Well i was creating a program in c++ .Then i noticed that there were some error due to which my program was not functioning correctly
compiler used:- Dev c++
Error was this:-
Suppose n1=274877906944 which is 2^38. so log(n1) should be 38 which is correct. now let n2=274877906942 which is smaller than n1.
So that means if we calculate log(n2) then it must give me less than log(n1).But log(n2) gave me the same result as log(n1) which is 38. Which is wrong!!!
Someone please explain this stuff..
You see the result that you do because of rounding. If you increase your precision, it'll be okay (note that the log2 function in <cmath> will cast your integers to double):
std::cout << std::fixed;
std::cout << std::setprecision(16);
std::cout << static_cast<double>(274877906944) << std::endl;
std::cout << static_cast<double>(274877906942) << std::endl;
std::cout << static_cast<double>(274877906948) << std::endl;
std::cout << log2(274877906944) << std::endl;
std::cout << log2(274877906942) << std::endl;
std::cout<< log2(274877906948) << std::endl;
Produces:
274877906944.0000000000000000
274877906942.0000000000000000
274877906948.0000000000000000
38.0000000000000000
37.9999999999895053
38.0000000000209965