# Tutorial :Position of least significant bit that is set ### Question:

I am looking for an efficient way to determine the position of the least significant bit that is set in an integer, e.g. for 0x0FF0 it would be 4.

A trivial implementation is this:

``unsigned GetLowestBitPos(unsigned value)  {     assert(value != 0); // handled separately       unsigned pos = 0;     while (!(value & 1))     {        value >>= 1;        ++pos;     }     return pos;  }  ``

Any ideas how to squeeze some cycles out of it?

(Note: this question is for people that enjoy such things, not for people to tell me xyzoptimization is evil.)

 Thanks everyone for the ideas! I've learnt a few other things, too. Cool!

### Solution:1

Bit Twiddling Hacks offers an excellent collection of, er, bit twiddling hacks, with performance/optimisation discussion attached. My favourite solution for your problem (from that site) is Â«multiply and lookupÂ»:

``unsigned int v;  // find the number of trailing zeros in 32-bit v   int r;           // result goes here  static const int MultiplyDeBruijnBitPosition =   {    0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,     31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9  };  r = MultiplyDeBruijnBitPosition[((uint32_t)((v & -v) * 0x077CB531U)) >> 27];  ``

### Solution:2

Why not use the built-in ffs? (I grabbed a man page from Linux, but it's more widely available than that.)

## ffs(3) - Linux man page

### Name

ffs - find first bit set in a word

### Synopsis

``#include <strings.h>  int ffs(int i);  #define _GNU_SOURCE  #include <string.h>  int ffsl(long int i);  int ffsll(long long int i);  ``

### Description

The ffs() function returns the position of the first (least significant) bit set in the word i. The least significant bit is position 1 and the most significant position e.g. 32 or 64. The functions ffsll() and ffsl() do the same but take arguments of possibly different size.

### Return Value

These functions return the position of the first bit set, or 0 if no bits are set in i.

### Conforming to

4.3BSD, POSIX.1-2001.

### Notes

BSD systems have a prototype in `<string.h>`.

### Solution:3

There is an x86 assembly instruction (`bsf`) that will do it. :)

More optimized?!

## Side Note:

Optimization at this level is inherently architecture dependent. Today's processors are too complex (in terms of branch prediction, cache misses, pipelining) that it's so hard to predict which code is executed faster on which architecture. Decreasing operations from 32 to 9 or things like that might even decrease the performance on some architectures. Optimized code on a single architecture might result in worse code in the other. I think you'd either optimize this for a specific CPU or leave it as it is and let the compiler to choose what it thinks it's better.

### Solution:4

Most modern architectures will have some instruction for finding the position of the lowest set bit, or the highest set bit, or counting the number of leading zeroes etc.

If you have any one instruction of this class you can cheaply emulate the others.

Take a moment to work through it on paper and realise that `x & (x-1)` will clear the lowest set bit in x, and `( x & ~(x-1) )` will return just the lowest set bit, irrespective of achitecture, word length etc. Knowing this, it is trivial to use hardware count-leading-zeroes / highest-set-bit to find the lowest set bit if there is no explicit instruction to do so.

If there is no relevant hardware support at all, the multiply-and-lookup implementation of count-leading-zeroes given here or one of the ones on the Bit Twiddling Hacks page can trivially be converted to give lowest set bit using the above identities and has the advantage of being branchless.

### Solution:5

The fastest (non-intrinsic/non-assembler) solution to this is to find the lowest-byte and then use that byte in a 256-entry lookup table. This gives you a worst-case performance of four conditional instructions and a best-case of 1. Not only is this the least amount of instructions, but the least amount of branches which is super-important on modern hardware.

Your table (256 8-bit entries) should contain the index of the LSB for each number in the range 0-255. You check each byte of your value and find the lowest non-zero byte, then use this value to lookup the real index.

This does require 256-bytes of memory, but if the speed of this function is so important then that 256-bytes is well worth it,

E.g.

