# Pi

The Pi language is a public domain esoteric programming language idealized by Daniel Lopes Parra and invented by Marcelo Aires Caetano and Paulo Matias in 2006.

See here for an example of a Hello World program written in Pi

Pi is based on the brainfuck language and uses the same instructions as it. Pi works by calculating pi digits and introducing errors in some random digits of them, encoding obfuscated brainfuck instructions.

Instructions are encoded as below:

```'>' '<' '+' '-' '.' ',' '[' ']'
0   1   2   3   4   5   6   7   8
```

But, as we need to identify which pi digits are incorrect, we move each instruction in the table one position to the right starting at the position that is initially over the correct pi digit that is where we are inserting the instruction.

For example, if the pi digit in the position we are inserting the instruction is 4, the table would be moved as follows:

```'>' '<' '+' '-'     '.' ',' '[' ']'
0   1   2   3   4   5   6   7   8
```

Then the instruction would be converted to a digit that would be inserted replacing the correct digit.

## Brainfuck converter

A program written in Python for converting brainfuck programs to Pi programs and interpreting them is given as follows (available at IDEOne)

```#! /usr/bin/env python
"""
Pi In Bf interpreter
@author stranjo and thotypous
"""
import sys, random

def bf(string):

dpointer = pointer = 0
plist = *3000
stack = []
string = list(string)

while pointer < len(string):
if pointer == 0:
stack.append(-1)

if string[pointer] == '+':
plist[dpointer] +=1
plist[dpointer] &= 0xFF

elif string[pointer] == '-':
plist[dpointer] -= 1
plist[dpointer] &= 0xFF

elif string[pointer] == '>':
dpointer += 1

elif string[pointer] == '<':
dpointer-=1
if dpointer < 0: dpointer = 0

elif string[pointer] == ']':
pointer = stack.pop()

elif string[pointer] == '[':
if plist[dpointer]:
stack.append(pointer-1)
else:
while string[pointer] != ']': pointer+=1

elif string[pointer] == '.':
sys.stdout.write(chr(plist[dpointer]))
sys.stdout.flush()
elif string[pointer] == ',':
sys.stdin.flush()
pointer+=1

def pi2bf(string):
out = ""
t = { 0:'>', 1:'<', 2:'+', 3:'-', 4:'.', 5:',', 6:'[', 7:']' }
k, a, b, a1, b1, r = 2, 4, 1, 12, 4, True
while r:
p, q, k = k*k, 2*k+1, k+1
a, b, a1, b1 = a1, b1, p*a+q*a1, p*b+q*b1
d = int(a / b)
d1 = int(a1 / b1)
while d == d1:
if len(string):
c = string
string = string[1:]
else: c = ""
if len(c) == 0:
r = False
break
try: c = int(c)
except: continue
if c != d: out += t[c - (c > d)]
a, a1 = 10*(a%b), 10*(a1%b1)
d, d1 = int(a/b), int(a1/b1)
return out

def bf2pi(string):
random.seed()
out = ""
t = { '>':0, '<':1, '+':2, '-':3, '.':4, ',':5, '[':6, ']':7 }
k, a, b, a1, b1, cl, r = 2, 4, 1, 12, 4, random.randint(20,30), True
while r:
p, q, k = k*k, 2*k+1, k+1
a, b, a1, b1 = a1, b1, p*a+q*a1, p*b+q*b1
d = int(a / b)
d1 = int(a1 / b1)
while d == d1:
if cl:
out+= str(d)
cl -= 1
else:
if len(string):
c = string
string = string[1:]
else: c = ""
if len(c) == 0:
r = False
break
try: c = t[c]
except: continue
out += str(c + (c >= d))
cl = random.randint(2,7)
a, a1 = 10*(a%b), 10*(a1%b1)
d, d1 = int(a/b), int(a1/b1)
return "%s.%s"%(out,out[1:])

if __name__ == '__main__':
if len(sys.argv) == 1:

elif sys.argv == '-':
bf(pi2bf(" ".join(sys.argv[2:])))
elif sys.argv == '-bf':
bf(" ".join(sys.argv[2:]))
elif sys.argv == '--bf':
f = open(sys.argv)
elif sys.argv == '--convert':
f = open(sys.argv)
elif sys.argv == '-c':
print(bf2pi(" ".join(sys.argv[2:])))
elif sys.argv == '--tobf':
f = open(sys.argv)
elif sys.argv == '-2bf':
print(pi2bf(" ".join(sys.argv[2:])))
elif sys.argv == '-h' or sys.argv == '--help':
print("""pi language commands:
* -bf: parses a bf command
* --bf: parses a bf file
* - : parses a pi number from command line
* -h --help: displays dis help
* --convert: convert a bf file into pi
* -c: convert a bf command into pi
* --tobf convert a pi file into bf
* -2bf convert a pi command into bf""")
else:
f = open(sys.argv)