Bit Bashing Fun

[ShannonSmith]

I am currently doing an optimised sin using a lookup table and given I have seen some bitwise magic posted before I was wondering what people could come up with for this problem:

Given power of 2 sized table containing a quarter sine wave what is the best way to get the table index/sign for the output.

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static final float[] TABLE; // a power of 2 length quarter wave sine table // phase goes from 0.0f->1.0f public static float sin(float phase){   }

Now you can just use conditionals to calculate each of the quadrants but if you convert phase to an integer using TABLE.length*4 the top two bits give you the sign and flip for the quarter wave. I have come up with some mashing that gives you the index and sign but I'm sure there is an easier way two exploit 2's compliment and modular to get the answer.  Bonus points for efficient linear interpolation.

[Riven]

Well, if you want performance, you just make your table 4 times as big. You are trashing your cache anyway.

http://riven8192.blogspot.com/2009/08/fastmath-sincos-lookup-tables.html

I do a multiplication, a cast and a mask. It doesn't get faster than that.

[Riven]

If you want bit magic for the fun of it...

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int sign = magic >>> 31; int flip = magic >>> 30; int offset = magic & mask; int invert = sign^flip; return TABLE[TABLE.length*invert - offset*((invert<<1)-1)]

I think...

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[ShannonSmith]

The reason I wanted to use quarter wave is because I assumed it would have an effect on cache performance, I will have to try measuring it and see what the actual difference is.

[Jono]

Do you know if a floatToRawIntBits can be performed faster than a float->int cast? I might try comparing them at some point, but if it can be then:

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public static float sin(float phase){  return TABLE[(Float.floatToRawIntBits(1.0f+f) >> 15) & 0xFF]; }

for a 256 length table. For 512 then shift by 14, and mask with 0x1FF, etc. The idea being to keep the float within one power-of-two fraction, and just use the most significant mantissa bits.

This assumes that the range is from 0-1.0f, excluding 1.0f.

Edit: This isn't actually answering the original question, sorry. Just a thought of an alternative to the float cast.