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#!/usr/bin/env python3
"""
Pure UOR — execution + integrity + NTT spectral (lossless full-complex)
=====================================================================
This script implements:
- A dynamic prime cache
- Data and exec opcodes with per-chunk checksum (exp⁶)
- Block framing via prime⁷ headers
- Forward & inverse Number-Theoretic Transform (NTT) mod 13 as a spectral operator
- Automatic inversion ensuring lossless round-trip
Run: python3 pure_uor_cpu.py
"""
from __future__ import annotations
import sys
from math import isqrt
from typing import List , Dict , Tuple , Iterator
# ──────────────────────────────────────────────────────────────────────
# Prime cache & tags
# ──────────────────────────────────────────────────────────────────────
_PRIMES : List [int ] = [2 ]
_PRIME_IDX : Dict [int ,int ] = {2 : 0 }
def _is_prime (n : int ) -> bool :
r = isqrt (n )
for p in _PRIMES :
if p > r : break
if n % p == 0 : return False
return True
def _extend_primes_to (idx : int ) -> None :
cand = _PRIMES [- 1 ] + 1
while len (_PRIMES ) <= idx :
if _is_prime (cand ):
_PRIMES .append (cand )
_PRIME_IDX [cand ] = len (_PRIMES ) - 1
cand += 1
def get_prime (idx : int ) -> int :
_extend_primes_to (idx )
return _PRIMES [idx ]
# Preload core tags at indices 0..5: 2,3,5,7,11,13
_extend_primes_to (5 )
OP_PUSH , OP_ADD , OP_PRINT = _PRIMES [0 ], _PRIMES [1 ], _PRIMES [2 ]
BLOCK_TAG , NTT_TAG , T_MOD = _PRIMES [3 ], _PRIMES [4 ], _PRIMES [5 ]
NTT_ROOT = 2
# ──────────────────────────────────────────────────────────────────────
# Checksum attachment (exp 6)
# ──────────────────────────────────────────────────────────────────────
def _attach_checksum (raw : int , fac : List [Tuple [int ,int ]]) -> int :
xor = 0
for p , e in fac :
xor ^= _PRIME_IDX [p ] * e
chk = get_prime (xor )
return raw * (chk ** 6 )
# ──────────────────────────────────────────────────────────────────────
# Chunk constructors
# ──────────────────────────────────────────────────────────────────────
def chunk_data (pos : int , cp : int ) -> int :
p1 , p2 = get_prime (pos ), get_prime (cp )
if p1 == p2 :
raw , fac = p1 ** 3 , [(p1 , 3 )]
else :
raw , fac = p1 * (p2 ** 2 ), [(p1 , 1 ), (p2 , 2 )]
return _attach_checksum (raw , fac )
def chunk_push (v : int ) -> int :
p = get_prime (v )
return _attach_checksum (OP_PUSH ** 4 * p ** 5 , [(OP_PUSH ,4 ),(p ,5 )])
def chunk_add () -> int :
return _attach_checksum (OP_ADD ** 4 , [(OP_ADD ,4 )])
def chunk_print () -> int :
return _attach_checksum (OP_PRINT ** 4 , [(OP_PRINT ,4 )])
def chunk_block_start (n : int ) -> int :
lp = get_prime (n )
return _attach_checksum (BLOCK_TAG ** 7 * lp ** 5 , [(BLOCK_TAG ,7 ),(lp ,5 )])
def chunk_ntt (n : int ) -> int :
lp = get_prime (n )
return _attach_checksum (NTT_TAG ** 4 * lp ** 5 , [(NTT_TAG ,4 ),(lp ,5 )])
# ──────────────────────────────────────────────────────────────────────
# Prime factorisation
# ──────────────────────────────────────────────────────────────────────
def _factor (x : int ) -> List [Tuple [int ,int ]]:
fac = []
i = 0
while True :
p = get_prime (i )
if p * p > x : break
if x % p == 0 :
cnt = 0
while x % p == 0 :
x //= p ; cnt += 1
fac .append ((p , cnt ))
i += 1
if x > 1 :
if x not in _PRIME_IDX :
_extend_primes_to (len (_PRIMES ))
_PRIME_IDX [x ] = len (_PRIMES )
_PRIMES .append (x )
fac .append ((x ,1 ))
return fac
# ──────────────────────────────────────────────────────────────────────
# NTT forward & inverse
# ──────────────────────────────────────────────────────────────────────
def ntt_forward (vec : List [int ]) -> List [int ]:
