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e.i.1: Improved

initial writing: 2004-08-18 last updated: 2005-04-21

The dyad e.i.1: (and others, see below) are now supported by special code. These are similar to the dyads previously described in J5.02 and J5.03. A complete table of such dyads are as follows:

f i. 0:		i.&0@:f		first place where not x f y
f i. 1:		i.&1@:f		first place where x f y
f i: 0:		i:&0@:f		last place where not x f y
f i: 1:		i:&1@:f		last place where x f y
[: + / f		+ /@:f		number of places where x f y
[: +./ f		+./@:f		x f y anywhere?
[: *./ f		*./@:f		x f y everywhere?
[: I.  f		I. @:f		indices where x f y

Notes:
	•		f is one of the verbs = ~: < <: > >: E. e.
	•		Special code is available only for Boolean, integer, floating point, literal, and symbol arguments
	•		Special code is used only for atoms and lists if f is not e.
	•		If f is E. , special code only for   E.i.1:  +/@:E.  +./@:E.  I.@:E.

Moreover, if f is e. and the right argument is fixed, that is, (e.i.0:)&m , then that also is supported by special code. (See details here.)

The following benchmarks demonstrate the improvement:

x=: 1e6 ?.@$ 1e6
y=: 1e3 ?.@$ 1e4

a=: 'abcdefghijklmnopqrstuvwxyz'
c=: a {~ 1e5 4 ?.@$ #a
d=: a {~ 1e4 4 ?.@$ #a

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

Expression		J 5.04				J 5.03				Ratio
x(e.i.1:)y		0.0000119		17664		0.0309512		5244160		2600.01		296.88
x(e.i:1:)y		0.0000123		17664		0.0308734		5244160		2509.46		296.88
x +/@:e. y		0.0027426		17792		0.0248151		2098496		9.05		117.95
x I.@e. y		0.0031021		4211648		0.0265907		2098112		8.57		0.50
c(e.i.1:)d		0.0002968		132352		0.0045880		656640		15.46		4.96
c(e.i:1:)d		0.0002963		132352		0.0046068		656640		15.55		4.96
c +/@:e. d		0.0032609		132480		0.0039788		263488		1.22		1.99
c I.@e. d		0.0033605		656320		0.0041747		263104		1.24		0.40

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