Speed-coding for the 6502 – a simple example

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JKCalhoun

Games that needed trig in the 90's often used SIN/COS lookup-tables. To keep memory down:

1) you only need the first 1/4 of the Sine table since the remaining 3/4 are either the first 1/4 in reverse and/or with the sign flipped.

2) and of course Sine can also be used as a Cosine lookup if you add pi/2 radians to the cosine angle (wrapping around of course).

3) to avoid the size needed for a table of floats you can of course use integers (scaled by some factor) or fixed-point values.

4) and simple interpolation would get you seemingly more precision.

(Combining all the above was a bit gross so documentation and a good SPI helped.)

Joker_vD

I wonder if building this table can be sped up by noticing a recurring pattern?

    x    0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 ... 254 255
    f(x) 0  0  1  2  3  3  4  5  6  6  7  8  9  9 10 11 12 12 ... 190 191

So something like

    sta table,y
    iny
    sta table,y
    adc $0
    iny    
    sta table,y
    adc $0
    iny    
    sta table,y
    adc $0
    iny

used as the loop body that should be repeated 64 times, should work. Will it take less than 6000 cycles total?

anyfoo

Very neat. Breaking up multiplications and divisions into bit shifts, and lookup table to trade off memory for runtime, are indeed nothing new to engineers working on the low level, but this paints a very pretty picture of how this looks in practice.

rbanffy

What a delightful short read.

They could go one step further and calculate the table as needed and use it as a cache.

For an single image scaling it might get a little bit better.

spc476

If you read the entire article, they do that at the end of the article.

anyfoo

Not quite. They build the entire table upfront, whether any individual entry is needed or not.

Making it an on-demand cache instead is a neat next step. Whether it helps or hurts depends on the actual input: If the input image uses every pixel value anyway, the additional overhead of checking whether the table entry is computed is just unnecessary extra with no value.

But if a typical image only uses a few pixel values, then the amortized cost of just calculating the few needed table entries may very well be significantly below the cost of the current algorithm.

If images are somewhere in between, or their characteristics not well known, then simply trying out both approaches with typical input data is a good approach!

Unless you’re perfectly happy with 0.2 seconds, for example because the runtime of some other parts take so long that dwarfs those 0.2s, then why bother.

egypturnash

Even if you could get the "is this cell of the table calculated?" check down to one cycle (which you can't, 6502 branch instructions take 2-4 cycles, plus a few more operations to check the table calculation status), it's still gonna add one cycle to a hot loop that's done 43k times. Pre-calcing the entire table only burns 6k cycles, and can probably be done while displaying some transitional effect that requires very little CPU.

If we presume this scaling operation will be done more than one time (which it probably will be if it's getting this level of optimization) then it gets even worse.

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HN

Speed-coding for the 6502 – a simple example

Speed-coding for the 6502 – a simple example