How to represent this???

by: rsalzmannPosted on 2004-05-25 at 12:03:31ID: 11155137

See if this helps:
import java.util.*;

public class BitWiseDemo {
private static final int MAXNEG_INT = -2147483648;
private static final int MAXPOS_INT = 2147483647;
private static final long MAXNEG_LONG = -9223372036854775808L;
private static final long MAXPOS_LONG = 9223372036854775807L;

//experiment with this value to see the effect on
//the shift operations.
private static final int SHIFT_FACTOR = 3;

public static void main(String[] args) {
Random randomNumeral = new Random();
performIntOperations(randomNumeral);

performLongOperations(randomNumeral);
}

private static void performLongOperations(Random randomNumeral) {
long randomNumeralLongx = randomNumeral.nextLong();
long randomNumeralLongy = randomNumeral.nextLong();
longOperation("-1L", -1L);
longOperation("+1L", +1L);
longOperation("maxpos", MAXPOS_LONG);
longOperation("maxneg", MAXNEG_LONG);
longOperation("l", randomNumeralLongx);
longOperation("~l", ~randomNumeralLongx);
longOperation("-l", -randomNumeralLongx);
longOperation("m", randomNumeralLongy);
longOperation("l & m", randomNumeralLongx & randomNumeralLongy);
longOperation("l | m", randomNumeralLongx | randomNumeralLongy);
longOperation("l ^ m", randomNumeralLongx ^ randomNumeralLongy);
longOperation("l << shiftFactor", randomNumeralLongx << SHIFT_FACTOR);
longOperation("l >> shiftFactor", randomNumeralLongx >> SHIFT_FACTOR);
longOperation("(~l) >> shiftFactor", (~randomNumeralLongx) >> SHIFT_FACTOR);
longOperation("l >>> shiftFactor", randomNumeralLongx >>> SHIFT_FACTOR);
longOperation("(~l) >>> shiftFactor", (~randomNumeralLongx) >>> SHIFT_FACTOR);
}

private static void performIntOperations(Random randomNumeral) {
int randomNumeralIntx = randomNumeral.nextInt();
int randomNumeralInty = randomNumeral.nextInt();
intOperation("-1", -1);
intOperation("+1", +1);
intOperation("maxpos", MAXPOS_INT);
intOperation("maxneg", MAXNEG_INT);
intOperation("i", randomNumeralIntx);
intOperation("~i", ~randomNumeralIntx);
intOperation("-i", -randomNumeralIntx);
intOperation("j", randomNumeralInty);
intOperation("i & j", randomNumeralIntx & randomNumeralInty);
intOperation("i | j", randomNumeralIntx | randomNumeralInty);
intOperation("i ^ j", randomNumeralIntx ^ randomNumeralInty);
intOperation("i << shiftFactor", randomNumeralIntx << SHIFT_FACTOR);
intOperation("i >> shiftFactor", randomNumeralIntx >> SHIFT_FACTOR);
intOperation("(~i) >> shiftFactor", (~randomNumeralIntx) >> SHIFT_FACTOR);
intOperation("i >>> shiftFactor", randomNumeralIntx >>> SHIFT_FACTOR);
intOperation("(~i) >>> shiftFactor", (~randomNumeralIntx) >>> SHIFT_FACTOR);
}
static void intOperation(String s, int i) {
System.out.println(
s + ", int: " + i + ", binary: ");
System.out.print(" ");
for(int j = 31; j >=0; j--)
if(((1 << j) & i) != 0)
System.out.print("1");
else
System.out.print("0");
System.out.println();
}
static void longOperation(String s, long l) {
System.out.println(
s + ", long: " + l + ", binary: ");
System.out.print(" ");
for(int i = 63; i >=0; i--)
if(((1L << i) & l) != 0)
System.out.print("1");
else
System.out.print("0");
System.out.println();
}
}

~robb

by: girionisPosted on 2004-05-25 at 12:11:22ID: 11155194

Take a look here for a bit of theory: http://mindprod.com/jgloss/binary.html

by: maheshexpPosted on 2004-05-25 at 17:40:25ID: 11157215

thanks friends, i will look over it and reply to u all back....

by: maheshexpPosted on 2004-05-25 at 17:55:01ID: 11157283

is it better to use BitSet if u need to do bit operation which consist of > 1000 bits or shall i use integer arrays like

sizeof( int ) = 4 bytes = 32 bits, hence for 3200 bits, i need 10 int[]...

which one to choose

by: maheshexpPosted on 2004-05-25 at 18:04:00ID: 11157312

rsalzmann, ur code shows me the demo of bitwise operators but my problem is using those operators how to represent the binary arithmetic operators

for eg: 2 + 3, how to do this with the bitwise operators...

by: girionisPosted on 2004-05-26 at 00:44:13ID: 11159395

BitSet internally implements a bit-vector that can grow dynamically while when you're using arrays you get a fixed size. So the choice comes down to whether the size is going to grow dynamically or not.

