Digital to Analog Conversion using Cordic

Question

I am a newbie with DACs, but basically, I have a FPGA (DE1-SOC) running Linux. Hooked up to it is a LTC2607 DAC. Everything is operating smoothly as far as Linux recognizing the DAC over I2C and everything.

My question is regarding how to generate a sinusoidal waveform using the cordic algorithm. I have an algorithm that outputs an array of 16 hex values.

{0x00003243, 0x00001DAC, 0x00000FAD, 0x000007F5, etc...}

The code that runs the I2c/DAC accepts a 16-bit "DAC Code", which then is converted to an analog output:

uint16_t LTC2607_code(float dac_voltage, float LTC2607_lsb, float LTC2607_offset)
{
  uint16_t dac_code;
  float float_code;
  float_code = (dac_voltage - LTC2607_offset) / LTC2607_lsb;                                      // Calculate the DAC code
  float_code = (float_code > (floor(float_code) + 0.5)) ? ceil(float_code) : floor(float_code);   // Round
  if (float_code >= 65535.0)                                                                      // Limits the DAC code to 16 bits
    float_code = 65535.0;
  dac_code = (uint16_t) (float_code);                                                             // Convert to unsigned integer
  return (dac_code);
}

I know for direct digital synthesis you have to "interpolate" the points (voltage levels) along the sinusoid. My thinking is that I would send those value across the I2C, one-by-one, and however fast those 16 hex values are passed across the I2C (set by the Master (FPGA) clock @ ~10MHz) is what frequency the sin wave will be?

The code for writing to the DAC is as follows:

int8_t LTC2607_write(uint8_t i2c_address, uint8_t dac_command, uint8_t dac_address, uint16_t dac_code)
{
    int fd;
    int ret;
    char *device;
    uint8_t command_byte;
    uint8_t buffer[3];

    command_byte = dac_command | dac_address; // Build the DAC command byte

    // Open the I2C device
    device = LTC2607_get_device_name();
    fd = open(device, O_RDWR);
    if (fd < 0)
    {
        return (1);
    }

    // Select the desired address
    ret = ioctl(fd, I2C_SLAVE, i2c_address);
    if (ret < 0)
    {
        close(fd);
        return (1);
    }

    // Build the I2C command
    buffer[0] = command_byte;
    buffer[1] = (dac_code >> 8) & 0xFF;
    buffer[2] = dac_code & 0xFF;

   // Write the command to the I2C bus
   ret = write(fd, buffer, 3);
   if (ret < 3)
   {
     close(fd);
     return (1);
   }

   // Close the device
   close(fd);

   return (0);
 }

How would I convert that string of 16 hex values into a sinusoid using the above LTC2607_write function?