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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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