C语言中的无穷正弦生成

Question

double time;
void control_loop() {
    time += 30e-6;
    double sine = sin(2 * M_PI * 280 * time);
    ...
}

null

Answer 1

static const double dx = cos(2 * M_PI * 280 * 30e-6);
static const double dy = sin(2 * M_PI * 280 * 30e-6);
double x = 1, y = 0; // complex x + iy
int counter = 0;

void control_loop() {
    double xx = dx*x - dy*y;
    double yy = dx*y + dy*x;
    x = xx, y = yy;

    // renormalize once in a while, based on
    // https://www.gamedev.net/forums/topic.asp?topic_id=278849
    if((counter++ & 0xff) == 0) {
        double d = 1 - (x*x + y*y - 1)/2;
        x *= d, y *= d;
    }

    double sine = y; // this is your sine
}

xx = cos((n+1)*a) = cos(n*a)*cos(a) - sin(n*a)*sin(a) = x*dx - y*dy
yy = sin((n+1)*a) = sin(n*a)*cos(a) + cos(n*a)*sin(a) = y*dx + x*dy

double d = 1/sqrt(x*x + y*y);
x *= d, y *= d;

d = 1 - (x*x + y*y - 1)/2