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Why am I not able to mask 32 bits on a long data type in Java

I cannot figure out why this works. I am attempting to mask the least significant 32 bits of java on a long but it does not properly AND the 33rd and 34th bit and further. Here is my example
class Main {
public static void main(String[] args) {
long someVal = 17592096894893l; //hex 0xFFFFAAFAFAD
long mask = 0xFF; //binary
long result = mask & someVal;
System.out.println("Example 1 this works on one byte");
System.out.printf("\n%x %s", someVal, Long.toBinaryString(someVal) );
System.out.printf("\n%x %s", result, Long.toBinaryString(result) );
long someVal2 = 17592096894893l; //hex 0xFFFFAAFAFAD
mask = 0xFFFFFFFF; //binary
result = mask & someVal2;
System.out.println("\nExample 2 - this does not work");
System.out.printf("\n%x %s", someVal2, Long.toBinaryString(someVal2) );
System.out.printf("\n%x %s", result, Long.toBinaryString(result) );
}
}
I was expecting the results to drop the most significant byte to be a zero since the AND operation did it on 32 bits. Here is the output I get.
Example 1 - this works
ffffaafafad 11111111111111111010101011111010111110101101
ad 10101101
Example 2 - this does not work
ffffaafafad 11111111111111111010101011111010111110101101
ffffaafafad 11111111111111111010101011111010111110101101
I would like to be able to mask the first least significant 4 bytes of the long value.

I believe what you’re seeing here is the fact that Java converts integers to longs using sign extension.
For starters, what should this code do?
int myInt = -1;
long myLong = myInt;
System.out.println(myLong);
This should intuitively print out -1, and that’s indeed what happens. I mean, it would be kinda weird if in converting an int to a long, we didn’t get the same number we started with.
Now, let’s take this code:
int myInt = 0xFFFFFFFF;
long myLong = myInt;
System.out.println(myLong);
What does this print? Well, 0xFFFFFFFF is the hexadecimal version of the signed 32-bit number -1. That means that this code is completely equivalent to the above code, so it should (and does) print the same value, -1.
But the value -1, encoded as a long, doesn’t have representation 0x00000000FFFFFFFF. That would be 232 - 1, not -1. Rather, since it’s 64 bits long, -1 is represented as 0xFFFFFFFFFFFFFFFFF. Oops - all the upper bits just got activated! That makes it not very effective as a bitmask.
The rule in Java is that if you convert an int to a long, if the very first bit of the int is 1, then all 32 upper bits of the long will get set to 1 as well. That’s in place so that converting an integer to a long preserves the numeric value.
If you want to make a bitmask that’s actually 64 bits long, initialize it with a long literal rather than an int literal:
mask = 0xFFFFFFFFL; // note the L
Why does this make a difference? Without the L, Java treats the code as
Create the integer value 0xFFFFFFFF = -1, giving 32 one bits.
Convert that integer value into a long. To do so, use sign extension to convert it to the long value -1, giving 64 one bits in a row.
However, if you include the L, Java interprets things like this:
Create the long value 0xFFFFFFFF = 232 - 1, which is 32 zero bits followed by 32 one bits.
Assign that value to mask.
Hope this helps!

Multiply an int in Java by itself

Why if I multiply int num = 2,147,483,647 by the same int num is it returning 1 as result? Note that I am in the limit of the int possible value.
I already try to catch the exception but still give the result as 1.

Before any multiplication java translates ints to binary numbers. So you are actually trying to multiply 01111111111111111111111111111111 by 01111111111111111111111111111111. The result of this is something like
1111111111111111111111111111111000000000000000000000000000000001. The int can hold just 32 bits, so in fact you get 00000000000000000000000000000001 which is =1 in decimal.

