How do you randomly zero a bit in an integer?

Question

Updated with newer answer and better test

Let's say I have the number 382 which is 101111110.

How could I randomly turn a bit which is not 0 to 0?

The why;

Since people ask me why, I simply need to do this, removing a bit from an integer.

based on the answer here is the result(working one)
I ran this

using System;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using System.Diagnostics;

namespace ConsoleApplication1
{
    class Program
    {
        static Random random;
        static void Main(string[] args)
        {
            Stopwatch sw;
            int[] test = new int[10] { 382, 256, 1, 257, 999, 555, 412, 341, 682, 951 };

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    Perturb(test[j]);
                sw.Stop();
                Console.WriteLine("Perturb " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> Perturb " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    FastPerturb(test[j]);
                sw.Stop();
                Console.WriteLine("FastPerturb " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> FastPerturb " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    SetRandomTrueBitToFalse(test[j]);
                sw.Stop();
                Console.WriteLine("SetRandomTrueBitToFalse " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> SetRandomTrueBitToFalse " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    flipRandomBit(test[j]);
                sw.Stop();
                Console.WriteLine("flipRandomBit " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> flipRandomBit " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    oneBitsIndexes(test[j]);
                sw.Stop();
                Console.WriteLine("oneBitsIndexes " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> oneBitsIndexes " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    ClearOneBit(test[j]);
                sw.Stop();
                Console.WriteLine("ClearOneBit " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> ClearOneBit " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    FlipRandomTrueBit(test[j]);
                sw.Stop();
                Console.WriteLine("FlipRandomTrueBit " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> FlipRandomTrueBit " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            random = new Random(42);
            for (int j = 0; j < 10; j++)
            {
                sw = Stopwatch.StartNew();
                for (int i = 0; i < 1000000; i++)
                    ClearRandomBit(test[j]);
                sw.Stop();
                Console.WriteLine("ClearRandomBit " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString());
                Debug.WriteLine("> ClearRandomBit " + sw.Elapsed.TotalSeconds.ToString("0.#######") + " seconds for " + test[j].ToString() + "  ");
            }

            Console.Read();
        }
        public static int Perturb(int data)
        {
            if (data == 0) return 0;

            int minBits = (data & 0xFFFF0000) == 0 ? 16 : 32;

            int newData = data;
            do
            {
                newData &= ~(1 << random.Next(minBits));
            } while (newData == data);

            return newData;
        }

        public static int FastPerturb(int data)
        {
            if (data == 0) return 0;

            int bit = 0;
            while (0 == (data & (bit = 1 << random.Next(32)))) ;

            return data & ~bit;
        }

        private static Int32 SetRandomTrueBitToFalse(Int32 p)
        {
            List<int> trueBits = new List<int>();
            for (int i = 0; i < 31; i++)
            {
                if ((p >> i & 1) == 1)
                {
                    trueBits.Add(i);
                }
            }
            if (trueBits.Count > 0)
            {
                int index = random.Next(0, trueBits.Count);
                return p & ~(1 << trueBits[index]);
            }
            return p;
        }

        public static int getBitCount(int bits)
        {
            bits = bits - ((bits >> 1) & 0x55555555);
            bits = (bits & 0x33333333) + ((bits >> 2) & 0x33333333);
            return ((bits + (bits >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
        }

        public static int flipRandomBit(int data)
        {
            int index = random.Next(getBitCount(data));
            int mask = data;

            for (int i = 0; i < index; i++)
                mask &= mask - 1;
            mask ^= mask & (mask - 1);

            return data ^ mask;
        }

        public static int oneBitsIndexes(int data)
        {
            if (data > 0)
            {
                var oneBitsIndexes = Enumerable.Range(0, 31)
                                               .Where(i => ((data >> i) & 0x1) != 0).ToList();
                // pick a random index and update the source value bit there from 1 to 0
                data &= ~(1 << oneBitsIndexes[random.Next(oneBitsIndexes.Count)]);
            }
            return data;
        }

        static private int ClearOneBit(int originalValue)
        {
            if (originalValue == 0)
                return 0; // All bits are already set to 0, nothing to do