``byte lowestBitTable = {  .... // left as an exercise for the reader to generate  };    unsigned GetLowestBitPos(unsigned value)  {    // note that order to check indices will depend whether you are on a big     // or little endian machine. This is for little-endian    byte* bytes = (byte*)value;    if (bytes)      return lowestBitTable[bytes];    else if (bytes)        return lowestBitTable[bytes] + 8;    else if (bytes)        return lowestBitTable[bytes] + 16;    else        return lowestBitTable[bytes] + 24;    }  ``

### Solution:6

Weee, loads of solutions and not a benchmark in sight. You people should be ashamed of yourselves ;-)

My machine is an Intel i530 (2.9 GHz), running Windows 7 64-bit. I compiled with a 32-bit version of MinGW.

``\$ gcc --version  gcc.exe (GCC) 4.7.2    \$ gcc bench.c -o bench.exe -std=c99 -Wall -O2  \$ bench  Naive loop.         Time = 2.91  (Original questioner)  De Bruijn multiply. Time = 1.16  (Tykhyy)  Lookup table.       Time = 0.36  (Andrew Grant)  FFS instruction.    Time = 0.90  (ephemient)  Branch free mask.   Time = 3.48  (Dan / Jim Balter)  Double hack.        Time = 3.41  (DocMax)    \$ gcc bench.c -o bench.exe -std=c99 -Wall -O2 -march=native  \$ bench  Naive loop.         Time = 2.92  De Bruijn multiply. Time = 0.47  Lookup table.       Time = 0.35  FFS instruction.    Time = 0.68  Branch free mask.   Time = 3.49  Double hack.        Time = 0.92  ``

My code:

