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## bug#22689: 25.1.50; implement logcount

**From**: |
Mark Oteiza |

**Subject**: |
bug#22689: 25.1.50; implement logcount |

**Date**: |
Mon, 15 Feb 2016 18:18:56 -0500 |

Wishlist:
Logcount, AKA popcount, Hamming weight, sideways sum. Basically,
counting the number of 1s in a number's binary representation. The
concept is similar to that in `bool-vector-count-population', except the
argument would be a number, presumably a non-negative integer.
There are a number of ways to go about it, and beyond that I'm not sure
how to write it into data.c:
- Some compilers have a __builtin_popcount (gcc since 2004 and llvm
since 2005)
- gmp has a popcount function
- lots of algorithms implementing it
Many are given here:
https://en.wikipedia.org/wiki/Hamming_weight
another resource:
http://rosettacode.org/wiki/Population_count
Guile's implementation uses table lookup:
http://git.savannah.gnu.org/cgit/guile.git/tree/libguile/numbers.c#n5234
When I needed it, I just naïvely ported an algorithm to elisp (in
particular ignoring the case of negative numbers):
(let ((m1 #x555555555555555)
(m2 #x333333333333333)
(m4 #x0f0f0f0f0f0f0f0f)
(h01 #x0101010101010101))
(setq x (- x (logand (lsh x -1) m1)))
(setq x (+ (logand x m2) (logand (lsh x -2) m2)))
(setq x (logand (+ x (lsh x -4)) m4))
(lsh (* x h01) -56))
The table lookup isn't so different
(defvar logtab [0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4])
(let ((count 0))
(while (not (zerop x))
(setq count (+ count (aref logtab (logand 15 x))))
(setq x (lsh x -4)))
count)
I couldn't find any implementation of this in calc either, but such a
function/operation would fit in calc-bin.

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**bug#22689: 25.1.50; implement logcount**,
*Mark Oteiza* **<=**