ruby/sample/trick2015/kinaba/remarks.markdown

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 suitable for Rubyists to memorize the digits of 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 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.