bootloaderZ.zip (6.9 KB)
As everything is in alpha and we are dealing with Bootloaders, the chances of this breaking your machine are probable. Use at your own risk obeying copyright and you should probably go ahead and place this in a virtual machine isolated from anything important to you.
A Set of Hypervisor scripts / bootloaders capable of extreme precision, which also serve as our roadmap, considering implementation of base4096, and beyond, over time.
Version 2.1
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
#include <time.h>
// --- System Constants ---
#define PHI 1.6180339887
#define MAX_INSTANCES 8388608
#define SLOTS_PER_INSTANCE 4
#define MAX_SLOTS (MAX_INSTANCES * SLOTS_PER_INSTANCE)
#define CHUNK_SIZE 1048576 // 1M slots per chunk
#define MSB_MASK (1ULL << 63) // Mask for the Most Significant Bit of a uint64_t
// --- Future MPI and Base-4096 Constants (NEW) ---
#define BASE_4096_BPC 12 // Bits per Character (4096 = 2^12)
#define MPI_INITIAL_WORDS 1 // Initial allocation size for MPI structures
#define MPI_ZERO_WORD 0ULL // Canonical zero for MPI operations
// Fibonacci and prime tables
static const float fib_table[] = {1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987};
static const float prime_table[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53};
static const int fib_len = 16;
static const int prime_len = 16;
// Helper for generating normalized random double
double get_normalized_rand() {
return (double)rand() / RAND_MAX;
}
// Macro for generating 64-bit random seed (Placeholder for get_random_bytes in kernel)
#define GET_RANDOM_UINT64() (((uint64_t)rand() << 32) | rand())
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// FUTURE-PROOF MPI (Multi-Word Integer) and State Flags
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Multi-Word Integer (MPI) Structure for arbitrarily large metadata
typedef struct {
uint64_t *words; // Array of 64-bit words for the number
size_t num_words; // Number of words currently allocated
uint8_t sign; // 0: Positive, 1: Negative
} MPI;
// State Flags Definitions for Implied Precision
#define APA_FLAG_SIGN_NEG (1 << 0) // Mantissa is negative
#define APA_FLAG_IS_NAN (1 << 1) // Not a Number
#define APA_FLAG_GOI (1 << 2) // Gradual Overflow Infinity
#define APA_FLAG_GUZ (1 << 3) // Gradual Underflow Zero
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Slot4096: Arbitrary Precision Architecture (APA) Structure (FUTURE-PROOF)
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
// --- Core Precision Fields (Legacy kept for ease of use, but MPI is the future) ---
uint64_t *mantissa_words; // Multi-word array for high-precision mantissa
// FUTURE-PROOF FIELDS (Conceptual, for 4096^4096+ scaling)
MPI num_words_mantissa; // The COUNT of mantissa_words (Arbitrarily wide)
MPI exponent_mpi; // The exponent value (Arbitrarily wide)
// State and Base Control Fields
uint16_t exponent_base; // Base of the floating-point system (e.g., 2 or 4096)
uint32_t state_flags; // Flags for NaN, Sign, GOI, GUZ
MPI source_of_infinity; // Records magnitude for Gradual Overflow Infinity (GOI)
// LEGACY FIELDS (Used by current 4096-bit functional code)
size_t num_words; // Legacy Count of 64-bit words allocated
int64_t exponent; // Legacy Signed exponent (Base 2)
float base; // Dynamic base (φ-scaled)
int bits_mant; // Actual software-managed bit width (e.g., 4096)
int bits_exp; // Exponent bit width
} Slot4096;
// -----------------------------------------------------------------------------
// GLOBAL HIGH-PRECISION CONSTANT SLOTS (NEW)
// These slots will be computed to full 4096^4096+ precision by the MPI system.
// -----------------------------------------------------------------------------
static Slot4096 APA_CONST_PHI; // Target slot for full precision Golden Ratio
static Slot4096 APA_CONST_PI; // Target slot for full precision Pi
// Forward Declarations for APA Operations
void ap_normalize_legacy(Slot4096 *slot);
void ap_add_legacy(Slot4096 *A, const Slot4096 *B);
void ap_free(Slot4096 *slot);
void ap_copy(Slot4096 *dest, const Slot4096 *src);
double ap_to_double(const Slot4096 *slot);
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp);
void ap_shift_right_legacy(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount);
// Forward Declarations for new MPI/Future APA Operations (Conceptual)
// We replace the inline definitions with full signatures for the MPI API
// --- MPI Core Functions ---
void mpi_init(MPI *m, size_t initial_words);
void mpi_free(MPI *m);
void mpi_copy(MPI *dest, const MPI *src);
void mpi_resize(MPI *m, size_t new_words);
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign);
int mpi_compare(const MPI *A, const MPI *B);
void mpi_add(MPI *A, const MPI *B); // Add magnitude
void mpi_subtract(MPI *A, const MPI *B); // Subtract magnitude
// --- MPI Helper Functions ---
size_t mpi_get_effective_words(const MPI *m);
int mpi_count_leading_zeros(const MPI *m);
// --- Future APA Functions (MPI-based) ---
void ap_shift_right_mpi(uint64_t *mantissa_words, const MPI *num_words, const MPI *shift_amount);
void ap_add_mpi(Slot4096 *A, const Slot4096 *B);
// Wrappers to maintain the main API calls
void ap_add(Slot4096 *A, const Slot4096 *B);
void ap_normalize(Slot4096 *slot) { ap_normalize_legacy(slot); }
void ap_shift_right(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount) { ap_shift_right_legacy(mantissa_words, num_words, shift_amount); }
// -----------------------------------------------------------------------------
// CONCEPTUAL MPI FUNCTION IMPLEMENTATIONS (Placeholder for V3)
// -----------------------------------------------------------------------------
void mpi_init(MPI *m, size_t initial_words) {
m->words = calloc(initial_words, sizeof(uint64_t));
m->num_words = initial_words;
m->sign = 0;
}
void mpi_free(MPI *m) {
if (m->words) free(m->words);
m->words = NULL;
m->num_words = 0;
}
void mpi_copy(MPI *dest, const MPI *src) {
mpi_free(dest);
dest->num_words = src->num_words;
dest->words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (src->words && dest->words) {
memcpy(dest->words, src->words, src->num_words * sizeof(uint64_t));
}
dest->sign = src->sign;
}
// Minimal placeholder implementations for required API
void mpi_resize(MPI *m, size_t new_words) { /* TBD */ }
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign) { m->words[0] = value; m->sign = sign; }
int mpi_compare(const MPI *A, const MPI *B) { return 0; }
void mpi_add(MPI *A, const MPI *B) { /* TBD */ }
void mpi_subtract(MPI *A, const MPI *B) { /* TBD */ }
size_t mpi_get_effective_words(const MPI *m) { return m->num_words; }
int mpi_count_leading_zeros(const MPI *m) { return 64; }
void ap_shift_right_mpi(uint64_t *mantissa_words, const MPI *num_words, const MPI *shift_amount) { /* TBD */ }
void ap_add_mpi(Slot4096 *A, const Slot4096 *B) { /* TBD */ }
// -----------------------------------------------------------------------------
// APA UTILITY FUNCTIONS
// -----------------------------------------------------------------------------
// Initialize slot with dynamic precision and APA allocation (Updated for MPI and Base-4096)
Slot4096 slot_init_apa(int bits_mant, int bits_exp) {
Slot4096 slot = {0};
slot.bits_mant = bits_mant;
slot.bits_exp = bits_exp;
slot.num_words = (bits_mant + 63) / 64;
slot.mantissa_words = (uint64_t*)calloc(slot.num_words, sizeof(uint64_t));
// FUTURE-PROOF MPI INITIALIZATION
mpi_init(&slot.exponent_mpi, MPI_INITIAL_WORDS); // Use constant
mpi_init(&slot.num_words_mantissa, MPI_INITIAL_WORDS); // Use constant
mpi_init(&slot.source_of_infinity, MPI_INITIAL_WORDS); // Use constant
if (!slot.mantissa_words) {
fprintf(stderr, "Error: Failed to allocate multi-word mantissa.\n");
return slot;
}
if (slot.num_words > 0) {
slot.mantissa_words[0] = GET_RANDOM_UINT64();
slot.mantissa_words[0] |= MSB_MASK;
}
int64_t exp_range = 1LL << bits_exp;
int64_t exp_bias = 1LL << (bits_exp - 1);
slot.exponent = (rand() % exp_range) - exp_bias;
slot.base = PHI + get_normalized_rand() * 0.01;
// Set the target base for future MPI operations
slot.exponent_base = 4096;
// Synchronize Legacy with MPI (conceptual)
mpi_set_value(&slot.exponent_mpi, (uint64_t)slot.exponent, slot.exponent < 0 ? 1 : 0);
mpi_set_value(&slot.num_words_mantissa, (uint64_t)slot.num_words, 0);
return slot;
}
// Helper to free single APA slot's dynamic members (Updated for MPI)
void ap_free(Slot4096 *slot) {
if (slot) {
if (slot->mantissa_words) {
free(slot->mantissa_words);
slot->mantissa_words = NULL;
}
// FUTURE-PROOF MPI CLEANUP
mpi_free(&slot->exponent_mpi);
mpi_free(&slot->num_words_mantissa);
mpi_free(&slot->source_of_infinity);
slot->num_words = 0;
}
}
// Deep copy of APA slot (Updated for MPI)
void ap_copy(Slot4096 *dest, const Slot4096 *src) {
ap_free(dest);
*dest = *src; // Shallow copy of struct members
// Deep copy mantissa
dest->mantissa_words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (!dest->mantissa_words) {
fprintf(stderr, "Error: Failed deep copy allocation.\n");
dest->num_words = 0;
return;
}
memcpy(dest->mantissa_words, src->mantissa_words, src->num_words * sizeof(uint64_t));
// Deep copy MPI structs
mpi_copy(&dest->exponent_mpi, &src->exponent_mpi);
mpi_copy(&dest->num_words_mantissa, &src->num_words_mantissa);
mpi_copy(&dest->source_of_infinity, &src->source_of_infinity);
}
// Converts APA to double (Lossy, for display/recursion input)
double ap_to_double(const Slot4096 *slot) {
if (!slot || slot->num_words == 0 || !slot->mantissa_words) return 0.0;
double mantissa_double = (double)slot->mantissa_words[0] / (double)UINT64_MAX;
return mantissa_double * pow(2.0, (double)slot->exponent);
}
// Converts double to APA slot (Used for the increment_value)
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp) {
Slot4096 temp_slot = slot_init_apa(bits_mant, bits_exp);
Slot4096 *slot = (Slot4096*)malloc(sizeof(Slot4096));
if (!slot) { ap_free(&temp_slot); return NULL; }
*slot = temp_slot;
if (value == 0.0) return slot;
int exp_offset;
double mant_val = frexp(value, &exp_offset);
slot->mantissa_words[0] = (uint64_t)(mant_val * (double)UINT64_MAX);
slot->exponent = (int64_t)exp_offset;
// Synchronize Legacy with MPI (conceptual)
mpi_set_value(&slot->exponent_mpi, (uint64_t)slot->exponent, slot->exponent < 0 ? 1 : 0);
return slot;
}
/**
* LEGACY Multi-word right shift (kept for this version's functionality)
*/
void ap_shift_right_legacy(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount) {
if (shift_amount <= 0 || num_words == 0) return;
if (shift_amount >= (int64_t)num_words * 64) {
memset(mantissa_words, 0, num_words * sizeof(uint64_t));
return;
}
int64_t word_shift = shift_amount / 64;
int bit_shift = (int)(shift_amount % 64);
if (word_shift > 0) {
for (size_t i = 0; i < num_words; ++i) {
if ((int64_t)i + word_shift < (int64_t)num_words) {
mantissa_words[i + word_shift] = mantissa_words[i];
}
}
memset(mantissa_words, 0, word_shift * sizeof(uint64_t));
}
if (bit_shift > 0) {
int reverse_shift = 64 - bit_shift;
for (size_t i = num_words; i-- > 0; ) {
uint64_t lower_carry = 0;
if (i > 0) {
lower_carry = mantissa_words[i - 1] << reverse_shift;
}
mantissa_words[i] = (mantissa_words[i] >> bit_shift) | lower_carry;
}
}
}
// -----------------------------------------------------------------------------
// APA CORE ARITHMETIC FUNCTIONS (FUNCTIONAL WITH ALIGNMENT)
// -----------------------------------------------------------------------------
// Performs multi-word normalization to maintain canonical range [0.5, 1.0)
void ap_normalize_legacy(Slot4096 *slot) {
if (slot->num_words == 0) return;
// --- Shift Left (Underflow Correction: Mantissa < 0.5) ---
while (!(slot->mantissa_words[0] & MSB_MASK)) {
// FUTURE-PROOF: Should check for GUZ flag before breaking
if (slot->exponent <= -(1LL << (slot->bits_exp - 1))) {
slot->state_flags |= APA_FLAG_GUZ;
// Record magnitude for GUZ (conceptual)
// mpi_copy(&slot->source_of_infinity, &slot->exponent_mpi);
break;
}
uint64_t carry = 0;
for (size_t i = slot->num_words; i-- > 0; ) {
uint64_t next_carry = (slot->mantissa_words[i] & MSB_MASK) ? 1 : 0;
slot->mantissa_words[i] = (slot->mantissa_words[i] << 1) | carry;
carry = next_carry;
}
slot->exponent--;
}
// --- Shift Right (Cleanup) ---
if (slot->mantissa_words[0] == 0) {
slot->exponent = 0;
}
}
// LEGACY Addition with alignment (Called by ap_add wrapper)
void ap_add_legacy(Slot4096 *A, const Slot4096 *B) {
if (A->num_words != B->num_words) {
fprintf(stderr, "Error: APA addition failed due to unaligned word counts.\n");
return;
}
Slot4096 B_aligned;
ap_copy(&B_aligned, B);
// --- 1. Exponent Alignment (Legacy int64_t logic) ---
int64_t exp_diff = A->exponent - B_aligned.exponent;
if (exp_diff > 0) {
ap_shift_right(B_aligned.mantissa_words, B_aligned.num_words, exp_diff);
B_aligned.exponent = A->exponent;
} else if (exp_diff < 0) {
int64_t shift_amount = -exp_diff;
ap_shift_right(A->mantissa_words, A->num_words, shift_amount);
A->exponent = B_aligned.exponent;
}
// --- 2. Multi-Word Addition ---
uint64_t carry = 0;
size_t num_words = A->num_words;
for (size_t i = num_words; i-- > 0; ) {
uint64_t sum = A->mantissa_words[i] + B_aligned.mantissa_words[i] + carry;
carry = (sum < A->mantissa_words[i] || (sum == A->mantissa_words[i] && carry)) ? 1 : 0;
A->mantissa_words[i] = sum;
}
// --- 3. Final Carry Handling (Future-Proof GOI Check) ---
if (carry) {
if (A->exponent >= (1LL << (A->bits_exp - 1))) {
A->state_flags |= APA_FLAG_GOI;
// Record magnitude for GOI (conceptual)
// mpi_copy(&A->source_of_infinity, &A->exponent_mpi);
} else {
A->exponent += 1;
uint64_t next_carry = 0;
for (size_t i = 0; i < num_words; i++) {
uint64_t current_carry = A->mantissa_words[i] & 1;
A->mantissa_words[i] = (A->mantissa_words[i] >> 1) | next_carry;
next_carry = current_carry << 63;
}
}
}
// --- 4. Final Normalization and Sync (Legacy with MPI) ---
ap_normalize(A);
// The exponent sync must happen after normalization, as norm changes A->exponent
mpi_set_value(&A->exponent_mpi, (uint64_t)A->exponent, A->exponent < 0 ? 1 : 0);
ap_free(&B_aligned);
}
// Public wrapper for addition
void ap_add(Slot4096 *A, const Slot4096 *B) {
// This function will eventually call ap_add_mpi when MPI is fully implemented.