``#include <stdio.h>  #include <stdlib.h>  #include <time.h>      #define ARRAY_SIZE 65536  #define NUM_ITERS 5000  // Number of times to process array      int find_first_bits_naive_loop(unsigned nums[ARRAY_SIZE])  {      int total = 0; // Prevent compiler from optimizing out the code      for (int j = 0; j < NUM_ITERS; j++) {          for (int i = 0; i < ARRAY_SIZE; i++) {              unsigned value = nums[i];              if (value == 0)                  continue;              unsigned pos = 0;              while (!(value & 1))              {                  value >>= 1;                  ++pos;              }              total += pos + 1;          }      }        return total;  }      int find_first_bits_de_bruijn(unsigned nums[ARRAY_SIZE])  {      static const int MultiplyDeBruijnBitPosition =       {         1, 2, 29, 3, 30, 15, 25, 4, 31, 23, 21, 16, 26, 18, 5, 9,          32, 28, 14, 24, 22, 20, 17, 8, 27, 13, 19, 7, 12, 6, 11, 10      };        int total = 0; // Prevent compiler from optimizing out the code      for (int j = 0; j < NUM_ITERS; j++) {          for (int i = 0; i < ARRAY_SIZE; i++) {              unsigned int c = nums[i];              total += MultiplyDeBruijnBitPosition[((unsigned)((c & -c) * 0x077CB531U)) >> 27];          }      }        return total;  }      unsigned char lowestBitTable;  int get_lowest_set_bit(unsigned num) {      unsigned mask = 1;      for (int cnt = 1; cnt <= 32; cnt++, mask <<= 1) {          if (num & mask) {              return cnt;          }      }        return 0;  }  int find_first_bits_lookup_table(unsigned nums[ARRAY_SIZE])  {      int total = 0; // Prevent compiler from optimizing out the code      for (int j = 0; j < NUM_ITERS; j++) {          for (int i = 0; i < ARRAY_SIZE; i++) {              unsigned int value = nums[i];              // note that order to check indices will depend whether you are on a big               // or little endian machine. This is for little-endian              unsigned char *bytes = (unsigned char *)&value;              if (bytes)                  total += lowestBitTable[bytes];              else if (bytes)                total += lowestBitTable[bytes] + 8;              else if (bytes)                total += lowestBitTable[bytes] + 16;              else                total += lowestBitTable[bytes] + 24;          }      }        return total;  }      int find_first_bits_ffs_instruction(unsigned nums[ARRAY_SIZE])  {      int total = 0; // Prevent compiler from optimizing out the code      for (int j = 0; j < NUM_ITERS; j++) {          for (int i = 0; i < ARRAY_SIZE; i++) {              total +=  __builtin_ffs(nums[i]);          }      }        return total;  }      int find_first_bits_branch_free_mask(unsigned nums[ARRAY_SIZE])  {      int total = 0; // Prevent compiler from optimizing out the code      for (int j = 0; j < NUM_ITERS; j++) {          for (int i = 0; i < ARRAY_SIZE; i++) {              unsigned value = nums[i];              int i16 = !(value & 0xffff) << 4;              value >>= i16;                int i8 = !(value & 0xff) << 3;              value >>= i8;                int i4 = !(value & 0xf) << 2;              value >>= i4;                int i2 = !(value & 0x3) << 1;              value >>= i2;                int i1 = !(value & 0x1);                int i0 = (value >> i1) & 1? 0 : -32;                total += i16 + i8 + i4 + i2 + i1 + i0 + 1;          }      }        return total;  }      int find_first_bits_double_hack(unsigned nums[ARRAY_SIZE])  {      int total = 0; // Prevent compiler from optimizing out the code      for (int j = 0; j < NUM_ITERS; j++) {          for (int i = 0; i < ARRAY_SIZE; i++) {              unsigned value = nums[i];              double d = value ^ (value - !!value);               total += (((int*)&d)>>20)-1022;           }      }        return total;  }      int main() {      unsigned nums[ARRAY_SIZE];      for (int i = 0; i < ARRAY_SIZE; i++) {          nums[i] = rand() + (rand() << 15);      }        for (int i = 0; i < 256; i++) {          lowestBitTable[i] = get_lowest_set_bit(i);      }          clock_t start_time, end_time;      int result;        start_time = clock();      result = find_first_bits_naive_loop(nums);      end_time = clock();      printf("Naive loop.         Time = %.2f, result = %d\n",           (end_time - start_time) / (double)(CLOCKS_PER_SEC), result);        start_time = clock();      result = find_first_bits_de_bruijn(nums);      end_time = clock();      printf("De Bruijn multiply. Time = %.2f, result = %d\n",           (end_time - start_time) / (double)(CLOCKS_PER_SEC), result);        start_time = clock();      result = find_first_bits_lookup_table(nums);      end_time = clock();      printf("Lookup table.       Time = %.2f, result = %d\n",           (end_time - start_time) / (double)(CLOCKS_PER_SEC), result);        start_time = clock();      result = find_first_bits_ffs_instruction(nums);      end_time = clock();      printf("FFS instruction.    Time = %.2f, result = %d\n",           (end_time - start_time) / (double)(CLOCKS_PER_SEC), result);        start_time = clock();      result = find_first_bits_branch_free_mask(nums);      end_time = clock();      printf("Branch free mask.   Time = %.2f, result = %d\n",           (end_time - start_time) / (double)(CLOCKS_PER_SEC), result);        start_time = clock();      result = find_first_bits_double_hack(nums);      end_time = clock();      printf("Double hack.        Time = %.2f, result = %d\n",           (end_time - start_time) / (double)(CLOCKS_PER_SEC), result);  }  ``

### Solution:7

OMG has this just spiraled.

What most of these examples are lacking is a little understanding about how all hardware works.

Anytime you have a branch, the CPU has to guess which branch will be taken. The instruction pipe is loaded with the instructions that lead down the guessed path. If the CPU has guessed wrong then the instruction pipe gets flushed, and the other branch must be loaded.

Consider the simple while loop at the top. The guess will be to stay within the loop. It will be wrong at least once when it leaves the loop. This WILL flush the instruction pipe. This behavior is slightly better than guessing that it will leave the loop, in which case it would flush the instruction pipe on every iteration.

The amount of CPU cycles that are lost varies highly from one type of processor to the next. But you can expect between 20 and 150 lost CPU cycles.

