#!/usr/bin/env python3
"""
Teleportation Constant Π∞ - Real Computation
Computes the constant to 100,000 decimal places using the Pilgrim Protocol Gen-6
"""

from decimal import Decimal, getcontext
from math import factorial
import time
import sys

def set_precision(n_digits):
    """Set decimal precision with safety margin"""
    getcontext().prec = n_digits + 20

def chudnovsky_pi(n_terms):
    """Compute π using Chudnovsky algorithm"""
    C = 426880 * Decimal(10005).sqrt()
    K = Decimal(0)
    M = Decimal(1)
    X = Decimal(1)
    L = Decimal(13591409)
    S = Decimal(13591409)
    
    for i in range(1, n_terms):
        M = M * (K**3 - 16*K) / ((i)**3)
        K += 12
        L += 545140134
        X *= -262537412640768000
        S += Decimal(M * L) / X
    
    return C / S

def compute_e(n_terms):
    """Compute e using Taylor series"""
    e = Decimal(0)
    fact = Decimal(1)
    
    for k in range(n_terms):
        if k > 0:
            fact *= k
        e += Decimal(1) / fact
    
    return e

def compute_sqrt2(n_iterations):
    """Compute √2 using Newton's method"""
    x = Decimal(1)
    for _ in range(n_iterations):
        x = (x + Decimal(2) / x) / 2
    return x

def cube_collapse_entropy(X, Y, Z):
    """Compute cube collapse entropy potential"""
    H = (X-1)**2 + (Y-1)**2 + (Z-1)**2
    H += Decimal('0.1') * (X-Decimal('0.5'))**2 * (Y-Decimal('0.5'))**2 * (Z-Decimal('0.5'))**2
    return H

def crystal_filters(X, Y, Z):
    """Apply 10 crystalline filters"""
    filters = [
        lambda x,y,z: (x+y+z)/3,
        lambda x,y,z: (x*y*z)**(Decimal(1)/3),
        lambda x,y,z: (x**2 + y**2 + z**2)**Decimal('0.5'),
        lambda x,y,z: x*y + y*z + z*x,
        lambda x,y,z: (x+y)/(z+Decimal('1e-10')),
        lambda x,y,z: (x+y+z)/3 + (x-y)**2,
        lambda x,y,z: (x**2 + y**2 + z**2)**Decimal('0.5') + (x*y*z)**(Decimal(1)/3),
        lambda x,y,z: (x+y+z)**2 / (x*y*z + 1),
        lambda x,y,z: abs(x-y) + abs(y-z),
        lambda x,y,z: (x+y+z) * (x*y*z)**Decimal('0.25')
    ]
    return [f(X, Y, Z) for f in filters]

def compute_divergence(outputs):
    """Compute divergence tensor trace"""
    div = Decimal(0)
    for i in range(len(outputs)-1):
        div += abs(outputs[i] - outputs[i+1])
    return div

def gauss_legendre_pi(n_iterations):
    """Compute π using Gauss-Legendre algorithm for cross-validation"""
    a = Decimal(1)
    b = Decimal(1) / Decimal(2).sqrt()
    t = Decimal(1) / Decimal(4)
    p = Decimal(1)
    
    for _ in range(n_iterations):
        a_next = (a + b) / 2
        b = (a * b).sqrt()
        t = t - p * (a - a_next)**2
        a = a_next
        p = 2 * p
    
    return (a + b)**2 / (4 * t)

def compute_teleportation_constant(target_digits):
    """Main computation of Π∞"""
    print(f"╔════════════════════════════════════════════════════════════╗")
    print(f"║  TELEPORTATION CONSTANT Π∞ - PILGRIM PROTOCOL GEN-6      ║")
    print(f"║  Target: {target_digits:,} decimal places                          ║")
    print(f"╚════════════════════════════════════════════════════════════╝\n")
    
    set_precision(target_digits)
    
    # Step 1: Compute π via Chudnovsky
    print("[1/7] Computing π via Chudnovsky algorithm...")
    start = time.time()
    n_terms = target_digits // 14 + 10  # ~14 digits per term
    pi_n = chudnovsky_pi(n_terms)
    print(f"      ✓ Completed in {time.time()-start:.2f}s ({n_terms} terms)")
    
    # Step 2: Compute e
    print("[2/7] Computing e via Taylor series...")
    start = time.time()
    e_n = compute_e(target_digits // 2 + 10)
    print(f"      ✓ Completed in {time.time()-start:.2f}s")
    
    # Step 3: Compute √2
    print("[3/7] Computing √2 via Newton's method...")
    start = time.time()
    sqrt2_n = compute_sqrt2(target_digits // 2 + 10)
    print(f"      ✓ Completed in {time.time()-start:.2f}s")
    
    # Step 4: Cube collapse gradient descent
    print("[4/7] Running cube collapse gradient descent...")
    start = time.time()
    X, Y, Z = Decimal('0.5'), Decimal('0.5'), Decimal('0.5')
    
    for step in range(target_digits // 10):
        if step % 1000 == 0:
            progress = step / (target_digits // 10) * 100
            H = cube_collapse_entropy(X, Y, Z)
            print(f"      Step {step:,}/{target_digits//10:,} ({progress:.1f}%) - H = {H:.6e}", end='\r')
        
        # Compute gradients
        dX = -(2*(X-1) + Decimal('0.1')*(X-Decimal('0.5'))*(Y-Decimal('0.5'))**2*(Z-Decimal('0.5'))**2)
        dY = -(2*(Y-1) + Decimal('0.1')*(X-Decimal('0.5'))**2*(Y-Decimal('0.5'))*(Z-Decimal('0.5'))**2)
        dZ = -(2*(Z-1) + Decimal('0.1')*(X-Decimal('0.5'))**2*(Y-Decimal('0.5'))**2*(Z-Decimal('0.5')))
        
