Thread:User talk:Rednaxela/FastTrig/Faster normalXAngle -- faster sin,cos,tan/reply

Further experimentation with the profiler tells me that our lookup-table sin and cos are actually slower than an expanded polynomial version, I suspect this is due to occasional cache misses. However, the faster normalRelativeAngle code is still useful, here are my latest sin/cos implementations:

 public static final double sin(double d) {
      d += Math.PI;
      double x2 = Math.floor(d*(1/(2*Math.PI)));
      d -= x2*(2*Math.PI);
      d-=Math.PI;
   
      x2 = d * d;
   
      return //accurate to 6.82e-8, 3.3x faster than Math.sin, 
         //faster than lookup table in real-world conditions due to no cache misses
         //all values from "Fast Polynomial Approximations to Sine and Cosine", Garret, C. K., 2012
         (((((-2.05342856289746600727e-08*x2 + 2.70405218307799040084e-06)*x2
         - 1.98125763417806681909e-04)*x2 + 8.33255814755188010464e-03)*x2
         - 1.66665772196961623983e-01)*x2 + 9.99999707044156546685e-01)*d;
   }


   public static final double cos(double d) {
      d += Math.PI;
      double x2 = Math.floor(d*(1/(2*Math.PI)));
      d -= x2*(2*Math.PI);
      d-=Math.PI;
   
      d *= d;
   
      return //max error 5.6e-7, 4x faster than Math.cos, 
         //faster than lookup table in real-world conditions due to less cache misses
         //all values from "Fast Polynomial Approximations to Sine and Cosine", Garret, C. K., 2012
         ((((- 2.21941782786353727022e-07*d + 2.42532401381033027481e-05)*d
         - 1.38627507062573673756e-03)*d + 4.16610337354021107429e-02)*d
         - 4.99995582499065048420e-01)*d + 9.99999443739537210853e-01;
   }