In integer arithmetic, Java doesn't throw an exception when an overflow occurs. Instead, it just the 32 least significant bits of the outcome, or equivalently, it "wraps around". That is, if you calculate 2147483647 + 1, the outcome is -2147483648.
2,147,483,647 squared happens to be, in binary:
11111111111111111111111111111100000000000000000000000000000001
The least significant 32 bits of the outcome are equal to the value 1.
If you want to calculate with values which don't fit in 32 bits, you have to use either long (if 64 bits are sufficient) or java.math.BigInteger (if not).

int cannot handle just any large value.Look here. In JAVA you have an exclusive class for this problem which comes quite handy
import java.math.BigInteger;
public class BigIntegerDemo {
public static void main(String[] args) {
BigInteger b1 = new BigInteger("987654321987654321000000000"); //change it to your number
BigInteger b2 = new BigInteger("987654321987654321000000000"); //change it to your number
BigInteger product = b1.multiply(b2);
BigInteger division = b1.divide(b2);
System.out.println("product = " + product);
System.out.println("division = " + division);
}
}
Source : Using BigInteger In JAVA

The Java Language Specification exactly rules what should happen in the given case.
If an integer multiplication overflows, then the result is the low-order bits of the mathematical product as represented in some sufficiently large two's-complement format. As a result, if overflow occurs, then the sign of the result may not be the same as the sign of the mathematical product of the two operand values.
It means, that when you multiply two ints, the result will be represented in a long value first (that type holds sufficient bits to represent the result). Then, because you assign it to an int variable, the lower bits are kept for your int.
The JLS also says:
Despite the fact that overflow, underflow, or loss of information may occur, evaluation of a multiplication operator * never throws a run-time exception.
That's why you never get an exception.
My guess: Store the result in a long, and check what happens if you downcast to int. For example:
int num = 2147483647;
long result = num * num;
if (result != (long)((int)result)) {
// overflow happened
}
To really follow the arithmetics, let's follow the calculation:
((2^n)-1) * ((2^n)-1) =
2^(2n) - 2^n - 2^n + 1 =
2^(2n) - 2^(n+1) + 1
In your case, n=31 (your number is 2^31 - 1). The result is 2^62 + 2^32 + 1. In bits it looks like this (split by the 32bit boundary):
01000000000000000000000000000001 00000000000000000000000000000001
From this number, you get the rightmost part, which equals to 1.

It seems that the issue is because the int can not handle such a large value. Based on this link from oracle regarding the primitive types, the maximum range of values allowed is 2^31 -1 (2,147,483,647) which is exactly the same value that you want to multiply.
So, in this case is recommended to use the next primitive type with greater capacity, for example you could change your "int" variables to "long" which have a bigger range between -2^63 to 2^63-1 (-9223372036854775808 to 9223372036854775807).
For example:
public static void main(String[] args) {
long num = 2147483647L;
long total = num * num;
System.out.println("total: " + total);
}
And the output is:
total: 4611686014132420609
I hope this can help you.
Regards.

According to this link, a Java 'int' signed is 2^31 - 1. Which is equal to 2,147,483,647.
So if you are already at the max for int, and if you multiply it by anything, I would expect an error.

Arithmetic Operation in Java

Assume that I have one arithmetic function which will add two long variables and return a long value. If pass Long.MaxValue() as an argument it wont give a perfect result. What will be the solution for that? The code below explains what I mean:
public class ArithmaticExample {
public static void main(String[] args) {
System.out.println(ArithmaticExample.addLong(Long.MAX_VALUE, Long.MAX_VALUE));
}
public static long addLong(long a,long b){
return a+b;
}
}

So you can see the wood from the trees, let's recast the problem using byte rather than long and consider
byte a = 0b01111111; // i.e. 127, the largest value of a `byte`.
byte b = 0b01111111;
byte c = (byte)(a + b);
where you need the explicit cast to circumvent conversion of a + b to an int.
Computing c by hand gives you 0b11111110. This is, of course, the bitwise representation of -2 in an 8 bit 2's complement type.
So the answer for the byte case is -2. And the same holds true for a long: there are just more 1 bits to contend with in your addition.
Note that although all this is perfectly well-defined in Java, the same cannot be said for C and C++.
If you need to add two long values of such magnitude then consider using BigInteger.