            int mask = 0;
            do
            {
                int n = random.Next(32);
                mask = 1 << n;
            } while ((mask & originalValue) == 0); // check that this bit is not 0

            int newValue = originalValue & ~mask; // clear this bit
            return newValue;
        }

        public static BitArray FlipRandomTrueBit(BitArray bits)
        {
            List<int> trueBits = new List<int>();

            for (int i = 0; i < bits.Count; i++)
                if (bits[i])
                    trueBits.Add(i);

            if (trueBits.Count > 0)
            {
                int index = random.Next(0, trueBits.Count);
                bits[trueBits[index]] = false;
            }

            return bits;
        }

        public static int FlipRandomTrueBit(int input)
        {
            BitArray bits = new BitArray(new int[] { input });
            BitArray flipedBits = FlipRandomTrueBit(bits);

            byte[] bytes = new byte[4];
            flipedBits.CopyTo(bytes, 0);

            int result = BitConverter.ToInt32(bytes, 0);
            return result;
        }

        static int ClearRandomBit(int value)
        {
            return unchecked((int)ClearRandomBit((ulong)(uint)value));
        }
        static ulong ClearRandomBit(ulong value)
        {
            // Algorithm from http://graphics.stanford.edu/~seander/bithacks.html
            //
            //   "Select the bit position (from the most-significant bit) with the 
            //   given count (rank)."
            //   
            //   The following 64-bit code selects the position of the rth 1 bit when
            //   counting from the left. In other words if we start at the most 
            //   significant bit and proceed to the right, counting the number of bits
            //   set to 1 until we reach the desired rank, r, then the position where 
            //   we stop will be the final value given to s.

            // Do a normal parallel bit count for a 64-bit integer,                     
            // but store all intermediate steps.
            ulong v = value;
            ulong a = v - ((v >> 1) & ~0UL / 3);
            ulong b = (a & ~0UL / 5) + ((a >> 2) & ~0UL / 5);
            ulong c = (b + (b >> 4)) & ~0UL / 0x11;
            ulong d = (c + (c >> 8)) & ~0UL / 0x101;
            ulong t = (uint)((d >> 32) + (d >> 48));

            // Choose a random r in the range [1-bitCount]
            int bitCount = (int)((d * (~0UL / 255)) >> 56);
            int randomRank = 1 + random.Next(bitCount);
            ulong r = (ulong)randomRank;

            // Compute s                                       
            ulong s = 64;
            s -= ((t - r) & 256UL) >> 3;
            r -= (t & ((t - r) >> 8));
            t = (d >> (int)(s - 16)) & 0xff;
            s -= ((t - r) & 256UL) >> 4;
            r -= (t & ((t - r) >> 8));
            t = (c >> (int)(s - 8)) & 0xf;
            s -= ((t - r) & 256UL) >> 5;
            r -= (t & ((t - r) >> 8));
            t = (b >> (int)(s - 4)) & 0xf;
            s -= ((t - r) & 256UL) >> 6;
            r -= (t & ((t - r) >> 8));
            t = (a >> (int)(s - 2)) & 0x3;
            s -= ((t - r) & 256UL) >> 7;
            r -= (t & ((t - r) >> 8));
            t = (v >> (int)(s - 1)) & 0x1;
            s -= ((t - r) & 256UL) >> 8;
            s = 65 - s;

            // Clear the selected bit
            return value & ~(1UL << (int)(64 - s));
        }
    }
}

result;

