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Gerd Isenberg

Joined: 08 Mar 2006
Posts: 1785
Location: Hattingen, Germany

Post subject: Re: Resource for bit twiddlers    Posted: Mon May 28, 2007 12:40 pm

 jwes wrote: I just ran accross this. It is a preprint of part of Knuth's Art of Computer Programming, Vol 4, and covers bit twiddling tricks and techniques. http://www-cs-faculty.stanford.edu/~knuth/fasc1a.ps.gz

This is really a great ressource - thanks for providing the link.

"tweaking several bytes at once" (page 19), nicely explains some SWAR (SIMD within a regsiter) tricks suggested by H.G. Dietz.

 Code: SWAR add z = x + y      z = ((x &~H) + (y &~H)) ^ ((x ^ y) & H) SWAR sub z = x - y     z = ((x | H) - (y &~H)) ^ ((x ^~y) & H) SWAR average z = (x+y)/2 based on x + y = (x^y) + 2*(x&y)     z = (x & y) + (((x ^ y) & ~L) >> 1)

For bytewise math, H = 0x8080808080808080 and L = 0x0101010101010101. But one can use arbitrary masks for other sizes such as 6*10 or 5*12 bit as well - or even 64-bit structures with mixed "word"-sizes.

Performing bytewise or rankwise sub using the o ^(o-2r)-trick saves some instructions compared to one Kogge-Stone attack getter, even with general purpose registers:
 Code: u64 eastAttacks(u64 rooks, u64 empty) {     empty  = empty &  0xfefefefefefefefe;     rooks |= empty & (rooks << 1);     empty  = empty & (empty << 1);     rooks |= empty & (rooks << 2);     empty  = empty & (empty << 2);     rooks |= empty & (rooks << 4);     return (rooks << 1) & 0xfefefefefefefefe; }

 Code: u64 eastAttacks(u64 rooks, u64 empty) {     const u64 H     = 0x8080808080808080;     u64 occupied    = rooks | ~empty;     u64 occNoRook   = rooks ^ occupied;     u64 difference  = ((occNoRook | H) - (rooks & ~H))                     ^  (~occupied & H);     return occupied ^ difference; }

Gerd
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
Subject Author Date/Time
J. Wesley Cleveland Fri May 04, 2007 1:55 am
Re: Resource for bit twiddlers Gerd Isenberg Mon May 28, 2007 12:40 pm
Gerd Isenberg Mon May 28, 2007 3:16 pm
Gerd Isenberg Mon May 28, 2007 4:35 pm
Gerd Isenberg Wed May 30, 2007 5:55 pm
Pradu Kannan Wed May 30, 2007 10:51 pm
Gerd Isenberg Thu May 31, 2007 6:17 am
Pradu Kannan Fri Jun 01, 2007 12:16 am
Gerd Isenberg Fri Jun 01, 2007 8:19 am
Gerd Isenberg Mon Jun 04, 2007 2:58 pm

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