ap_add_legacy(A, B);
}
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// HDGL Lattice (Modified to use APA)
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
Slot4096 *slots;
size_t allocated;
} HDGLChunk;
typedef struct {
HDGLChunk **chunks;
int num_chunks;
int num_instances;
int slots_per_instance;
double omega;
double time;
} HDGLLattice;
// Initialize lattice
HDGLLattice* lattice_init(int num_instances, int slots_per_instance) {
HDGLLattice *lat = malloc(sizeof(HDGLLattice));
if (!lat) return NULL;
lat->num_instances = num_instances;
lat->slots_per_instance = slots_per_instance;
lat->omega = 0.0;
lat->time = 0.0;
int total_slots = num_instances * slots_per_instance;
lat->num_chunks = (total_slots + CHUNK_SIZE - 1) / CHUNK_SIZE;
lat->chunks = calloc(lat->num_chunks, sizeof(HDGLChunk*));
if (!lat->chunks) { free(lat); return NULL; }
return lat;
}
// Get chunk, allocate if needed
HDGLChunk* lattice_get_chunk(HDGLLattice *lat, int chunk_idx) {
if (chunk_idx >= lat->num_chunks) return NULL;
if (!lat->chunks[chunk_idx]) {
HDGLChunk *chunk = malloc(sizeof(HDGLChunk));
if (!chunk) return NULL;
chunk->allocated = CHUNK_SIZE;
chunk->slots = (Slot4096*)malloc(CHUNK_SIZE * sizeof(Slot4096));
if (!chunk->slots) { free(chunk); return NULL; }
for (int i = 0; i < CHUNK_SIZE; i++) {
int bits_mant = 4096 + (i % 8) * 64;
int bits_exp = 16 + (i % 8) * 2;
chunk->slots[i] = slot_init_apa(bits_mant, bits_exp);
}
lat->chunks[chunk_idx] = chunk;
}
return lat->chunks[chunk_idx];
}
// Get slot pointer
Slot4096* lattice_get_slot(HDGLLattice *lat, int idx) {
int chunk_idx = idx / CHUNK_SIZE;
int local_idx = idx % CHUNK_SIZE;
HDGLChunk *chunk = lattice_get_chunk(lat, chunk_idx);
if (!chunk) return NULL;
return &chunk->slots[local_idx];
}
// Prismatic recursion function (MUST use lossy double for calculation input)
double prismatic_recursion(HDGLLattice *lat, int idx, double val) {
double phi_harm = pow(PHI, (double)(idx % 16));
double fib_harm = fib_table[idx % fib_len];
double dyadic = (double)(1 << (idx % 16));
double prime_harm = prime_table[idx % prime_len];
double omega_val = 0.5 + 0.5 * sin(lat->time + idx * 0.01);
double r_dim = pow(val, (double)((idx % 7) + 1));
return sqrt(phi_harm * fib_harm * dyadic * prime_harm * omega_val) * r_dim;
}
// CPU step with APA processing
void lattice_step_cpu(HDGLLattice *lat, double tick) {
int total_slots = lat->num_instances * lat->slots_per_instance;
for (int i = 0; i < total_slots; i++) {
Slot4096 *slot = lattice_get_slot(lat, i);
if (!slot) continue;
// Check for Implied Precision State
if (slot->state_flags & (APA_FLAG_GOI | APA_FLAG_IS_NAN)) {
// Skip computation if state is implied infinity or NaN
continue;
}
double val = ap_to_double(slot);
double r = prismatic_recursion(lat, i, val);
double increment_value = pow(slot->base, (double)slot->exponent) * tick + 0.05 * r;
Slot4096 *increment_apa = ap_from_double(
increment_value, slot->bits_mant, slot->bits_exp
);
if (!increment_apa) continue;
ap_add(slot, increment_apa);
ap_free(increment_apa);
free(increment_apa);
}
lat->omega += 0.01 * tick;
lat->time += tick;
}
// Prismatic folding: double instance count
void lattice_fold(HDGLLattice *lat) {
int old_instances = lat->num_instances;
int new_instances = old_instances * 2;
if (new_instances > MAX_INSTANCES) return;
int old_total = old_instances * lat->slots_per_instance;
int new_total = new_instances * lat->slots_per_instance;
int old_chunks = lat->num_chunks;
int new_chunks = (new_total + CHUNK_SIZE - 1) / CHUNK_SIZE;
HDGLChunk **new_chunks_ptr = realloc(lat->chunks, new_chunks * sizeof(HDGLChunk*));
if (!new_chunks_ptr) {
fprintf(stderr, "Failed to allocate memory for folding\n");
return;
}
lat->chunks = new_chunks_ptr;
for (int i = old_chunks; i < new_chunks; i++) {
lat->chunks[i] = NULL;
}
for (int i = 0; i < old_total; i++) {
Slot4096 *old_slot = lattice_get_slot(lat, i);
Slot4096 *new_slot = lattice_get_slot(lat, old_total + i);
if (old_slot && new_slot) {
ap_copy(new_slot, old_slot);
double perturbation = fib_table[i % fib_len] * 0.01;
Slot4096 *pert_apa = ap_from_double(perturbation, new_slot->bits_mant, new_slot->bits_exp);
if (pert_apa) {
ap_add(new_slot, pert_apa);
ap_free(pert_apa);
free(pert_apa);
}
new_slot->base += get_normalized_rand() * 0.001;
}
}
lat->num_instances = new_instances;
lat->num_chunks = new_chunks;
}
// Free lattice: MUST handle freeing multi-word mantissa in every slot
void lattice_free(HDGLLattice *lat) {
if (!lat) return;
for (int i = 0; i < lat->num_chunks; i++) {
if (lat->chunks[i]) {
for (size_t j = 0; j < CHUNK_SIZE; j++) {
ap_free(&lat->chunks[i]->slots[j]);
}
free(lat->chunks[i]->slots);
free(lat->chunks[i]);
}
}
free(lat->chunks);
free(lat);
}
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Bootloader Integration and Main Demo
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// New function to initialize the high-precision constant slots
void init_apa_constants() {
// These calls allocate and initialize the slots to a base precision
// The mantissa_words will be zeroed out for a precise value to be loaded later.
APA_CONST_PHI = slot_init_apa(4096, 16);
APA_CONST_PI = slot_init_apa(4096, 16);
// FUTURE: Load the actual (4096^4096) values here using MPI.
// Placeholder: Set with double precision for demonstration
// ap_from_double will overwrite the initial random mantissa
Slot4096 *temp_phi = ap_from_double(1.6180339887, APA_CONST_PHI.bits_mant, APA_CONST_PHI.bits_exp);
ap_copy(&APA_CONST_PHI, temp_phi);
ap_free(temp_phi);
free(temp_phi);
Slot4096 *temp_pi = ap_from_double(3.1415926535, APA_CONST_PI.bits_mant, APA_CONST_PI.bits_exp);
ap_copy(&APA_CONST_PI, temp_pi);
ap_free(temp_pi);
free(temp_pi);
printf("[Bootloader] High-precision constant slots (PHI, PI) initialized.\n");
}
void bootloader_init_lattice(HDGLLattice *lat, int steps) {
printf("[Bootloader] Initializing HDGL lattice with FUTURE-PROOF APA V2.1...\n");
if (!lat) { printf("[Bootloader] ERROR: Lattice allocation failed.\n"); return; }
init_apa_constants(); // Initialize the global constants
printf("[Bootloader] %d instances, %d total slots\n",
lat->num_instances, lat->num_instances * lat->slots_per_instance);
for (int i = 0; i < steps; i++) {
lattice_step_cpu(lat, 0.01);
}
printf("[Bootloader] Lattice seeded with %d steps\n", steps);
printf("[Bootloader] Omega: %.6f, Time: %.6f\n", lat->omega, lat->time);
}
int main() {
srand(time(NULL));
printf("=== HDGL Unified System (Future-Proof APA V2.1: MPI API Defined) ===\n\n");
HDGLLattice *lat = lattice_init(4096, 4);
if (!lat) { fprintf(stderr, "Fatal: Could not initialize lattice.\n"); return 1; }
bootloader_init_lattice(lat, 50);
// Show high-precision constant values
printf("\nHigh-Precision Constants (Legacy Display):\n");
printf(" PHI: value=%.10e exp=%ld words=%zu\n", ap_to_double(&APA_CONST_PHI), APA_CONST_PHI.exponent, APA_CONST_PHI.num_words);
printf(" PI: value=%.10e exp=%ld words=%zu\n", ap_to_double(&APA_CONST_PI), APA_CONST_PI.exponent, APA_CONST_PI.num_words);
// Show some slot values (Display is lossy, but internal state is 4096-bit)
printf("\nFirst 8 slot values (after seeding):\n");
for (int i = 0; i < 8; i++) {
Slot4096 *slot = lattice_get_slot(lat, i);
if (slot) {
printf(" D%d: value=%.6e base=%.6f exp=%ld bits=%d/%d words=%zu flags=%d\n",
i+1, ap_to_double(slot), slot->base, slot->exponent,
slot->bits_mant, slot->bits_exp, slot->num_words, slot->state_flags);
}
}
printf("\nTesting prismatic folding...\n");
lattice_fold(lat);
printf(" After: %d instances\n", lat->num_instances);
// Clean up global constants
ap_free(&APA_CONST_PHI);
ap_free(&APA_CONST_PI);
lattice_free(lat);
printf("\n=== System is structurally ready for MPI scaling to 4096^4096 ===\n");
return 0;
}
Version 3.0
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
#include <time.h>
// --- System Constants ---
#define PHI 1.6180339887
#define MAX_INSTANCES 8388608
#define SLOTS_PER_INSTANCE 4
#define MAX_SLOTS (MAX_INSTANCES * SLOTS_PER_INSTANCE)
#define CHUNK_SIZE 1048576 // 1M slots per chunk
#define MSB_MASK (1ULL << 63) // Mask for the Most Significant Bit of a uint64_t
// --- Future MPI and Base-4096 Constants (V3 ADDITIONS) ---
#define BASE_4096_BPC 12 // Bits per Character (4096 = 2^12)
#define MPI_INITIAL_WORDS 1 // Initial allocation size for MPI structures
#define MPI_ZERO_WORD 0ULL // Canonical zero for MPI operations
// MPI Bit Extraction Helpers (NEW for V3)
#define MPI_GET_MSB(word) ((word) >> 63)
// Note: MPI_IS_NON_ZERO now relies on mpi_get_effective_words which is implemented below
// Fibonacci and prime tables
static const float fib_table[] = {1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987};
static const float prime_table[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53};
static const int fib_len = 16;
static const int prime_len = 16;
// Helper for generating normalized random double
double get_normalized_rand() {
return (double)rand() / RAND_MAX;
}
// Macro for generating 64-bit random seed (Placeholder for get_random_bytes in kernel)
#define GET_RANDOM_UINT64() (((uint64_t)rand() << 32) | rand())
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// FUTURE-PROOF MPI (Multi-Word Integer) and State Flags
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Multi-Word Integer (MPI) Structure for arbitrarily large metadata (Exponent, Word Count)
typedef struct {
uint64_t *words; // Array of 64-bit words for the number
size_t num_words; // Number of words currently allocated
uint8_t sign; // 0: Positive, 1: Negative (Magnitude is always stored in words)
} MPI;
// State Flags Definitions for Implied Precision
#define APA_FLAG_SIGN_NEG (1 << 0) // Mantissa is negative
#define APA_FLAG_IS_NAN (1 << 1) // Not a Number
#define APA_FLAG_GOI (1 << 2) // Gradual Overflow Infinity
#define APA_FLAG_GUZ (1 << 3) // Gradual Underflow Zero
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Slot4096: Arbitrary Precision Architecture (APA) Structure (FUTURE-PROOF)
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
// --- Core Precision Fields ---
uint64_t *mantissa_words; // Multi-word array for high-precision mantissa
// FUTURE-PROOF FIELDS (Conceptual, for 4096^4096+ scaling)
MPI num_words_mantissa; // The COUNT of mantissa_words (Arbitrarily wide, V3)
MPI exponent_mpi; // The exponent value (Arbitrarily wide, V3)
// State and Base Control Fields
uint16_t exponent_base; // Base of the floating-point system (e.g., 2 or 4096)
uint32_t state_flags; // Flags for NaN, Sign, GOI, GUZ
MPI source_of_infinity; // Records magnitude for Gradual Overflow Infinity (GOI)
// LEGACY FIELDS (Used by current 4096-bit functional code)
size_t num_words; // Legacy Count of 64-bit words allocated
int64_t exponent; // Legacy Signed exponent (Base 2)
float base; // Dynamic base (φ-scaled)
int bits_mant; // Actual software-managed bit width (e.g., 4096)
int bits_exp; // Exponent bit width
} Slot4096;
// -----------------------------------------------------------------------------
// GLOBAL HIGH-PRECISION CONSTANT SLOTS
// -----------------------------------------------------------------------------
static Slot4096 APA_CONST_PHI; // Target slot for full precision Golden Ratio
static Slot4096 APA_CONST_PI; // Target slot for full precision Pi
// Forward Declarations for APA Operations
void ap_normalize_legacy(Slot4096 *slot);
void ap_add_legacy(Slot4096 *A, const Slot4096 *B);
void ap_free(Slot4096 *slot);
void ap_copy(Slot4096 *dest, const Slot4096 *src);
double ap_to_double(const Slot4096 *slot);
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp);
void ap_shift_right_legacy(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount);
// Forward Declarations for new MPI/Future APA Operations
// --- MPI Core Functions ---
void mpi_init(MPI *m, size_t initial_words);
void mpi_free(MPI *m);
void mpi_copy(MPI *dest, const MPI *src);
void mpi_resize(MPI *m, size_t new_words);
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign);
int mpi_compare(const MPI *A, const MPI *B);
void mpi_add(MPI *A, const MPI *B); // Add magnitude
void mpi_subtract(MPI *A, const MPI *B); // Subtract magnitude
// --- MPI Helper Functions ---
size_t mpi_get_effective_words(const MPI *m);
int mpi_count_leading_zeros(const MPI *m);
// --- Future APA Functions (MPI-based) ---
void ap_shift_right_mpi(uint64_t *mantissa_words, const MPI *num_words, const MPI *shift_amount);
void ap_add_mpi(Slot4096 *A, const Slot4096 *B);
// Wrappers to maintain the main API calls
void ap_add(Slot4096 *A, const Slot4096 *B);
void ap_normalize(Slot4096 *slot) { ap_normalize_legacy(slot); }
void ap_shift_right(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount) { ap_shift_right_legacy(mantissa_words, num_words, shift_amount); }
// -----------------------------------------------------------------------------
// MPI FUNCTION IMPLEMENTATIONS (V3: ARITHMETIC CORE ENABLED)
// -----------------------------------------------------------------------------
void mpi_init(MPI *m, size_t initial_words) {
m->words = calloc(initial_words, sizeof(uint64_t));
m->num_words = initial_words;
m->sign = 0;
}
void mpi_free(MPI *m) {
if (m->words) free(m->words);
m->words = NULL;
m->num_words = 0;
}
void mpi_copy(MPI *dest, const MPI *src) {
mpi_free(dest);
dest->num_words = src->num_words;
dest->words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (src->words && dest->words) {
memcpy(dest->words, src->words, src->num_words * sizeof(uint64_t));
}
dest->sign = src->sign;
}
// Function to resize the MPI word array, zero-filling new words
void mpi_resize(MPI *m, size_t new_words) {
if (new_words == m->num_words) return;
if (new_words == 0) {
mpi_free(m);
return;
}
size_t old_words = m->num_words;
m->words = (uint64_t*)realloc(m->words, new_words * sizeof(uint64_t));
if (new_words > old_words) {
// Zero-fill new words if growing
memset(m->words + old_words, 0, (new_words - old_words) * sizeof(uint64_t));
}
m->num_words = new_words;
}
// Set MPI to a simple uint64_t value
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign) {
if (m->num_words < 1) mpi_resize(m, 1);
m->words[0] = value;
m->sign = sign;
// Zero out remaining words if they exist (ensuring canonical form)
if (m->num_words > 1) {
memset(m->words + 1, 0, (m->num_words - 1) * sizeof(uint64_t));
}
}
// Determines the highest index of a non-zero word
size_t mpi_get_effective_words(const MPI *m) {
if (!m->words) return 0;
size_t i = m->num_words;
while (i > 0 && m->words[i - 1] == 0) {
i--;
}
return i;
}
// Compares the magnitudes of A and B. Returns 1 if A > B, -1 if A < B, 0 if A = B.
