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diff --git a/sample/trick2015/kinaba/remarks.markdown b/sample/trick2015/kinaba/remarks.markdown new file mode 100644 index 0000000000..6316c51fb6 --- /dev/null +++ b/sample/trick2015/kinaba/remarks.markdown @@ -0,0 +1,85 @@ +### 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. |