ignore: 34568730
Time using bool: 2359
Time using char: 3116

Obviously, the vector<bool> wins in both cases--by around 15% with VC++, and over 30% with gcc. Also note that in this case, I've chosen the size to show vector<char> in quite favorable light. If, for example, I reduce number from 100000000 to 10000000, the time differential becomes much larger:

ignore: 3987474
Time using bool: 72
Time using char: 249

Although I haven't done a lot of work to confirm, I'd guess that in this case, the version using vector<bool> is saving enough space that the array fits entirely in the cache, while the vector<char> is large enough to overflow the cache, and involve a great deal of main memory access.

Answer 2

You should usually avoid std::vector<bool> because it is not a standard container. It's a packed version, so it breaks some valuable guarantees usually given by a vector. A valid alternative would be to use std::vector<char> which is what Herb Sutter recommends.

You can read more about it in his GotW on the subject.

Update:

As has been pointed out, vector<bool> can be used to good effect, as a packed representation improves locality on large data sets. It may very well be the fastest alternative depending on circumstances. However, I would still not recommend it by default since it breaks many of the promises established by std::vector and the packing is a speed/memory tradeoff which may be beneficial in both speed and memory.

If you choose to use it, I would do so after measuring it against vector<char> for your application. Even then, I'd recommend using a typedef to refer to it via a name which does not seem to make the guarantees which it does not hold.

Answer 3

It appears that the size of a dynamic bitset cannot be changed: "The dynamic_bitset class is nearly identical to the std::bitset class. The difference is that the size of the dynamic_bitset (the number of bits) is specified at run-time during the construction of a dynamic_bitset object, whereas the size of a std::bitset is specified at compile-time through an integer template parameter." (from http://www.boost.org/doc/libs/1_36_0/libs/dynamic_bitset/dynamic_bitset.html) As such, it should be slightly faster since it will have slightly less overhead than a vector, but you lose the ability to insert elements.

Answer 4

#include "boost/dynamic_bitset.hpp"
#include <chrono>
#include <iostream>
#include <random>
#include <vector>

int main(int, char*[])
{
    auto gen = std::bind(std::uniform_int_distribution<>(0, 1), std::default_random_engine());
    std::vector<char> randomValues(1000000);
    for (char & randomValue : randomValues)
    {
        randomValue = static_cast<char>(gen());
    }

    // many accesses, few initializations
    auto start = std::chrono::high_resolution_clock::now();
    for (int i = 0; i < 500; ++i)
    {
        std::vector<bool> test(1000000, false);
        for (int j = 0; j < test.size(); ++j)
        {
            test[j] = static_cast<bool>(randomValues[j]);
        }
    }
    auto end = std::chrono::high_resolution_clock::now();
    std::cout << "Time taken1: " << std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count()
              << " milliseconds" << std::endl;
    auto start2 = std::chrono::high_resolution_clock::now();
    for (int i = 0; i < 500; ++i)
    {
        boost::dynamic_bitset<> test(1000000, false);
        for (int j = 0; j < test.size(); ++j)
        {
            test[j] = static_cast<bool>(randomValues[j]);
        }
    }
    auto end2 = std::chrono::high_resolution_clock::now();
    std::cout << "Time taken2: " << std::chrono::duration_cast<std::chrono::milliseconds>(end2 - start2).count()
              << " milliseconds" << std::endl;
    auto start3 = std::chrono::high_resolution_clock::now();
    for (int i = 0; i < 500; ++i)
    {
        std::vector<char> test(1000000, false);
        for (int j = 0; j < test.size(); ++j)
        {
            test[j] = static_cast<bool>(randomValues[j]);
        }
    }
    auto end3 = std::chrono::high_resolution_clock::now();
    std::cout << "Time taken3: " << std::chrono::duration_cast<std::chrono::milliseconds>(end3 - start3).count()
              << " milliseconds" << std::endl;

    // few accesses, many initializations
    auto start4 = std::chrono::high_resolution_clock::now();
    for (int i = 0; i < 1000000; ++i)
    {
        std::vector<bool> test(1000000, false);
        for (int j = 0; j < 500; ++j)
        {
            test[j] = static_cast<bool>(randomValues[j]);
        }
    }
    auto end4 = std::chrono::high_resolution_clock::now();
    std::cout << "Time taken4: " << std::chrono::duration_cast<std::chrono::milliseconds>(end4 - start4).count()
              << " milliseconds" << std::endl;
    auto start5 = std::chrono::high_resolution_clock::now();
    for (int i = 0; i < 1000000; ++i)
    {
        boost::dynamic_bitset<> test(1000000, false);
        for (int j = 0; j < 500; ++j)
        {
            test[j] = static_cast<bool>(randomValues[j]);
        }
    }
    auto end5 = std::chrono::high_resolution_clock::now();
    std::cout << "Time taken5: " << std::chrono::duration_cast<std::chrono::milliseconds>(end5 - start5).count()
              << " milliseconds" << std::endl;
    auto start6 = std::chrono::high_resolution_clock::now();
    for (int i = 0; i < 1000000; ++i)
    {
        std::vector<char> test(1000000, false);
        for (int j = 0; j < 500; ++j)
        {
            test[j] = static_cast<bool>(randomValues[j]);
        }
    }
    auto end6 = std::chrono::high_resolution_clock::now();
    std::cout << "Time taken6: " << std::chrono::duration_cast<std::chrono::milliseconds>(end6 - start6).count()
              << " milliseconds" << std::endl;
    return EXIT_SUCCESS;
}

