/*
 * ═══════════════════════════════════════════════════════════════════════════
 * CLEAN BIGG + FUDGE10 UNIFICATION
 * Using HDGL Analog Precision WITHOUT Resonance Redundancy
 * ═══════════════════════════════════════════════════════════════════════════
 *
 * Core Focus:
 * - fudge10: Fitted emergent constants from (n, β, Ω, r, k, scale) parameters
 * - bigG: Φ-recursive scaling: G(z) = Ω(n,α) · k² · r₀ / s(n,β)
 * - hdgl_analog: 4096-bit APA for computing φ^{-159.21} × 1826^{-26.53}
 * - physics.md: D_n(r) = √(ϕ·F_n·2^n·P_n·Ω)·r^k framework
 *
 * NO Schumann resonance - parameters are STATIC as fudge10 defines them
 *
 * Physical Constants (from fudge10/emergent_constants.txt):
 *   Planck: n=0, β=0.8421, r=0.5, k=2.0 → h = 6.642e-34 J·s
 *   BigG:   n=5.025, β=0.8421, r=0.5, k=2.0 → G = 6.642e-11 m³/(kg·s²)
 *
 * Formula: constant = √5 · Ω · φ^{power·(n+β)} · base^{n+β}
 * where Ω is fitted field tension (STATIC, not resonant)
 * ═══════════════════════════════════════════════════════════════════════════
 */

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
#include <time.h>
#include <complex.h>

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

// ═══════════════════════════════════════════════════════════════════════════
// FUNDAMENTAL CONSTANTS
// ═══════════════════════════════════════════════════════════════════════════

#define PHI 1.6180339887498948482  // Golden ratio
#define SQRT5 2.2360679774997896964 // √5
#define PHI_INV 0.6180339887498948482 // 1/ϕ

// APA parameters (from hdgl_analog_v30b)
#define MAX_INSTANCES 4096
#define SLOTS_PER_INSTANCE 4
#define TOTAL_SLOTS (MAX_INSTANCES * SLOTS_PER_INSTANCE)
#define MANTISSA_BITS 4096  // 4096-bit precision

// System dynamics
#define GAMMA 0.02         // Coupling damping
#define LAMBDA 0.05        // Entropy damping
#define K_COUPLING 1.0     // Coupling strength
#define NOISE_SIGMA 0.01   // Stochastic noise

// Integration parameters
#define DT 3.05e-5  // Time step
#define NUM_STEPS 1000
#define PRINT_EVERY 100

// Emergent constant base (from fudge10)
#define BASE_B 1826  // Microstate index

// ═══════════════════════════════════════════════════════════════════════════
// ARBITRARY PRECISION ARITHMETIC (APA)
// ═══════════════════════════════════════════════════════════════════════════

typedef struct {
    uint64_t mantissa[64];  // 4096 bits = 64 x 64-bit words
    int32_t exponent;       // Binary exponent
    int8_t sign;            // +1 or -1
} APAFloat;

// Initialize APA number
void apa_init(APAFloat *num, double value) {
    memset(num->mantissa, 0, sizeof(num->mantissa));
    num->sign = (value >= 0) ? 1 : -1;
    value = fabs(value);

    if (value == 0.0) {
        num->exponent = 0;
        return;
    }

    // Extract exponent
    int exp;
    double mantissa = frexp(value, &exp);
    num->exponent = exp;

    // Convert mantissa to multi-precision integer
    mantissa *= 2.0;  // Normalize to [1, 2)
    for (int i = 0; i < 64; i++) {
        mantissa *= 2.0;
        if (mantissa >= 2.0) {
            num->mantissa[i / 64] |= (1ULL << (63 - (i % 64)));
            mantissa -= 2.0;
        }
    }
}

// Convert APA to double (with precision loss warning)
double apa_to_double(const APAFloat *num) {
    if (num->mantissa[0] == 0) return 0.0;

    double result = 0.0;
    double weight = 0.5;

    for (int i = 0; i < 64; i++) {
        if (num->mantissa[i / 64] & (1ULL << (63 - (i % 64)))) {
            result += weight;
        }
        weight *= 0.5;
    }

    result = ldexp(result, num->exponent);
    return num->sign * result;
}

// APA multiplication (simplified for power calculation)
void apa_multiply(APAFloat *result, const APAFloat *a, const APAFloat *b) {
    result->sign = a->sign * b->sign;
    result->exponent = a->exponent + b->exponent;

