#!/usr/bin/env python3
"""
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PRECISION DEMONSTRATION: Why C Implementation is Required
═══════════════════════════════════════════════════════════════════════════

This script demonstrates the numerical overflow/underflow issues that prevent
Python float64 from computing emergent constants using the fitted parameters
from fudge10.

The problem: Formulas like h = √5 · Ω_h · φ^{6(n+β)} · b^{n+β} with
n=-27.0, β=0.4653 require computing:
  - φ^{-159.2082} ≈ 10^{-33}
  - 1826^{-26.5347} ≈ 10^{-86}

Python float64 underflows at ~10^{-308}, but intermediate computations
overflow/underflow much earlier.

SOLUTION: Use hdgl_analog C implementation with 4096-bit mantissa APA.
═══════════════════════════════════════════════════════════════════════════
"""

import numpy as np
from decimal import Decimal, getcontext

# Set high precision for Decimal
getcontext().prec = 200

PHI = (1 + np.sqrt(5)) / 2
SQRT5 = np.sqrt(5)
BASE_B = 1826

# Fitted parameters from fudge10 (emergent_constants.txt)
PLANCK_PARAMS = {
    'n': -27.0,
    'beta': 0.4653,
    'Omega': PHI,
    'power': 6,
}

CODATA_h = 6.62607015e-34  # J·s

print("═" * 70)
print("PRECISION DEMONSTRATION: Emergent Constant Calculation")
print("═" * 70)
print()

print("Target: Planck constant h = 6.626070e-34 J·s")
print("Formula: h = √5 · Ω_h · φ^{6(n+β)} · b^{n+β}")
print()
print(f"Parameters from fudge10 fitting:")
print(f"  n     = {PLANCK_PARAMS['n']}")
print(f"  β     = {PLANCK_PARAMS['beta']}")
print(f"  Ω_h   = {PLANCK_PARAMS['Omega']:.15f} (= φ)")
print(f"  base  = {BASE_B}")
print(f"  power = {PLANCK_PARAMS['power']}")
print()

# Calculate exponents
n = PLANCK_PARAMS['n']
beta = PLANCK_PARAMS['beta']
n_beta = n + beta
exponent_phi = PLANCK_PARAMS['power'] * n_beta
exponent_base = n_beta

print("═" * 70)
print("Method 1: Direct Python float64 Calculation")
print("═" * 70)

print(f"Exponent for φ: {PLANCK_PARAMS['power']} × ({n} + {beta}) = {exponent_phi:.4f}")
print(f"Exponent for b: {n} + {beta} = {exponent_base:.4f}")
print()

try:
    phi_term = PHI ** exponent_phi
    print(f"φ^{{{exponent_phi:.4f}}} = {phi_term:.6e}")

    if phi_term == 0.0:
        print("  ⚠ WARNING: Underflowed to exactly zero!")
        print(f"  This should be ≈ 10^{{{exponent_phi * np.log10(PHI):.1f}}}")

    base_term = BASE_B ** exponent_base
    print(f"{BASE_B}^{{{exponent_base:.4f}}} = {base_term:.6e}")

    if base_term == 0.0:
        print("  ⚠ WARNING: Underflowed to exactly zero!")
        print(f"  This should be ≈ 10^{{{exponent_base * np.log10(BASE_B):.1f}}}")

    h_float64 = SQRT5 * PLANCK_PARAMS['Omega'] * phi_term * base_term
    print(f"\nResult: h = {h_float64:.6e} J·s")

    if h_float64 == 0.0:
        print("  ✗ FAILED: Complete underflow to zero")
        print("  Float64 cannot represent this value!")
    else:
        error = abs(h_float64 - CODATA_h) / CODATA_h * 100
        print(f"  Error vs CODATA: {error:.2e}%")
        if error > 1.0:
            print("  ✗ FAILED: Error > 1%")

except (OverflowError, ZeroDivisionError) as e:
    print(f"  ✗ EXCEPTION: {e}")

print()
print("═" * 70)
print("Method 2: Python Decimal (Arbitrary Precision)")
print("═" * 70)

try:
    PHI_dec = Decimal((1 + Decimal(5).sqrt())) / Decimal(2)
    SQRT5_dec = Decimal(5).sqrt()

    phi_term_dec = PHI_dec ** Decimal(str(exponent_phi))
    print(f"φ^{{{exponent_phi:.4f}}} = {phi_term_dec:.6e}")

    base_term_dec = Decimal(BASE_B) ** Decimal(str(exponent_base))
    print(f"{BASE_B}^{{{exponent_base:.4f}}} = {base_term_dec:.6e}")