Time taken1: 1821 milliseconds

Time taken2: 1722 milliseconds

Time taken3: 25 milliseconds

Time taken4: 1987 milliseconds

Time taken5: 1993 milliseconds

Time taken6: 10970 milliseconds

dynamic_bitset = std::vector<bool>

if you allocate many times but you only access the array that you created few times, go for std::vector<bool> because it has lower allocation/initialization time.

if you allocate once and access many times, go for std::vector<char>, because of faster access

Also keep in mind that std::vector<bool> is NOT safe to be used is in multithreading because you might write to different bits but it might be the same byte.

Answer 5

UPDATE: I just realize that OP was asking about vector<bool> vs bitset, and my answer does not answer the question, but I think I should leave it, if you search for c++ vector bool slow, you end up here.

vector<bool> is terribly slow. At least on my Arch Linux system (you can probably get a better implementation or something... but I was really surprised). If anybody has any suggestions why this is so slow, I'm all ears! (Sorry for the blunt beginning, here's the more professional part.)

I've written two implementations of the SOE, and the 'close to metal' C implementation is 10 times faster. sievec.c is the C implementation, and sievestl.cpp is the C++ implementation. I just compiled with make (implicit rules only, no makefile): and the results were 1.4 sec for the C version, and 12 sec for the C++/STL version:

sievecmp % make -B sievec && time ./sievec 27
cc     sievec.c   -o sievec
aa 1056282
./sievec 27  1.44s user 0.01s system 100% cpu 1.455 total

and

sievecmp % make -B sievestl && time ./sievestl 27
g++     sievestl.cpp   -o sievestl
1056282./sievestl 27  12.12s user 0.01s system 100% cpu 12.114 total

sievec.c is as follows:

#include <stdio.h>
#include <stdlib.h>

typedef unsigned long prime_t;
typedef unsigned long word_t;
#define LOG_WORD_SIZE 6

#define INDEX(i) ((i)>>(LOG_WORD_SIZE))
#define MASK(i) ((word_t)(1) << ((i)&(((word_t)(1)<<LOG_WORD_SIZE)-1)))
#define GET(p,i) (p[INDEX(i)]&MASK(i))
#define SET(p,i) (p[INDEX(i)]|=MASK(i))
#define RESET(p,i) (p[INDEX(i)]&=~MASK(i))
#define p2i(p) ((p)>>1) // (((p-2)>>1)) 
#define i2p(i) (((i)<<1)+1) // ((i)*2+3)

unsigned long find_next_zero(unsigned long from,
                    unsigned long *v,
                    size_t N){
  size_t i;
  for (i = from+1; i < N; i++) {
    if(GET(v,i)==0) return i;
  }

  return -1;
}

int main(int argc, char *argv[])
{

  size_t N = atoi(argv[1]);
  N = 1lu<<N;
  // printf("%u\n",N);
  unsigned long *v = malloc(N/8);
  for(size_t i = 0; i < N/64; i++) v[i]=0;

  unsigned long p = 3;
  unsigned long pp = p2i(p * p);

  while( pp <= N){

    for(unsigned long q = pp; q < N; q += p ){
      SET(v,q);
    }
    p = p2i(p);
    p = find_next_zero(p,v,N);
    p = i2p(p);
    pp = p2i(p * p);
  }

  unsigned long sum = 0;
  for(unsigned long i = 0; i+2 < N; i++)
    if(GET(v,i)==0 && GET(v,i+1)==0) {
      unsigned long p = i2p(i);
      // cout << p << ", " << p+2 << endl;
      sum++;
    }
  printf("aa %lu\n",sum);
  // free(v);
  return 0;
}

sievestl.cpp is as follows:

#include <iostream>
#include <vector>
#include <sstream>

using namespace std;

inline unsigned long i2p(unsigned long i){return (i<<1)+1; }
inline unsigned long p2i(unsigned long p){return (p>>1); }
inline unsigned long find_next_zero(unsigned long from, vector<bool> v){
  size_t N = v.size();
  for (size_t i = from+1; i < N; i++) {
    if(v[i]==0) return i;
  }

  return -1;
}

int main(int argc, char *argv[])
{
  stringstream ss;
  ss << argv[1];
  size_t N;
  ss >> N;
  N = 1lu<<N;
  // cout << N << endl;
  vector<bool> v(N);

  unsigned long p = 3;
  unsigned long pp = p2i(p * p);

  while( pp <= N){

    for(unsigned long q = pp; q < N; q += p ){
      v[q] = 1;
    }
    p = p2i(p);
    p = find_next_zero(p,v);
    p = i2p(p);
    pp = p2i(p * p);
  }

  unsigned sum = 0;
  for(unsigned long i = 0; i+2 < N; i++)
    if(v[i]==0 and v[i+1]==0) {
      unsigned long p = i2p(i);
      // cout << p << ", " << p+2 << endl;
      sum++;
    }
  cout << sum;
  return 0;
}