The next worse group is where you think your going to save a few iterations by splitting the value in to smaller pieces and adding several more branches. Each of these branches adds an additional opportunity to flush the instruction pipe and cost another 20 to 150 clock cycles.

Lets consider what happens when you look up a value in a table. Chances are the value is not currently in cache, at least not the first time your function is called. This means that the CPU gets stalled while the value is loaded from cache. Again this varies from one machine to the next. The new Intel chips actually use this as an opportunity to swap threads while the current thread is waiting for the cache load to complete. This could easily be more expensive than an instruction pipe flush, however if you are performing this operation a number of times it is likely to only occur once.

Clearly the fastest constant time solution is one which involves deterministic math. A pure and elegant solution.

My apologies if this was already covered.

Every compiler I use, except XCODE AFAIK, has compiler intrinsics for both the forward bitscan and the reverse bitscan. These will compile to a single assembly instruction on most hardware with no Cache Miss, no Branch Miss-Prediction and No other programmer generated stumbling blocks.

For Microsoft compilers use _BitScanForward & _BitScanReverse.
For GCC use __builtin_ffs, __builtin_clz, __builtin_ctz.

Additionally, please refrain from posting an answer and potentially misleading newcomers if you are not adequately knowledgeable about the subject being discussed.

Sorry I totally forgot to provide a solution.. This is the code I use on the IPAD which has no assembly level instruction for the task:

``unsigned BitScanLow_BranchFree(unsigned value)  {      bool bwl = (value & 0x0000ffff) == 0;      unsigned I1 = (bwl * 15);      value = (value >> I1) & 0x0000ffff;        bool bbl = (value & 0x00ff00ff) == 0;      unsigned I2 = (bbl * 7);      value = (value >> I2) & 0x00ff00ff;        bool bnl = (value & 0x0f0f0f0f) == 0;      unsigned I3 = (bnl * 3);      value = (value >> I3) & 0x0f0f0f0f;        bool bsl = (value & 0x33333333) == 0;      unsigned I4 = (bsl * 1);      value = (value >> I4) & 0x33333333;        unsigned result = value + I1 + I2 + I3 + I4 - 1;        return result;  }  ``

The thing to understand here is that it is not the compare that is expensive, but the branch that occurs after the compare. The comparison in this case is forced to a value of 0 or 1 with the .. == 0, and the result is used to combine the math that would have occurred on either side of the branch.

Edit:

The code above is totally broken. This code works and is still branch-free (if optimized):

``int BitScanLow_BranchFree(ui value)  {      int i16 = !(value & 0xffff) << 4;      value >>= i16;        int i8 = !(value & 0xff) << 3;      value >>= i8;        int i4 = !(value & 0xf) << 2;      value >>= i4;        int i2 = !(value & 0x3) << 1;      value >>= i2;        int i1 = !(value & 0x1);        int i0 = (value >> i1) & 1? 0 : -32;        return i16 + i8 + i4 + i2 + i1 + i0;  }  ``

This returns -1 if given 0. If you don't care about 0 or are happy to get 31 for 0, remove the i0 calculation, saving a chunk of time.

### Solution:8

Inspired by this similar post that involves searching for a set bit, I offer the following:

``unsigned GetLowestBitPos(unsigned value)  {     double d = value ^ (value - !!value);      return (((int*)&d)>>20)-1023;   }  ``

Pros:

• no loops
• no branching
• runs in constant time
• handles value=0 by returning an otherwise-out-of-bounds result
• only two lines of code

Cons:

• assumes little endianness as coded (can be fixed by changing the constants)
• assumes that double is a real*8 IEEE float (IEEE 754)

Update: As pointed out in the comments, a union is a cleaner implementation (for C, at least) and would look like:

``unsigned GetLowestBitPos(unsigned value)  {      union {          int i;          double d;      } temp = { .d = value ^ (value - !!value) };      return (temp.i >> 20) - 1023;  }  ``

This assumes 32-bit ints with little-endian storage for everything (think x86 processors).

