mirror of
https://github.com/ruby/ruby.git
synced 2022-11-09 12:17:21 -05:00
86 lines
3.1 KiB
Markdown
86 lines
3.1 KiB
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](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.
|