Hi André,
I have some comments to the sinf implementation. First of all,
calculating the factorials in separate function is quite inefficient,
since you repeat multiplication of what has already been multiplied.
Slightly better would be to declare local variable and calculate the
factorial in the for loop:
float fact = 1;
float y = 1;
float res = y;
for(int i = 1; i < 6; i++)
{
y *= x;
fact *= i;
res += y/fact;
}
this is rather an example for exp function, sine would require a
modification. And since you only calculate 6 values, it would be even
better to precalculate them and hardcode them in a table.
However, calculating goniometric functions from Taylor expansion is
quite inefficient and slow in general. In your algorithm, you use 6
values and power of 11, which itself introduces some error. The accuracy
of your implementation is 4 decimal digits at pi/2, where I believe the
deviation is the highest.
I suggest the following formula for calculating sine at (0, pi/2)
interval:
sin(x) = (0.99996736*x - 0.09779183*x^2 - 0.12839086*x^3 +
0.01826627*x^4) / (1 - 0.09809942*x + 0.03936879*x^2)
This is accurate at 6 decimal digits in the whole interval, moreover it
matches the values at 0, pi/12, pi/6, pi/4, pi/3, 5*pi/12 and pi/2
exactly. The highest deviation magnitude is about 7.8e-7. I have derived
the coefficients using R.
cosine can be then calculated as sin(pi/2 - x) at the (0, pi/2)
interval.
So I hope it might help you.
Pavel
On Mon, 2014-06-16 at 23:04 +0200, André Hentschel wrote:
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> Am 16.06.2014 21:51, schrieb Kai Tietz:
> > 2014-06-16 21:16 GMT+02:00 André Hentschel <[email protected]>:
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> >> Please review this initial implementation for the remaining math functions
> >> I'm unsure about the folder name and the license for taylor_private.h, it
> >> mostly contains
> >> defines/typedefs/consts from FreeBSD...
> >
> > Well, license is BSD. That's actuallly ok.
>
> ok, true
>
> > What is about the accuracy of the sinf/cosf implementation?
> > It might be of interest to replace for x64 the current x87
> > implementation by soft-float, too.
>
> As discussed on IRC i'll continue the plan of bringing the algorithms and
> build system changes in and later we see what we can do for amd64
>
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