short buffer[44100];
float frequency = 440.0f;
float sampling_ratio = 44100.0f;
float amplitude = 0.5f;
float t;
for (int i = 0; i < 44100; i++)
{
    float theta = ((float)i / sampling_ratio) * PI;
    buffer[i] = (short)(sin(theta * frequency) * 32767.0f * amplitude);
}

void add_sine_wave(short* buffer, int buffer_length, float frequency, float sampling_ratio, float amplitude)
{
    for (int i = 0; i < buffer_length; i++)
    {
        float theta = ((float)i / sampling_ratio) * M_PI;
        t = (sin(theta * frequency) * 32767.0f * amplitude);
        if(t>SHRT_MAX) t = SHRT_MAX; // overflow check
        if(t<SHRT_MIN) t = SHRT_MIN; // underflow check
        buffer[i] += (short) t;`
    }
}

short buffer[44100];
memset(buffer, 0, sizeof(buffer));
// Create an A Major chord
add_sine_wave(buffer, 44100, 440.0f, 44100.0f, 0.5f);
add_sine_wave(buffer, 44100, 554.37f, 44100.0f, 0.5f);
add_sine_wave(buffer, 44100, 659.26f, 44100.0f, 0.5f);