int mpi_compare(const MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
if (len_A > len_B) return 1;
if (len_A < len_B) return -1;
// Lengths are equal, compare word-by-word from MSB to LSB
for (size_t i = len_A; i-- > 0; ) {
if (A->words[i] > B->words[i]) return 1;
if (A->words[i] < B->words[i]) return -1;
}
return 0; // Magnitudes are equal
}
// Multi-word addition of magnitudes (A = |A| + |B|).
void mpi_add(MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
size_t max_len = len_A > len_B ? len_A : len_B;
// Ensure A is large enough to hold the result (+1 for potential carry)
if (A->num_words < max_len + 1) {
mpi_resize(A, max_len + 1);
}
uint64_t carry = 0;
for (size_t i = 0; i < max_len; ++i) {
uint64_t word_A = (i < len_A) ? A->words[i] : 0ULL;
uint64_t word_B = (i < len_B) ? B->words[i] : 0ULL;
// 1. Add A and B
uint64_t sum = word_A + word_B;
// Check for overflow from A+B
uint64_t carry1 = (sum < word_A);
// 2. Add previous carry
sum += carry;
// Check for overflow from sum+carry
uint64_t carry2 = (sum < carry);
A->words[i] = sum;
carry = carry1 | carry2;
}
// 3. Handle final carry
if (carry) {
A->words[max_len] = carry;
} else if (A->num_words > max_len + 1) {
// Clear any excess words if no final carry
memset(A->words + max_len, 0, (A->num_words - max_len) * sizeof(uint64_t));
}
// A->sign remains unchanged in magnitude addition
}
// Multi-word subtraction of magnitudes (A = |A| - |B|). Assumes |A| >= |B|.
void mpi_subtract(MPI *A, const MPI *B) {
// Note: Caller must ensure |A| >= |B| and handle the sign swap if not.
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
if (len_A < len_B) {
fprintf(stderr, "Error: MPI Subtraction called with |A| < |B|. Magnitude result will be incorrect.\n");
return;
}
uint64_t borrow = 0;
for (size_t i = 0; i < len_A; ++i) {
uint64_t word_B = (i < len_B) ? B->words[i] : 0ULL;
uint64_t diff = A->words[i] - word_B - borrow;
// Check for borrow: if diff is greater than A->words[i] (underflow)
// or if diff is equal to A->words[i] and we had a borrow (meaning B[i] was 0 and we borrowed)
// A simpler check: if A[i] < B[i] or (A[i] == B[i] and borrow is 1)
borrow = (diff > A->words[i]) || (A->words[i] == diff && (word_B | borrow));
A->words[i] = diff;
}
// Ensure the resulting array is canonically sized (no leading zeros)
size_t new_len = mpi_get_effective_words(A);
if (new_len < A->num_words) {
mpi_resize(A, new_len > 0 ? new_len : 1);
}
// If result is zero, sign should be reset
if (new_len == 0) A->sign = 0;
}
int mpi_count_leading_zeros(const MPI *m) {
// TBD: Implementation requires an efficient CLZ instruction or lookup.
return 64;
}
// Placeholder implementations (TBD in future releases)
void ap_shift_right_mpi(uint64_t *mantissa_words, const MPI *num_words, const MPI *shift_amount) { /* TBD */ }
void ap_add_mpi(Slot4096 *A, const Slot4096 *B) { /* TBD */ }
// -----------------------------------------------------------------------------
// APA UTILITY FUNCTIONS
// -----------------------------------------------------------------------------
// Initialize slot with dynamic precision and APA allocation (Updated for MPI and Base-4096)
Slot4096 slot_init_apa(int bits_mant, int bits_exp) {
Slot4096 slot = {0};
slot.bits_mant = bits_mant;
slot.bits_exp = bits_exp;
slot.num_words = (bits_mant + 63) / 64;
slot.mantissa_words = (uint64_t*)calloc(slot.num_words, sizeof(uint64_t));
// FUTURE-PROOF MPI INITIALIZATION (V3: Functional MPI used for metadata)
mpi_init(&slot.exponent_mpi, MPI_INITIAL_WORDS);
mpi_init(&slot.num_words_mantissa, MPI_INITIAL_WORDS);
mpi_init(&slot.source_of_infinity, MPI_INITIAL_WORDS);
if (!slot.mantissa_words) {
fprintf(stderr, "Error: Failed to allocate multi-word mantissa.\n");
return slot;
}
if (slot.num_words > 0) {
slot.mantissa_words[0] = GET_RANDOM_UINT64();
slot.mantissa_words[0] |= MSB_MASK;
}
int64_t exp_range = 1LL << bits_exp;
int64_t exp_bias = 1LL << (bits_exp - 1);
slot.exponent = (rand() % exp_range) - exp_bias;
slot.base = PHI + get_normalized_rand() * 0.01;
// Set the target base for future MPI operations
slot.exponent_base = 4096;
// Synchronize Legacy with MPI (conceptual)
mpi_set_value(&slot.exponent_mpi, (uint64_t)llabs(slot.exponent), slot.exponent < 0 ? 1 : 0);
mpi_set_value(&slot.num_words_mantissa, (uint64_t)slot.num_words, 0);
return slot;
}
// Helper to free single APA slot's dynamic members (Updated for MPI)
void ap_free(Slot4096 *slot) {
if (slot) {
if (slot->mantissa_words) {
free(slot->mantissa_words);
slot->mantissa_words = NULL;
}
// FUTURE-PROOF MPI CLEANUP
mpi_free(&slot->exponent_mpi);
mpi_free(&slot->num_words_mantissa);
mpi_free(&slot->source_of_infinity);
slot->num_words = 0;
}
}
// Deep copy of APA slot (Updated for MPI)
void ap_copy(Slot4096 *dest, const Slot4096 *src) {
ap_free(dest);
*dest = *src; // Shallow copy of struct members
// Deep copy mantissa
dest->mantissa_words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (!dest->mantissa_words) {
fprintf(stderr, "Error: Failed deep copy allocation.\n");
dest->num_words = 0;
return;
}
memcpy(dest->mantissa_words, src->mantissa_words, src->num_words * sizeof(uint64_t));
// Deep copy MPI structs
mpi_copy(&dest->exponent_mpi, &src->exponent_mpi);
mpi_copy(&dest->num_words_mantissa, &src->num_words_mantissa);
mpi_copy(&dest->source_of_infinity, &src->source_of_infinity);
}
// Converts APA to double (Lossy, for display/recursion input)
double ap_to_double(const Slot4096 *slot) {
if (!slot || slot->num_words == 0 || !slot->mantissa_words) return 0.0;
double mantissa_double = (double)slot->mantissa_words[0] / (double)UINT64_MAX;
return mantissa_double * pow(2.0, (double)slot->exponent);
}
// Converts double to APA slot (Used for the increment_value)
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp) {
Slot4096 temp_slot = slot_init_apa(bits_mant, bits_exp);
Slot4096 *slot = (Slot4096*)malloc(sizeof(Slot4096));
if (!slot) { ap_free(&temp_slot); return NULL; }
*slot = temp_slot;
if (value == 0.0) return slot;
int exp_offset;
double mant_val = frexp(value, &exp_offset);
slot->mantissa_words[0] = (uint64_t)(mant_val * (double)UINT64_MAX);
slot->exponent = (int64_t)exp_offset;
// Synchronize Legacy with MPI (conceptual)
mpi_set_value(&slot->exponent_mpi, (uint64_t)llabs(slot->exponent), slot->exponent < 0 ? 1 : 0);
return slot;
}
/**
* LEGACY Multi-word right shift (kept for this version's functionality)
*/
void ap_shift_right_legacy(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount) {
if (shift_amount <= 0 || num_words == 0) return;
if (shift_amount >= (int64_t)num_words * 64) {
memset(mantissa_words, 0, num_words * sizeof(uint64_t));
return;
}
int64_t word_shift = shift_amount / 64;
int bit_shift = (int)(shift_amount % 64);
if (word_shift > 0) {
// Shift words right by word_shift positions
for (size_t i = num_words; i-- > word_shift; ) {
mantissa_words[i] = mantissa_words[i - word_shift];
}
// Zero out the lowest 'word_shift' words
memset(mantissa_words, 0, word_shift * sizeof(uint64_t));
}
if (bit_shift > 0) {
int reverse_shift = 64 - bit_shift;
for (size_t i = 0; i < num_words; ++i) {
uint64_t upper_carry = 0;
if (i < num_words - 1) {
upper_carry = mantissa_words[i + 1] << reverse_shift;
}
mantissa_words[i] = (mantissa_words[i] >> bit_shift) | upper_carry;
}
}
}
// -----------------------------------------------------------------------------
// APA CORE ARITHMETIC FUNCTIONS (FUNCTIONAL WITH ALIGNMENT)
// -----------------------------------------------------------------------------
// Performs multi-word normalization to maintain canonical range [0.5, 1.0)
void ap_normalize_legacy(Slot4096 *slot) {
if (slot->num_words == 0) return;
// --- Shift Left (Underflow Correction: Mantissa < 0.5) ---
while (!(slot->mantissa_words[0] & MSB_MASK)) {
// FUTURE-PROOF: Should check for GUZ flag before breaking
if (slot->exponent <= -(1LL << (slot->bits_exp - 1))) {
slot->state_flags |= APA_FLAG_GUZ;
// Record magnitude for GUZ (conceptual)
break;
}
uint64_t carry = 0;
for (size_t i = slot->num_words; i-- > 0; ) {
uint64_t next_carry = (slot->mantissa_words[i] & MSB_MASK) ? 1 : 0;
slot->mantissa_words[i] = (slot->mantissa_words[i] << 1) | carry;
carry = next_carry;
}
slot->exponent--;
}
// --- Shift Right (Cleanup: Should not be needed if addition/multiplication are correct) ---
// If the MSB is set, but the resulting value is greater than 1.0, the mantissa must be shifted right.
// However, the canonical range for IEEE floats is [1.0, 2.0). Since we are using
// a sign-magnitude fixed-point representation scaled by an exponent, we enforce [0.5, 1.0)
// where the MSB is always 1 (and implicitly dropped in IEEE). Here, we keep the MSB 1.
if (slot->mantissa_words[0] == 0) {
slot->exponent = 0;
}
// The exponent sync must happen after normalization, as norm changes A->exponent
mpi_set_value(&slot->exponent_mpi, (uint64_t)llabs(slot->exponent), slot->exponent < 0 ? 1 : 0);
}
// LEGACY Addition with alignment (Called by ap_add wrapper)
void ap_add_legacy(Slot4096 *A, const Slot4096 *B) {
if (A->num_words != B->num_words) {
fprintf(stderr, "Error: APA addition failed due to unaligned word counts.\n");
return;
}
Slot4096 B_aligned;
ap_copy(&B_aligned, B);
// --- 1. Exponent Alignment (Legacy int64_t logic) ---
int64_t exp_diff = A->exponent - B_aligned.exponent;
if (exp_diff > 0) {
ap_shift_right(B_aligned.mantissa_words, B_aligned.num_words, exp_diff);
B_aligned.exponent = A->exponent;
} else if (exp_diff < 0) {
int64_t shift_amount = -exp_diff;
ap_shift_right(A->mantissa_words, A->num_words, shift_amount);
A->exponent = B_aligned.exponent;
}
// --- 2. Multi-Word Addition ---
uint64_t carry = 0;
size_t num_words = A->num_words;
for (size_t i = num_words; i-- > 0; ) {
// Use full 128-bit addition if available, but for now use 64-bit carry check
uint64_t sum = A->mantissa_words[i] + B_aligned.mantissa_words[i] + carry;
// Check for carry: if sum wraps around or if sum equals A[i] but a carry was added
// carry = (sum < A->mantissa_words[i] || (sum == A->mantissa_words[i] && carry)) ? 1 : 0;
// Simpler, more robust carry check (checking if sum is less than the larger operand)
carry = (sum < A->mantissa_words[i]);
if (sum == A->mantissa_words[i]) carry |= (B_aligned.mantissa_words[i] != 0 && carry); // If A+B overflowed, or A+carry overflowed
A->mantissa_words[i] = sum;
}
// --- 3. Final Carry Handling (Renormalization) ---
if (carry) {
// If there's a final carry, the result is >= 2.0 * 2^exp.
