builtin.hpp

ctz

int ctz32(unsigned x);
int ctz64(unsigned long long x);

Slow than __builtin_ctz and __builtin_ctzll but funny.

bitCount

we may use __builtin_popcount, or __builtin_popcountll in g++(but not in clang++), but it is slower than the following methods

int bitCount(unsigned n);  
int bitCountll(unsigned long long n); // The fastest so far for 64bit
int BitCountTable(unsigned n);    // The fastest so far for 32bit
int BitCountTablell(unsigned long long n);

bitCountTable use static Table of length 256, and bitCount and bitCountll use MIT HAKMEM, since $2^6 = 64 > 32$, and $2^8 = 256 > 64$

parity

bool parity(unsigned n);
bool parityll(unsigned long long n);
bool parityTable(unsigned n);
bool parityTablell(unsigned long long n);
bool parityMIT(unsigned n);
bool parityMITll(unsigned long long n);

All above are sightly slow than __builtin_parity and __builtin_parityll

acos, asin