Perturb 0.1704681 seconds for 382
Perturb 0.9307034 seconds for 256
Perturb 0.932266 seconds for 1
Perturb 0.4896138 seconds for 257
Perturb 0.1541828 seconds for 999
Perturb 0.2222421 seconds for 555
Perturb 0.2370868 seconds for 412
Perturb 0.2229154 seconds for 341
Perturb 0.2233445 seconds for 682
Perturb 0.1554396 seconds for 951
FastPerturb 0.2988974 seconds for 382
FastPerturb 1.8008209 seconds for 256
FastPerturb 1.7966043 seconds for 1
FastPerturb 0.9255025 seconds for 257
FastPerturb 0.2708695 seconds for 999
FastPerturb 0.4036553 seconds for 555
FastPerturb 0.401872 seconds for 412
FastPerturb 0.4042984 seconds for 341
FastPerturb 0.4028209 seconds for 682
FastPerturb 0.2688467 seconds for 951
SetRandomTrueBitToFalse 0.6127648 seconds for 382
SetRandomTrueBitToFalse 0.4432519 seconds for 256
SetRandomTrueBitToFalse 0.4193295 seconds for 1
SetRandomTrueBitToFalse 0.4543657 seconds for 257
SetRandomTrueBitToFalse 0.6270696 seconds for 999
SetRandomTrueBitToFalse 0.5891294 seconds for 555
SetRandomTrueBitToFalse 0.5910375 seconds for 412
SetRandomTrueBitToFalse 0.6104247 seconds for 341
SetRandomTrueBitToFalse 0.6249519 seconds for 682
SetRandomTrueBitToFalse 0.6142904 seconds for 951
flipRandomBit 0.1624584 seconds for 382
flipRandomBit 0.1284565 seconds for 256
flipRandomBit 0.13208 seconds for 1
flipRandomBit 0.1383649 seconds for 257
flipRandomBit 0.1658636 seconds for 999
flipRandomBit 0.1563506 seconds for 555
flipRandomBit 0.1588513 seconds for 412
flipRandomBit 0.1561841 seconds for 341
flipRandomBit 0.1562256 seconds for 682
flipRandomBit 0.167605 seconds for 951
oneBitsIndexes 2.1871352 seconds for 382
oneBitsIndexes 1.8677352 seconds for 256
oneBitsIndexes 1.8389871 seconds for 1
oneBitsIndexes 1.8729746 seconds for 257
oneBitsIndexes 2.1821771 seconds for 999
oneBitsIndexes 2.1300304 seconds for 555
oneBitsIndexes 2.1098191 seconds for 412
oneBitsIndexes 2.0836421 seconds for 341
oneBitsIndexes 2.0803612 seconds for 682
oneBitsIndexes 2.1684378 seconds for 951
ClearOneBit 0.3005068 seconds for 382
ClearOneBit 1.7872318 seconds for 256
ClearOneBit 1.7902597 seconds for 1
ClearOneBit 0.9243212 seconds for 257
ClearOneBit 0.2666008 seconds for 999
ClearOneBit 0.3929297 seconds for 555
ClearOneBit 0.3964557 seconds for 412
ClearOneBit 0.3945432 seconds for 341
ClearOneBit 0.3936286 seconds for 682
ClearOneBit 0.2686803 seconds for 951
FlipRandomTrueBit 1.5828644 seconds for 382
FlipRandomTrueBit 1.3162437 seconds for 256
FlipRandomTrueBit 1.2944724 seconds for 1
FlipRandomTrueBit 1.3305612 seconds for 257
FlipRandomTrueBit 1.5845461 seconds for 999
FlipRandomTrueBit 1.5252726 seconds for 555
FlipRandomTrueBit 1.5786568 seconds for 412
FlipRandomTrueBit 1.5314749 seconds for 341
FlipRandomTrueBit 1.5311035 seconds for 682
FlipRandomTrueBit 1.6164142 seconds for 951
ClearRandomBit 0.2681578 seconds for 382
ClearRandomBit 0.2728117 seconds for 256
ClearRandomBit 0.2685423 seconds for 1
ClearRandomBit 0.2626029 seconds for 257
ClearRandomBit 0.2623253 seconds for 999
ClearRandomBit 0.274382 seconds for 555
ClearRandomBit 0.2644288 seconds for 412
ClearRandomBit 0.2667171 seconds for 341
ClearRandomBit 0.264912 seconds for 682
ClearRandomBit 0.2666491 seconds for 951

so in the end, Kyteland is now the winner.