Not sure if you could do a 2 + 3 operation using bitwise operators. There should be a way that I probably don't know. But you can take a look here: http://c.ittoolbox.com/code/d.asp?d=2522&a=s for a c programme and maybe you can convert it in Java.

by: maheshexpPosted on 2004-05-27 at 19:01:59ID: 11176888

is it possible to do fast squaring i.e x^2 without any multipication, using only binary and bits...

by: girionisPosted on 2004-05-28 at 00:19:04ID: 11177939

There is no easy way to do it. Take a look here:

http://mindprod.com/jgloss/power.html

Also for subtraction take a look here: http://mathforum.org/library/drmath/view/55733.html

IF you go to the home page of the above page you will find loads of examples on binary.

by: maheshexpPosted on 2004-05-28 at 06:46:13ID: 11180194

>>>ttp://mindprod.com/jgloss/power.html
i had already look at it....thanks friend.

by: rsalzmannPosted on 2004-05-28 at 08:50:59ID: 11181512

Maheshexp makes my point very well. I did my best to represent what you want to show in code, but as you see, most of the actual mechanics of this type of code is lower level or theory based. Backgroiund knowledge of assembly, cpu register, & binary math operations helps understand this as it is somewhat cryptic when viewed from a high level language perspective.

Best wishes, robb

by: girionisPosted on 2004-05-28 at 09:09:49ID: 11181690

To be honest I am not sure if you can subtract or add numbers by using the logical operators. Maybe someone with more low-level knowledge can shed some light.

by: maheshexpPosted on 2004-05-28 at 09:32:28ID: 11181905

>> To be honest I am not sure if you can subtract or add numbers by using the *logical operators*
not using logical, using *bitwise*

by: maheshexpPosted on 2004-05-29 at 02:08:34ID: 11186320

at last found a way to find the fast modulo...it's intresting and fast...have a look at this link

http://mersenneforum.org/showthread.php?t=1955

can things be possible liek this (not same like this, but to say...) to make fast multiplication division etc....

by: girionisPosted on 2004-05-31 at 11:34:16ID: 11198088

You can do fast multiplication and division by 2 if you left or right shift a number, but again, I am not sure how you could multiply two other numbers using bitwise.

by: maheshexpPosted on 2004-05-31 at 19:21:10ID: 11199761

i found something from Knuth's Seminumerical algorithms....numbers can be multiplied faster if it is expressed in the form

(A1 * 2^n + A2 ) = A
(B1 * 2^n + B2 ) = B

i.e (A1 * 2^n + A2 ) * (B1 * 2^n + B2) = (A1 * B1)*2^(2n) + ((A1 * B2) + ( A2 * B1)) * 2^n + A2 * B2

after reductions

= (A1*B1)*(2^(2n)+2^n) + (A1-A2)*(B2-B1)*2^n + (A2*B2)*(2^n+1)
= (A1*B1)<<(2n) + (A1*B2)<<n + (A1-A2)*(B2-B1)<<n + (A2*B2)<<n + (A2*B2)

Thus the most expensive operation ---multiplication---
need only be computed three times:
1. A1*B1
2. (A1-A2)*(B2-B1)
3. A2*B2

if tired using BigIntegers,it's really faster, but when A1,A2 or B1,B2 is significantly big, it slows down , but it is really faster than normal multiplication provided by BigInteger

by: girionisPosted on 2004-05-31 at 23:32:02ID: 11200531

Ok, but this is not using the bitwise operators except the ^.

by: maheshexpPosted on 2004-06-01 at 01:49:28ID: 11201105

>> Ok, but this is not using the bitwise operators except the ^.
????

by: girionisPosted on 2004-06-01 at 02:22:55ID: 11201199

Ehhmm.. I have either misunderstood your question or you meant something else.

> i need to represent +, - , * , / in terms of &,|,^, ~ etc...

I can't see how the following is represented in terms of &, ~ etc.

> (A1*B1)*(2^(2n)+2^n) + (A1-A2)*(B2-B1)*2^n + (A2*B2)*(2^n+1)

by: maheshexpPosted on 2004-06-01 at 03:28:24ID: 11201420

oh god really confused a lot....

^ symbol in the expression is meant for the power i.e pow()

i asked this question to make fast multiplications, additions and subtractions. anyway i had found some stuff from ur links too...thanks friend

by: girionisPosted on 2004-06-01 at 03:45:50ID: 11201519

Yes I know the ^ symbol. Thing is I can't see how A1*B1 could be represented using & or some other bitwise operator for example. I really don't think computers use bitwise operators to do addition for instance but rather a built in mechanism that adds each bit seperately. But again I am not very good at low-level stuff, I might be wrong.

by: maheshexpPosted on 2004-06-01 at 06:22:05ID: 11202460

ok...anyway it's time to close

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How to represent this???

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