sed and gawk use fastmap in regex, but grep does not.  By using fastmap,
I expect that grep speeds up for patterns as regex is used.

before:
$ time -p env LC_ALL=ja_JP.eucjp src/grep '\([a-b]\)\1' k
real 7.83
user 7.62
sys 0.07

after:
$ time -p env LC_ALL=ja_JP.eucjp src/grep '\([a-b]\)\1' k
real 0.46
user 0.38
sys 0.07

However, if grep uses fastmap, fails in case-fold-titlecase test.  It
means that grep's behavior differ from sed and gawk, as they use fastmap,
although it seems to be a bug in regex.