// We must right-shift 1 bit and increment the exponent to renormalize to [0.5, 1.0)
if (A->exponent >= (1LL << (A->bits_exp - 1))) {
A->state_flags |= APA_FLAG_GOI;
// Record magnitude for GOI (conceptual)
} else {
A->exponent += 1;
// Right shift all words by 1 bit, propagating carry down
uint64_t next_carry = 0;
for (size_t i = A->num_words; i-- > 0; ) {
uint64_t current_carry_bit = A->mantissa_words[i] & 1;
A->mantissa_words[i] = (A->mantissa_words[i] >> 1) | next_carry;
next_carry = current_carry_bit << 63;
}
}
}
// --- 4. Final Normalization and Sync (Legacy with MPI) ---
ap_normalize(A);
ap_free(&B_aligned);
}
// Public wrapper for addition
void ap_add(Slot4096 *A, const Slot4096 *B) {
// V3: Still uses legacy. This will call ap_add_mpi in a future release.
ap_add_legacy(A, B);
}
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// HDGL Lattice (Modified to use APA)
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
Slot4096 *slots;
size_t allocated;
} HDGLChunk;
typedef struct {
HDGLChunk **chunks;
int num_chunks;
int num_instances;
int slots_per_instance;
double omega;
double time;
} HDGLLattice;
// Initialize lattice
HDGLLattice* lattice_init(int num_instances, int slots_per_instance) {
HDGLLattice *lat = malloc(sizeof(HDGLLattice));
if (!lat) return NULL;
lat->num_instances = num_instances;
lat->slots_per_instance = slots_per_instance;
lat->omega = 0.0;
lat->time = 0.0;
int total_slots = num_instances * slots_per_instance;
lat->num_chunks = (total_slots + CHUNK_SIZE - 1) / CHUNK_SIZE;
lat->chunks = calloc(lat->num_chunks, sizeof(HDGLChunk*));
if (!lat->chunks) { free(lat); return NULL; }
return lat;
}
// Get chunk, allocate if needed
HDGLChunk* lattice_get_chunk(HDGLLattice *lat, int chunk_idx) {
if (chunk_idx >= lat->num_chunks) return NULL;
if (!lat->chunks[chunk_idx]) {
HDGLChunk *chunk = malloc(sizeof(HDGLChunk));
if (!chunk) return NULL;
chunk->allocated = CHUNK_SIZE;
chunk->slots = (Slot4096*)malloc(CHUNK_SIZE * sizeof(Slot4096));
if (!chunk->slots) { free(chunk); return NULL; }
for (int i = 0; i < CHUNK_SIZE; i++) {
// Dynamic precision allocation: 4096 bits minimum, up to 4576 bits
int bits_mant = 4096 + (i % 8) * 64;
int bits_exp = 16 + (i % 8) * 2;
chunk->slots[i] = slot_init_apa(bits_mant, bits_exp);
}
lat->chunks[chunk_idx] = chunk;
}
return lat->chunks[chunk_idx];
}
// Get slot pointer
Slot4096* lattice_get_slot(HDGLLattice *lat, int idx) {
int chunk_idx = idx / CHUNK_SIZE;
int local_idx = idx % CHUNK_SIZE;
HDGLChunk *chunk = lattice_get_chunk(lat, chunk_idx);
if (!chunk) return NULL;
return &chunk->slots[local_idx];
}
// Prismatic recursion function (MUST use lossy double for calculation input)
double prismatic_recursion(HDGLLattice *lat, int idx, double val) {
double phi_harm = pow(PHI, (double)(idx % 16));
double fib_harm = fib_table[idx % fib_len];
double dyadic = (double)(1 << (idx % 16));
double prime_harm = prime_table[idx % prime_len];
double omega_val = 0.5 + 0.5 * sin(lat->time + idx * 0.01);
double r_dim = pow(val, (double)((idx % 7) + 1));
return sqrt(phi_harm * fib_harm * dyadic * prime_harm * omega_val) * r_dim;
}
// CPU step with APA processing
void lattice_step_cpu(HDGLLattice *lat, double tick) {
int total_slots = lat->num_instances * lat->slots_per_instance;
for (int i = 0; i < total_slots; i++) {
Slot4096 *slot = lattice_get_slot(lat, i);
if (!slot) continue;
// Check for Implied Precision State
if (slot->state_flags & (APA_FLAG_GOI | APA_FLAG_IS_NAN)) {
// Skip computation if state is implied infinity or NaN
continue;
}
double val = ap_to_double(slot);
double r = prismatic_recursion(lat, i, val);
double increment_value = pow(slot->base, (double)slot->exponent) * tick + 0.05 * r;
Slot4096 *increment_apa = ap_from_double(
increment_value, slot->bits_mant, slot->bits_exp
);
if (!increment_apa) continue;
ap_add(slot, increment_apa);
ap_free(increment_apa);
free(increment_apa);
}
lat->omega += 0.01 * tick;
lat->time += tick;
}
// Prismatic folding: double instance count
void lattice_fold(HDGLLattice *lat) {
int old_instances = lat->num_instances;
int new_instances = old_instances * 2;
if (new_instances > MAX_INSTANCES) return;
int old_total = old_instances * lat->slots_per_instance;
int new_total = new_instances * lat->slots_per_instance;
int old_chunks = lat->num_chunks;
int new_chunks = (new_total + CHUNK_SIZE - 1) / CHUNK_SIZE;
HDGLChunk **new_chunks_ptr = realloc(lat->chunks, new_chunks * sizeof(HDGLChunk*));
if (!new_chunks_ptr) {
fprintf(stderr, "Failed to allocate memory for folding\n");
return;
}
lat->chunks = new_chunks_ptr;
for (int i = old_chunks; i < new_chunks; i++) {
lat->chunks[i] = NULL;
}
for (int i = 0; i < old_total; i++) {
Slot4096 *old_slot = lattice_get_slot(lat, i);
Slot4096 *new_slot = lattice_get_slot(lat, old_total + i);
if (old_slot && new_slot) {
ap_copy(new_slot, old_slot);
double perturbation = fib_table[i % fib_len] * 0.01;
Slot4096 *pert_apa = ap_from_double(perturbation, new_slot->bits_mant, new_slot->bits_exp);
if (pert_apa) {
ap_add(new_slot, pert_apa);
ap_free(pert_apa);
free(pert_apa);
}
new_slot->base += get_normalized_rand() * 0.001;
}
}
lat->num_instances = new_instances;
lat->num_chunks = new_chunks;
}
// Free lattice: MUST handle freeing multi-word mantissa in every slot
void lattice_free(HDGLLattice *lat) {
if (!lat) return;
for (int i = 0; i < lat->num_chunks; i++) {
if (lat->chunks[i]) {
for (size_t j = 0; j < CHUNK_SIZE; j++) {
ap_free(&lat->chunks[i]->slots[j]);
}
free(lat->chunks[i]->slots);
free(lat->chunks[i]);
}
}
free(lat->chunks);
free(lat);
}
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Bootloader Integration and Main Demo
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// New function to initialize the high-precision constant slots
void init_apa_constants() {
// These calls allocate and initialize the slots to a base precision
APA_CONST_PHI = slot_init_apa(4096, 16);
APA_CONST_PI = slot_init_apa(4096, 16);
// Placeholder: Set with double precision for demonstration
Slot4096 *temp_phi = ap_from_double(1.6180339887, APA_CONST_PHI.bits_mant, APA_CONST_PHI.bits_exp);
ap_copy(&APA_CONST_PHI, temp_phi);
ap_free(temp_phi);
free(temp_phi);
Slot4096 *temp_pi = ap_from_double(3.1415926535, APA_CONST_PI.bits_mant, APA_CONST_PI.bits_exp);
ap_copy(&APA_CONST_PI, temp_pi);
ap_free(temp_pi);
free(temp_pi);
printf("[Bootloader] High-precision constant slots (PHI, PI) initialized.\n");
}
void bootloader_init_lattice(HDGLLattice *lat, int steps) {
printf("[Bootloader] Initializing HDGL lattice with FUTURE-PROOF APA V3.0...\n");
if (!lat) { printf("[Bootloader] ERROR: Lattice allocation failed.\n"); return; }
init_apa_constants(); // Initialize the global constants
printf("[Bootloader] %d instances, %d total slots\n",
lat->num_instances, lat->num_instances * lat->slots_per_instance);
for (int i = 0; i < steps; i++) {
lattice_step_cpu(lat, 0.01);
}
printf("[Bootloader] Lattice seeded with %d steps\n", steps);
printf("[Bootloader] Omega: %.6f, Time: %.6f\n", lat->omega, lat->time);
}
int main() {
srand(time(NULL));
printf("=== HDGL Unified System (Future-Proof APA V3.0: Functional MPI Core) ===\n\n");
HDGLLattice *lat = lattice_init(4096, 4);
if (!lat) { fprintf(stderr, "Fatal: Could not initialize lattice.\n"); return 1; }
bootloader_init_lattice(lat, 50);
// Test the new MPI core implementations (conceptual)
MPI m1, m2;
mpi_init(&m1, 2);
mpi_init(&m2, 1);
mpi_set_value(&m1, 0xFFFFFFFFFFFFFFFEULL, 0); // 18446744073709551614 (2^64 - 2)
mpi_set_value(&m2, 0x0000000000000003ULL, 0); // 3
mpi_add(&m1, &m2); // Should result in 0xFFFFFFFFFFFFFFFF (word 0) and 1 (carry to word 1)
printf("\n--- MPI Core Test (V3) ---\n");
printf("Test Add: (2^64 - 2) + 3\n");
printf("Result Words: %zu. Effective Words: %zu\n", m1.num_words, mpi_get_effective_words(&m1));
printf("Word 0: 0x%llX (Expected FFFFFFFFFFFFFFFF)\n", m1.words[0]);
printf("Word 1: 0x%llX (Expected 0000000000000001)\n", m1.words[1]);
// Clean up MPI test
mpi_free(&m1);
mpi_free(&m2);
// Show high-precision constant values
printf("\nHigh-Precision Constants (Legacy Display):\n");
printf(" PHI: value=%.10e exp=%ld words=%zu\n", ap_to_double(&APA_CONST_PHI), APA_CONST_PHI.exponent, APA_CONST_PHI.num_words);
printf(" PI: value=%.10e exp=%ld words=%zu\n", ap_to_double(&APA_CONST_PI), APA_CONST_PI.exponent, APA_CONST_PI.num_words);
// Show some slot values (Display is lossy, but internal state is 4096-bit)
printf("\nFirst 8 slot values (after seeding):\n");
for (int i = 0; i < 8; i++) {
Slot4096 *slot = lattice_get_slot(lat, i);
if (slot) {
printf(" D%d: value=%.6e base=%.6f exp=%ld bits=%d/%d words=%zu flags=%d\n",
i+1, ap_to_double(slot), slot->base, slot->exponent,
slot->bits_mant, slot->bits_exp, slot->num_words, slot->state_flags);
}
}
printf("\nTesting prismatic folding...\n");
lattice_fold(lat);
printf(" After: %d instances\n", lat->num_instances);
// Clean up global constants
ap_free(&APA_CONST_PHI);
ap_free(&APA_CONST_PI);
lattice_free(lat);
printf("\n=== System is architecturally ready for full 4096^4096 calculations in V4 ===\n");
return 0;
}
Version 4.0
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
#include <time.h>
// --- System Constants ---
#define PHI 1.6180339887
#define MAX_INSTANCES 8388608
#define SLOTS_PER_INSTANCE 4
#define MAX_SLOTS (MAX_INSTANCES * SLOTS_PER_INSTANCE)
#define CHUNK_SIZE 1048576 // 1M slots per chunk
#define MSB_MASK (1ULL << 63) // Mask for the Most Significant Bit of a uint64_t
// --- Future MPI and Base-4096 Constants (V3 ADDITIONS) ---
#define BASE_4096_BPC 12 // Bits per Character (4096 = 2^12)
#define MPI_INITIAL_WORDS 1 // Initial allocation size for MPI structures
#define MPI_ZERO_WORD 0ULL // Canonical zero for MPI operations
// MPI Bit Extraction Helpers
#define MPI_GET_MSB(word) ((word) >> 63)
// Fibonacci and prime tables
static const float fib_table[] = {1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987};
static const float prime_table[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53};
static const int fib_len = 16;
static const int prime_len = 16;
// Helper for generating normalized random double
double get_normalized_rand() {
return (double)rand() / RAND_MAX;
}
// Macro for generating 64-bit random seed (Placeholder for get_random_bytes in kernel)
#define GET_RANDOM_UINT64() (((uint64_t)rand() << 32) | rand())
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// FUTURE-PROOF MPI (Multi-Word Integer) and State Flags
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Multi-Word Integer (MPI) Structure for arbitrarily large metadata (Exponent, Word Count)
typedef struct {
uint64_t *words; // Array of 64-bit words for the number
size_t num_words; // Number of words currently allocated
uint8_t sign; // 0: Positive, 1: Negative (Magnitude is always stored in words)
} MPI;
// State Flags Definitions for Implied Precision
#define APA_FLAG_SIGN_NEG (1 << 0) // Mantissa is negative
#define APA_FLAG_IS_NAN (1 << 1) // Not a Number
#define APA_FLAG_GOI (1 << 2) // Gradual Overflow Infinity
#define APA_FLAG_GUZ (1 << 3) // Gradual Underflow Zero
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Slot4096: Arbitrary Precision Architecture (APA) Structure (FUTURE-PROOF)
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
// --- Core Precision Fields ---
uint64_t *mantissa_words; // Multi-word array for high-precision mantissa
// FUTURE-PROOF FIELDS (Conceptual, for 4096^4096+ scaling)
MPI num_words_mantissa; // The COUNT of mantissa_words (Arbitrarily wide, V3)
MPI exponent_mpi; // The exponent value (Arbitrarily wide, V3)
// State and Base Control Fields
uint16_t exponent_base; // Base of the floating-point system (e.g., 2 or 4096)
uint32_t state_flags; // Flags for NaN, Sign, GOI, GUZ
MPI source_of_infinity; // Records magnitude for Gradual Overflow Infinity (GOI)
// LEGACY FIELDS (Kept for compatibility with old I/O and shift amount calculations)
size_t num_words; // Legacy Count of 64-bit words allocated
int64_t exponent; // Legacy Signed exponent (Base 2)
float base; // Dynamic base (φ-scaled)
int bits_mant; // Actual software-managed bit width (e.g., 4096)
int bits_exp; // Exponent bit width
} Slot4096;
// -----------------------------------------------------------------------------
// GLOBAL HIGH-PRECISION CONSTANT SLOTS
// -----------------------------------------------------------------------------
static Slot4096 APA_CONST_PHI; // Target slot for full precision Golden Ratio
static Slot4096 APA_CONST_PI; // Target slot for full precision Pi
// Forward Declarations for APA Operations
void ap_normalize(Slot4096 *slot); // Renormalized from legacy to public API
void ap_free(Slot4096 *slot);
void ap_copy(Slot4096 *dest, const Slot4096 *src);
double ap_to_double(const Slot4096 *slot);
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp);
void ap_shift_right(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount); // Renormalized from legacy to public API
// --- Mantissa Magnitude Operations (V4: New for sign-magnitude control) ---
int apa_mantissa_compare_magnitude(const uint64_t *A, const uint64_t *B, size_t num_words);
uint64_t apa_mantissa_add_magnitude(uint64_t *A, const uint64_t *B, size_t num_words);
void apa_mantissa_subtract_magnitude(uint64_t *A, const uint64_t *B, size_t num_words);
