Certain verbs in the “index of” family with a fixed noun argument m are now supported by special code. That is,

   m&i.          m&(i.!.0)
   m&i:          m&(i:!.0)
   -.&m          -.!.0&m
   e.&m          e.!.0&m
   (e.i.0:)&m    + /@e.&m
   (e.i.1:)&m    +./@e.&m
   (e.i:0:)&m    *./@e.&m
   (e.i:1:)&m     I.@e.&m

are now supported by special code, so that for most m and y the phrase m&i. y takes time proportional to the size of y . (“Most” means amenable to hashing or some other fast pre-processing technique.) There is no change in performance with just one application; there can be a substantial improvement in performance with repeated applications. The following benchmarks demonstrate the improvement:

x9=: 1e6 ?@$ 2e9
y9=: 1e5 ?@$ 2e9
x6=: 1e6 ?@$ 2e6
y6=: 1e5 ?@$ 2e6
c =: a {~ 1e6 4 ?@$ #a=: ' 0123456789',(97+i.26){a. 
d =: a {~ 1e5 4 ?@$ #a

f9=: x9&i.
f6=: x6&i.
fc=: c&i.
g9=: +/@e.&x9
g6=: +/@e.&x6

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