How Can I Efficiently Find the Position of the Least Significant Set Bit in an Integer?

Determining the Position of the Least Significant Set Bit

In programming, determining the position of the least significant bit (LSB) that is set in an integer can be a useful operation. A trivial implementation involves repeatedly masking the integer with 1 and shifting it right until the result becomes non-zero, but this method can be slow for large integers.

Bit Twiddling Optimization

Bit twiddling hacks provide an efficient alternative. One such hack, known as the "multiply and lookup" method, exploits the properties of the de Bruijn sequence to perform the calculation in a single step.

Code Implementation

unsigned int v;  // find the number of trailing zeros in 32-bit v
int r;           // result goes here
static const int MultiplyDeBruijnBitPosition[32] = 
{
  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];

Explanation

This code works by multiplying the integer v by a magic constant and then performing a bit shift on the result. The MultiplyDeBruijnBitPosition array maps the result of the multiplication to the desired position of the LSB.

Benefits and References

This method is significantly faster than the trivial implementation, especially for large integers. For more insights and detailed explanations of this technique, refer to:

• "Using de Bruijn Sequences to Index a 1 in a Computer Word"
• "Board Representation > Bitboards > BitScan"

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