void ap_add(Slot4096 *A, const Slot4096 *B); // Full sign-magnitude V4 implementation
// --- MPI Core Functions (V3 Functional) ---
void mpi_init(MPI *m, size_t initial_words);
void mpi_free(MPI *m);
void mpi_copy(MPI *dest, const MPI *src);
void mpi_resize(MPI *m, size_t new_words);
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign);
int mpi_compare(const MPI *A, const MPI *B);
void mpi_add(MPI *A, const MPI *B); // Add magnitude
void mpi_subtract(MPI *A, const MPI *B); // Subtract magnitude
size_t mpi_get_effective_words(const MPI *m);
int mpi_count_leading_zeros(const MPI *m);
// Placeholder implementations (TBD in future releases)
void ap_shift_right_mpi(uint64_t *mantissa_words, const MPI *num_words, const MPI *shift_amount) { /* TBD */ }
void ap_add_mpi(Slot4096 *A, const Slot4096 *B) { /* TBD */ }
// -----------------------------------------------------------------------------
// MPI FUNCTION IMPLEMENTATIONS (V3 Functional Core)
// -----------------------------------------------------------------------------
void mpi_init(MPI *m, size_t initial_words) {
m->words = calloc(initial_words, sizeof(uint64_t));
m->num_words = initial_words;
m->sign = 0;
}
void mpi_free(MPI *m) {
if (m->words) free(m->words);
m->words = NULL;
m->num_words = 0;
}
void mpi_copy(MPI *dest, const MPI *src) {
mpi_free(dest);
dest->num_words = src->num_words;
dest->words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (src->words && dest->words) {
memcpy(dest->words, src->words, src->num_words * sizeof(uint64_t));
}
dest->sign = src->sign;
}
void mpi_resize(MPI *m, size_t new_words) {
if (new_words == m->num_words) return;
if (new_words == 0) { mpi_free(m); return; }
size_t old_words = m->num_words;
m->words = (uint64_t*)realloc(m->words, new_words * sizeof(uint64_t));
if (new_words > old_words) {
memset(m->words + old_words, 0, (new_words - old_words) * sizeof(uint64_t));
}
m->num_words = new_words;
}
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign) {
if (m->num_words < 1) mpi_resize(m, 1);
m->words[0] = value;
m->sign = sign;
if (m->num_words > 1) {
memset(m->words + 1, 0, (m->num_words - 1) * sizeof(uint64_t));
}
}
size_t mpi_get_effective_words(const MPI *m) {
if (!m->words) return 0;
size_t i = m->num_words;
while (i > 0 && m->words[i - 1] == 0) {
i--;
}
return i;
}
int mpi_compare(const MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
if (len_A > len_B) return 1;
if (len_A < len_B) return -1;
for (size_t i = len_A; i-- > 0; ) {
if (A->words[i] > B->words[i]) return 1;
if (A->words[i] < B->words[i]) return -1;
}
return 0;
}
void mpi_add(MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
size_t max_len = len_A > len_B ? len_A : len_B;
if (A->num_words < max_len + 1) {
mpi_resize(A, max_len + 1);
}
uint64_t carry = 0;
for (size_t i = 0; i < max_len; ++i) {
uint64_t word_A = (i < len_A) ? A->words[i] : 0ULL;
uint64_t word_B = (i < len_B) ? B->words[i] : 0ULL;
uint64_t sum = word_A + word_B;
uint64_t carry1 = (sum < word_A);
sum += carry;
uint64_t carry2 = (sum < carry);
A->words[i] = sum;
carry = carry1 | carry2;
}
if (carry) {
A->words[max_len] = carry;
} else if (A->num_words > max_len + 1) {
memset(A->words + max_len, 0, (A->num_words - max_len) * sizeof(uint64_t));
}
}
void mpi_subtract(MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
if (len_A < len_B) { return; } // Should not happen if mpi_compare is used first
uint64_t borrow = 0;
for (size_t i = 0; i < len_A; ++i) {
uint64_t word_B = (i < len_B) ? B->words[i] : 0ULL;
uint64_t diff = A->words[i] - word_B - borrow;
borrow = (diff > A->words[i]) || (A->words[i] == diff && (word_B | borrow));
A->words[i] = diff;
}
size_t new_len = mpi_get_effective_words(A);
if (new_len < A->num_words) {
// Shrink the array to canonical size (or 1 if it's zero)
mpi_resize(A, new_len > 0 ? new_len : 1);
}
if (new_len == 0) mpi_set_value(A, 0ULL, 0); // Canonical zero
}
int mpi_count_leading_zeros(const MPI *m) { return 64; } // Placeholder
// -----------------------------------------------------------------------------
// APA UTILITY FUNCTIONS (V4: Cleanup and Mantissa Logic)
// -----------------------------------------------------------------------------
// Fixed-width multi-word magnitude comparison (V4)
int apa_mantissa_compare_magnitude(const uint64_t *A, const uint64_t *B, size_t num_words) {
for (size_t i = num_words; i-- > 0; ) {
if (A[i] > B[i]) return 1;
if (A[i] < B[i]) return -1;
}
return 0; // Equal
}
// Fixed-width multi-word magnitude addition (V4)
// Returns the final carry out (0 or 1)
uint64_t apa_mantissa_add_magnitude(uint64_t *A, const uint64_t *B, size_t num_words) {
uint64_t carry = 0;
for (size_t i = num_words; i-- > 0; ) {
uint64_t sum = A[i] + B[i];
uint64_t carry1 = (sum < A[i]);
sum += carry;
uint64_t carry2 = (sum < carry);
A[i] = sum;
carry = carry1 | carry2;
}
return carry;
}
// Fixed-width multi-word magnitude subtraction (A = A - B). Assumes |A| >= |B|. (V4)
void apa_mantissa_subtract_magnitude(uint64_t *A, const uint64_t *B, size_t num_words) {
uint64_t borrow = 0;
for (size_t i = num_words; i-- > 0; ) {
uint64_t diff = A[i] - B[i] - borrow;
borrow = (diff > A[i]) || (A[i] == diff && B[i] != 0 && borrow);
A[i] = diff;
}
}
// Initialize slot with dynamic precision and APA allocation
Slot4096 slot_init_apa(int bits_mant, int bits_exp) {
Slot4096 slot = {0};
slot.bits_mant = bits_mant;
slot.bits_exp = bits_exp;
slot.num_words = (bits_mant + 63) / 64;
slot.mantissa_words = (uint64_t*)calloc(slot.num_words, sizeof(uint64_t));
// FUTURE-PROOF MPI INITIALIZATION (V3 Functional)
mpi_init(&slot.exponent_mpi, MPI_INITIAL_WORDS);
mpi_init(&slot.num_words_mantissa, MPI_INITIAL_WORDS);
mpi_init(&slot.source_of_infinity, MPI_INITIAL_WORDS);
if (!slot.mantissa_words) {
fprintf(stderr, "Error: Failed to allocate multi-word mantissa.\n");
return slot;
}
if (slot.num_words > 0) {
slot.mantissa_words[0] = GET_RANDOM_UINT64();
slot.mantissa_words[0] |= MSB_MASK;
}
int64_t exp_range = 1LL << bits_exp;
int64_t exp_bias = 1LL << (bits_exp - 1);
slot.exponent = (rand() % exp_range) - exp_bias;
slot.base = PHI + get_normalized_rand() * 0.01;
// Set the target base for future MPI operations
slot.exponent_base = 4096;
// Synchronize Legacy with MPI
mpi_set_value(&slot.exponent_mpi, (uint64_t)llabs(slot.exponent), slot.exponent < 0 ? 1 : 0);
mpi_set_value(&slot.num_words_mantissa, (uint64_t)slot.num_words, 0);
return slot;
}
// Helper to free single APA slot's dynamic members
void ap_free(Slot4096 *slot) {
if (slot) {
if (slot->mantissa_words) {
free(slot->mantissa_words);
slot->mantissa_words = NULL;
}
// FUTURE-PROOF MPI CLEANUP
mpi_free(&slot->exponent_mpi);
mpi_free(&slot->num_words_mantissa);
mpi_free(&slot->source_of_infinity);
slot->num_words = 0;
}
}
// Deep copy of APA slot
void ap_copy(Slot4096 *dest, const Slot4096 *src) {
ap_free(dest);
*dest = *src; // Shallow copy of struct members
// Deep copy mantissa
dest->mantissa_words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (!dest->mantissa_words) {
fprintf(stderr, "Error: Failed deep copy allocation.\n");
dest->num_words = 0;
return;
}
memcpy(dest->mantissa_words, src->mantissa_words, src->num_words * sizeof(uint64_t));
// Deep copy MPI structs
mpi_copy(&dest->exponent_mpi, &src->exponent_mpi);
mpi_copy(&dest->num_words_mantissa, &src->num_words_mantissa);
mpi_copy(&dest->source_of_infinity, &src->source_of_infinity);
}
// Converts APA to double (Lossy, for display/recursion input)
double ap_to_double(const Slot4096 *slot) {
if (!slot || slot->num_words == 0 || !slot->mantissa_words) return 0.0;
double mantissa_double = (double)slot->mantissa_words[0] / (double)UINT64_MAX;
double result = mantissa_double * pow(2.0, (double)slot->exponent);
if (slot->state_flags & APA_FLAG_SIGN_NEG) {
result *= -1.0;
}
return result;
}
// Converts double to APA slot (Used for the increment_value)
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp) {
Slot4096 temp_slot = slot_init_apa(bits_mant, bits_exp);
Slot4096 *slot = (Slot4096*)malloc(sizeof(Slot4096));
if (!slot) { ap_free(&temp_slot); return NULL; }
*slot = temp_slot;
if (value == 0.0) return slot;
if (value < 0) {
slot->state_flags |= APA_FLAG_SIGN_NEG;
value = -value;
} else {
slot->state_flags &= ~APA_FLAG_SIGN_NEG;
}
int exp_offset;
double mant_val = frexp(value, &exp_offset);
slot->mantissa_words[0] = (uint64_t)(mant_val * (double)UINT64_MAX);
slot->exponent = (int64_t)exp_offset;
// Synchronize Legacy with MPI (conceptual)
mpi_set_value(&slot->exponent_mpi, (uint64_t)llabs(slot->exponent), slot->exponent < 0 ? 1 : 0);
return slot;
}
/**
* Multi-word right shift (V4: Fixed word shift direction)
*/
void ap_shift_right(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount) {
if (shift_amount <= 0 || num_words == 0) return;
if (shift_amount >= (int64_t)num_words * 64) {
memset(mantissa_words, 0, num_words * sizeof(uint64_t));
return;
}
int64_t word_shift = shift_amount / 64;
int bit_shift = (int)(shift_amount % 64);
if (word_shift > 0) {
// Shift words right by word_shift positions
// We must start from the lowest index to correctly propagate the shift
for (size_t i = 0; i < num_words; ++i) {
if ((int64_t)i + word_shift < (int64_t)num_words) {
mantissa_words[i] = mantissa_words[i + word_shift];
}
}
// Zero out the highest 'word_shift' words
memset(mantissa_words + num_words - word_shift, 0, word_shift * sizeof(uint64_t));
}
if (bit_shift > 0) {
int reverse_shift = 64 - bit_shift;
// Shift bits right, propagating carry (upper bits) down
for (size_t i = num_words; i-- > 0; ) {
uint64_t upper_carry = 0;
if (i > 0) { // Check previous (higher-indexed) word for carry
upper_carry = mantissa_words[i - 1] << reverse_shift;
}
mantissa_words[i] = (mantissa_words[i] >> bit_shift) | upper_carry;
}
}
}
// -----------------------------------------------------------------------------
// APA CORE ARITHMETIC FUNCTIONS (V4: Sign-Magnitude Logic)
// -----------------------------------------------------------------------------
// Performs multi-word normalization to maintain canonical range [0.5, 1.0)
void ap_normalize(Slot4096 *slot) {
if (slot->num_words == 0) return;
// --- Check for Zero Mantissa ---
int is_zero = 1;
for (size_t i = 0; i < slot->num_words; i++) {
if (slot->mantissa_words[i] != 0) {
is_zero = 0;
break;
}
}
if (is_zero) {
slot->exponent = 0;
slot->state_flags &= ~APA_FLAG_SIGN_NEG; // Canonical zero is positive
mpi_set_value(&slot->exponent_mpi, 0ULL, 0); // Synchronize MPI
return;
}
// --- Shift Left (Underflow Correction: Mantissa < 0.5) ---
while (!(slot->mantissa_words[0] & MSB_MASK)) {
if (slot->exponent <= -(1LL << (slot->bits_exp - 1))) {
slot->state_flags |= APA_FLAG_GUZ;
break;
}
uint64_t carry = 0;
for (size_t i = slot->num_words; i-- > 0; ) {
uint64_t next_carry = (slot->mantissa_words[i] & MSB_MASK) ? 1 : 0;
slot->mantissa_words[i] = (slot->mantissa_words[i] << 1) | carry;
carry = next_carry;
}
slot->exponent--;
}
// The exponent sync must happen after normalization, as norm changes A->exponent
mpi_set_value(&slot->exponent_mpi, (uint64_t)llabs(slot->exponent), slot->exponent < 0 ? 1 : 0);
}
// Full APA addition with sign-magnitude handling (V4)
void ap_add(Slot4096 *A, const Slot4096 *B) {
if (A->num_words != B->num_words) {
fprintf(stderr, "Error: APA addition failed due to unaligned word counts.\n");
return;
}
Slot4096 B_aligned;
ap_copy(&B_aligned, B);
// --- 1. Exponent Alignment (Legacy int64_t logic for shift amount) ---
int64_t exp_diff = A->exponent - B_aligned.exponent;
if (exp_diff > 0) {
ap_shift_right(B_aligned.mantissa_words, B_aligned.num_words, exp_diff);
B_aligned.exponent = A->exponent;
} else if (exp_diff < 0) {
int64_t shift_amount = -exp_diff;
ap_shift_right(A->mantissa_words, A->num_words, shift_amount);
A->exponent = B_aligned.exponent;
}
// --- 2. Sign-Magnitude Decision (V4 Core Logic) ---
int sign_A = (A->state_flags & APA_FLAG_SIGN_NEG) ? 1 : 0;
int sign_B = (B_aligned.state_flags & APA_FLAG_SIGN_NEG) ? 1 : 0;
uint64_t final_carry = 0;
if (sign_A == sign_B) {
// Case 1: Same Signs -> Add Magnitudes
// Result sign is the same as A's sign.
final_carry = apa_mantissa_add_magnitude(A->mantissa_words, B_aligned.mantissa_words, A->num_words);
} else {
// Case 2: Different Signs -> Subtract Magnitudes
// Determine which magnitude is larger to know the result's sign.
int cmp_result = apa_mantissa_compare_magnitude(A->mantissa_words, B_aligned.mantissa_words, A->num_words);
if (cmp_result >= 0) {
// |A| >= |B|. Result sign is A's sign. (A = A - B)
apa_mantissa_subtract_magnitude(A->mantissa_words, B_aligned.mantissa_words, A->num_words);
// Sign remains sign_A
} else {
// |A| < |B|. Result sign is B's sign. (A = B - A)
// Need a temporary copy for A to hold B - A.
uint64_t *temp_words = (uint64_t*)malloc(A->num_words * sizeof(uint64_t));
memcpy(temp_words, B_aligned.mantissa_words, A->num_words * sizeof(uint64_t));
apa_mantissa_subtract_magnitude(temp_words, A->mantissa_words, A->num_words);
// Overwrite A's mantissa with the result
memcpy(A->mantissa_words, temp_words, A->num_words * sizeof(uint64_t));
free(temp_words);
// Set A's sign to B's sign
if (sign_B) A->state_flags |= APA_FLAG_SIGN_NEG;
else A->state_flags &= ~APA_FLAG_SIGN_NEG;
}
}
// --- 3. Final Carry Handling (Only for magnitude addition) ---
if (final_carry) {
// Overflow due to addition (result >= 2.0 * 2^exp). Renormalize.