Answer 1

EDIT : fixed to take into account the constraint "a bit which is not 0"

Pick a random number N between 0 and 31 (for a 32 bit integer), and use it to generate a bitmask by shifting 1 N times to the left. Repeat until bit N is not 0 in the original number. Negate the bitmask to have only 1 bit set to 0 and combine it with your original number with the & operator :

private int ClearOneBit(int originalValue)
{
    if (originalValue == 0)
        return 0; // All bits are already set to 0, nothing to do

    Random rnd = new Random();
    int mask = 0;
    do
    {
        int n = rnd.Next(32);
        mask = 1 << n;
    } while ((mask & originalValue) == 0); // check that this bit is not 0

    int newValue = originalValue & ~mask; // clear this bit
    return newValue;
}

Answer 2

You can turn on any bit by OR'ing it with 1 and turn it off by AND'ing with the bitwise complement.

Here's an example that selects a random 1-bit and turns it off.

var rand = new Random();
int myValue = 0x017E; // 101111110b
// identify which indexes are one-bits (if any, thanks Doc)
if( myValue > 0 )
{
    var oneBitsIndexes = Enumerable.Range( 0, 31 )
                                   .Where(i => ((myValue >> i) & 0x1) !=0).ToList();
    // pick a random index and update the source value bit there from 1 to 0
    myValue &= ~(1 << oneBitsIndexes[rand.Next(oneBitsIndexes.Count)]);
}
// otherwise, there are no bits to turn off...

Answer 3

Try the following code

public static int ChangeOneBit(int data)
{
    if (data == 0)
    {
        return data;
    }

    var random = new Random();
    int bit = 0;
    do
    {
        var shift = random.Next(31);
        bit = data >> shift;
        bit = bit & 0x00000001;
    } while (bit == 0);
    var ret = data & (~(1 << bit));
    return ret;
}

Answer 4

EDIT: Fixed some logic.

BitArray bits = new BitArray(new int[] { number } );

randomIndex = new Random().Next(32);

// check if bit is true, if not, goes to next bit and wraps around as well.
for(int i = 0; i < 32; i++)
{
    if(bits[randomIndex] == false)
    {
    randomIndex = (randomIndex + 1) % 32;
    }
    else
    {
        break;
    }
}

bits[randomIndex] = false;

Answer 5

Count all the 1's in your integer. Choose a random number using your favorite random number generator between 1 and the first count. Create a mask for Random-th 1 in your integer. OR your integer with the mask.

Answer 6

int changeBit(int a)
{
    a = ~a;
    int temp = a;
    while(temp == a)
    {
        r = Math.pow(2,(int)(32*random.next()));
        a = a || r;    
    }

    return ~a;
}

Answer 7

static Random random = new Random();

public static int Perturb(int data)
{
    if (data == 0) return 0;

    // attempt to pick a more narrow search space
    int minBits = (data & 0xFFFF0000) == 0 ? 16 : 32;

    // int used = 0; // Uncomment for more-bounded performance
    int newData = data;
    do
    {
        // Unbounded performance guarantees
        newData &= ~(1 << random.Next(minBits));

        // // More-bounded performance:
        // int bit = 1 << random.Next(minBits);
        // if ((used & bit) == bit) continue;
        // used |= bit;
        // newData &= ~bit;
    } while (newData == data); // XXX: we know we've inverted at least one 1
                               // when the new value differs

    return newData;
}

Update: added code above which can be used for more-bounded performance guarantees (or less unbounded if you want to think of it that way). Interestingly enough this performs better than the original uncommented version.

Below is an alternate approach that is fast but without bounded performance guarantees:

public static int FastPerturb(int data)
{
    if (data == 0) return 0;

    int bit = 0;
    while (0 == (data & (bit = 1 << random.Next(32))));

    return data & ~bit;
}

Answer 8

Ok, a lot of wrong answers. Here's one that works:

1. determine which bit to flip. Do this randomly. I won't supply the code, it's pretty straightforward.
2. setup a bitmask with all zeros, with a 1 for the bit in question. So for example, if it's the 3rd bit, your bitmask might be 00000100. Again, this doesn't require code.
3. bitwise XOR your number with the bit mask. If you're unfamiliar with the operator it's the hat operator: ^

Here's some sample code:

int myInt; // set this up with your original value
int myBitmask; // set this up with the bit mask via steps 1 and 2.
int randomlyZeroedBitInt = myInt ^ myBitmask;

Edit: On a fifth read of the question, I have a question in return: you are wanting to do which of the following:

1. Randomly zero a bit, but only if that bit is already 1. In other words, if the bit in question isn't already 1, the operation is a no-op.
2. Randomly choose a bit that is 1 and zero it. This operation always chooses a bit that is already 1 and always zeros it. The operation is only a no-op if the original value is 0.

