[are the mailing lists having hiccups? I sent something yesterday and it
didn't show up]
>> José Fonseca <[EMAIL PROTECTED]> writes:
> +#if 0
> #define DIV255(X) (((X) << 8) + (X) + 256) >> 16
> +#else
> + const GLint temp;
> +#define DIV255(X) (temp = (X), ((temp << 8) + temp + 256) >> 16)
> +#endif
> +#if 0
This function introduces a slight error (+-1) for about half the cases.
This instead:
DIV255(X) ((X) + ((X) >> 8) + 0x80) >> 8
introduces a slight error (-1) for 0.2% of the cases in the input range
[0, 0xFE01]. It uses only 16 bits instead of 24 bits as the original.
If someone is insterested:
x/255
= x/256*256/255
= x/256 + x/(256*255)
= x/256 + x/256**2 + x/(256**2*255)
approx = x/256 + x/256**2
= (x + x/256)/256
and the 0x80 is needed to account for rounding up when using interger
arithmetic. The error introduced by the approximation is at most
255/256**2 but becomes more significant when using the last expression.
The error introduced by this approximation occurs only on the upper
half of the range of interest and is well spread all over it. Like I
said before, it's always -1. The accumulated error varies between
unnoticeable to quite annoying. The only way I've found to avoid the
error is to use a 64 kB lookup table to perform the division. The
speed difference is not significant and the accumulated error shows up
much later.
Cheers,
Marcelo
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