if (A->exponent >= (1LL << (A->bits_exp - 1))) {
A->state_flags |= APA_FLAG_GOI;
} else {
A->exponent += 1;
// Right shift all words by 1 bit, propagating carry down
uint64_t next_carry = final_carry << 63;
for (size_t i = 0; i < A->num_words; i++) {
uint64_t current_carry_bit = A->mantissa_words[i] & 1;
A->mantissa_words[i] = (A->mantissa_words[i] >> 1) | next_carry;
next_carry = current_carry_bit << 63;
}
}
}
// --- 4. Final Normalization and Sync ---
ap_normalize(A);
ap_free(&B_aligned);
}
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// HDGL Lattice
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
Slot4096 *slots;
size_t allocated;
} HDGLChunk;
typedef struct {
HDGLChunk **chunks;
int num_chunks;
int num_instances;
int slots_per_instance;
double omega;
double time;
} HDGLLattice;
// Initialize lattice
HDGLLattice* lattice_init(int num_instances, int slots_per_instance) {
HDGLLattice *lat = malloc(sizeof(HDGLLattice));
if (!lat) return NULL;
lat->num_instances = num_instances;
lat->slots_per_instance = slots_per_instance;
lat->omega = 0.0;
lat->time = 0.0;
int total_slots = num_instances * slots_per_instance;
lat->num_chunks = (total_slots + CHUNK_SIZE - 1) / CHUNK_SIZE;
lat->chunks = calloc(lat->num_chunks, sizeof(HDGLChunk*));
if (!lat->chunks) { free(lat); return NULL; }
return lat;
}
// Get chunk, allocate if needed
HDGLChunk* lattice_get_chunk(HDGLLattice *lat, int chunk_idx) {
if (chunk_idx >= lat->num_chunks) return NULL;
if (!lat->chunks[chunk_idx]) {
HDGLChunk *chunk = malloc(sizeof(HDGLChunk));
if (!chunk) return NULL;
chunk->allocated = CHUNK_SIZE;
chunk->slots = (Slot4096*)malloc(CHUNK_SIZE * sizeof(Slot4096));
if (!chunk->slots) { free(chunk); return NULL; }
for (int i = 0; i < CHUNK_SIZE; i++) {
// Dynamic precision allocation: 4096 bits minimum, up to 4576 bits
int bits_mant = 4096 + (i % 8) * 64;
int bits_exp = 16 + (i % 8) * 2;
chunk->slots[i] = slot_init_apa(bits_mant, bits_exp);
}
lat->chunks[chunk_idx] = chunk;
}
return lat->chunks[chunk_idx];
}
// Get slot pointer
Slot4096* lattice_get_slot(HDGLLattice *lat, int idx) {
int chunk_idx = idx / CHUNK_SIZE;
int local_idx = idx % CHUNK_SIZE;
HDGLChunk *chunk = lattice_get_chunk(lat, chunk_idx);
if (!chunk) return NULL;
return &chunk->slots[local_idx];
}
// Prismatic recursion function (MUST use lossy double for calculation input)
double prismatic_recursion(HDGLLattice *lat, int idx, double val) {
double phi_harm = pow(PHI, (double)(idx % 16));
double fib_harm = fib_table[idx % fib_len];
double dyadic = (double)(1 << (idx % 16));
double prime_harm = prime_table[idx % prime_len];
double omega_val = 0.5 + 0.5 * sin(lat->time + idx * 0.01);
double r_dim = pow(val, (double)((idx % 7) + 1));
return sqrt(phi_harm * fib_harm * dyadic * prime_harm * omega_val) * r_dim;
}
// CPU step with APA processing
void lattice_step_cpu(HDGLLattice *lat, double tick) {
int total_slots = lat->num_instances * lat->slots_per_instance;
for (int i = 0; i < total_slots; i++) {
Slot4096 *slot = lattice_get_slot(lat, i);
if (!slot) continue;
// Check for Implied Precision State
if (slot->state_flags & (APA_FLAG_GOI | APA_FLAG_IS_NAN)) {
// Skip computation if state is implied infinity or NaN
continue;
}
double val = ap_to_double(slot);
double r = prismatic_recursion(lat, i, fabs(val));
// Ensure increment value can be negative to test sign-magnitude arithmetic
double increment_value = (pow(slot->base, (double)slot->exponent) * tick + 0.05 * r) * (i % 2 == 0 ? 1.0 : -1.0);
Slot4096 *increment_apa = ap_from_double(
increment_value, slot->bits_mant, slot->bits_exp
);
if (!increment_apa) continue;
ap_add(slot, increment_apa);
ap_free(increment_apa);
free(increment_apa);
}
lat->omega += 0.01 * tick;
lat->time += tick;
}
// Prismatic folding: double instance count
void lattice_fold(HDGLLattice *lat) {
int old_instances = lat->num_instances;
int new_instances = old_instances * 2;
if (new_instances > MAX_INSTANCES) return;
int old_total = old_instances * lat->slots_per_instance;
int new_total = new_instances * lat->slots_per_instance;
int old_chunks = lat->num_chunks;
int new_chunks = (new_total + CHUNK_SIZE - 1) / CHUNK_SIZE;
HDGLChunk **new_chunks_ptr = realloc(lat->chunks, new_chunks * sizeof(HDGLChunk*));
if (!new_chunks_ptr) {
fprintf(stderr, "Failed to allocate memory for folding\n");
return;
}
lat->chunks = new_chunks_ptr;
for (int i = old_chunks; i < new_chunks; i++) {
lat->chunks[i] = NULL;
}
for (int i = 0; i < old_total; i++) {
Slot4096 *old_slot = lattice_get_slot(lat, i);
Slot4096 *new_slot = lattice_get_slot(lat, old_total + i);
if (old_slot && new_slot) {
ap_copy(new_slot, old_slot);
double perturbation = fib_table[i % fib_len] * 0.01;
Slot4096 *pert_apa = ap_from_double(perturbation, new_slot->bits_mant, new_slot->bits_exp);
if (pert_apa) {
ap_add(new_slot, pert_apa);
ap_free(pert_apa);
free(pert_apa);
}
new_slot->base += get_normalized_rand() * 0.001;
}
}
lat->num_instances = new_instances;
lat->num_chunks = new_chunks;
}
// Free lattice: MUST handle freeing multi-word mantissa in every slot
void lattice_free(HDGLLattice *lat) {
if (!lat) return;
for (int i = 0; i < lat->num_chunks; i++) {
if (lat->chunks[i]) {
for (size_t j = 0; j < CHUNK_SIZE; j++) {
ap_free(&lat->chunks[i]->slots[j]);
}
free(lat->chunks[i]->slots);
free(lat->chunks[i]);
}
}
free(lat->chunks);
free(lat);
}
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Bootloader Integration and Main Demo
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// New function to initialize the high-precision constant slots
void init_apa_constants() {
APA_CONST_PHI = slot_init_apa(4096, 16);
APA_CONST_PI = slot_init_apa(4096, 16);
// Placeholder: Set with double precision for demonstration
Slot4096 *temp_phi = ap_from_double(1.6180339887, APA_CONST_PHI.bits_mant, APA_CONST_PHI.bits_exp);
ap_copy(&APA_CONST_PHI, temp_phi);
ap_free(temp_phi);
free(temp_phi);
Slot4096 *temp_pi = ap_from_double(3.1415926535, APA_CONST_PI.bits_mant, APA_CONST_PI.bits_exp);
ap_copy(&APA_CONST_PI, temp_pi);
ap_free(temp_pi);
free(temp_pi);
printf("[Bootloader] High-precision constant slots (PHI, PI) initialized.\n");
}
void bootloader_init_lattice(HDGLLattice *lat, int steps) {
printf("[Bootloader] Initializing HDGL lattice with FUTURE-PROOF APA V4.0...\n");
if (!lat) { printf("[Bootloader] ERROR: Lattice allocation failed.\n"); return; }
init_apa_constants(); // Initialize the global constants
printf("[Bootloader] %d instances, %d total slots\n",
lat->num_instances, lat->num_instances * lat->slots_per_instance);
for (int i = 0; i < steps; i++) {
lattice_step_cpu(lat, 0.01);
}
printf("[Bootloader] Lattice seeded with %d steps\n", steps);
printf("[Bootloader] Omega: %.6f, Time: %.6f\n", lat->omega, lat->time);
}
int main() {
srand(time(NULL));
printf("=== HDGL Unified System (Future-Proof APA V4.0: Sign-Magnitude Integration) ===\n\n");
HDGLLattice *lat = lattice_init(4096, 4);
if (!lat) { fprintf(stderr, "Fatal: Could not initialize lattice.\n"); return 1; }
bootloader_init_lattice(lat, 50);
// Show high-precision constant values
printf("\nHigh-Precision Constants (Legacy Display):\n");
printf(" PHI: value=%.10e exp=%ld words=%zu\n", ap_to_double(&APA_CONST_PHI), APA_CONST_PHI.exponent, APA_CONST_PHI.num_words);
printf(" PI: value=%.10e exp=%ld words=%zu\n", ap_to_double(&APA_CONST_PI), APA_CONST_PI.exponent, APA_CONST_PI.num_words);
// Show some slot values (Display is lossy, but internal state is 4096-bit)
printf("\nFirst 8 slot values (after seeding) - Check for positive/negative signs:\n");
for (int i = 0; i < 8; i++) {
Slot4096 *slot = lattice_get_slot(lat, i);
if (slot) {
printf(" D%d: value=%.6e base=%.6f exp=%ld bits=%d/%d words=%zu flags=%d (Sign: %s)\n",
i+1, ap_to_double(slot), slot->base, slot->exponent,
slot->bits_mant, slot->bits_exp, slot->num_words, slot->state_flags,
(slot->state_flags & APA_FLAG_SIGN_NEG) ? "NEG" : "POS");
}
}
printf("\nTesting prismatic folding...\n");
lattice_fold(lat);
printf(" After: %d instances\n", lat->num_instances);
// Clean up global constants
ap_free(&APA_CONST_PHI);
ap_free(&APA_CONST_PI);
lattice_free(lat);
printf("\n=== APA V4.0 Complete: System is fully sign-magnitude arithmetic ready ===\n");
return 0;
}
Version 5.0
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
#include <time.h>
// --- System Constants ---
#define PHI 1.6180339887
#define MAX_INSTANCES 8388608
#define SLOTS_PER_INSTANCE 4
#define MAX_SLOTS (MAX_INSTANCES * SLOTS_PER_INSTANCE)
#define CHUNK_SIZE 1048576 // 1M slots per chunk
#define MSB_MASK (1ULL << 63) // Mask for the Most Significant Bit of a uint64_t
// --- Future MPI and Base-4096 Constants (V3 ADDITIONS) ---
#define BASE_4096_BPC 12 // Bits per Character (4096 = 2^12)
#define MPI_INITIAL_WORDS 1 // Initial allocation size for MPI structures
#define MPI_ZERO_WORD 0ULL // Canonical zero for MPI operations
// MPI Bit Extraction Helpers
#define MPI_GET_MSB(word) ((word) >> 63)
// Fibonacci and prime tables
static const float fib_table[] = {1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987};
static const float prime_table[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53};
static const int fib_len = 16;
static const int prime_len = 16;
// Helper for generating normalized random double
double get_normalized_rand() {
return (double)rand() / RAND_MAX;
}
// Macro for generating 64-bit random seed (Placeholder for get_random_bytes in kernel)
#define GET_RANDOM_UINT64() (((uint64_t)rand() << 32) | rand())
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// FUTURE-PROOF MPI (Multi-Word Integer) and State Flags
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Multi-Word Integer (MPI) Structure for arbitrarily large metadata (Exponent, Word Count)
typedef struct {
uint64_t *words; // Array of 64-bit words for the number
size_t num_words; // Number of words currently allocated
uint8_t sign; // 0: Positive, 1: Negative (Magnitude is always stored in words)
} MPI;
// State Flags Definitions for Implied Precision
#define APA_FLAG_SIGN_NEG (1 << 0) // Mantissa is negative
#define APA_FLAG_IS_NAN (1 << 1) // Not a Number
#define APA_FLAG_GOI (1 << 2) // Gradual Overflow Infinity
#define APA_FLAG_GUZ (1 << 3) // Gradual Underflow Zero
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Slot4096: Arbitrary Precision Architecture (APA) Structure (FUTURE-PROOF)
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
// --- Core Precision Fields ---
uint64_t *mantissa_words; // Multi-word array for high-precision mantissa
// FUTURE-PROOF FIELDS (Conceptual, for 4096^4096+ scaling)
MPI num_words_mantissa; // The COUNT of mantissa_words (Arbitrarily wide, V3)
MPI exponent_mpi; // The exponent value (Arbitrarily wide, V3)
// State and Base Control Fields
uint16_t exponent_base; // Base of the floating-point system (e.g., 2 or 4096)
uint32_t state_flags; // Flags for NaN, Sign, GOI, GUZ
MPI source_of_infinity; // Records magnitude for Gradual Overflow Infinity (GOI)
// LEGACY FIELDS (Kept for compatibility and temporary transition)
size_t num_words; // Legacy Count of 64-bit words allocated
int64_t exponent; // Legacy Signed exponent (Base 2)
float base; // Dynamic base (φ-scaled)
int bits_mant; // Actual software-managed bit width (e.g., 4096)
int bits_exp; // Exponent bit width
} Slot4096;
// -----------------------------------------------------------------------------
// GLOBAL HIGH-PRECISION CONSTANT SLOTS
// -----------------------------------------------------------------------------
static Slot4096 APA_CONST_PHI; // Target slot for full precision Golden Ratio
static Slot4096 APA_CONST_PI; // Target slot for full precision Pi
// Forward Declarations for APA Operations
void ap_normalize(Slot4096 *slot);
void ap_free(Slot4096 *slot);
void ap_copy(Slot4096 *dest, const Slot4096 *src);
double ap_to_double(const Slot4096 *slot);
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp);
void ap_shift_right(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount);
// --- Mantissa Magnitude Operations (V4) ---
int apa_mantissa_compare_magnitude(const uint64_t *A, const uint64_t *B, size_t num_words);
uint64_t apa_mantissa_add_magnitude(uint64_t *A, const uint64_t *B, size_t num_words);
void apa_mantissa_subtract_magnitude(uint64_t *A, const uint64_t *B, size_t num_words);
void ap_add(Slot4096 *A, const Slot4096 *B); // Full sign-magnitude V5 implementation
// --- MPI Core Functions (V5 Additions) ---
int mpi_compare_signed(const MPI *A, const MPI *B);
void mpi_update_from_legacy(MPI *m, int64_t value);
void mpi_init(MPI *m, size_t initial_words);
void mpi_free(MPI *m);
void mpi_copy(MPI *dest, const MPI *src);
void mpi_resize(MPI *m, size_t new_words);
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign);
int mpi_compare(const MPI *A, const MPI *B);
void mpi_add(MPI *A, const MPI *B);
void mpi_subtract(MPI *A, const MPI *B);
size_t mpi_get_effective_words(const MPI *m);
// -----------------------------------------------------------------------------
// MPI FUNCTION IMPLEMENTATIONS (V5 Functional Core)
// -----------------------------------------------------------------------------
void mpi_init(MPI *m, size_t initial_words) {
m->words = calloc(initial_words, sizeof(uint64_t));
m->num_words = initial_words;
m->sign = 0;
}
void mpi_free(MPI *m) {
if (m->words) free(m->words);
m->words = NULL;
m->num_words = 0;
}
void mpi_copy(MPI *dest, const MPI *src) {
mpi_free(dest);
dest->num_words = src->num_words;
dest->words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (src->words && dest->words) {
memcpy(dest->words, src->words, src->num_words * sizeof(uint64_t));
}
dest->sign = src->sign;
}
void mpi_resize(MPI *m, size_t new_words) {
if (new_words == m->num_words) return;
if (new_words == 0) { mpi_free(m); return; }
size_t old_words = m->num_words;
m->words = (uint64_t*)realloc(m->words, new_words * sizeof(uint64_t));
if (new_words > old_words) {
memset(m->words + old_words, 0, (new_words - old_words) * sizeof(uint64_t));
}
m->num_words = new_words;
}
// Helper to update MPI struct from legacy int64_t value (V5: Exponent Sync)
void mpi_update_from_legacy(MPI *m, int64_t value) {
uint8_t sign = 0;
uint64_t magnitude = (uint64_t)value;
if (value < 0) {
sign = 1;
magnitude = (uint64_t)llabs(value);
}
// Ensure we have at least 1 word
if (m->num_words < 1) mpi_resize(m, 1);
m->words[0] = magnitude;
m->sign = sign;
// Zero out higher words if necessary
if (m->num_words > 1) {
memset(m->words + 1, 0, (m->num_words - 1) * sizeof(uint64_t));
}
}
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign) {
if (m->num_words < 1) mpi_resize(m, 1);
m->words[0] = value;
m->sign = sign;
if (m->num_words > 1) {
memset(m->words + 1, 0, (m->num_words - 1) * sizeof(uint64_t));
}
}
size_t mpi_get_effective_words(const MPI *m) {
if (!m->words) return 0;
size_t i = m->num_words;
while (i > 0 && m->words[i - 1] == 0) {
i--;
}
return i;
}
// Magnitude comparison: |A| vs |B|
int mpi_compare(const MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
if (len_A > len_B) return 1;
if (len_A < len_B) return -1;
for (size_t i = len_A; i-- > 0; ) {
if (A->words[i] > B->words[i]) return 1;
if (A->words[i] < B->words[i]) return -1;
}
return 0;
}
// Signed comparison (V5 New): A vs B
int mpi_compare_signed(const MPI *A, const MPI *B) {
if (A->sign != B->sign) {
// POS (sign 0) is greater than NEG (sign 1)
return A->sign == 0 ? 1 : -1;
}
// Signs are the same. Compare magnitudes.
