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Matt Taylor was involved in forum discussions on low level optimization and x86 assembly language issues. Beside other things Matt was busy to optimize a minimal perfect hashing scheme for bitscan purposes.

BitScan

Based on ideas of Walter Faxon and De Bruijn Multiplication, Matt came up with a genius folding trick as a quintessence ^[1]:

const int lsb_64_table[64] =
{
   63, 30,  3, 32, 59, 14, 11, 33,
   60, 24, 50,  9, 55, 19, 21, 34,
   61, 29,  2, 53, 51, 23, 41, 18,
   56, 28,  1, 43, 46, 27,  0, 35,
   62, 31, 58,  4,  5, 49, 54,  6,
   15, 52, 12, 40,  7, 42, 45, 16,
   25, 57, 48, 13, 10, 39,  8, 44,
   20, 47, 38, 22, 17, 37, 36, 26
};
 
/**
 * bitScanForward
 * @author Matt Taylor (2003)
 * @param bb bitboard to scan
 * @precondition bb != 0
 * @return index (0..63) of least significant one bit
 */
int bitScanForward(U64 bb) {
   unsigned int folded;
   assert (bb != 0);
   bb ^= bb - 1;
   folded = (int) bb ^ (bb >> 32);
   return lsb_64_table[folded * 0x78291ACF >> 26];
}

Forum Posts

• Bitscan Conclusions by Matt Taylor, CCC, January 05, 2003
• Cleverness, Please! by Matt Taylor, CCC, January 22, 2003
• Bitscan by Matt Taylor, CCC, February 11, 2003
• Bit magic by Matt Taylor, comp.lang.asm.x86, June 26, 2003
• Re: Static memory allocation by Matt Taylor, comp.lang.asm.x86, July 03, 2004

References

1. ^ Bit magic by Matt Taylor, comp.lang.asm.x86, June 26, 2003

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