boost::dynamic_bitset inconsistent result with std::vector<bool>?

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I look up the boost's implementation of the dynamic_bitset and find that they compares the underlying integer storage type to improve the operator< performance, I test the correctness with following code and get the inconsistent result. Is this a bug?

std::vector<bool>       v1, v2;
v1.push_back(0); v1.push_back(1);
v2.push_back(1); v2.push_back(0);
std::cout << (v1 < v2) << '\n';

boost::dynamic_bitset<> b1, b2;
b1.push_back(0); b1.push_back(1);
b2.push_back(1); b2.push_back(0);
std::cout << (b1 < b2) << '\n';

I expect the output of both to be 1, but the second output is 0.

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Look at the bitset from most significant bits to the least significant ones

#include <iostream> 
#include <boost/dynamic_bitset.hpp> 
int main(int, char*[]) {
boost::dynamic_bitset<> x(5); // all 0's by default 
x[0] = 1; 
x[1] = 1; 
x[4] = 1;  
std::cout << x << "\n"; 
return EXIT_SUCCESS;
}

The output is

10011

The operator<<for dynamic_bitset prints the bitset from most-significant to least-significant, since that is the format most people are use to reading.

And this is what you are doing

b1.push_back(0); b1.push_back(1);//b1 = 10    
b2.push_back(1); b2.push_back(0);//b2 = 01

Boost is correct. You should change the order of push_backs to get what you intended. Boost