### Solution:9

It can be done with a worst case of less than 32 operations:

Principle: Checking for 2 or more bits is just as efficient as checking for 1 bit.

So for example there's nothing stopping you from checking for which grouping its in first, then checking each bit from smallest to biggest in that group.

So...
if you check 2 bits at a time you have in the worst case (Nbits/2) + 1 checks total.
if you check 3 bits at a time you have in the worst case (Nbits/3) + 2 checks total.
...

Optimal would be to check in groups of 4. Which would require in the worst case 11 operations instead of your 32.

The best case goes from your algorithms's 1 check though to 2 checks if you use this grouping idea. But that extra 1 check in best case is worth it for the worst case savings.

Note: I write it out in full instead of using a loop because it's more efficient that way.

``int getLowestBitPos(unsigned int value)  {      //Group 1: Bits 0-3      if(value&0xf)      {          if(value&0x1)              return 0;          else if(value&0x2)              return 1;          else if(value&0x4)              return 2;          else              return 3;      }        //Group 2: Bits 4-7      if(value&0xf0)      {          if(value&0x10)              return 4;          else if(value&0x20)              return 5;          else if(value&0x40)              return 6;          else              return 7;      }        //Group 3: Bits 8-11      if(value&0xf00)      {          if(value&0x100)              return 8;          else if(value&0x200)              return 9;          else if(value&0x400)              return 10;          else              return 11;      }        //Group 4: Bits 12-15      if(value&0xf000)      {          if(value&0x1000)              return 12;          else if(value&0x2000)              return 13;          else if(value&0x4000)              return 14;          else              return 15;      }        //Group 5: Bits 16-19      if(value&0xf0000)      {          if(value&0x10000)              return 16;          else if(value&0x20000)              return 17;          else if(value&0x40000)              return 18;          else              return 19;      }        //Group 6: Bits 20-23      if(value&0xf00000)      {          if(value&0x100000)              return 20;          else if(value&0x200000)              return 21;          else if(value&0x400000)              return 22;          else              return 23;      }        //Group 7: Bits 24-27      if(value&0xf000000)      {          if(value&0x1000000)              return 24;          else if(value&0x2000000)              return 25;          else if(value&0x4000000)              return 26;          else              return 27;      }        //Group 8: Bits 28-31      if(value&0xf0000000)      {          if(value&0x10000000)              return 28;          else if(value&0x20000000)              return 29;          else if(value&0x40000000)              return 30;          else              return 31;      }        return -1;  }  ``

### Solution:10

Why not use binary search? This will always complete after 5 operations (assuming int size of 4 bytes):

``if (0x0000FFFF & value) {      if (0x000000FF & value) {          if (0x0000000F & value) {              if (0x00000003 & value) {                  if (0x00000001 & value) {                      return 1;                  } else {                      return 2;                  }              } else {                  if (0x0000004 & value) {                      return 3;                  } else {                      return 4;                  }              }          } else { ...      } else { ...  } else { ...  ``

### Solution:11

Another method (modulus division and lookup) deserves a special mention here from the same link provided by @anton-tykhyy. this method is very similar in performance to DeBruijn multiply and lookup method with a slight but important difference.

modulus division and lookup

`` unsigned int v;  // find the number of trailing zeros in v      int r;           // put the result in r      static const int Mod37BitPosition[] = // map a bit value mod 37 to its position      {        32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13, 4,        7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9, 5,        20, 8, 19, 18      };      r = Mod37BitPosition[(-v & v) % 37];  ``

modulus division and lookup method returns different values for v=0x00000000 and v=FFFFFFFF whereas DeBruijn multiply and lookup method returns zero on both inputs.

test:-

``unsigned int n1=0x00000000, n2=0xFFFFFFFF;    MultiplyDeBruijnBitPosition[((unsigned int )((n1 & -n1) * 0x077CB531U)) >> 27]); /* returns 0 */  MultiplyDeBruijnBitPosition[((unsigned int )((n2 & -n2) * 0x077CB531U)) >> 27]); /* returns 0 */  Mod37BitPosition[(((-(n1) & (n1))) % 37)]); /* returns 32 */  Mod37BitPosition[(((-(n2) & (n2))) % 37)]); /* returns 0 */  ``

### Solution:12

According to the Chess Programming BitScan page and my own measurements, subtract and xor is faster than negate and mask.

