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how to locate right slot in a range with right-shifting and offset?

Hi all,

Assume I non-uniformally break down a range from 0 to (2^10)-1 into
(2^4)-1 blocks.

|----|---|------|---|......|--|
0    5   7                   (2^10)-1

For a given value x (x may be from 0 to 2^10-1), I would like to
locate what block x should be in. For example if x is 6, I want to
find the second block (from 5 to 7) in the above figure. ( x is
integers).

In a technical report, for this task, I see they use the operator:

block_address=x >> shift_amount + offset_amount.

(>> is right shift).
where shift_amount and offset_amount are the same for all values of x.
(all operation is implemented in binary).

Can you please explain how this way works? and how to determine
shift_amount and offset_amount?
Honestly, I do not understand how this algorithm works. Do you see any
thing like this for block location? (I mean using right shift and
offset)?

In your case when  you implement an interpolation in hardware, how do
you search for the boundary for a given input?

Thank you very much.
0
aelover11 (81)
1/11/2009 11:56:04 PM
comp.programming 11491 articles. 2 followers. Post Follow

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"A.E lover" <aelover11@gmail.com> writes:

> Hi all,
>
> Assume I non-uniformally break down a range from 0 to (2^10)-1 into
> (2^4)-1 blocks.
>
> |----|---|------|---|......|--|
> 0    5   7                   (2^10)-1
>
> For a given value x (x may be from 0 to 2^10-1), I would like to
> locate what block x should be in. For example if x is 6, I want to
> find the second block (from 5 to 7) in the above figure. ( x is
> integers).
>
> In a technical report, for this task, I see they use the operator:
>
> block_address=x >> shift_amount + offset_amount.
>
> (>> is right shift).
> where shift_amount and offset_amount are the same for all values of x.
> (all operation is implemented in binary).
>
> Can you please explain how this way works? and how to determine
> shift_amount and offset_amount?
> Honestly, I do not understand how this algorithm works. Do you see any
> thing like this for block location? (I mean using right shift and
> offset)?

In this case, the break down is uniform.

           (x >> n)  ==  (x / 2^n)

so all blocks will have the same size, 2^b.


If your blocks have random sizes (even if increasing), then the best you
can do is to keep the block boundaries sorted in apply a DICHOTOMY to
find out in which block your number lie.


On the other hand, if your block boundaries are generated with a
function easily inversible, for example, 

    boundary(block_number)     = 2^block_number

then you can easily find the block_number of a number by using the
inverse:

         boundary(block_number(x)) <= x < boundary(block_number(x)+1)
     <=> 2^block_number(x) <= x < 2^(block_number(x)+1)
     <=> log2(2^block_number(x)) <= log2(x) <log2(2^(block_number(x)+1))
     <=> block_number(x) <= log2(x) < block_number(x)+1)
     <=> block_number(x) = floor(log2(x))
              
But as long as you use a function to generate the boundaries, I'd say
there's some level of "uniformity" in their repartition...


> In your case when  you implement an interpolation in hardware, how do
> you search for the boundary for a given input?

This qualification is meaningless.  It makes no difference whether it's
implemented in software, in hardware, in firmware, in wetware,
whatever.  Hardware contains much more software than you think.


-- 
__Pascal Bourguignon__
0
pjb (7869)
1/12/2009 7:18:47 AM
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