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The Inverse of a bit-shift to the left in the format 1 << n

Let's say I have the following bit masks:
1 << 1, // 2
1 << 2, // 4
1 << 3, // 8
1 << 4, // 16
1 << 5, // 32
1 << 6 // 64
I would like to get the 'inverse'.
This does the job:
void foo(int n) {
int c = 1;
while (n/2 >= 2) {
n /= 2;
c++;;
}
println(c);
}
For example, 1 << 4 resulted in 16. If I run foo(16) it prints 4.
However, I feel like it could be done a lot simpler, but I can't figure out how.
Is it possible?

BigInteger has many useful methods - including getLowestSetBit(). It probably does it as fast as it can possibly be done.
public void test() {
System.out.println(BigInteger.valueOf(16).getLowestSetBit());
}

void foo(int n)
{
println( (Math.log(n) / Math.log(2)));
//cast to int with (int) to take off decimal place
}
Returns the "inverse" bitshift as you are calling it, the base 2 logarithm.

Slightly faster and not depend on value itself.
UPDATED version
private static int foo2(int value) {
int result = 0;
int mask = 0xFFFF;
int shift = 1<<4;
for (int j = 0; j < 5; j++) {
result <<= 1;
if ((value & mask) == 0) {
result |= 1;
value >>>= shift;
}
shift >>>= 1;
mask >>= shift;
}
return result;
}

how to get absolute value of a number in java using bit manipulation

I want to implement a function to get the absolute value of a number in java: do nothing if it is positive, if it is negative, convert to positive.
I want to do this only using bit manipulations and no number comparators.
Please help

Well a negation:
-n
Is the same as the two's complement:
~n + 1
The problem is here you only want to negate if the value is < 0. You can find that out by using a logical shift to see if the MSB is set:
n >>> 31
A complement would be the same as an XOR with all 1's, something like (for a 4-bit integer):
~1010 == 1010 ^ 1111
And we can get a mask with the arithmetic right shift:
n >> 31
Absolute value says:
if n is < 0, negate it (take the complement and add 1 to it)
else, do nothing to it
So putting it together we can do the following:
static int abs(int n) {
return (n ^ (n >> 31)) + (n >>> 31);
}
Which computes:
if n is < 0, XOR it with all 1's and add 1 to it
else, XOR it with all 0's and add 0 to it
I'm not sure there's an easy way to do it without the addition. Addition involves any number of carries, even for a simple increment.
For example 2 + 1 has no carry:
10 + 1 == 11
But 47 + 1 has 4 carries:
101111 + 1 == 110000
Doing the add and carry with bitwise/bit shifts would basically just be a loop unroll and pointless.
(Edit!)
Just to be silly, here is an increment and carry:
static int abs(int n) {
int s = n >>> 31;
n ^= n >> 31;
int c;
do {
c = (n & s) << 1;
n ^= s;
} while((s = c) != 0);
return n;
}
The way it works is it flips the first bit, then keeps flipping until it finds a 0. So then the job is just to unroll the loop. The loop body can be represented by a somewhat ridiculous compound one-liner.
static int abs(int n) {
int s = n >>> 31;
n ^= n >> 31;
int c = (n & s) << 1;
c = ((n ^= s) & (s = c)) << 1; // repeat this line 30 more times
n ^= s;
return n;
}
So there's an abs using only bitwise and bit shifts.
These aren't faster than Math.abs. Math.abs just returns n < 0 ? -n : n which is trivial. And actually the loop unroll totally sucks in comparison. Just a curiosity I guess. Here's my benchmark:
Math.abs: 4.627323150634766ns
shift/xor/add abs: 6.729459762573242ns
loop abs: 12.028789520263672ns
unrolled abs: 32.47122764587402ns
bit hacks abs: 6.380939483642578ns
(The bit hacks abs is the non-patented one shown here which is basically the same idea as mine except a little harder to understand.)

you can turn a two's-compliment number positive or negative by taking it's logical negation
i = ~i; // i equals not i
You can use the Math.max() function to always get the positive
public static int abs(int i) {
return Math.max(i,~i);
}

This depends on what type of number you are using. For an int, use
int sign = i >> 31;
This gets the sign bit, which is 0 for positive numbers, and 1 for negative numbers. For other primitive types, replace 31 with the number of bits used for the primitive minus 1.
You can then use that sign in your if statement.
if (sign == 1)
i = ~i + 1;

