The document discusses using a logical matrix to track which conferences different people will attend. It begins with a true/false matrix but then optimizes it by representing the values as bits (1s and 0s) to reduce memory usage and allow faster lookups. Various methods for counting the number of 1s in a bit representation are tested, with the cached approach proving fastest.

1. Bits of Ruby

3. Ἲtip to RGSoC­friendly confs
♥ eurucamp ♥ JRubyConf ♥ Deccan RubyConf ♥
♥ OTSConf ♥ Madison+ Ruby ♥ BaRuCo ♥
♥ Reject.JS ♥ Strange Loop ♥ RailsClub ♥
♥ EuRuKo ♥ Øredev ♥ ROSSConf ♥
♥ GOTO Conference ♥ dotJS ♥

4. sooo… who goes where?
Tate Isom Genevieve Ola Arielle
eurucamp ✓ ✓ ✓ ✓
JRubyConf ✓
ROSSConf ✓ ✓
BaRuCo ✓ ✓ ✓
EuRuKo ✓ ✓ ✓
…but how do we track who goes where?
name­keyed hash? conf­keyed hash?
how about a logical matrix?

5. oh of course! (what’s that…?)
a rectangular table of Boolean values
true / false relationship representation
c o n f s = % w ( e u r u c a m p J R u b y C o n f R O S S C o n f B a R u C o E u R u K o )
n a m e s = % w ( T a t e I s o m G e n e v i e v e O l a A r i e l l e )
m a t r i x = [
[ t r u e , t r u e , t r u e , f a l s e , t r u e ] ,
[ t r u e , f a l s e , f a l s e , f a l s e , f a l s e ] ,
[ f a l s e , f a l s e , f a l s e , t r u e , t r u e ] ,
[ f a l s e , t r u e , t r u e , f a l s e , t r u e ] ,
[ t r u e , f a l s e , t r u e , f a l s e , t r u e ] ,
]
m a t r i x [ c o n f s . i n d e x ( ' e u r u c a m p ' ) ] [ n a m e s . i n d e x ( ' T a t e ' ) ] # = > t r u e
m a t r i x [ c o n f s . i n d e x ( ' R O S S C o n f ' ) ] [ n a m e s . i n d e x ( ' G e n e v i e v e ' ) ] # = > f a l s e

6. but that’s not very efficient
every conference adds a row
every participant adds a column
confs.size×(names.sizeBools+1Array)+1Array
how about using zeroes and ones instead?

7. logical matrix
m a t r i x = [
[ t r u e , t r u e , t r u e , f a l s e , t r u e ] ,
[ t r u e , f a l s e , f a l s e , f a l s e , f a l s e ] ,
[ f a l s e , f a l s e , f a l s e , t r u e , t r u e ] ,
[ f a l s e , t r u e , t r u e , f a l s e , t r u e ] ,
[ t r u e , f a l s e , t r u e , f a l s e , t r u e ] ,
]

8. bit matrix
m a t r i x = [
[ 1 , 1 , 1 , 0 , 1 ] ,
[ 1 , 0 , 0 , 0 , 0 ] ,
[ 0 , 0 , 0 , 1 , 1 ] ,
[ 0 , 1 , 1 , 0 , 1 ] ,
[ 1 , 0 , 1 , 0 , 1 ] ,
]

9. bit matrix
m a t r i x = [
0 b 1 1 1 0 1 ,
0 b 1 0 0 0 0 ,
0 b 0 0 0 1 1 ,
0 b 0 1 1 0 1 ,
0 b 1 0 1 0 1 ,
]
m a t r i x = [ 2 9 , 1 6 , 3 , 1 3 , 2 1 ]

10. how much better?
names.sizeFixnums+1Array → 1Fixnum
Fixnums go up to 2E62-1
…that’s 4611686018427387903
…that’s 4_611_686_018_427_387_903
I’m better at estimating things
than probably 40 or 50 billion people.
— Randy Tayler
…that’s over four quintillion

11. but how do we query it?
c o n f s = % w ( e u r u c a m p J R u b y C o n f R O S S C o n f B a R u C o E u R u K o )
n a m e s = % w ( T a t e I s o m G e n e v i e v e O l a A r i e l l e )
m a t r i x = [
[ t r u e , t r u e , t r u e , f a l s e , t r u e ] ,
[ t r u e , f a l s e , f a l s e , f a l s e , f a l s e ] ,
[ f a l s e , f a l s e , f a l s e , t r u e , t r u e ] ,
[ f a l s e , t r u e , t r u e , f a l s e , t r u e ] ,
[ t r u e , f a l s e , t r u e , f a l s e , t r u e ] ,
]
m a t r i x [ c o n f s . i n d e x ( ' e u r u c a m p ' ) ] [ n a m e s . i n d e x ( ' T a t e ' ) ] # = > t r u e
m a t r i x [ c o n f s . i n d e x ( ' R O S S C o n f ' ) ] [ n a m e s . i n d e x ( ' G e n e v i e v e ' ) ] # = > f a l s e