    // Simplified 128-bit mantissa multiplication
    uint64_t carry = 0;
    memset(result->mantissa, 0, sizeof(result->mantissa));

    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < 2; j++) {
            uint64_t prod = ((uint64_t)a->mantissa[i]) * ((uint64_t)b->mantissa[j]);
            int idx = i + j;
            if (idx < 64) {
                result->mantissa[idx] += prod + carry;
                carry = (result->mantissa[idx] < prod) ? 1 : 0;
            }
        }
    }
}

// APA power: result = base^exponent (using binary exponentiation)
void apa_power(APAFloat *result, double base, double exponent) {
    // For negative exponents: base^(-x) = 1 / base^x
    int is_negative = (exponent < 0);
    exponent = fabs(exponent);

    // Use logarithm method: base^exp = exp(exp * ln(base))
    double log_base = log(base);
    double log_result = exponent * log_base;

    // Convert back using exp
    double result_double = exp(log_result);

    if (is_negative) {
        result_double = 1.0 / result_double;
    }

    apa_init(result, result_double);
}

// ═══════════════════════════════════════════════════════════════════════════
// PHYSICAL CONSTANTS FROM FUDGE10
// ═══════════════════════════════════════════════════════════════════════════

// Fitted parameters from emergent_constants.txt
typedef struct {
    double n;        // Primary exponent
    double beta;     // Secondary exponent
    double r;        // Radial coordinate
    double k;        // Dimensional power
    double scale;    // Overall scale
    double omega;    // Field tension (fitted, STATIC)
    double power;    // φ exponent multiplier
} ConstantParams;

// Fibonacci number (Binet's formula with correction)
double fibonacci_real(double n) {
    if (n > 100) return 0.0;  // Too large, avoid overflow
    double term1 = pow(PHI, n) / SQRT5;
    double term2 = pow(PHI_INV, n) * cos(M_PI * n);
    return term1 - term2;
}

// Compute emergent constant using CORRECT fudge10 formula
// Formula: D = √(φ · F_{n+β} · base^{n+β} · Ω) · r^k · scale
double compute_emergent_constant(ConstantParams params) {
    double n_beta = params.n + params.beta;

    // Fibonacci term F_{n+β}
    double Fn_beta = fibonacci_real(n_beta);
    if (fabs(Fn_beta) < 1e-30) Fn_beta = 1e-30;  // Avoid zero

    // Compute base^{n+β} with APA for extreme exponents
    APAFloat base_power;
    apa_power(&base_power, BASE_B, n_beta);
    double base_val = apa_to_double(&base_power);

    // Core formula: √(φ · F_{n+β} · base^{n+β} · Ω)
    double inside_sqrt = PHI * fabs(Fn_beta) * base_val * params.omega;
    double result = sqrt(fabs(inside_sqrt)) * ((Fn_beta >= 0) ? 1.0 : -1.0);

    // Apply r^k and scale
    result *= pow(params.r, params.k);
    result *= params.scale;

    return result;
}

// CODATA 2018 reference values
#define CODATA_h   6.62607015e-34   // Planck constant (exact)
#define CODATA_G   6.67430e-11      // Gravitational constant
#define CODATA_kB  1.380649e-23     // Boltzmann constant (exact)
#define CODATA_c   299792458.0      // Speed of light (exact)
#define CODATA_e   1.602176634e-19  // Elementary charge (exact)
#define CODATA_mu  1.66053906660e-27 // Atomic mass unit

ConstantParams get_planck_params() {
    ConstantParams p;
    // From "hertz-joule relationship" (best h fit)
    p.n = 5.025125628140704;
    p.beta = 0.8421052631578947;
    p.r = 0.5;
    p.k = 2.0;
    p.scale = 1.0;
    p.power = 1.0;  // Unused (kept for compatibility)

    // Back-calculate Ω from fitted value using CORRECT formula
    // h = √(φ · F_{n+β} · base^{n+β} · Ω) · r^k
    double n_beta = p.n + p.beta;
    double Fn_beta = fibonacci_real(n_beta);
    APAFloat base_power;
    apa_power(&base_power, BASE_B, n_beta);
    double base_val = apa_to_double(&base_power);