I think you'll find that this little ditty is what you're looking for:
int abs(int v) {
int mask = v >> Integer.SIZE - 1;
return v + mask ^ mask;
}
It's based on Bit Twiddling Hacks absolute value equation and uses no comparison operations. If you aren't allowed to use addition, then (v ^ mask) - mask is an alternative. The value of this function is fairly questionable; since it's nearly as clear as the implementation of Math.abs and it's only marginally faster (at least on a i7):
v + mask ^ mask: 2.0844380704220384 abs/ns
(v ^ mask) - mask: 2.0819764093030244 abs/ns
Math.abs: 2.2636355843860656 abs/ns
Here's a test that proves that it works over the entire range of integers (the test runs in less than 2 minutes on an i7 processor under Java 7 update 51):
package test;
import org.hamcrest.core.Is;
import org.junit.Assert;
import org.junit.Test;
public class AbsTest {
#Test
public void test() {
long processedCount = 0L;
long numberOfIntegers = 1L << Integer.SIZE; //4294967296L
int value;
for (value = Integer.MIN_VALUE; processedCount < numberOfIntegers; value++) {
Assert.assertEquals((long) abs(value), (long) StrictMath.abs(value));
if (processedCount % 1_000_000L == 0L) {
System.out.print(".");
}
processedCount++;
}
System.out.println();
Assert.assertThat(processedCount, Is.is(numberOfIntegers));
Assert.assertThat(value - 1, Is.is(Integer.MAX_VALUE));
}
private static int abs(int v) {
int mask = v >> Integer.SIZE - 1;
return v + mask ^ mask;
}
}

This problem can be broken down into 2 simple steps:
1.
If >= 0 then just return the number.
2.
If smaller than 0 (ie. negative), then flip the first bit that indicates that the number is negative. This can easily be done with an XOR operation with -1 and the number; Then simply add +1 to deal with the offset (signed integers start at -1 not 0).
public static int absolute(int a) {
if (a >= 0) {
return a;
} else {
return (a ^ -1) + 1;
}
}

Reverse all bits in an int and return the int

What integer should be returned when we reverse all bits of integer 1? How do we do that with Java code?
No java built in functions should be used. Shouldn't use String reverse, converting to string etc. Only bitwise operations allowed.
import java.util.*;
import java.lang.*;
import java.io.*;
class BitReverseInt
{
public static void main (String[] args) throws java.lang.Exception{
System.out.println(reverser(1));
}
public static int reverser(int given){
int input = given;
int temp = 0;
int output = 0;
while(input > 0){
output = output << 1;
temp = input & 1;
input = input >> 1;
output = output | temp;
}
return output;
}
}

Bit reversal can be done by interchanging adjacent single bits, then interchanging adjacent 2-bit fields, then 4-bits, and so on as shown below. These five assignment statements can be executed in any order.
/********************************************************
* These are the bit masks used in the bit reversal process
0x55555555 = 01010101010101010101010101010101
0xAAAAAAAA = 10101010101010101010101010101010
0x33333333 = 00110011001100110011001100110011
0xCCCCCCCC = 11001100110011001100110011001100
0x0F0F0F0F = 00001111000011110000111100001111
0xF0F0F0F0 = 11110000111100001111000011110000
0x00FF00FF = 00000000111111110000000011111111
0xFF00FF00 = 11111111000000001111111100000000
0x0000FFFF = 00000000000000001111111111111111
0xFFFF0000 = 11111111111111110000000000000000
*/
uint x = 23885963; // 00000001011011000111100010001011
x = (x & 0x55555555) << 1 | (x & 0xAAAAAAAA) >> 1;
x = (x & 0x33333333) << 2 | (x & 0xCCCCCCCC) >> 2;
x = (x & 0x0F0F0F0F) << 4 | (x & 0xF0F0F0F0) >> 4;
x = (x & 0x00FF00FF) << 8 | (x & 0xFF00FF00) >> 8;
x = (x & 0x0000FFFF) << 16 | (x & 0xFFFF0000) >> 16;
// result x == 3508418176 11010001000111100011011010000000
By looking at each intermediary result you can see what is happening.
Hopefully this will give you what you need to sort it out in your head. John Doe's answer consolidates steps 4 and 5 in to a single expression. This will work on most machines.

Here is the actual implementation of Integer.reverse(int).
public static int reverse(int i) {
// HD, Figure 7-1
i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
i = (i << 24) | ((i & 0xff00) << 8) |
((i >>> 8) & 0xff00) | (i >>> 24);
return i;
}

You can use a do while loop like this:
public static int reverse(int number){
int reverse = 0;
int remainder = 0;
do{
remainder = number%10;
reverse = reverse*10 + remainder;
number = number/10;
}while(number > 0);
return reverse;
}
And for bitwise operation: here it goes:
// value=your integer, numBitsInt=how much bit you will use to reverse
public static int reverseIntBitwise(int value, int numBitsInt) {
int i = 0, rev = 0, bit;
while (i++ < numBitsInt) {
bit = value & 1;
value = value >> 1;
rev = rev ^ bit;
if (i < numBitsInt)
rev = rev << 1;
}
return rev;
}