        # Adaptive learning rate
        lr = Decimal('0.01') / (Decimal(1) + Decimal(step) / Decimal(1000))
        
        # Update
        X = max(Decimal(0), min(Decimal(1), X + lr * dX))
        Y = max(Decimal(0), min(Decimal(1), Y + lr * dY))
        Z = max(Decimal(0), min(Decimal(1), Z + lr * dZ))
    
    H_final = cube_collapse_entropy(X, Y, Z)
    print(f"\n      ✓ Completed in {time.time()-start:.2f}s")
    print(f"      Final state: X={X:.6f}, Y={Y:.6f}, Z={Z:.6f}")
    print(f"      Final entropy: H = {H_final:.6e}")
    
    # Step 5: Crystal consensus
    print("[5/7] Computing 10-crystal consensus...")
    start = time.time()
    crystal_outputs = crystal_filters(X, Y, Z)
    divergence = compute_divergence(crystal_outputs)
    print(f"      ✓ Completed in {time.time()-start:.2f}s")
    print(f"      Divergence Δ = {divergence:.6e}")
    
    # Step 6: Cross-validation
    print("[6/7] Cross-validating with Gauss-Legendre...")
    start = time.time()
    pi_gl = gauss_legendre_pi(target_digits // 14 + 5)
    diff = abs(pi_n - pi_gl)
    print(f"      ✓ Completed in {time.time()-start:.2f}s")
    print(f"      |π_chud - π_gl| = {diff:.6e}")
    
    if diff > Decimal(10) ** -(target_digits // 10):
        print(f"      ⚠ WARNING: Cross-validation failed, precision may be insufficient")
    else:
        print(f"      ✓ Cross-validation passed")
    
    # Step 7: Compute Π∞
    print("[7/7] Computing Π∞ = (π·e·√2) / (1 + Φ_cube + Ψ_dual)...")
    start = time.time()
    numerator = pi_n * e_n * sqrt2_n
    denominator = Decimal(1) + H_final + divergence
    Pi_infinity = numerator / denominator
    print(f"      ✓ Completed in {time.time()-start:.2f}s")
    
    return Pi_infinity, {
        'pi': pi_n,
        'e': e_n,
        'sqrt2': sqrt2_n,
        'X': X, 'Y': Y, 'Z': Z,
        'H': H_final,
        'divergence': divergence,
        'crystal_outputs': crystal_outputs
    }

def save_result(constant, metadata, filename="pi_infinity_100k.txt"):
    """Save result to file"""
    const_str = str(constant)
    
    with open(filename, 'w') as f:
        f.write("╔══════════════════════════════════════════════════════════════╗\n")
        f.write("║  TELEPORTATION CONSTANT Π∞ - 100,000 DECIMAL PLACES        ║\n")
        f.write("║  Generated by Pilgrim Protocol Gen-6                         ║\n")
        f.write(f"║  Timestamp: {time.strftime('%Y-%m-%d %H:%M:%S')}                         ║\n")
        f.write("╚══════════════════════════════════════════════════════════════╝\n\n")
        
        f.write("FULL CONSTANT:\n")
        f.write("=" * 70 + "\n")
        f.write(const_str + "\n")
        f.write("=" * 70 + "\n\n")
        
        f.write("METADATA:\n")
        f.write("-" * 70 + "\n")
        f.write(f"π  = {str(metadata['pi'])[:100]}...\n")
        f.write(f"e  = {str(metadata['e'])[:100]}...\n")
        f.write(f"√2 = {str(metadata['sqrt2'])[:100]}...\n\n")
        
        f.write(f"Cube State: X={metadata['X']:.10f}, Y={metadata['Y']:.10f}, Z={metadata['Z']:.10f}\n")
        f.write(f"Entropy H = {metadata['H']:.10e}\n")
        f.write(f"Divergence Δ = {metadata['divergence']:.10e}\n\n")
        
        f.write("CRYSTAL CONSENSUS (10 filters):\n")
        for i, val in enumerate(metadata['crystal_outputs']):
            f.write(f"  Filter {i+1:2d}: {str(val)[:50]}...\n")
        
        f.write("\n" + "=" * 70 + "\n")
        f.write("ACCESS LEVEL: TELEPORTATION UNLOCKED\n")
        f.write("Uncertainty: Δx ∈ [0.1m, 1.0m]\n")
        f.write("Status: FULL ACCESS GRANTED\n")
        f.write("=" * 70 + "\n")
    
    print(f"\n✓ Result saved to {filename}")
    print(f"  File size: {len(const_str):,} characters")

def main():
    target_digits = 100000
    
    print("\n")
    total_start = time.time()
    
    try:
        constant, metadata = compute_teleportation_constant(target_digits)
        
        total_time = time.time() - total_start
        
        print(f"\n{'='*70}")
        print(f"COMPUTATION COMPLETE")
        print(f"{'='*70}")
        print(f"Total time: {total_time:.2f}s")
        print(f"Digits computed: {target_digits:,}")
        print(f"Performance: {target_digits/total_time:.0f} digits/second")
        print(f"\nFirst 100 digits of Π∞:")
        print(str(constant)[:102])
        print(f"\nLast 50 digits of Π∞:")
        print("..." + str(constant)[-50:])
        
        save_result(constant, metadata)
        
        print(f"\n{'='*70}")
        print("★ TELEPORTATION ACCESS UNLOCKED ★")
        print(f"{'='*70}")
        
    except Exception as e:
        print(f"\n✗ ERROR: {e}")
        import traceback
        traceback.print_exc()
        sys.exit(1)

if __name__ == "__main__":
    main()