(Note than if you are going to count the trailing zeros in `0`, the method as I have it returns `63` whereas the negate and mask returns `0`.)

Here is a 64-bit subtract and xor:

``unsigned long v;  // find the number of trailing zeros in 64-bit v   int r;            // result goes here  static const int MultiplyDeBruijnBitPosition =   {    0, 47, 1, 56, 48, 27, 2, 60, 57, 49, 41, 37, 28, 16, 3, 61,    54, 58, 35, 52, 50, 42, 21, 44, 38, 32, 29, 23, 17, 11, 4, 62,    46, 55, 26, 59, 40, 36, 15, 53, 34, 51, 20, 43, 31, 22, 10, 45,    25, 39, 14, 33, 19, 30, 9, 24, 13, 18, 8, 12, 7, 6, 5, 63  };  r = MultiplyDeBruijnBitPosition[((uint32_t)((v ^ (v-1)) * 0x03F79D71B4CB0A89U)) >> 58];  ``

For reference, here is a 64-bit version of the negate and mask method:

``unsigned long v;  // find the number of trailing zeros in 64-bit v   int r;            // result goes here  static const int MultiplyDeBruijnBitPosition =   {    0, 1, 48, 2, 57, 49, 28, 3, 61, 58, 50, 42, 38, 29, 17, 4,    62, 55, 59, 36, 53, 51, 43, 22, 45, 39, 33, 30, 24, 18, 12, 5,    63, 47, 56, 27, 60, 41, 37, 16, 54, 35, 52, 21, 44, 32, 23, 11,    46, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6  };  r = MultiplyDeBruijnBitPosition[((uint32_t)((v & -v) * 0x03F79D71B4CB0A89U)) >> 58];  ``

### Solution:13

You could check if any of the lower order bits are set. If so then look at the lower order of the remaining bits. e.g.,:

32bit int - check if any of the first 16 are set. If so, check if any of the first 8 are set. if so, ....

if not, check if any of the upper 16 are set..

Essentially it's binary search.

### Solution:14

See my answer here for how to do it with a single x86 instruction, except that to find the least significant set bit you'll want the `BSF` ("bit scan forward") instruction instead of `BSR` described there.

### Solution:15

Yet another solution, not the fastest possibly, but seems quite good.
At least it has no branches. ;)

``uint32 x = ...;  // 0x00000001  0x0405a0c0  0x00602000  x |= x <<  1;    // 0x00000003  0x0c0fe1c0  0x00e06000  x |= x <<  2;    // 0x0000000f  0x3c3fe7c0  0x03e1e000  x |= x <<  4;    // 0x000000ff  0xffffffc0  0x3fffe000  x |= x <<  8;    // 0x0000ffff  0xffffffc0  0xffffe000  x |= x << 16;    // 0xffffffff  0xffffffc0  0xffffe000    // now x is filled with '1' from the least significant '1' to bit 31    x = ~x;          // 0x00000000  0x0000003f  0x00001fff    // now we have 1's below the original least significant 1  // let's count them    x = x & 0x55555555 + (x >>  1) & 0x55555555;                   // 0x00000000  0x0000002a  0x00001aaa    x = x & 0x33333333 + (x >>  2) & 0x33333333;                   // 0x00000000  0x00000024  0x00001444    x = x & 0x0f0f0f0f + (x >>  4) & 0x0f0f0f0f;                   // 0x00000000  0x00000006  0x00000508    x = x & 0x00ff00ff + (x >>  8) & 0x00ff00ff;                   // 0x00000000  0x00000006  0x0000000d    x = x & 0x0000ffff + (x >> 16) & 0x0000ffff;                   // 0x00000000  0x00000006  0x0000000d  // least sign.bit pos. was:  0           6          13  ``