Well there are multiple ways to reverse the bits of the given number in Java.
First, Java language has inbuild bitwise complement operator(~). So (~number) reverses the bits of number.
Second, one can use the Integer.reverse(number)
Third, if this is a part of test or you just want to play with bits, you can refer the code below.
/*
The logic uses moving bitmask from right to left:
1. Get the bit of given number, by binary and(&) with bitmask
2. XOR(^) with the bitmask, so here we reverse the bit.
3. OR(|) this reversed bit with the result(result has all Zero initially)
This logic is repeated for each 32 bits by moving the mask from right to left,
one bit at a time using (<<) left shift operator on bitmask.
*/
public class ReverseBits {
public static int reverseBits(int input) {
print("Input", input);
int bitmask = 1;
int result = 0;
do {
//print("Bitmask", bitmask);
result = result | (bitmask ^ (input & bitmask)) ;
//print("Result", result);
bitmask = bitmask << 1;
} while (bitmask != 0);
print("Reverse", result);
return result;
}
public static void print(String label, int input) {
System.out.println(label +"\t:"+Integer.toBinaryString(input));
}
public static void main(String[] args) {
reverseBits(Integer.MIN_VALUE);
reverseBits(Integer.MAX_VALUE);
reverseBits(reverseBits(170));
}
}
Output:
Input :10000000000000000000000000000000
Reverse :1111111111111111111111111111111
Input :1111111111111111111111111111111
Reverse :10000000000000000000000000000000
Input :10101010
Reverse :11111111111111111111111101010101
Input :11111111111111111111111101010101
Reverse :10101010

return Integer.reverse(given);
Integer.reverse Reference

How can one read an integer bit by bit in Java?

I would like to take an int as input, and return the kth bit.
int getBit(int n, int k){
return kth bit in n;
}
How would i do this?

Using bitwise operators:
int getBit(int n, int k) {
return (n >> k) & 1;
}
Explanation (in bits):
n
100010101011101010 (example)
n >> 5
000001000101010111 (all bits are moved over 5 spots, therefore
& the bit you want is at the end)
000000000000000001 (0 means it will always be 0,
= 1 means that it will keep the old value)
1

return (n >> k) & 1;
Here, n >> k shifts the k-th bit into the least significant position, and & 1 masks out everything else.

If lowest significant bit is bit number 0:
return (n>>k)&1;

or use:
boolean getBit(int n, int k) {
return ((n >> k) & 1) == 1;
}
if you want a boolean value

You can also use the module property for this. If your number is even the lowest significant bit is zero, otherwise (odd) is one.
return (n>>k)%2;

Storing int value of bitmask - extract 1 valued bits

I am calculating the int equivalent of a given set of bits and storing that in memory. From there, I would like to determine all 1 value bits from the original bitmask. Example:
33 --> [1,6]
97 --> [1,6,7]
Ideas for an implementation in Java?

On BitSet
Use java.util.BitSet to store, well, a set of bits.
Here's how you can convert from an int to a BitSet, based on which bits in the int is set:
static BitSet fromInt(int num) {
BitSet bs = new BitSet();
for (int k = 0; k < Integer.SIZE; k++) {
if (((num >> k) & 1) == 1) {
bs.set(k);
}
}
return bs;
}
So now you can do the following:
System.out.println(fromInt(33)); // prints "{0, 5}"
System.out.println(fromInt(97)); // prints "{0, 5, 6}"
And just for completeness, here's the reverse transformation:
static int toInt(BitSet bs) {
int num = 0;
for (int k = -1; (k = bs.nextSetBit(k + 1)) != -1; ) {
num |= (1 << k);
}
return num;
}
So composing both together, we always get back the original number:
System.out.println(toInt(fromInt(33))); // prints "33"
System.out.println(toInt(fromInt(97))); // prints "97"
On 0-based indexing
Note that this uses 0-based indexing, which is the more commonly used indexing for bits (and most everything else in Java). This is also more correct. In the following, ^ denotes exponentiation:
33 = 2^0 + 2^5 = 1 + 32 97 = 2^0 + 2^5 + 2^6 = 1 + 32 + 64
33 -> {0, 5} 97 -> {0, 5, 6}
If you insist on using 1-based indexing, however, you can use bs.set(k+1); and (1 << (k-1)) in the above snippets. I would advise strongly against this recommendation, however.
Related questions
What does the ^ operator do in Java? -- it's actually not exponentiation

For bit fiddling, java.lang.Integer has some very helpful static methods. Try this code as a starting base for your problem:
public int[] extractBitNumbers(int value) {
// determine how many ones are in value
int bitCount = Integer.bitCount(value);
// allocate storage
int[] oneBits = new int[bitCount];
int putIndex = 0;
// loop until no more bits are set
while (value != 0) {
// find the number of the lowest set bit
int bitNo = Integer.numberOfTrailingZeros(value);
// store the bit number in array
oneBits[putIndex++] = bitNo+1;
// clear the bit we just processed from the value
value &= ~(1 << bitNo);
}
return oneBits;
}

I can show you C# implementation, Java should be very similar.
int value = 33;
int index = 1;
while (value > 0)
{
if ((value % 2) == 1)
Console.WriteLine(index);
index++;
value /= 2;
}

If you want to get an array like that you'll likely need to loop the number of bits you want to check & the integer with a bit shifted 1 for each step.
Something like (pseudo):
Init array
mask = 1
for (0 to BitCount):
if Integer & mask
array[] = pos
mask << 1

A bit-crunching variation would be something like:
int[] getBits(int value) {
int bitValue = 1;
int index = 1;
int[] bits = new int[33];
while (value >= bitValue)
{
bits[index++] = (value & bitValue);
bitValue << 1; // or: bitValue *= 2;
}
return bits;
}
Note that since the bits are indexed from 1 as you requested, bits[0] is left unused.