will this sinus approximation be faster than a shader CG sinus function?

I have some functions that are not really sines but they are a lot quicker than conventional processing, they are simple parabole functions.

Will this be faster on a graphics processor than the built-in graphics sinus function:

    float  par (float xx){////// sinus approximation
        half xd =((fmod(abs(xx), 2.4)) - 1.2);
        if ( fmod (abs(xx) , 4.8)  > 2.4) { xd=(-xd*xd)+2.88;}
        else {xd = xd*xd;}
        xd = -xd*0.694444444+1;
        if (  (xx<0) ) { xd=-xd;}
        return xd;
    }

MAIN ANSWER

There is absolutely no way your function will be faster than the built in sin/cos functions on any graphics cards.

The shader instructions sin ,cos & tan are single-cycle instructions on just about EVERY graphics card ever manufactured. You certainly cannot purchase a graphics card today where it isn't a single-cycle.

To put your question in perspective - on a graphics card, it takes the same time to multiple 2 numbers (mul instruction) as it does to get the sinus (sin function) - a single GPU cycle.

When writing your shaders have a look at the command line options for your compiler. There will be options to output the assembly code generated, and most compilers even provide totals for the shortest path (number of instructions and cycles) and the longest path. These totals are not guaranteed durations because things like fetch can stall a pipeline, but they answer the type of question you are now asking.

Shader instruction do vary from card to card, but I think the longest single instruction is 4 GPU cycles.

If you took a look at the shader compiler assembly output for your function you are calling lots of instructions, using lots of cycles, and then asking if it could be executed more quickly than a single cycle instruction.

The whole purpose of Graphics Chips is that they are very fast and very parallel at running their instruction sets (however complex those instructions may be on other processors). When programming shaders focus your code on what the processor is designed to do. Shader programming is a different mind set from the programming you do elsewhere in software development, but once you start thinking about counting cycles, and minimizing fetch stalls, you'll soon start to open the true power of shader processing.

Best of luck.