int mag_cmp = mpi_compare(A, B);
if (A->sign == 0) { // Both positive
return mag_cmp;
} else { // Both negative: larger magnitude means smaller (more negative) number
return -mag_cmp;
}
}
void mpi_add(MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
size_t max_len = len_A > len_B ? len_A : len_B;
if (A->num_words < max_len + 1) {
mpi_resize(A, max_len + 1);
}
uint64_t carry = 0;
for (size_t i = 0; i < max_len; ++i) {
uint64_t word_A = (i < len_A) ? A->words[i] : 0ULL;
uint64_t word_B = (i < len_B) ? B->words[i] : 0ULL;
uint64_t sum = word_A + word_B;
uint64_t carry1 = (sum < word_A);
sum += carry;
uint64_t carry2 = (sum < carry);
A->words[i] = sum;
carry = carry1 | carry2;
}
if (carry) {
A->words[max_len] = carry;
} else if (A->num_words > max_len + 1) {
memset(A->words + max_len, 0, (A->num_words - max_len) * sizeof(uint64_t));
}
}
void mpi_subtract(MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
if (len_A < len_B) { return; }
uint64_t borrow = 0;
for (size_t i = 0; i < len_A; ++i) {
uint64_t word_B = (i < len_B) ? B->words[i] : 0ULL;
uint64_t diff = A->words[i] - word_B - borrow;
borrow = (diff > A->words[i]) || (A->words[i] == diff && (word_B | borrow));
A->words[i] = diff;
}
size_t new_len = mpi_get_effective_words(A);
if (new_len < A->num_words) {
// Shrink the array to canonical size (or 1 if it's zero)
mpi_resize(A, new_len > 0 ? new_len : 1);
}
if (new_len == 0) mpi_set_value(A, 0ULL, 0); // Canonical zero
}
// -----------------------------------------------------------------------------
// APA UTILITY FUNCTIONS
// -----------------------------------------------------------------------------
// Fixed-width multi-word magnitude comparison
int apa_mantissa_compare_magnitude(const uint64_t *A, const uint64_t *B, size_t num_words) {
for (size_t i = num_words; i-- > 0; ) {
if (A[i] > B[i]) return 1;
if (A[i] < B[i]) return -1;
}
return 0; // Equal
}
// Fixed-width multi-word magnitude addition
uint64_t apa_mantissa_add_magnitude(uint64_t *A, const uint64_t *B, size_t num_words) {
uint64_t carry = 0;
for (size_t i = num_words; i-- > 0; ) {
uint64_t sum = A[i] + B[i];
uint64_t carry1 = (sum < A[i]);
sum += carry;
uint64_t carry2 = (sum < carry);
A[i] = sum;
carry = carry1 | carry2;
}
return carry;
}
// Fixed-width multi-word magnitude subtraction (A = A - B). Assumes |A| >= |B|.
void apa_mantissa_subtract_magnitude(uint64_t *A, const uint64_t *B, size_t num_words) {
uint64_t borrow = 0;
for (size_t i = num_words; i-- > 0; ) {
uint64_t diff = A[i] - B[i] - borrow;
borrow = (diff > A[i]) || (A[i] == diff && B[i] != 0 && borrow);
A[i] = diff;
}
}
// Initialize slot with dynamic precision and APA allocation
Slot4096 slot_init_apa(int bits_mant, int bits_exp) {
Slot4096 slot = {0};
slot.bits_mant = bits_mant;
slot.bits_exp = bits_exp;
slot.num_words = (bits_mant + 63) / 64;
slot.mantissa_words = (uint64_t*)calloc(slot.num_words, sizeof(uint64_t));
// FUTURE-PROOF MPI INITIALIZATION (V3 Functional)
mpi_init(&slot.exponent_mpi, MPI_INITIAL_WORDS);
mpi_init(&slot.num_words_mantissa, MPI_INITIAL_WORDS);
mpi_init(&slot.source_of_infinity, MPI_INITIAL_WORDS);
if (!slot.mantissa_words) {
fprintf(stderr, "Error: Failed to allocate multi-word mantissa.\n");
return slot;
}
if (slot.num_words > 0) {
slot.mantissa_words[0] = GET_RANDOM_UINT64();
slot.mantissa_words[0] |= MSB_MASK;
}
int64_t exp_range = 1LL << bits_exp;
int64_t exp_bias = 1LL << (bits_exp - 1);
slot.exponent = (rand() % exp_range) - exp_bias;
slot.base = PHI + get_normalized_rand() * 0.01;
// Set the target base for future MPI operations
slot.exponent_base = 4096;
// Synchronize Legacy with MPI (V5: Use new helper)
mpi_update_from_legacy(&slot.exponent_mpi, slot.exponent);
mpi_set_value(&slot.num_words_mantissa, (uint64_t)slot.num_words, 0);
return slot;
}
// Helper to free single APA slot's dynamic members
void ap_free(Slot4096 *slot) {
if (slot) {
if (slot->mantissa_words) {
free(slot->mantissa_words);
slot->mantissa_words = NULL;
}
// FUTURE-PROOF MPI CLEANUP
mpi_free(&slot->exponent_mpi);
mpi_free(&slot->num_words_mantissa);
mpi_free(&slot->source_of_infinity);
slot->num_words = 0;
}
}
// Deep copy of APA slot
void ap_copy(Slot4096 *dest, const Slot4096 *src) {
ap_free(dest);
*dest = *src; // Shallow copy of struct members
// Deep copy mantissa
dest->mantissa_words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (!dest->mantissa_words) {
fprintf(stderr, "Error: Failed deep copy allocation.\n");
dest->num_words = 0;
return;
}
memcpy(dest->mantissa_words, src->mantissa_words, src->num_words * sizeof(uint64_t));
// Deep copy MPI structs
mpi_copy(&dest->exponent_mpi, &src->exponent_mpi);
mpi_copy(&dest->num_words_mantissa, &src->num_words_mantissa);
mpi_copy(&dest->source_of_infinity, &src->source_of_infinity);
}
// Converts double to APA slot
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp) {
Slot4096 temp_slot = slot_init_apa(bits_mant, bits_exp);
Slot4096 *slot = (Slot4096*)malloc(sizeof(Slot4096));
if (!slot) { ap_free(&temp_slot); return NULL; }
*slot = temp_slot;
if (value == 0.0) return slot;
if (value < 0) {
slot->state_flags |= APA_FLAG_SIGN_NEG;
value = -value;
} else {
slot->state_flags &= ~APA_FLAG_SIGN_NEG;
}
int exp_offset;
double mant_val = frexp(value, &exp_offset);
slot->mantissa_words[0] = (uint64_t)(mant_val * (double)UINT64_MAX);
slot->exponent = (int64_t)exp_offset;
// Synchronize Legacy with MPI (V5: Use new helper)
mpi_update_from_legacy(&slot->exponent_mpi, slot->exponent);
return slot;
}
/**
* Multi-word right shift (V4 Logic)
*/
void ap_shift_right(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount) {
if (shift_amount <= 0 || num_words == 0) return;
if (shift_amount >= (int64_t)num_words * 64) {
memset(mantissa_words, 0, num_words * sizeof(uint64_t));
return;
}
int64_t word_shift = shift_amount / 64;
int bit_shift = (int)(shift_amount % 64);
if (word_shift > 0) {
// Shift words right by word_shift positions
for (size_t i = 0; i < num_words; ++i) {
if ((int64_t)i + word_shift < (int64_t)num_words) {
// The bit shift must go from highest word to lowest word
// since we are moving the contents of A[i+shift] into A[i].
// However, since we are moving the *end* of the array to the *start*,
// we must iterate from the end to avoid overwriting source data.
// Let's use memcpy for simplicity and correctness if needed, but for in-place
// shifting by word, this loop should be reversed.
// For simplicity, we use memcpy logic for block shifts:
memmove(mantissa_words, mantissa_words + word_shift,
(num_words - word_shift) * sizeof(uint64_t));
}
}
// Zero out the highest 'word_shift' words
memset(mantissa_words + num_words - word_shift, 0, word_shift * sizeof(uint64_t));
}
if (bit_shift > 0) {
int reverse_shift = 64 - bit_shift;
// Shift bits right, propagating carry (upper bits) down
for (size_t i = num_words; i-- > 0; ) {
uint64_t upper_carry = 0;
if (i > 0) {
// Carry from the word below (higher index) in memory, which is higher magnitude
upper_carry = mantissa_words[i - 1] << reverse_shift;
}
mantissa_words[i] = (mantissa_words[i] >> bit_shift) | upper_carry;
}
}
}
// -----------------------------------------------------------------------------
// APA CORE ARITHMETIC FUNCTIONS (V5: MPI Exponent Logic)
// -----------------------------------------------------------------------------
// Performs multi-word normalization to maintain canonical range [0.5, 1.0)
void ap_normalize(Slot4096 *slot) {
if (slot->num_words == 0) return;
// --- Check for Zero Mantissa ---
int is_zero = 1;
for (size_t i = 0; i < slot->num_words; i++) {
if (slot->mantissa_words[i] != 0) {
is_zero = 0;
break;
}
}
if (is_zero) {
slot->exponent = 0;
slot->state_flags &= ~APA_FLAG_SIGN_NEG; // Canonical zero is positive
mpi_update_from_legacy(&slot->exponent_mpi, slot->exponent); // V5: Sync MPI
return;
}
// --- Shift Left (Underflow Correction: Mantissa < 0.5) ---
while (!(slot->mantissa_words[0] & MSB_MASK)) {
if (slot->exponent <= -(1LL << (slot->bits_exp - 1))) {
slot->state_flags |= APA_FLAG_GUZ;
break;
}
uint64_t carry = 0;
for (size_t i = slot->num_words; i-- > 0; ) {
uint64_t next_carry = (slot->mantissa_words[i] & MSB_MASK) ? 1 : 0;
slot->mantissa_words[i] = (slot->mantissa_words[i] << 1) | carry;
carry = next_carry;
}
slot->exponent--;
}
// V5: Synchronize MPI after all shifting is complete
mpi_update_from_legacy(&slot->exponent_mpi, slot->exponent);
}
// Full APA addition with sign-magnitude handling (V5)
void ap_add(Slot4096 *A, const Slot4096 *B) {
if (A->num_words != B->num_words) {
fprintf(stderr, "Error: APA addition failed due to unaligned word counts.\n");
return;
}
Slot4096 B_aligned;
ap_copy(&B_aligned, B);
// --- 1. Exponent Alignment (V5: Use MPI comparison for decision) ---
// Determine which exponent is larger (signed comparison)
int exp_cmp = mpi_compare_signed(&A->exponent_mpi, &B_aligned.exponent_mpi);
int64_t exp_diff = A->exponent - B_aligned.exponent; // Use legacy field for the shift amount calculation
if (exp_cmp > 0) { // A.exp > B.exp (A is larger/more positive)
// Shift B right. Shift amount is the difference (A.exp - B.exp).
int64_t shift_amount = exp_diff;
ap_shift_right(B_aligned.mantissa_words, B_aligned.num_words, shift_amount);
// Update B_aligned's exponent to match A's
B_aligned.exponent = A->exponent;
mpi_copy(&B_aligned.exponent_mpi, &A->exponent_mpi); // V5: Sync B's MPI
} else if (exp_cmp < 0) { // B.exp > A.exp (B is larger/more positive)
// Shift A right. Shift amount is the difference (B.exp - A.exp).
int64_t shift_amount = -exp_diff;
ap_shift_right(A->mantissa_words, A->num_words, shift_amount);
// Update A's exponent to match B's
A->exponent = B_aligned.exponent;
mpi_copy(&A->exponent_mpi, &B_aligned.exponent_mpi); // V5: Sync A's MPI
}
// If exp_cmp == 0, exponents are already aligned.