Edit 2:

2 is correct,(15chars) – Fredou

In that case, my general algorithm stands; merely choose the bit in step 1 with internal logic. Alternatively, choose a fully random bit in step 1 and repeat until the value of myInt and randomlyZeroedBitInt are not equal.

Unfortunately either case means a more complex algorithm, as you'll either need to iterate over every bit in your value to determine which to flip, or you'll need to loop the algorithm until a bit is flipped.

Answer 9

OK:

    private static Random rnd = new Random((int)DateTime.Now.Ticks);

    private static Int32 SetRandomTrueBitToFalse(Int32 p)
    {
        List<int> trueBits = new List<int>();
        for (int i = 0; i < 31; i++)
        {
            if ((p>>i&1) == 1){
                trueBits.Add(i);
            }
        }
        if (trueBits.Count>0){
            int index = rnd.Next(0, trueBits.Count);
            return p & ~(1 << trueBits[index]);
        }
        return p;
    }

But I would love to know: Why do you need/want this?

Answer 10

 int val=382

 int mask = ~(1 << N)   

 // this would turn-off nth bit (0 to 31)
 NewVal = (int) ((uint)val & (uint)mask} 

Answer 11

You can generalize this by using BitArray.

public static BitArray FlipRandomTrueBit(BitArray bits)
{
    List<int> trueBits = new List<int>();

    for (int i = 0; i < bits.Count; i++)
        if (bits[i])
            trueBits.Add(i);

    if (trueBits.Count > 0)
    {
        int index = rnd.Next(0, trueBits.Count);
        bits[trueBits[index]] = false;
    }

    return bits;
}

However then you will have to write helper functions for simple data types.

public static int FlipRandomTrueBit(int input)
{
    BitArray bits = new BitArray(new int[] { input });
    BitArray flipedBits = FlipRandomTrueBit(bits);

    byte[] bytes = new byte[4];
    flipedBits.CopyTo(bytes, 0);

    int result = BitConverter.ToInt32(bytes, 0);
    return result;
}

If your using a large bit array you could save memory by iterating twice.

public static void FlipRandomTrueBitLowMem(ref BitArray bits)
{
    int trueBits = 0;

    for (int i = 0; i < bits.Count; i++)
        if (bits[i])
            trueBits++;

    if (trueBits > 0)
    {
        int flip = rnd.Next(0, trueBits);

        for (int i = 0; i < bits.Count; i++)
        {
            if (bits[i])
            {
                if (flip == 0)
                {
                    bits[i] = false;
                    break;
                }

                flip--;
            }
        }
    }
}

Test Program.

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

namespace bitarray
{
    class Program
    {
        private static Random rnd = new Random((int)DateTime.Now.Ticks);

        public static BitArray FlipRandomTrueBit(BitArray bits)
        {
            List<int> trueBits = new List<int>();

            for (int i = 0; i < bits.Count; i++)
                if (bits[i])
                    trueBits.Add(i);

            if (trueBits.Count > 0)
            {
                int index = rnd.Next(0, trueBits.Count);
                bits[trueBits[index]] = false;
            }

            return bits;
        }

        public static int FlipRandomTrueBit(int input)
        {
            BitArray bits = new BitArray(new int[] { input });
            BitArray flipedBits = FlipRandomTrueBit(bits);

            byte[] bytes = new byte[4];
            flipedBits.CopyTo(bytes, 0);

            int result = BitConverter.ToInt32(bytes, 0);
            return result;
        }

        static void Main(string[] args)
        {
            int test = 382;
            for (int n = 0; n < 200; n++)
            {
                int result = FlipRandomTrueBit(test);
                Console.WriteLine(result);
            }

            Console.ReadLine();
        }
    }
}

Answer 12

Here's a slightly more efficient version using bit twiddling.