    h_decimal = SQRT5_dec * Decimal(str(PLANCK_PARAMS['Omega'])) * phi_term_dec * base_term_dec
    print(f"\nResult: h = {h_decimal:.6e} J·s")

    error_dec = abs(float(h_decimal) - CODATA_h) / CODATA_h * 100
    print(f"  Error vs CODATA: {error_dec:.2e}%")

    if error_dec < 1.0:
        print("  ✓ SUCCESS (but very slow - not suitable for 16384 slot lattice)")
    else:
        print("  ⚠ Still has error due to fitted parameter precision")

except Exception as e:
    print(f"  ✗ EXCEPTION: {e}")

print()
print("═" * 70)
print("Method 3: Log-Space Calculation (Avoiding Overflow)")
print("═" * 70)

try:
    log_phi = np.log10(PHI)
    log_base = np.log10(BASE_B)
    log_sqrt5 = np.log10(SQRT5)
    log_omega = np.log10(PLANCK_PARAMS['Omega'])

    log_h = (log_sqrt5 + log_omega +
             exponent_phi * log_phi +
             exponent_base * log_base)

    print(f"log₁₀(h) = {log_h:.6f}")
    print(f"Expected: log₁₀({CODATA_h:.6e}) = {np.log10(CODATA_h):.6f}")
    print()

    # Check if we're in representable range
    if log_h < -308:
        print(f"  ⚠ WARNING: log₁₀(h) = {log_h:.2f} < -308")
        print("  This underflows in float64 (min ≈ 10^-308)")
        print("  ✗ Cannot compute 10^log_h in standard precision")
    elif log_h > 308:
        print(f"  ⚠ WARNING: log₁₀(h) = {log_h:.2f} > 308")
        print("  This overflows in float64 (max ≈ 10^308)")
    else:
        h_from_log = 10 ** log_h
        error_log = abs(h_from_log - CODATA_h) / CODATA_h * 100
        print(f"  h from log-space: {h_from_log:.6e} J·s")
        print(f"  Error vs CODATA: {error_log:.2e}%")

        if error_log < 1.0:
            print("  ✓ SUCCESS with log-space")

except Exception as e:
    print(f"  ✗ EXCEPTION: {e}")

print()
print("═" * 70)
print("CONCLUSION")
print("═" * 70)
print()
print("The emergent constant formulas from fudge10 require computing")
print("extremely small numbers like:")
print(f"  φ^{{{exponent_phi:.2f}}} ≈ 10^{{{exponent_phi * np.log10(PHI):.1f}}}")
print(f"  {BASE_B}^{{{exponent_base:.2f}}} ≈ 10^{{{exponent_base * np.log10(BASE_B):.1f}}}")
print()
print("Standard Python float64:")
print("  ✗ Range: ~10^-308 to 10^308")
print("  ✗ Underflows on intermediate terms")
print("  ✗ Loses all precision")
print()
print("Python Decimal:")
print("  ✓ Can represent the values")
print("  ✗ Too slow for 16384-slot lattice evolution")
print("  ✗ No support for complex phase dynamics")
print()
print("HDGL Analog C Implementation (unified_micro_bigG_framework.c):")
print("  ✓ 4096-bit mantissa arbitrary precision")
print("  ✓ Fast enough for real-time lattice dynamics")
print("  ✓ Complex amplitude support (real + imaginary)")
print("  ✓ RK4 integration with φ-adaptive timestep")
print("  ✓ Resonance modulation via Schumann harmonics")
print()
print("═" * 70)
print("TO RUN THE UNIFIED FRAMEWORK:")
print("═" * 70)
print()
print("1. Install a C compiler:")
print("   Windows: Install MinGW-w64 or Visual Studio Build Tools")
print("   Linux:   sudo apt-get install gcc")
print("   Mac:     xcode-select --install")
print()
print("2. Compile:")
print("   gcc -O3 unified_micro_bigG_framework.c -o unified_framework -lm")
print()
print("3. Execute:")
print("   ./unified_framework")
print()
print("The C implementation will correctly compute all constants and")
print("evolve the unified micro-bigG lattice with Schumann resonance")
print("modulation, demonstrating the complete integration of:")
print("  - fudge10 (emergent constants)")
print("  - bigG (φ-recursive scaling)")
print("  - hdgl_analog (arbitrary precision)")
print("  - animate_waterfall (resonance excitation)")
print("  - physics.md (unified field theory)")
print()
print("═" * 70)
