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### Remarks
Just run it with no argument:
$ ruby entry.rb
I confirmed the following implementation/platform:
- ruby 2.2.3p173 (2015-08-18 revision 51636) [x64-mingw32]
### Description
The program is a [Piphilology](https://en.wikipedia.org/wiki/Piphilology#Examples_in_English)
suitable for Rubyists to memorize the digits of [Pi](https://en.wikipedia.org/wiki/Pi).
In English, the poems for memorizing Pi start with a word consisting of 3-letters,
1-letter, 4-letters, 1-letter, 5-letters, ... and so on. 10-letter words are used for the
digit `0`. In Ruby, the lengths of the lexical tokens tell you the number.
$ ruby -r ripper -e \
'puts Ripper.tokenize(STDIN).grep(/\S/).map{|t|t.size%10}.join' < entry.rb
31415926535897932384626433832795028841971693993751058209749445923078164062862...
The program also tells you the first 10000 digits of Pi, by running.
$ ruby entry.rb
31415926535897932384626433832795028841971693993751058209749445923078164062862...
### Internals
Random notes on what you might think interesting:
- The 10000 digits output of Pi is seriously computed with no cheets. It is calculated
by the formula `Pi/2 = 1 + 1/3 + 1/3*2/5 + 1/3*2/5*3/7 + 1/3*2/5*3/7*4/9 + ...`.
- Lexical tokens are not just space-separated units. For instance, `a*b + cdef` does
not represent [3,1,4]; rather it's [1,1,1,1,4]. The token length
burden imposes hard constraints on what we can write.
- That said, Pi is [believed](https://en.wikipedia.org/wiki/Normal_number) to contain
all digit sequences in it. If so, you can find any program inside Pi in theory.
In practice it isn't that easy particularly under the TRICK's 4096-char
limit rule. Suppose we want to embed `g += hij`. We have to find [1,2,3] from Pi.
Assuming uniform distribution, it occurs once in 1000 digits, which already consumes
5000 chars in average to reach the point. We need some TRICK.
- `alias` of global variables was useful. It allows me to access the same value from
different token-length positions.
- `srand` was amazingly useful. Since it returns the "previous seed", the token-length
`5` essentially becomes a value-store that can be written without waiting for the
1-letter token `=`.
- Combination of these techniques leads to a carefully chosen 77-token Pi computation
program (quoted below), which is embeddable to the first 242 tokens of Pi.
Though the remaining 165 tokens are just no-op fillers, it's not so bad compared to
the 1000/3 = 333x blowup mentioned above.
big, temp = Array 100000000**0x04e2
srand big
alias $curTerm $initTerm
big += big
init ||= big
$counter ||= 02
while 0x00012345 >= $counter
numbase = 0x0000
$initTerm ||= Integer srand * 0x00000002
srand $counter += 0x00000001
$sigmaTerm ||= init
$curTerm /= srand
pi, = Integer $sigmaTerm
$counter += 1
srand +big && $counter >> 0b1
num = numbase |= srand
$sigmaTerm += $curTerm
pi += 3_3_1_3_8
$curTerm *= num
end
print pi
- By the way, what's the blowup ratio of the final code, then?
It's 242/77, whose first three digits are, of course, 3.14.
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