### Solution:16

``unsigned GetLowestBitPos(unsigned value)  {      if (value & 1) return 1;      if (value & 2) return 2;      if (value & 4) return 3;      if (value & 8) return 4;      if (value & 16) return 5;      if (value & 32) return 6;      if (value & 64) return 7;      if (value & 128) return 8;      if (value & 256) return 9;      if (value & 512) return 10;      if (value & 1024) return 11;      if (value & 2048) return 12;      if (value & 4096) return 13;      if (value & 8192) return 14;      if (value & 16384) return 15;      if (value & 32768) return 16;      if (value & 65536) return 17;      if (value & 131072) return 18;      if (value & 262144) return 19;      if (value & 524288) return 20;      if (value & 1048576) return 21;      if (value & 2097152) return 22;      if (value & 4194304) return 23;      if (value & 8388608) return 24;      if (value & 16777216) return 25;      if (value & 33554432) return 26;      if (value & 67108864) return 27;      if (value & 134217728) return 28;      if (value & 268435456) return 29;      if (value & 536870912) return 30;      return 31;  }  ``

50% of all numbers will return on the first line of code.

75% of all numbers will return on the first 2 lines of code.

87% of all numbers will return in the first 3 lines of code.

94% of all numbers will return in the first 4 lines of code.

97% of all numbers will return in the first 5 lines of code.

etc.

I think people that are complaining on how inefficient the worst case scenario for this code don't understand how rare that condition will happen.

### Solution:17

Found this clever trick using 'magic masks' in "The art of programming, part 4", which does it in O(log(n)) time for n-bit number. [with log(n) extra space]. Typical solutions checking for the set bit is either O(n) or need O(n) extra space for a look up table, so this is a good compromise.

``m0 = (...............01010101)    m1 = (...............00110011)  m2 = (...............00001111)    m3 = (.......0000000011111111)  ....  ``

Key idea: No of trailing zeros in x = 1 * [(x & m0) = 0] + 2 * [(x & m1) = 0] + 4 * [(x & m2) = 0] + ...

``int lastSetBitPos(const uint64_t x) {      if (x == 0)  return -1;        //For 64 bit number, log2(64)-1, ie; 5 masks needed      int steps = log2(sizeof(x) * 8); assert(steps == 6);      //magic masks      uint64_t m[] = { 0x5555555555555555, //     .... 010101                       0x3333333333333333, //     .....110011                       0x0f0f0f0f0f0f0f0f, //     ...00001111                       0x00ff00ff00ff00ff, //0000000011111111                        0x0000ffff0000ffff,                        0x00000000ffffffff };        //Firstly extract only the last set bit      uint64_t y = x & -x;        int trailZeros = 0, i = 0 , factor = 0;      while (i < steps) {          factor = ((y & m[i]) == 0 ) ? 1 : 0;          trailZeros += factor * pow(2,i);          ++i;      }      return (trailZeros+1);  }  ``

### Solution:18

If C++11 is available for you, a compiler sometimes can do the task for you :)

``constexpr std::uint64_t lssb(const std::uint64_t value)  {      return !value ? 0 : (value % 2 ? 1 : lssb(value >> 1) + 1);  }  ``

Result is 1-based index.

### Solution:19

This is in regards of @Anton Tykhyy answer

Here is my C++11 constexpr implementation doing away with casts and removing a warning on VC++17 by truncating a 64bit result to 32 bits:

``constexpr uint32_t DeBruijnSequence =  {      0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,      31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9  };  constexpr uint32_t ffs ( uint32_t value )  {      return  DeBruijnSequence[           (( ( value & ( -static_cast<int32_t>(value) ) ) * 0x077CB531ULL ) & 0xFFFFFFFF)              >> 27];  }  ``

To get around the issue of 0x1 and 0x0 both returning 0 you can do:

``constexpr uint32_t ffs ( uint32_t value )  {      return (!value) ? 32 : DeBruijnSequence[           (( ( value & ( -static_cast<int32_t>(value) ) ) * 0x077CB531ULL ) & 0xFFFFFFFF)              >> 27];  }  ``

but if the compiler can't or won't preprocess the call it will add a couple of cycles to the calculation.