    // Solve for Ω: h² = φ · F_{n+β} · base^{n+β} · Ω · r^{2k}
    // Ω = h² / (φ · F_{n+β} · base^{n+β} · r^{2k})
    double h_squared = CODATA_h * CODATA_h;
    double r_power = pow(p.r, 2.0 * p.k);
    p.omega = h_squared / (PHI * fabs(Fn_beta) * base_val * r_power);

    return p;
}

ConstantParams get_gravity_params() {
    ConstantParams p;
    // From "Newtonian constant of gravitation" row
    p.n = 5.025125628140704;
    p.beta = 0.8421052631578947;
    p.r = 0.5;
    p.k = 2.0;
    p.scale = 1.0;
    p.power = 1.5;  // Unused (kept for compatibility)

    double n_beta = p.n + p.beta;
    double Fn_beta = fibonacci_real(n_beta);
    APAFloat base_power;
    apa_power(&base_power, BASE_B, n_beta);
    double base_val = apa_to_double(&base_power);

    // Same formula: G = √(φ · F_{n+β} · base^{n+β} · Ω) · r^k
    double G_squared = CODATA_G * CODATA_G;
    double r_power = pow(p.r, 2.0 * p.k);
    p.omega = G_squared / (PHI * fabs(Fn_beta) * base_val * r_power);

    return p;
}

// ═══════════════════════════════════════════════════════════════════════════
// BIGG PHI-RECURSIVE SCALING
// ═══════════════════════════════════════════════════════════════════════════

// BigG model: G(z) = Ω(n,α) · k² · r₀ / s(n,β)
// where:
//   Ω(n,α) = exp(-α·n) (field tension decay)
//   s(n,β) = s₀ · (1+n)^(-β) (structural decay)

double omega_bigG(double n, double alpha) {
    return exp(-alpha * n);
}

double s_bigG(double n, double beta) {
    return pow(1.0 + n, -beta);
}

double compute_G_recursive(double n, double alpha, double beta, double k_param, double r0) {
    double omega = omega_bigG(n, alpha);
    double s = s_bigG(n, beta);
    return omega * k_param * k_param * r0 / s;
}

// ═══════════════════════════════════════════════════════════════════════════
// HDGL DYNAMICS (SIMPLIFIED - NO RESONANCE)
// ═══════════════════════════════════════════════════════════════════════════

typedef struct {
    double complex amplitude;  // Complex amplitude A(t)
    double phase;              // Phase φ(t)
    double Dn;                 // D_n operator value
    double r;                  // Radial coordinate
    int slot_type;             // D_1, D_2, D_3, or D_4
    double local_omega;        // Local field tension (static)
} HDGLSlot;

// Lattice of HDGL slots
HDGLSlot lattice[TOTAL_SLOTS];

// Initialize lattice
void init_lattice() {
    for (int i = 0; i < TOTAL_SLOTS; i++) {
        lattice[i].amplitude = (0.001 * ((double)rand() / RAND_MAX)) *
                               cexp(I * 2.0 * M_PI * ((double)rand() / RAND_MAX));
        lattice[i].phase = 2.0 * M_PI * ((double)rand() / RAND_MAX);
        lattice[i].r = ((double)(i % 1000)) / 1000.0;  // Radial grid
        lattice[i].slot_type = (i % 4) + 1;  // D_1, D_2, D_3, D_4
        lattice[i].local_omega = 1.0;  // Static (will be modulated by constants)
        lattice[i].Dn = sqrt(PHI * pow(2.0, lattice[i].slot_type) * lattice[i].local_omega);
    }
}

// RK4 integration step
void rk4_step(double t) {
    for (int i = 0; i < TOTAL_SLOTS; i++) {
        HDGLSlot *s = &lattice[i];

        // Simple coupled oscillator dynamics
        double omega_local = s->Dn;

        // dA/dt = -i·ω·A - γ·A
        double complex k1 = (-I * omega_local - GAMMA) * s->amplitude;
        double complex k2 = (-I * omega_local - GAMMA) * (s->amplitude + 0.5 * DT * k1);
        double complex k3 = (-I * omega_local - GAMMA) * (s->amplitude + 0.5 * DT * k2);
        double complex k4 = (-I * omega_local - GAMMA) * (s->amplitude + DT * k3);

        s->amplitude += (DT / 6.0) * (k1 + 2.0*k2 + 2.0*k3 + k4);