The result is -2. This is not what is expected as it seems to be more an overflow than anything else, but this result is "normal".
Long.MAX_VALUE = 9223372036854775807
Long.MAX_VALUE + 1 = 9223372036854775807
Long.MAX_VALUE + Long.MAX_VALUE = -2

What is the fastest way to associate a boolean flag to every possible integer value?

If I had a byte instead of an integer, I could easily create a boolean array with 256 positions and check:
boolean[] allBytes = new boolean[256];
if (allBytes[value & 0xFF] == true) {
// ...
}
Because I have an integer, I can't have an array with size 2 billion. What is the fastest way to check if an integer is true or false? A set of Integers? A hashtable?
EDIT1: I want to associate for every possible integer (2 billion) a true or false flag.
EDIT2: I have ID X (integer) and I need a quick way to know if ID X is ON or OFF.

A BitSet can't handle negative numbers. But there's a simple way around:
class BigBitSet {
private final BitSet[] bitSets = new BitSet[] {new BitSet(), new BitSet()};
public boolean get(int bitIndex) {
return bitIndex < 0 ? bitSets[1].get(~bitIndex)
: bitSets[0].get(bitIndex);
}
...
}
The second BitSet is for negative numbers, which get translated via the '~' operator (that's better than simply negating as it works for Integer.MIN_VALUE, too).
The memory consumption may get up to 4 Gib, i.e., about 524 MB.

I feel stupid for even elaborating on this.
The smallest unit of information your computer can store is a bit, right? A bit has two states, you want two states, so lets just say bit=0 is false and bit=1 is true.
So you need as many bits as there are possible int's, 2^32 = 4,294,967,296. You can fit 8 bits into a byte, so you need only 2^32 / 8 = 536,870,912 bytes.
From that easily follows code to address each of these bits in the bytes...
byte[] store = new byte[1 << 29]; // 2^29 bytes provide 2^32 bits
void setBit(int i) {
int byteIndex = i >>> 3;
int bitMask = 1 << (i & 7);
store[byteIndex] |= bitMask;
}
boolean testBit(int i) {
int byteIndex = i >>> 3;
int bitMask = 1 << (i & 7);
return (store[byteIndex] & bitMask) != 0;
}
java.util.BitSet provides practically the same premade in a nice class, only you can use it to store a maximum of 2^31 bits since it does not work with negative bit indices.

Since you're using Java, use BitSet. It's fast and easy. If you prefer, you could also use an array of primitive longs or BigInteger, but this is really what BitSet is for.
http://docs.oracle.com/javase/7/docs/api/java/util/BitSet.html

Java - Explicit Conversion from Int to Short

Can someone please explain why this following statement:
short value = (short) 100000000;
System.out.println(value);
Gives me:
-7936
Knowing that the maximum value of a short in Java is 32767 correct?

With your value of 100 million, I get -7936. I can only get 16960 if I change 100 million to 1 million.
The reason is that short values are limited to -32768 to +32767, and Java only keeps the least significant 16 bits when casting to a short (a narrowing primitive conversion, JLS 5.1.3). Effectively this operation: 1 million mod 2^16 (16 bits in a short) is 16960.

The way you did it merely reinterprets a smaller number of bits at the same memory location. It does not change them.
You probably want to use the max and min functions to detect when the value lies beyond of short and assign the max or min value of the short when that happens.
int n = 1000000;
short value = n > Short.MAX_VALUE ? Short.MAX_VALUE : n < Short.MIN_VALUE ? Short.MIN_VALUE : (short)n;
Update: more compactly:
import static java.lang.Math.max;
import static java.lang.Math.min;
// ...
value = (short)min(max(value, Short.MIN_VALUE), Short.MAX_VALUE);
System.out.println(value);

Here's good article explaining narrowing and widening primitive conversions in Java.
short s = 696; // 0000 0010 1011 1000
byte x = (byte)s;
System.out.println("byte x = " + x);
Produces:
byte x = -72
Now you should understand why - because when we narrow short down to
the byte the JVM discards the most significant part (00000010) and the
result (in binary form) is 10111000. This is the same number we were
looking at before. And, as you can see, it is negative, unlike the
original value.