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u//. Improved

initial writing: 2007-07-31 last updated: 2007-08-01

The dyad x u//. y has been improved where u and y are one of the following combinations:

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

There is a generalization of a similar improvement in J 5.03 which was restricted to vector right arguments. The following benchmarks demonstrate the improvement:

x1=: 2e5 ?@$ 1e1
x2=: 2e5 ?@$ 1e2
x3=: 2e5 ?@$ 1e3
x4=: 2e5 ?@$ 1e4

b=: 2e5 5 ?@$ 2
i=: 2e5 5 ?@$ 1000
d=: 0.1 * i

ts=: 6!:2 , 7!:2@]  NB. time and space
ts 'Expression'

Expression		J 6.02				J 6.01				Ratio
x1 ~://. b		0.00277323		1536		0.02164587		4457984		7.81		2902.33
x2 ~://. b		0.00276233		3520		0.02522252		4458880		9.13		1266.73
x3 ~://. b		0.00285285		19648		0.02643234		4466048		9.27		227.30
x4 ~://. b		0.00375916		148672		0.03122265		4523392		8.31		30.43
x1 + //. i		0.00431878		2560		0.02990644		7603840		6.92		2970.25
x2 + //. i		0.00435932		11712		0.03602225		7605632		8.26		649.39
x3 + //. i		0.00529091		167104		0.03750901		7636352		7.09		45.70
x4 + //. i		0.01718684		1328320		0.04396052		7865728		2.56		5.92
x1 + //. d		0.00455240		2304		0.03985561		11798400		8.75		5120.83
x2 + //. d		0.00455401		9664		0.04259895		11801984		9.35		1221.23
x3 + //. d		0.00481319		134336		0.04401794		11863424		9.15		88.31
x4 + //. d		0.01125234		1066176		0.05060965		12322176		4.50		11.56

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