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On 30-Dec-08 13:00, Warp wrote:
> andrel <a_l### [at] hotmail com> wrote:
>> On 29-Dec-08 23:58, Warp wrote:
>>> clipka <nomail@nomail> wrote:
>>>> So yes, that should do: A loop typically taking less than two iterations (the
>>>> most expensive part probably being the RNG) and a square root. Quite
>>>> inexpensive after all.
>>> When you project the point to the hemisphere, you'll probably need three
>>> multiplications and a square root. That's going to be much more expensive
>>> than the RNG. (High-quality RNGs are very fast. They are faster than a LCG,
>>> which consists of one integer multiplication and addition.)
>
>> but sin and cos are (much?) more costly than sqrt and multiplication is
>> comparatively negligible.
>
> I was commenting to his estimation that the RNG would be the most
> expensive part of the calculation. Certainly not true. I would estimate
> that one single sqrt() call will be several times slower than pulling a
> value from a high-quality RNG.
>
sqrt has at worst N/2 iteration, with N the number of significant bits.
That is a naive implementation. I thought there are even faster
algorithms. Cheap calculators often have a button for sqrt, implying
probably that they have a (naive) hardware implementation. I don't know
if it is available also on more complex processors.
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