fast sin, cos, tan approximations without using crt

#ifndef M_PI
#define M_PI (3.1415926535897932384626433)
#endif
#define M_PI2 (M_PI/2)
#define M_2PI (2*M_PI)
#define _fmod(_x, _y) (   (_x) - (  (long long)((_x)/(_y)) * (_y)  )   )
//(you could switch floats with doubles here, though the approximation's
 //lack of precision prevents that switch from being all that useful)
float sinf_bhaskara(float x){
    //keep x within the domain of >=0  ->  <pi,
     //while preserving relevant info
    char negative = x<0.0f;
    if(x < 0.0f) x = -x; //x = fabsf(x);
    x = _fmod(x, M_2PI); //x %= 2pi
    //'if original value of x%(2pi) is between _ -> _, returned value will be _':
     //>-2pi -> <=-pi,  >=0
     //> -pi -> <=  0,  <=0
     //>=  0 -> <  pi,  >=0
     //>= pi -> < 2pi,  <=0
    negative ^= x>=M_PI;
    if(x >= M_PI) x -= M_PI; //x %= pi

    float result = 16*x * (M_PI-x);
    result /= 5*M_PI*M_PI - 4*x*(M_PI-x);
    return (negative) ? -result : result;

}

#define sinf sinf_bhaskara
#define cosf(_x) sinf((_x)+M_PI2)
#define tanf(_x) ( sinf(_x)/cosf(_x) )