>> 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)
That function introduces an small error (off by +-1) in about 50% of
the time for inputs in the range [0, 0xFFE1]. OTOH, this function (and
its optimized equivalent):
DIV255(X) ((X) + ((X) >> 8) + 0x80) >> 8
introduces an small error (off by -1) in 0.2% of the cases, the error
being the same as that introduced by the original function. This
approximation is obtained in the following way:
x/255
= x/256*256/255
= x/256 + x/(256*255)
= x/256 + x/(256*256) + x/(256*256*255)
the last factor is negligible in the range of interest. The expression
can be then approximated by:
(x + x/256)/256
Since we are performing integer arithmeric:
(x + x/256 + 128)/256
to account for rounding up. The error is well spread over the last
half of the range. This can be coded in 16 bit arithmetic while the
original needs 24 bits.
Cheers,
--
Marcelo
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