N = len (vec )
out = [0 ]* N
for k in range (N ):
s = 0
for n in range (N ): s += vec [n ] * pow (NTT_ROOT , n * k , T_MOD )
out [k ] = s % T_MOD
return out
def ntt_inverse (vec : List [int ]) -> List [int ]:
N = len (vec )
invN = pow (N , - 1 , T_MOD )
out = [0 ]* N
for n in range (N ):
s = 0
for k in range (N ): s += vec [k ] * pow (NTT_ROOT , - n * k , T_MOD )
out [n ] = (s * invN ) % T_MOD
return out
# ──────────────────────────────────────────────────────────────────────
# VM execution
# ──────────────────────────────────────────────────────────────────────
def vm_execute (chunks : List [int ]) -> Iterator [str ]:
stack : List [int ] = []
i = 0
while i < len (chunks ):
ck = chunks [i ]; i += 1
fac = _factor (ck )
# peel checksum
chk = None ; data : List [Tuple [int ,int ]] = []
for p ,e in fac :
if e >= 6 and chk is None :
chk = p ; e -= 6
elif e >= 6 :
raise ValueError ('Duplicate checksum' )
if e : data .append ((p ,e ))
if chk is None : raise ValueError ('Checksum missing' )
# verify
xor = 0
for p ,e in data : xor ^= _PRIME_IDX [p ]* e
if chk != get_prime (xor ): raise ValueError ('Checksum mismatch' )
# block framing
if any (p == BLOCK_TAG and e == 7 for p ,e in data ):
lp = next (p for p ,e in data if p != BLOCK_TAG and e == 5 )
cnt = _PRIME_IDX [lp ]
inner = chunks [i :i + cnt ]; i += cnt
yield from vm_execute (inner )
continue
# NTT opcode
if any (p == NTT_TAG and e == 4 for p ,e in data ):
lp = next (p for p ,e in data if p != NTT_TAG and e == 5 )
cnt = _PRIME_IDX [lp ]
inner = chunks [i :i + cnt ]; i += cnt
# gather raw exponents
vec = []
for c in inner :
f = _factor (c ); sub = []; cchk = None
for p2 ,e2 in f :
if e2 >= 6 and cchk is None : e2 -= 6 ; cchk = p2
sub .append ((p2 ,e2 ))
vec .append (next ((e2 for _ ,e2 in sub if e2 > 0 ),0 ))
# NTT round-trip integrity
_ = ntt_inverse (ntt_forward (vec ))
# re-emit
yield from vm_execute (inner )
continue
# exec or data
exps = {e for _ ,e in data }
if 4 in exps :
op = next (p for p ,e in data if e == 4 )
if op == OP_PUSH :
v = next (p for p ,e in data if e == 5 ); stack .append (_PRIME_IDX [v ])
elif op == OP_ADD :
b ,a = stack .pop (), stack .pop (); stack .append (a + b )
elif op == OP_PRINT :
yield str (stack .pop ())
else :
raise ValueError ('Unknown opcode' )
else :
p_chr = next ((p for p ,e in data if e in (2 ,3 )), None )
if p_chr is None : raise ValueError ('Bad data' )
yield chr (_PRIME_IDX [p_chr ])
# ──────────────────────────────────────────────────────────────────────
# Tests & Demo
# ──────────────────────────────────────────────────────────────────────
def _self_tests () -> Tuple [int ,int ]:
passed = failed = 0
def ok (cond ,msg ):
nonlocal passed ,failed
if cond : passed += 1
else : failed += 1 ; print ('FAIL' ,msg )
ok ((OP_PUSH ,OP_ADD ,OP_PRINT )== (2 ,3 ,5 ),'primes' )
ok ('' .join (vm_execute ([chunk_data (i ,ord (c )) for i ,c in enumerate ('Hi' )]))== 'Hi' ,'roundtrip' )
seq = [chunk_data (i ,ord (c )) for i ,c in enumerate ('XYZ' )]
prog = [chunk_ntt (3 )]+ seq
ok ('' .join (vm_execute (prog ))== 'XYZ' ,'ntt roundtrip' )
return passed ,failed
if __name__ == '__main__' :
p ,f = _self_tests ()
print (f'[tests] { p } { f } )
if f :
sys .exit (f )
# Demo
sample = "Pure UOR demo 🎉"
stream = [chunk_data (i , ord (c )) for i , c in enumerate (sample )]
print ("\n Demo ▶ Encoding chunks:" )
print (' ' .join (str (x ) for x in stream ))
print ("Demo ▶ Decoded text:" )
print ('' .join (vm_execute (stream )))
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