discrete-cos.cc

class DiscreteCos {
  public:
      DiscreteCos() { generate(); }
    static const unsigned int DC_2PI = 2048;
    static const unsigned int DC_PI  = 1024;
    static const unsigned int DC_PI2 = 512;

    int32_t cos(unsigned int t) {
        t %= DC_2PI;
        int32_t r;

        if (t < DC_PI2) {
            r = m_cosTable[t];
        } else if (t < DC_PI) {
            r = -m_cosTable[DC_PI - 1 - t];
        } else if (t < (DC_PI + DC_PI2)) {
            r = -m_cosTable[t - DC_PI];
        } else {
            r = m_cosTable[DC_2PI - 1 - t];
        }

        return r;
    }

    // sin(x) = cos(x - pi / 2)
    int32_t sin(unsigned int t) {
        t %= DC_2PI;

        if (t < DC_PI2)
            return cos(t + DC_2PI - DC_PI2);

        return cos(t - DC_PI2);
    }

  private:
    int32_t m_cosTable[512];

    // f(n) = cos(n * 2pi / 2048)
    // f(n) = 2 * f(1) * f(n - 1) - f(n - 2)
    void generate() {
        m_cosTable[0]             = 16777216; // 2^24 * cos(0 * 2pi / 2048)
        int64_t C = m_cosTable[1] = 16777137; // 2^24 * cos(1 * 2pi / 2048) = C = f(1);

        for (int i = 2; i < 512; i++)
            m_cosTable[i] = ((C * m_cosTable[i - 1]) >> 23) - m_cosTable[i - 2];

        m_cosTable[511] = 0;
    }
};

DiscreteCos dc;