AlliedModders - [INFO] Bitsums and Operators

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Re: [INFO] Bitsums and Operators

I also confirm that it works. (And also, thanks Damizean)

The improvement:

PHP Code:


		
			
date: Sun May 24 06:58:56 2009 map: de_dust2
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Re: [INFO] Bitsums and Operators

I understand the "x / 32" -> "x >> 5" because like you said, bitshifting is a power of 2.
x * power(2, y) = x << y
x / power(2, y) = x >> y

However, I don't understand why "x % 32" was changed to "x & 31".
I know that the & operator compares the bits, but it just doesn't make sense to me.

Re: [INFO] Bitsums and Operators

Quote:

Originally Posted by Exolent[jNr] (Post 833769)

x & 31 will translate always to a value between 0 and 31. That's part is obvious (And that's what we want). Then, the less obvious, is how the result value "cycles":

When x is a power of 2 bigger or equal to 32 (i.e. 32,64,128,...) , (x & 31) is 0

Code:

(32)

  0000011111

& 0000100000



(64)

  0000011111

& 0001000000



(128)

  0000011111

& 0010000000

When x grows after that, (x & 31) will grow equally until be again a power of 2.

Code:

(33) => (33 & 31) == 1

  0000011111

& 0000100001



(34) => (34 & 31) == 2

  0000011111

& 0000100010



(35) => (35 & 31) == 3

  0000011111

& 0000100011



...



(63) => (63 & 31) == 31

  0000011111

& 0000111111



(64) => (64 & 31) == 0

  0000011111

& 0001000000

So, basically it goes:

0 .. 31 , 0 ... 31

Re: [INFO] Bitsums and Operators

I pretty much understand it now, thanks.
I guess I need to brush up on my knowledge of bits.

Re: [INFO] Bitsums and Operators

Quote:

Originally Posted by Exolent[jNr] (Post 833804)

I pretty much understand it now, thanks.
I guess I need to brush up on my knowledge of bits.

I guess that this is pretty much advanced stuff. Probably this guy has some special knowledge on this topic

Re: [INFO] Bitsums and Operators

Here's a few examples of what is taking place:

Code:

34 & 31 = 2 === 34 % 32 = 2



The only matching bit (&) out of these two numbers is bit 2 which represents 2.

34 = 100010

31 = 011111

02 = 000010  =  Result of 34 & 31



34 modulus 32 = 2

Code:

19 & 31 = 19 === 19 % 32 = 19



The bits that match up in these two numbers represents 19.

19 = 10011

31 = 11111

19 = 10011  =  Result of 19 & 31



19 modulus 32 = 19

Code:

32 & 31 = 0 === 32 % 32 = 0



Notice that no bits match so the result of this is 0

32 = 100000

31 = 011111

00 = 000000  == Result of 32 & 31 



32 modulus 32 = 0

Here's a little web tool you can use to play with binary <-> decimal.
http://www.openstrike.co.uk/cgi-bin/decimalbinary.cgi

Here's a printout of the values for 0 - 34 comparing ( x & 31 ) and ( x % 32 )

Code:

0 & 31 = 0 === 0 % 32 = 0

1 & 31 = 1 === 1 % 32 = 1

2 & 31 = 2 === 2 % 32 = 2

3 & 31 = 3 === 3 % 32 = 3

4 & 31 = 4 === 4 % 32 = 4

5 & 31 = 5 === 5 % 32 = 5

6 & 31 = 6 === 6 % 32 = 6

7 & 31 = 7 === 7 % 32 = 7

8 & 31 = 8 === 8 % 32 = 8

9 & 31 = 9 === 9 % 32 = 9

10 & 31 = 10 === 10 % 32 = 10

11 & 31 = 11 === 11 % 32 = 11

12 & 31 = 12 === 12 % 32 = 12

13 & 31 = 13 === 13 % 32 = 13

14 & 31 = 14 === 14 % 32 = 14

15 & 31 = 15 === 15 % 32 = 15

16 & 31 = 16 === 16 % 32 = 16

17 & 31 = 17 === 17 % 32 = 17

18 & 31 = 18 === 18 % 32 = 18

19 & 31 = 19 === 19 % 32 = 19

20 & 31 = 20 === 20 % 32 = 20

21 & 31 = 21 === 21 % 32 = 21

22 & 31 = 22 === 22 % 32 = 22

23 & 31 = 23 === 23 % 32 = 23

24 & 31 = 24 === 24 % 32 = 24

25 & 31 = 25 === 25 % 32 = 25

26 & 31 = 26 === 26 % 32 = 26

27 & 31 = 27 === 27 % 32 = 27

28 & 31 = 28 === 28 % 32 = 28

29 & 31 = 29 === 29 % 32 = 29

30 & 31 = 30 === 30 % 32 = 30

31 & 31 = 31 === 31 % 32 = 31

32 & 31 = 0 === 32 % 32 = 0

33 & 31 = 1 === 33 % 32 = 1

34 & 31 = 2 === 34 % 32 = 2

Re: [INFO] Bitsums and Operators

Okay, I understand it now.
I was looking at it in a totally wrong way.

Re: [INFO] Bitsums and Operators

It didn't get through my thick skull until I saw this:

Quote:

Originally Posted by Bugsy (Post 833841)

Code:

34 & 31 = 2 === 34 % 32 = 2



The only matching bit (&) out of these two numbers is bit 2 which represents 2.

34 = 100010

31 = 011111

02 = 000010  =  Result of 34 & 31



34 modulus 32 = 2

Thanks for taking the time to explain this stuff, guys :up:

Re: [INFO] Bitsums and Operators

I recommend a good article about bits
http://www-graphics.stanford.edu/~seander/bithacks.html

Re: [INFO] Bitsums and Operators

Are you sure the next expressions are true, ot_207?

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