circle_test.cpp

#include <cstdio>
#include <cmath>

#define PI 3.14159265358979323846f
#define DEG2PI (PI / 180.0f)
#define PI2DEG (180.0f / PI)

#define EXTRA_PRECISION

#if 0

// https://stackoverflow.com/questions/2683588/what-is-the-fastest-way-to-compute-sin-and-cos-together/2683853#2683853
float sine(float x)
{
  if (x > PI)
    x -= 2 * PI;

  const float B = 4 / PI;
  const float C = -4 / (PI * PI);
  float y = B * x + C * x * std::abs(x);

#ifdef EXTRA_PRECISION
  //  const float Q = 0.775;
  const float P = 0.225;
  y = P * (y * abs(y) - y) + y;   // Q * y + P * y * abs(y)
#endif
  return y;
}

float cosine(float x)
{
  x += PI/2;
  return sine(x);
}


#else

// https://stackoverflow.com/a/53113880

// https://www.codeproject.com/Tips/700780/Fast-floor-ceiling-functions
template <typename T>
T myfloor(T x)
{
  return (int)(x + 32768.) - 32768;
}

// https://stackoverflow.com/a/28050328
template<typename T>
T cosine(T x)
{
  constexpr T tp = 1./(2.*PI);
  x *= tp;
  x -= T(.25) + myfloor(x + T(.25));
  x *= T(16.) * (std::abs(x) - T(.5));
#ifdef EXTRA_PRECISION
  x += T(.225) * x * (std::abs(x) - T(1.));
#endif
  return x;
}

template<typename T>
T sine(T x)
{
  return cosine(x - PI/2);
}

#endif

int main(int argc, char* argv[])
{
  std::FILE* f = std::fopen("test.csv", "w");

  for (int i=0; i<360; i += 4) {
    float rad = i * DEG2PI;
#if 0
    float x = std::sinf(rad);
    float y = std::cosf(rad);
#else
    float x = sine(rad);
    float y = cosine(rad);
#endif
    std::fprintf(f, "%.5f,%.5f\n", x, y);
  }

  std::fclose(f);
  return 0;
}