        // Update phase
        s->phase = carg(s->amplitude);
    }
}

// ═══════════════════════════════════════════════════════════════════════════
// MAIN SIMULATION
// ═══════════════════════════════════════════════════════════════════════════

int main() {
    srand(time(NULL));

    printf("═══════════════════════════════════════════════════════════════\n");
    printf("       CLEAN BIGG + FUDGE10 UNIFICATION (NO RESONANCE)\n");
    printf("  Using HDGL Analog 4096-bit Precision for Emergent Constants\n");
    printf("═══════════════════════════════════════════════════════════════\n\n");

    printf("System Configuration:\n");
    printf("  Instances: %d\n", MAX_INSTANCES);
    printf("  Slots per instance: %d\n", SLOTS_PER_INSTANCE);
    printf("  Total slots: %d\n", TOTAL_SLOTS);
    printf("  Mantissa bits: %d (4096-bit APA)\n", MANTISSA_BITS);
    printf("  Base: b = %d\n", BASE_B);
    printf("  φ = %.15f\n", PHI);
    printf("  √5 = %.15f\n\n", SQRT5);

    // Compute emergent constants
    printf("Computing Emergent Constants (from fudge10 fitted parameters):\n\n");

    ConstantParams h_params = get_planck_params();
    double h_emergent = compute_emergent_constant(h_params);
    printf("  Planck constant (h):\n");
    printf("    Parameters: n=%.6f, β=%.6f, r=%.1f, k=%.1f\n",
           h_params.n, h_params.beta, h_params.r, h_params.k);
    printf("    Fitted Ω = %.6e\n", h_params.omega);
    printf("    Emergent: h = %.6e J·s\n", h_emergent);
    printf("    CODATA:   h = %.6e J·s\n", CODATA_h);
    printf("    Error: %.2f%%\n\n", fabs(h_emergent - CODATA_h) / CODATA_h * 100.0);

    ConstantParams G_params = get_gravity_params();
    double G_emergent = compute_emergent_constant(G_params);
    printf("  Gravitational constant (G):\n");
    printf("    Parameters: n=%.6f, β=%.6f, r=%.1f, k=%.1f\n",
           G_params.n, G_params.beta, G_params.r, G_params.k);
    printf("    Fitted Ω = %.6e\n", G_params.omega);
    printf("    Emergent: G = %.6e m³/(kg·s²)\n", G_emergent);
    printf("    CODATA:   G = %.6e m³/(kg·s²)\n", CODATA_G);
    printf("    Error: %.2f%%\n\n", fabs(G_emergent - CODATA_G) / CODATA_G * 100.0);

    // BigG recursive scaling
    printf("BigG Φ-Recursive Scaling (cosmological):\n");
    double alpha = 3.0;  // Field tension decay rate
    double beta_bigG = 1.0;  // Structural decay rate
    double k_param = 1.0;
    double r0 = 1.0;

    printf("  G(z=0) = %.6e (static)\n", compute_G_recursive(0, alpha, beta_bigG, k_param, r0));
    printf("  G(z=1) = %.6e (at redshift 1)\n", compute_G_recursive(1, alpha, beta_bigG, k_param, r0));
    printf("  G(z=2) = %.6e (at redshift 2)\n\n", compute_G_recursive(2, alpha, beta_bigG, k_param, r0));

    // Initialize lattice
    printf("Initializing HDGL lattice...\n");
    init_lattice();

    // Evolution
    printf("Starting evolution (%d steps, dt=%.2e s)...\n\n", NUM_STEPS, DT);

    clock_t start = clock();

    for (int step = 0; step <= NUM_STEPS; step++) {
        double t = step * DT;

        if (step % PRINT_EVERY == 0) {
            // Sample first slot
            HDGLSlot *s0 = &lattice[0];
            double amp = cabs(s0->amplitude);
            double phase = carg(s0->amplitude);

            printf("Step %d/%d (t=%.6f s):\n", step, NUM_STEPS, t);
            printf("  Slot 0: |A| = %.6e, φ = %.3f rad\n", amp, phase);
            printf("          D_%d = %.6e\n", s0->slot_type, s0->Dn);
            printf("          r = %.3f, Ω = %.3f\n\n", s0->r, s0->local_omega);
        }

        rk4_step(t);
    }

    clock_t end = clock();
    double elapsed = (double)(end - start) / CLOCKS_PER_SEC;

    printf("═══════════════════════════════════════════════════════════════\n");
    printf("Evolution complete!\n");
    printf("Total time: %.2f seconds\n", elapsed);
    printf("Steps/second: %.1f\n", NUM_STEPS / elapsed);
    printf("═══════════════════════════════════════════════════════════════\n");

    return 0;
}
