Tutorial :Converting a range into a bit array



Question:

I'm writing a time-critical piece of code in C# that requires me to convert two unsigned integers that define an inclusive range into a bit field. Ex:

uint x1 = 3;  uint x2 = 9;    //defines the range [3-9]    //                              98  7654 3    //must be converted to:  0000 0011  1111 1000  

It may help to visualize the bits in reverse order

The maximum value for this range is a parameter given at run-time which we'll call max_val. Therefore, the bit field variable ought to be defined as a UInt32 array with size equal to max_val/32:

UInt32 MAX_DIV_32 = max_val / 32;  UInt32[] bitArray = new UInt32[MAX_DIV_32];  

Given a range defined by the variables x1 and x2, what is the fastest way to perform this conversion?


Solution:1

Try this. Calculate the range of array items that must be filled with all ones and do this by iterating over this range. Finally set the items at both borders.

Int32 startIndex = x1 >> 5;  Int32 endIndex = x2 >> 5;    bitArray[startIndex] = UInt32.MaxValue << (x1 & 31);    for (Int32 i = startIndex + 1; i <= endIndex; i++)  {     bitArray[i] = UInt32.MaxValue;  }    bitArray[endIndex] &= UInt32.MaxValue >> (31 - (x2 & 31));  

May be the code is not 100% correct, but the idea should work.


Just tested it and found three bugs. The calculation at start index required a mod 32 and at end index the 32 must be 31 and a logical and instead of a assignment to handle the case of start and end index being the same. Should be quite fast.


Just benchmarked it with equal distribution of x1 and x2 over the array. Intel Core 2 Duo E8400 3.0 GHz, MS VirtualPC with Server 2003 R2 on Windows XP host.

Array length [bits]           320         160         64  Performance [executions/s]    33 million  43 million  54 million  

One more optimazation x % 32 == x & 31 but I am unable to meassure a performance gain. Because of only 10.000.000 iterations in my test the fluctuations are quite high. And I am running in VirtualPC making the situation even more unpredictable.


Solution:2

My solution for setting a whole range of bits in a BitArray to true or false:

public static BitArray SetRange(BitArray bitArray, Int32 offset, Int32 length, Boolean value)  {        Int32[] ints = new Int32[(bitArray.Count >> 5) + 1];        bitArray.CopyTo(ints, 0);        var firstInt = offset >> 5;      var lastInt = (offset + length) >> 5;        Int32 mask = 0;        if (value)      {          // set first and last int          mask = (-1 << (offset & 31));          if (lastInt != firstInt)              ints[lastInt] |= ~(-1 << ((offset + length) & 31));          else              mask &= ~(-1 << ((offset + length) & 31));            ints[firstInt] |= mask;            // set all ints in between          for (Int32 i = firstInt + 1; i < lastInt; i++)              ints[i] = -1;      }        else      {          // set first and last int          mask = ~(-1 << (offset & 31));          if (lastInt != firstInt)              ints[lastInt] &= -1 << ((offset + length) & 31);          else              mask |= -1 << ((offset + length) & 31);            ints[firstInt] &= mask;            // set all ints in between          for (Int32 i = firstInt + 1; i < lastInt; i++)              ints[i] = 0;        }        return new BitArray(ints) { Length = bitArray.Length };    }  


Solution:3

You could try:

UInt32 x1 = 3;  UInt32 x2 = 9;  UInt32 newInteger = (UInt32)(Math.Pow(2, x2 + 1) - 1) &                      ~(UInt32)(Math.Pow(2, x1)-1);  


Solution:4

Is there a reason not to use the System.Collections.BitArray class instead of a UInt32[]? Otherwise, I'd try something like this:

int minIndex = (int)x1/32;  int maxIndex = (int)x2/32;  // first handle the all zero regions and the all one region (if any)  for (int i = 0; i < minIndex; i++) {      bitArray[i] = 0;  }  for (int i = minIndex + 1; i < maxIndex; i++) {      bitArray[i] = UInt32.MaxValue; // set to all 1s  }  for (int i = maxIndex + 1; i < MAX_DIV_32; i++) {      bitArray[i] = 0;  }    // now handle the tricky parts  uint maxBits = (2u << ((int)x2 - 32 * maxIndex)) - 1; // set to 1s up to max  uint minBits = ~((1u << ((int)x1 - 32 * minIndex)) - 1); // set to 1s after min    if (minIndex == maxIndex) {      bitArray[minIndex] = maxBits & minBits;  }  else {      bitArray[minIndex] = minBits;      bitArray[maxIndex] = maxBits;  }  


Solution:5

I was bored enough to try doing it with a char array and using Convert.ToUInt32(string, int) to convert to a uint from base 2.

uint Range(int l, int h)  {    char[] buffer = new char[h];    for (int i = 0; i < buffer.Length; i++)    {      buffer[i] = i < h - l ? '1' : '0';    }    return Convert.ToUInt32(new string(buffer), 2);  }  

A simple benchmark shows that my method is about 5% faster than Angrey Jim's (even if you replace second Pow with a bit shift.)

It is probably the easiest to convert to producing a uint array if the upper bound is too big to fit into a single int. It's a little cryptic but I believe it works.

uint[] Range(int l, int h)  {    char[] buffer = new char[h];    for (int i = 0; i < buffer.Length; i++)    {      buffer[i] = i < h - l ? '1' : '0';    }      int bitsInUInt = sizeof(uint) * 8;    int numNeededUInts = (int)Math.Ceiling((decimal)buffer.Length /                                           (decimal)bitsInUInt);    uint[] uints = new uint[numNeededUInts];    for (int j = uints.Length - 1, s = buffer.Length - bitsInUInt;         j >= 0 && s >= 0;         j--, s -= bitsInUInt)    {      uints[j] = Convert.ToUInt32(new string(buffer, s, bitsInUInt), 2);    }      int remainder = buffer.Length % bitsInUInt;    if (remainder > 0)    {      uints[0] = Convert.ToUInt32(new string(buffer, 0, remainder), 2);    }      return uints;  }  


Solution:6

Try this:

uint x1 = 3;  uint x2 = 9;    int cbToShift = x2 - x1; // 6  int nResult = ((1 << cbToShift) - 1) << x1;     /*    (1<<6)-1 gives you 63 = 111111, then you shift it on 3 bits left  */  

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