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u/. Improved

initial writing: 2003-09-03 last updated: 2007-07-31

The key adverb u/. has been made more efficient for the following cases:

• The dyad x #/. y
• The cases x </.i.#x and (</. i.@#) x (group the indices of identical items of x)
• The dyad x f//. y where y is a vector, and f and y are one of the following combinations:

  	verb f		y type
  	= <. >. + +. * *. ~:		Boolean
  	<. >. +		integer, floating-point
  	n b. for n= 17 22 23 25		integer

  (In J 6.02 the restriction that y be a vector is removed.)

The following benchmarks demonstrate the improvements in time and space.

x1=: ?1e6$10
x2=: ?1e6$100
x3=: ?1e6$1000
x4=: ?1e6$10000

c=: (?1e6$10000){a.{~?1e4 6$#a.
b=: ?1e6$2
i=: ?1e6$1000
d=: 0.01*?1e6$1e6

ts=: 6!:2 , 7!:2@]
ts 'Expression'

Expression		J 5.03			J 5.02			Ratio
x1 #/. i		0.054980	1088		0.142855	1.258374e7		2.60	11565.94
x2 #/. i		0.061149	1856		0.148341	1.258374e7		2.43	6780.03
x3 #/. i		0.057310	9024		0.151128	1.258374e7		2.64	1394.48
x4 #/. i		0.058312	131904		0.163465	1.258374e7		2.80	95.40
c  #/. i		0.466662	12583808		0.523424	1.258381e7		1.12	1.00
x1 </.i.#x1		0.146615	9.438592e6		0.541370	3.565293e7		3.69	3.78
x2 </.i.#x2		0.161843	1.075046e7		0.571060	3.696403e7		3.53	3.44
x3 </.i.#x3		0.173669	9.655296e6		0.603863	3.588218e7		3.48	3.72
x4 </.i.#x4		0.246410	9.731584e6		0.709207	3.582688e7		2.88	3.68
c  </.i.#c		0.738528	1.799411e7		1.094735	3.580832e7		1.48	1.99
(</. i.@#) x1		0.110250	5.244480e6		0.543262	3.565312e7		4.93	6.80
(</. i.@#) x2		0.117883	6.556352e6		0.571406	3.696422e7		4.85	5.64
(</. i.@#) x3		0.130114	5.461184e6		0.605503	3.588237e7		4.65	6.57
(</. i.@#) x4		0.203980	5.537472e6		0.716786	3.582707e7		3.51	6.47
(</. i.@#) c		0.651008	1.380013e7		1.101898	3.580864e7		1.69	2.59
x1 +//. i		0.089229	1472		0.489221	3.145965e7		5.48	21372.04
x2 +//. i		0.091571	2240		0.545150	3.277690e7		5.95	14632.54
x3 +//. i		0.089238	9408		0.580384	3.169478e7		6.50	3368.92
x4 +//. i		0.093303	132288		0.696549	3.237165e7		7.47	244.71
x1 +//. b		0.061756	1472		0.422279	2.438176e7		6.84	16563.70
x2 +//. b		0.061645	2240		0.494004	2.471597e7		8.01	11033.91
x3 +//. b		0.061742	9408		0.510600	2.489747e7		8.27	2646.41
x4 +//. b		0.065804	132288		0.639285	2.635066e7		9.71	199.19
x1 +.//. b		0.057070	1344		0.422874	2.438170e7		7.41	18141.14
x2 +.//. b		0.057171	1728		0.493326	2.471571e7		8.63	14303.07
x3 +.//. b		0.057439	5312		0.516077	2.489747e7		8.98	4687.02
x4 +.//. b		0.061470	33984		0.650361	2.630214e7		10.58	773.96
x1 23 b.//. i		0.088951	1856		0.514752	3.145997e7		5.79	16950.41
x2 23 b.//. i		0.088652	2816		0.541060	3.277722e7		6.10	11639.64
x3 23 b.//. i		0.091216	11776		0.580654	3.173197e7		6.37	2694.63
x4 23 b.//. i		0.092286	148992		0.696234	3.237453e7		7.54	217.29
x4 +//. d		0.099751	279744		0.740266	4.168851e7		7.42	149.02
c  +//. d		0.536441	12584192		1.096851	4.167213e7		2.04	3.31

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