Finally, if interested, here's a list of static asserts to check that the code does what is intended to:

``static_assert (ffs(0x1) == 0, "Find First Bit Set Failure.");  static_assert (ffs(0x2) == 1, "Find First Bit Set Failure.");  static_assert (ffs(0x4) == 2, "Find First Bit Set Failure.");  static_assert (ffs(0x8) == 3, "Find First Bit Set Failure.");  static_assert (ffs(0x10) == 4, "Find First Bit Set Failure.");  static_assert (ffs(0x20) == 5, "Find First Bit Set Failure.");  static_assert (ffs(0x40) == 6, "Find First Bit Set Failure.");  static_assert (ffs(0x80) == 7, "Find First Bit Set Failure.");  static_assert (ffs(0x100) == 8, "Find First Bit Set Failure.");  static_assert (ffs(0x200) == 9, "Find First Bit Set Failure.");  static_assert (ffs(0x400) == 10, "Find First Bit Set Failure.");  static_assert (ffs(0x800) == 11, "Find First Bit Set Failure.");  static_assert (ffs(0x1000) == 12, "Find First Bit Set Failure.");  static_assert (ffs(0x2000) == 13, "Find First Bit Set Failure.");  static_assert (ffs(0x4000) == 14, "Find First Bit Set Failure.");  static_assert (ffs(0x8000) == 15, "Find First Bit Set Failure.");  static_assert (ffs(0x10000) == 16, "Find First Bit Set Failure.");  static_assert (ffs(0x20000) == 17, "Find First Bit Set Failure.");  static_assert (ffs(0x40000) == 18, "Find First Bit Set Failure.");  static_assert (ffs(0x80000) == 19, "Find First Bit Set Failure.");  static_assert (ffs(0x100000) == 20, "Find First Bit Set Failure.");  static_assert (ffs(0x200000) == 21, "Find First Bit Set Failure.");  static_assert (ffs(0x400000) == 22, "Find First Bit Set Failure.");  static_assert (ffs(0x800000) == 23, "Find First Bit Set Failure.");  static_assert (ffs(0x1000000) == 24, "Find First Bit Set Failure.");  static_assert (ffs(0x2000000) == 25, "Find First Bit Set Failure.");  static_assert (ffs(0x4000000) == 26, "Find First Bit Set Failure.");  static_assert (ffs(0x8000000) == 27, "Find First Bit Set Failure.");  static_assert (ffs(0x10000000) == 28, "Find First Bit Set Failure.");  static_assert (ffs(0x20000000) == 29, "Find First Bit Set Failure.");  static_assert (ffs(0x40000000) == 30, "Find First Bit Set Failure.");  static_assert (ffs(0x80000000) == 31, "Find First Bit Set Failure.");  ``

### Solution:20

recently I see that singapore's premier posted a program he wrote on facebook, there is one line to mention it..

The logic is simply "value & -value", suppose you have 0x0FF0, then, 0FF0 & (F00F+1) , which equals 0x0010, that means the lowest 1 is in the 4th bit.. :)

### Solution:21

If you have the resources, you can sacrifice memory in order to improve the speed:

``static const unsigned bitPositions[MAX_INT] = { 0, 0, 1, 0, 2, /* ... */ };    unsigned GetLowestBitPos(unsigned value)  {      assert(value != 0); // handled separately      return bitPositions[value];  }  ``

Note: This table would consume at least 4 GB (16 GB if we leave the return type as `unsigned`). This is an example of trading one limited resource (RAM) for another (execution speed).

If your function needs to remain portable and run as fast as possible at any cost, this would be the way to go. In most real-world applications, a 4GB table is unrealistic.

Note:If u also have question or solution just comment us below or mail us on toontricks1994@gmail.com
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