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tried some optimizations of task 1 (rare numbers). All times are for n==8 or 9
I used Devel::NYTProf to profile each version, then made small optimizations,
then reprofiled. See "run.sh" for how to run a particular version through
the profiler, generate the report, and copy it into a web-accessible directory
for viewing:
ch-1.pl: the original, not optimized
time(8): 0:34.31
time(9): 5:56:10
ch-1a.pl: observation from rare numbers webpage ("Properties of.."
section): rare numbers start with even top digit
time(8): 0:24.46
time(9): 4:10.61
ch-1b.pl: only consider rare numbers starting with even top digit..
time(8): 0:15.35
time(9): 2:44.34
ch-1c.pl: lots of optimizations, especially 3 separate rare block
functions: rareblock(), rareblock05() and rareblock2378().
time(8): 0:06.35
time(9): 1:06.64
ch-1d.pl: lots more optimizations, especially: rather than generate x and
test x%10 == d, generate y (1/10th the range) and make
x = 10y + d: 1/10th the work, but same x's as before
time(8): 0:03.92
time(9): 0:40.21
ch-1e.pl: inlined israre() into the slowest rareblock2378() func
time(8): 0:03.39
time(9): 0:34.49
ch-1f.pl: inlined israre() into the next slowest rareblock05() func
time(8): 0:03.12
time(9): 0:31.47
ch-1g.pl: inlined israre() into the last rareblock() func
time(8): 0:02.94
time(9): 0:28.79
ch-1h.pl: inlined perfectsquare() everywhere
time(8): 0:02.15
time(9): 0:21.20
ch-1i.pl: reintroduced israre() but with two inlined calls to perfectsquare()
sweet spot: clear, shows problem structure nicely, plus pretty fast
time(8): 0:03.23
time(9): 0:32.34
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