NB. all calls to memoized(?) verbs are first calls after loading. Subsequent
calls are even more efficient.
===================
0. recursion with M. can be faster than a primitive.
-------------------
facM=:1:`(] * $:@<:)@.* M.
NB. \system\extras\help\dictionary\d212.htm
5 ts'! 2000x'
0.013499039 179136
ts'facM 2000x'
0.00063421529 8479616
(! -: facM) 2000x
1
'0.2,5.1,6.3' (8!:2) (,~*/)0.013499039 179136 % 0.00063421529 8479616
0.45 21.3 0.021
NB. relative performance, rel. execution time and rel. ex. space.
===================
1. you could have your own special code.
-------------------
antibsM=: 3 : 0 M. NB. equivalent to x #.^:_1 i.x^y or (y#x) #: i.x^y
2 antibsM y
:
ix=.i.x
if. y=1 do. ,.ix
else. ,/ ix,"1"0 _ x antibsM <:y
end.
)
5 ts'3 #.^:_1 y'[y=.i.3^10
0.02847991 4201536
ts'3 antibsM 10'
2.1428313e_5 9812096
(3 #.^:_1 i.3^10) -: 3 antibsM 10
1
'0.0,5.0,5.2' (8!:2) (,~*/)0.02847991 4201536 % 2.1428313e_5 9812096
569 1329 0.43
5 ts'#: y'[y=.i.2^20
0.047805544 33555008
ts'antibsM 20'
2.3639982e_5 1.1639277e8
(#:i.2^20) -: antibsM 20
1
'0,5.0,5.2'(8!:2) (,~*/)0.047805544 33555008 % 2.3639982e_5 1.1639277e8
583 2022 0.29
NB. relative performance, rel. execution time and rel. ex. space.
===================
2. (a lot of) performance records should be reconsidered.
-------------------
NB. \system\extras\help\dictionary\dmcapdot.htm
combM=: 4 : 0 M. NB. All size x combinations of i.y
if. (x>:y)+.0=x do. i.(x<:y),x else. (0,.x combM&.<: y),1+x combM y-1 end.
)
NB. http://www.jsoftware.com/jwiki/Essays/Combinations
comb2=: 4 : 0 NB. All size x combinations of y
d=. x-~#y
k=. |.(>:d),\y
z=. (d$<i.0 0),<i.1 0
for_j. k do. z=. j ,.&.> ,&.>/\. z end.
; z
)
5 ts'10 (comb2 i.) 20'
0.047006717 20793088
ts'10 combM 20'
3.3272275e_5 44555136
10 (combM -: (comb2 i.)) 20
1
'0,5.0,5.2'(8!:2) (,~*/)0.053603614 20793088 % 3.3272275e_5 44555136
752 1611 0.47
NB. relative performance, rel. execution time and rel. ex. space.
R.E. Boss
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