    public static int getBitCount(int bits)
    {
        bits = bits - ((bits >> 1) & 0x55555555);
        bits = (bits & 0x33333333) + ((bits >> 2) & 0x33333333);
        return ((bits + (bits >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
    }

    public static int flipRandomBit(int data)
    {
        int index = random.Next(getBitCount(data));
        int mask = data;

        for (int i = 0; i < index; i++)
            mask &= mask - 1;
        mask ^= mask & (mask - 1);

        return data ^ mask;
    }

Answer 13

Here is a version based on an algorithm from Bit Twiddling Hacks to select the nth set bit of an integer. For this case, we simply select n at random.

The code has been ported to C#, made to work directly on 32-bit signed integers, and count from the right instead of the left. Furthermore, the optimization to remove all branches has not been preserved here as it yielded slower code on my machine (Intel Core 2 Quad Q9450).

The description on the Bit Twiddling Hacks page does not give much insight into how the algorithm works. I have taken the time to step through and reverse engineer it and what I found is described in detail in the comments below.

In my tests, this algorithm performs very similarly to Kyteland's excellent flipRandomBit over input that is distributed randomly across the full range of 32-bit integers. However, flipRandomBit is slightly faster for numbers with significantly fewer set bits than cleared bits. Conversely, this algorithm is slightly faster for numbers with significantly more set bits than cleared bits.

The OP's benchmark consists entirely of small positive integers, which do not stress flipRandomBit's worst case. If this is an indication of the expected input, then all the more reason to prefer flipRandomBit.

static int ClearRandomSetBit(int input) {
    ///////////////////////////////////////////////////////////////////////
    // ** Step 1 **
    // Count the set bits
    ////////////////////////////////////////////////////////////////////////

    // magic numbers
    const int m2 = 0x55555555; // 1 zero,  1 one,  ...
    const int m4 = 0x33333333; // 2 zeros, 2 ones, ...
    const int m8 = 0x0f0f0f0f; // 4 zeros, 4 ones, ...

    // sequence of 2-bit values representing the counts of each 2 bits.
    int c2 = input - ((input >> 1) & m2);

    // sequence of 4-bit values representing the counts of each 4 bits.
    int c4 = (c2 & m4) + ((c2 >> 2) & m4);

    // sequence of 8-bit values representing the counts of each 8 bits.
    int c8 = (c4 + (c4 >> 4)) & m8;

    // count set bits in input.
    int bitCount = (c8 * 0x1010101) >> 24;

    ///////////////////////////////////////////////////////////////////////////////////
    // ** Step 2 ** 
    // Select a random set bit to clear and find it using binary search with our 
    // knowledge of the bit counts in the various regions.
    ///////////////////////////////////////////////////////////////////////////////////

    // count 16 right-most bits where we'll begin our search
    int count = (c8 + (c8 >> 8)) & 0xff;

    // position of target bit among the set bits
    int target = random.Next(bitCount);

    // distance in set bits from the current position to the target
    int distance = target + 1;

    // current bit position 
    int pos = 0;

    // if the target is not in the right-most 16 bits, move past them
    if (distance > count) { pos += 16; distance -= count; }

    // if the target is not in the next 8 bits, move past them
    count = (c8 >> pos) & 0xff;
    if (distance > count) { pos += 8; distance -= count; }

    // if the target is not in the next 4 bits, move past them
    count = (c4 >> pos) & 0xf;
    if (distance > count) { pos += 4; distance -= count; }

    // if the target is not in the next 2 bits, move past them
    count = (c2 >> pos) & 0x3;
    if (distance > count) { pos += 2; distance -= count; }

    // if the bit is not the next bit, move past it.
    //
    // Note that distance and count must be single bits by now.
    // As such, distance is greater than count if and only if 
    // distance equals 1 and count equals 0. This obversation
    // allows us to optimize away the final branch.
    Debug.Assert((distance & 0x1) == distance);
    Debug.Assert((count & 0x1) == count);
    count = (input >> pos) & 0x1;
    pos += (distance & (count ^ 1));

    Debug.Assert((input & (1 << pos)) != 0);
    return input ^ (1 << pos);
}