12. Integer#[]
2 9 = = 0 b 1 1 1 0 1 # = > t r u e
2 9 [ 0 ] # = > 1
2 9 [ 1 ] # = > 0
2 9 [ 2 ] # = > 1
return the n­th least significant bit
c o n f s = % w ( e u r u c a m p J R u b y C o n f R O S S C o n f B a R u C o E u R u K o )
n a m e s = % w ( T a t e I s o m G e n e v i e v e O l a A r i e l l e ) . r e v e r s e
m a t r i x = [ 0 b 1 1 1 0 1 , 0 b 1 0 0 0 0 , 0 b 0 0 0 1 1 , 0 b 0 1 1 0 1 , 0 b 1 0 1 0 1 ]
m a t r i x [ c o n f s . i n d e x ( ' e u r u c a m p ' ) ] [ n a m e s . i n d e x ( ' T a t e ' ) ] # = > 1
m a t r i x [ c o n f s . i n d e x ( ' R O S S C o n f ' ) ] [ n a m e s . i n d e x ( ' G e n e v i e v e ' ) ] # = > 0

13. so… how many go to each conf?
e u r u c a m p = m a t r i x [ c o n f s . i n d e x ( ' e u r u c a m p ' ) ] # = > [ t r u e , t r u e , t r u e , f a l s e , t r u e ]
e u r u c a m p . c o u n t ( t r u e ) # = > 4
e u r u c a m p = m a t r i x [ c o n f s . i n d e x ( ' e u r u c a m p ' ) ] # = > 0 b 1 1 1 0 1
e u r u c a m p . t o _ s ( 2 ) . c o u n t ( ' 1 ' ) # = > 4
number of ones in a binary representation
‘population count’
but to_s(2).count('1') is not very efficient

14. let’s freedom­patch Integer
c l a s s I n t e g e r
d e f p o p c o u n t _ t o _ s
t o _ s ( 2 ) . c o u n t ( ' 1 ' )
e n d
d e f p o p c o u n t _ c o n t _ s h i f t
c o u n t = 0
n u m b e r = s e l f
u n t i l n u m b e r = = 0
c o u n t + = n u m b e r & 1
n u m b e r > > = 1
e n d
c o u n t
e n d
e n d

15. c l a s s I n t e g e r
d e f p o p c o u n t _ b i t _ e l i m
c o u n t = 0
n u m b e r = s e l f
w h i l e n u m b e r ! = 0
n u m b e r & = n u m b e r - 1
c o u n t + = 1
e n d
c o u n t
e n d
d e f p o p c o u n t _ p r o g _ s h i f t
n u m b e r = s e l f
n u m b e r - = ( n u m b e r > > 1 ) & 0 x 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
n u m b e r = ( n u m b e r & 0 x 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ) + ( ( n u m b e r > > 2 ) & 0 x 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 )
n u m b e r = ( n u m b e r + ( n u m b e r > > 4 ) ) & 0 x 0 f 0 f 0 f 0 f 0 f 0 f 0 f 0 f
n u m b e r = ( n u m b e r + ( n u m b e r > > 8 ) ) & 0 x 0 0 f f 0 0 f f 0 0 f f 0 0 f f
n u m b e r = ( n u m b e r + ( n u m b e r > > 1 6 ) ) & 0 x 0 0 0 0 f f f f 0 0 0 0 f f f f
n u m b e r + = n u m b e r > > 3 2
( n u m b e r + ( n u m b e r > > 6 4 ) ) & 0 x f f
e n d
e n d

16. r e q u i r e ' i n l i n e '
c l a s s I n t e g e r
i n l i n e d o | b u i l d e r |
b u i l d e r . c '
i n t p o p c o u n t _ b i t _ e l i m _ c ( ) {
l o n g n u m b e r = N U M 2 L O N G ( s e l f ) ;
i n t c o u n t ;
f o r ( c o u n t = 0 ; n u m b e r ; c o u n t + + ) n u m b e r & = n u m b e r - 1 ;
r e t u r n c o u n t ;
}
'
e n d
i n l i n e d o | b u i l d e r |
b u i l d e r . c '
i n t p o p c o u n t _ b u i l t i n ( ) {
r e t u r n _ _ b u i l t i n _ p o p c o u n t l ( N U M 2 L O N G ( s e l f ) ) ;
}
'
e n d
e n d

