Mike, Here's my take on this:
bitcomb=: 13 :'(x=+/"1 #:i.2^y)#"2#:i.2^y'
(3 combbitub 5);3 bitcomb 5
┌─────────┬─────────┐
│1 1 1 0 0│0 0 1 1 1│
│1 1 0 1 0│0 1 0 1 1│
│1 1 0 0 1│0 1 1 0 1│
│1 0 1 1 0│0 1 1 1 0│
│1 0 1 0 1│1 0 0 1 1│
│1 0 0 1 1│1 0 1 0 1│
│0 1 1 1 0│1 0 1 1 0│
│0 1 1 0 1│1 1 0 0 1│
│0 1 0 1 1│1 1 0 1 0│
│0 0 1 1 1│1 1 1 0 0│
└─────────┴─────────┘
Mine are in numeric order for binary counting.
Linda
-----Original Message-----
From: Programming [mailto:[email protected]] On Behalf
Of 'Mike Day' via Programming
Sent: Friday, November 10, 2017 11:28 AM
To: [email protected]
Subject: Re: [Jprogramming] K-sets - bitmap representation of sets. WAS:
Partitions
Nice. Note that d doesn't need to be global.
The 63 bit (or 31 for older hardware) limit shouldn't be a problem in practice?!
Wondering if it was possible to avoid boxing, I've found this version - not
faster, though more parsimonious in space, so probably not for serious use:
combbitub =: 4 : 0
assert y<:<:##:_1 (32 b.) 1
lshift =.33 b.
or =.23 b.
k =. (y->:ix =. i.>:d=.y-x)lshift 1
z =. ,0
l =. 1#~ #k NB. "box-sizes" as successively 1s, i.#k, triangular nums etc.
for. i.x do.
nz =. _1 lshift z
z =. nz or {.k
for_j. }. i.#k do. NB. tack on the smaller "boxes"
z =. z, (j{k) or (-j{l) {. nz
end.
l =. +/\. l NB. bump up the box sizes
end.
#: z
)
3 (combbit -: combbitub) 5
1
Cheers,
Mike
10/11/2017 11:46, Erling Hellenäs wrote:
> Hi all!
>
> Bitmap version of comb. Unfortunately handles sets of max 63 items.
>
> I tried to make a general version, but hit the problem with #: .
>
> ts'5 combbit 10'
> 3.37831e_5 20864
> ts'5 combbool 10'
> 3.89148e_5 22400
> ts'5 combREBoss 10'
> 5.51649e_5 44416
> ts'5 comb 10'
> 3.76319e_5 50944
>
> ts'13 combbit 26'
> 0.44835 8.03039e8
> ts'13 combbool 26'
> 0.880373 1.4314e9
> ts'13 combREBoss 26'
> 2.39319 4.22297e9
> ts'13 comb 26'
> 2.59969 4.41693e9
>
> ts'60 combbit 63'
> 0.00416474 5.26221e6
> ts'60 combbool 63'
> 0.0534253 1.73281e7
> ts'60 combREBoss 63'
> 0.0344776 6.81943e7
> ts'60 comb 63'
> 0.310994 1.38554e8
>
> combbit=: 4 : 0
> assert y<:<:##:_1 (32 b.) 1
> lshift=.33 b.
> or=.23 b.
> k=.<"0 (y->:i.>:d=:y-x)lshift 1
> z=. (d$<i.0),<0
> for. i.x do. z=. k (or)&.> ,&.>/\. (_1&lshift)&.> z end.
> #: ;z
> )
>
> Cheers,
>
> Erling Hellenäs
>
>
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