I'm pretty sure it's not faster, but it was fun to write:

    float asin(float x) {
      float x2 = 1.0f-fabs(x);
      u32 i = bitcast(x2);
      i = 0x5f3759df - (i>>1);
      float inv = bitcast(i);
      return copysign(pi/2-pi/2*(x2*inv),x);
    }

Courtesy of evil floating point bithacks.