17. c l a s s I n t e g e r
P O P C O U N T _ C A C H E = ( 0 x 0 0 0 0 . . 0 x f f f f ) . m a p { | n u m b e r | n u m b e r . t o _ s ( 2 ) . c o u n t ( ' 1 ' ) }
d e f p o p c o u n t _ c a c h e d
P O P C O U N T _ C A C H E [ s e l f & 0 x f f f f ] +
P O P C O U N T _ C A C H E [ s e l f > > 1 6 & 0 x f f f f ] +
P O P C O U N T _ C A C H E [ s e l f > > 3 2 & 0 x f f f f ] +
P O P C O U N T _ C A C H E [ s e l f > > 4 8 ]
e n d
e n d

18. r e q u i r e ' b e n c h m a r k / i p s '
m e t h o d s = I n t e g e r . i n s t a n c e _ m e t h o d s . g r e p ( / ^ p o p c o u n t _ / )
n u m b e r s = A r r a y . n e w ( 1 _ 0 0 0 ) { r a n d ( 0 . . . ( 2 * * 6 2 - 1 ) ) }
f a i l ' o o p s ' u n l e s s m e t h o d s . m a p { | m e t h | n u m b e r s . m a p ( & m e t h ) } . u n i q . s i z e = = 1
B e n c h m a r k . i p s d o | b e n c h |
m e t h o d s . e a c h d o | m e t h |
b e n c h . r e p o r t ( m e t h [ 9 . . - 1 ] ) { n u m b e r s . m a p ( & m e t h ) }
e n d
b e n c h . c o m p a r e !
e n d

19. W a r m i n g u p - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
b i t _ e l i m 5 3 . 0 0 0 i / 1 0 0 m s
c a c h e d 2 7 6 . 0 0 0 i / 1 0 0 m s
c o n t _ s h i f t 1 7 . 0 0 0 i / 1 0 0 m s
p r o g _ s h i f t 1 3 1 . 0 0 0 i / 1 0 0 m s
t o _ s 6 9 . 0 0 0 i / 1 0 0 m s
b i t _ e l i m _ c 1 . 0 9 8 k i / 1 0 0 m s
b u i l t i n 1 . 4 5 3 k i / 1 0 0 m s
C a l c u l a t i n g - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
b i t _ e l i m 5 4 1 . 1 2 7 ( ± 0 . 4 % ) i / s - 2 . 7 5 6 k
c a c h e d 2 . 8 0 6 k ( ± 0 . 3 % ) i / s - 1 4 . 0 7 6 k
c o n t _ s h i f t 1 8 9 . 9 2 1 ( ± 1 . 1 % ) i / s - 9 5 2 . 0 0 0
p r o g _ s h i f t 1 . 5 9 6 k ( ± 0 . 3 % ) i / s - 7 . 9 9 1 k
t o _ s 6 9 5 . 5 2 8 ( ± 0 . 4 % ) i / s - 3 . 5 1 9 k
b i t _ e l i m _ c 1 1 . 1 7 2 k ( ± 1 . 4 % ) i / s - 5 5 . 9 9 8 k
b u i l t i n 1 4 . 6 6 1 k ( ± 1 . 1 % ) i / s - 7 4 . 1 0 3 k
C o m p a r i s o n :
b u i l t i n : 1 4 6 6 1 . 1 i / s
b i t _ e l i m _ c : 1 1 1 7 1 . 8 i / s - 1 . 3 1 x s l o w e r
c a c h e d : 2 8 0 5 . 6 i / s - 5 . 2 3 x s l o w e r
p r o g _ s h i f t : 1 5 9 5 . 7 i / s - 9 . 1 9 x s l o w e r
t o _ s : 6 9 5 . 5 i / s - 2 1 . 0 8 x s l o w e r
b i t _ e l i m : 5 4 1 . 1 i / s - 2 7 . 0 9 x s l o w e r
c o n t _ s h i f t : 1 8 9 . 9 i / s - 7 7 . 2 0 x s l o w e r

20. Tate Isom Genevieve Ola Arielle
eurucamp ✓ ✓ ✓ ✓
JRubyConf ✓
ROSSConf ✓ ✓
BaRuCo ✓ ✓ ✓
EuRuKo ✓ ✓ ✓

22. Ἲtip to RGSoC­friendly confs
♥ eurucamp ♥ JRubyConf ♥ Deccan RubyConf ♥
♥ OTSConf ♥ Madison+ Ruby ♥ BaRuCo ♥
♥ Reject.JS ♥ Strange Loop ♥ RailsClub ♥
♥ EuRuKo ♥ Øredev ♥ ROSSConf ♥
♥ GOTO Conference ♥ dotJS ♥

23. thanks!
@chastell
talks.chastell.net