jmasterx - 1 year ago 114

C Question

I have my own, very fast cos function:

`float sine(float x)`

{

const float B = 4/pi;

const float C = -4/(pi*pi);

float y = B * x + C * x * abs(x);

// const float Q = 0.775;

const float P = 0.225;

y = P * (y * abs(y) - y) + y; // Q * y + P * y * abs(y)

return y;

}

float cosine(float x)

{

return sine(x + (pi / 2));

}

But now when I profile, I see that acos() is killing the processor. I don't need intense precision. What is a fast way to calculate acos(x)

Thanks.

Answer Source

A simple cubic approximation, the Lagrange polynomial for x ∈ {-1, -½, 0, ½, 1}, is:

```
double acos(x) {
return (-0.69813170079773212 * x * x - 0.87266462599716477) * x + 1.5707963267948966;
}
```

It has a maximum error of about 0.18 rad.