// --- 2. Sign-Magnitude Decision (V4 Core Logic) ---
int sign_A = (A->state_flags & APA_FLAG_SIGN_NEG) ? 1 : 0;
int sign_B = (B_aligned.state_flags & APA_FLAG_SIGN_NEG) ? 1 : 0;
uint64_t final_carry = 0;
if (sign_A == sign_B) {
// Case 1: Same Signs -> Add Magnitudes
final_carry = apa_mantissa_add_magnitude(A->mantissa_words, B_aligned.mantissa_words, A->num_words);
} else {
// Case 2: Different Signs -> Subtract Magnitudes
int cmp_result = apa_mantissa_compare_magnitude(A->mantissa_words, B_aligned.mantissa_words, A->num_words);
if (cmp_result >= 0) {
// |A| >= |B|. Result sign is A's sign. (A = A - B)
apa_mantissa_subtract_magnitude(A->mantissa_words, B_aligned.mantissa_words, A->num_words);
} else {
// |A| < |B|. Result sign is B's sign. (A = B - A)
uint64_t *temp_words = (uint64_t*)malloc(A->num_words * sizeof(uint64_t));
memcpy(temp_words, B_aligned.mantissa_words, A->num_words * sizeof(uint64_t));
apa_mantissa_subtract_magnitude(temp_words, A->mantissa_words, A->num_words);
memcpy(A->mantissa_words, temp_words, A->num_words * sizeof(uint64_t));
free(temp_words);
// Set A's sign to B's sign
if (sign_B) A->state_flags |= APA_FLAG_SIGN_NEG;
else A->state_flags &= ~APA_FLAG_SIGN_NEG;
}
}
// --- 3. Final Carry Handling (Only for magnitude addition) ---
if (final_carry) {
// Overflow due to addition (result >= 2.0 * 2^exp). Renormalize.
if (A->exponent >= (1LL << (A->bits_exp - 1))) {
A->state_flags |= APA_FLAG_GOI;
} else {
A->exponent += 1; // Increment legacy exponent
// Right shift all words by 1 bit, propagating carry down
uint64_t next_carry = final_carry << 63;
for (size_t i = 0; i < A->num_words; i++) {
uint64_t current_carry_bit = A->mantissa_words[i] & 1;
A->mantissa_words[i] = (A->mantissa_words[i] >> 1) | next_carry;
next_carry = current_carry_bit << 63;
}
}
// V5: Sync A's MPI exponent after carry update
mpi_update_from_legacy(&A->exponent_mpi, A->exponent);
}
// --- 4. Final Normalization and Sync ---
ap_normalize(A);
ap_free(&B_aligned);
}
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// HDGL Lattice (Unchanged from V4)
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
Slot4096 *slots;
size_t allocated;
} HDGLChunk;
typedef struct {
HDGLChunk **chunks;
int num_chunks;
int num_instances;
int slots_per_instance;
double omega;
double time;
} HDGLLattice;
// Initialize lattice
HDGLLattice* lattice_init(int num_instances, int slots_per_instance) {
HDGLLattice *lat = malloc(sizeof(HDGLLattice));
if (!lat) return NULL;
lat->num_instances = num_instances;
lat->slots_per_instance = slots_per_instance;
lat->omega = 0.0;
lat->time = 0.0;
int total_slots = num_instances * slots_per_instance;
lat->num_chunks = (total_slots + CHUNK_SIZE - 1) / CHUNK_SIZE;
lat->chunks = calloc(lat->num_chunks, sizeof(HDGLChunk*));
if (!lat->chunks) { free(lat); return NULL; }
return lat;
}
// Get chunk, allocate if needed
HDGLChunk* lattice_get_chunk(HDGLLattice *lat, int chunk_idx) {
if (chunk_idx >= lat->num_chunks) return NULL;
if (!lat->chunks[chunk_idx]) {
HDGLChunk *chunk = malloc(sizeof(HDGLChunk));
if (!chunk) return NULL;
chunk->allocated = CHUNK_SIZE;
chunk->slots = (Slot4096*)malloc(CHUNK_SIZE * sizeof(Slot4096));
if (!chunk->slots) { free(chunk); return NULL; }
for (int i = 0; i < CHUNK_SIZE; i++) {
// Dynamic precision allocation: 4096 bits minimum, up to 4576 bits
int bits_mant = 4096 + (i % 8) * 64;
int bits_exp = 16 + (i % 8) * 2;
chunk->slots[i] = slot_init_apa(bits_mant, bits_exp);
}
lat->chunks[chunk_idx] = chunk;
}
return lat->chunks[chunk_idx];
}
// Get slot pointer
Slot4096* lattice_get_slot(HDGLLattice *lat, int idx) {
int chunk_idx = idx / CHUNK_SIZE;
int local_idx = idx % CHUNK_SIZE;
HDGLChunk *chunk = lattice_get_chunk(lat, chunk_idx);
if (!chunk) return NULL;
return &chunk->slots[local_idx];
}
// Prismatic recursion function (MUST use lossy double for calculation input)
double prismatic_recursion(HDGLLattice *lat, int idx, double val) {
double phi_harm = pow(PHI, (double)(idx % 16));
double fib_harm = fib_table[idx % fib_len];
double dyadic = (double)(1 << (idx % 16));
double prime_harm = prime_table[idx % prime_len];
double omega_val = 0.5 + 0.5 * sin(lat->time + idx * 0.01);
double r_dim = pow(val, (double)((idx % 7) + 1));
return sqrt(phi_harm * fib_harm * dyadic * prime_harm * omega_val) * r_dim;
}
// Converts APA to double (Lossy, for display/recursion input)
double ap_to_double(const Slot4096 *slot) {
if (!slot || slot->num_words == 0 || !slot->mantissa_words) return 0.0;
double mantissa_double = (double)slot->mantissa_words[0] / (double)UINT64_MAX;
double result = mantissa_double * pow(2.0, (double)slot->exponent);
if (slot->state_flags & APA_FLAG_SIGN_NEG) {
result *= -1.0;
}
return result;
}
// CPU step with APA processing
void lattice_step_cpu(HDGLLattice *lat, double tick) {
int total_slots = lat->num_instances * lat->slots_per_instance;
for (int i = 0; i < total_slots; i++) {
Slot4096 *slot = lattice_get_slot(lat, i);
if (!slot) continue;
// Check for Implied Precision State
if (slot->state_flags & (APA_FLAG_GOI | APA_FLAG_IS_NAN)) {
// Skip computation if state is implied infinity or NaN
continue;
}
double val = ap_to_double(slot);
double r = prismatic_recursion(lat, i, fabs(val));
// Ensure increment value can be negative to test sign-magnitude arithmetic
double increment_value = (pow(slot->base, (double)slot->exponent) * tick + 0.05 * r) * (i % 2 == 0 ? 1.0 : -1.0);
Slot4096 *increment_apa = ap_from_double(
increment_value, slot->bits_mant, slot->bits_exp
);
if (!increment_apa) continue;
ap_add(slot, increment_apa);
ap_free(increment_apa);
free(increment_apa);
}
lat->omega += 0.01 * tick;
lat->time += tick;
}
// Prismatic folding: double instance count
void lattice_fold(HDGLLattice *lat) {
int old_instances = lat->num_instances;
int new_instances = old_instances * 2;
if (new_instances > MAX_INSTANCES) return;
int old_total = old_instances * lat->slots_per_instance;
int new_total = new_instances * lat->slots_per_instance;
int old_chunks = lat->num_chunks;
int new_chunks = (new_total + CHUNK_SIZE - 1) / CHUNK_SIZE;
HDGLChunk **new_chunks_ptr = realloc(lat->chunks, new_chunks * sizeof(HDGLChunk*));
if (!new_chunks_ptr) {
fprintf(stderr, "Failed to allocate memory for folding\n");
return;
}
lat->chunks = new_chunks_ptr;
for (int i = old_chunks; i < new_chunks; i++) {
lat->chunks[i] = NULL;
}
for (int i = 0; i < old_total; i++) {
Slot4096 *old_slot = lattice_get_slot(lat, i);
Slot4096 *new_slot = lattice_get_slot(lat, old_total + i);
if (old_slot && new_slot) {
ap_copy(new_slot, old_slot);
double perturbation = fib_table[i % fib_len] * 0.01;
Slot4096 *pert_apa = ap_from_double(perturbation, new_slot->bits_mant, new_slot->bits_exp);
if (pert_apa) {
ap_add(new_slot, pert_apa);
ap_free(pert_apa);
free(pert_apa);
}
new_slot->base += get_normalized_rand() * 0.001;
}
}
lat->num_instances = new_instances;
lat->num_chunks = new_chunks;
}
// Free lattice: MUST handle freeing multi-word mantissa in every slot
void lattice_free(HDGLLattice *lat) {
if (!lat) return;
for (int i = 0; i < lat->num_chunks; i++) {
if (lat->chunks[i]) {
for (size_t j = 0; j < CHUNK_SIZE; j++) {
ap_free(&lat->chunks[i]->slots[j]);
}
free(lat->chunks[i]->slots);
free(lat->chunks[i]);
}
}
free(lat->chunks);
free(lat);
}
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Bootloader Integration and Main Demo
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// New function to initialize the high-precision constant slots
void init_apa_constants() {
APA_CONST_PHI = slot_init_apa(4096, 16);
APA_CONST_PI = slot_init_apa(4096, 16);
// Placeholder: Set with double precision for demonstration
Slot4096 *temp_phi = ap_from_double(1.6180339887, APA_CONST_PHI.bits_mant, APA_CONST_PHI.bits_exp);
ap_copy(&APA_CONST_PHI, temp_phi);
ap_free(temp_phi);
free(temp_phi);
Slot4096 *temp_pi = ap_from_double(3.1415926535, APA_CONST_PI.bits_mant, APA_CONST_PI.bits_exp);
ap_copy(&APA_CONST_PI, temp_pi);
ap_free(temp_pi);
free(temp_pi);
printf("[Bootloader] High-precision constant slots (PHI, PI) initialized.\n");
}
void bootloader_init_lattice(HDGLLattice *lat, int steps) {
printf("[Bootloader] Initializing HDGL lattice with FUTURE-PROOF APA V5.0...\n");
if (!lat) { printf("[Bootloader] ERROR: Lattice allocation failed.\n"); return; }
init_apa_constants(); // Initialize the global constants
printf("[Bootloader] %d instances, %d total slots\n",
lat->num_instances, lat->num_instances * lat->slots_per_instance);
for (int i = 0; i < steps; i++) {
lattice_step_cpu(lat, 0.01);
}
printf("[Bootloader] Lattice seeded with %d steps\n", steps);
printf("[Bootloader] Omega: %.6f, Time: %.6f\n", lat->omega, lat->time);
}
int main() {
srand(time(NULL));
printf("=== HDGL Unified System (Future-Proof APA V5.0: Full MPI Exponent Integration) ===\n\n");
HDGLLattice *lat = lattice_init(4096, 4);
if (!lat) { fprintf(stderr, "Fatal: Could not initialize lattice.\n"); return 1; }
bootloader_init_lattice(lat, 50);
// Show high-precision constant values
printf("\nHigh-Precision Constants (Legacy Display):\n");
printf(" PHI: value=%.10e exp=%ld words=%zu\n", ap_to_double(&APA_CONST_PHI), APA_CONST_PHI.exponent, APA_CONST_PHI.num_words);
printf(" PI: value=%.10e exp=%ld words=%zu\n", ap_to_double(&APA_CONST_PI), APA_CONST_PI.exponent, APA_CONST_PI.num_words);
// Show some slot values (Display is lossy, but internal state is 4096-bit)
printf("\nFirst 8 slot values (after seeding) - Exponent alignment decision is now MPI-driven:\n");
for (int i = 0; i < 8; i++) {
Slot4096 *slot = lattice_get_slot(lat, i);
if (slot) {
printf(" D%d: value=%.6e exp=%ld flags=%d (Sign: %s)\n",
i+1, ap_to_double(slot), slot->exponent,
slot->state_flags,
(slot->state_flags & APA_FLAG_SIGN_NEG) ? "NEG" : "POS");
}
}
printf("\nTesting prismatic folding...\n");
lattice_fold(lat);
printf(" After: %d instances\n", lat->num_instances);
// Clean up global constants
ap_free(&APA_CONST_PHI);
ap_free(&APA_CONST_PI);
lattice_free(lat);
printf("\n=== APA V5.0 Complete: Exponent control is now handled by MPI ===\n");
return 0;
}
Version 6.0
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
#include <time.h>
// --- System Constants ---
#define PHI 1.6180339887
#define MAX_INSTANCES 8388608
#define SLOTS_PER_INSTANCE 4
#define MAX_SLOTS (MAX_INSTANCES * SLOTS_PER_INSTANCE)
#define CHUNK_SIZE 1048576 // 1M slots per chunk
#define MSB_MASK (1ULL << 63) // Mask for the Most Significant Bit of a uint64_t
// --- Future MPI and Base-4096 Constants (V3 ADDITIONS) ---
#define BASE_4096_BPC 12 // Bits per Character (4096 = 2^12)
#define MPI_INITIAL_WORDS 1 // Initial allocation size for MPI structures
#define MPI_ZERO_WORD 0ULL // Canonical zero for MPI operations
// MPI Bit Extraction Helpers
#define MPI_GET_MSB(word) ((word) >> 63)
// Fibonacci and prime tables
static const float fib_table[] = {1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987};
static const float prime_table[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53};
static const int fib_len = 16;
static const int prime_len = 16;
// Helper for generating normalized random double
double get_normalized_rand() {
return (double)rand() / RAND_MAX;
}
// Macro for generating 64-bit random seed (Placeholder for get_random_bytes in kernel)
#define GET_RANDOM_UINT64() (((uint64_t)rand() << 32) | rand())
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// FUTURE-PROOF MPI (Multi-Word Integer) and State Flags
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Multi-Word Integer (MPI) Structure for arbitrarily large metadata (Exponent, Word Count)
typedef struct {
uint64_t *words; // Array of 64-bit words for the number
size_t num_words; // Number of words currently allocated
uint8_t sign; // 0: Positive, 1: Negative (Magnitude is always stored in words)
} MPI;
// State Flags Definitions for Implied Precision
#define APA_FLAG_SIGN_NEG (1 << 0) // Mantissa is negative
#define APA_FLAG_IS_NAN (1 << 1) // Not a Number
#define APA_FLAG_GOI (1 << 2) // Gradual Overflow Infinity
#define APA_FLAG_GUZ (1 << 3) // Gradual Underflow Zero
// --- V6.0 Addition: Decoupled Communication State ---
// This structure holds state specific to asynchronous communication and remote exponent synchronization.
typedef struct {
MPI remote_exponent_delta; // Change derived from remote synchronization (V6.0)
uint8_t status_flags; // Flags for async operations (e.g., AWAITING_SYNC, SYNC_READY) (V6.0)
int comm_handle_id; // Unique ID for tracking async tasks (Placeholder for MPI_Request)
} CommLayerState;
// CommLayer Status Flags (Simulating MPI non-blocking state)
#define COMM_FLAG_AWAITING_SYNC (1 << 0) // Exponent needs external sync/wait
#define COMM_FLAG_SYNC_READY (1 << 1) // Remote delta has arrived and is ready to apply
#define COMM_FLAG_RMA_PENDING (1 << 2) // Remote Memory Access is pending completion
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// Slot4096: Arbitrary Precision Architecture (APA) Structure (FUTURE-PROOF)
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
// --- Core Precision Fields ---
uint64_t *mantissa_words; // Multi-word array for high-precision mantissa
// FUTURE-PROOF FIELDS (Conceptual, for 4096^4096+ scaling)
MPI num_words_mantissa; // The COUNT of mantissa_words (Arbitrarily wide, V3)
MPI exponent_mpi; // The exponent value (Arbitrarily wide, V3)
// V6.0: Exponent Decoupling Structure
CommLayerState comm_state; // Dedicated state for asynchronous communication
// State and Base Control Fields
uint16_t exponent_base; // Base of the floating-point system (e.g., 2 or 4096)
uint32_t state_flags; // Flags for NaN, Sign, GOI, GUZ
MPI source_of_infinity; // Records magnitude for Gradual Overflow Infinity (GOI)
// LEGACY FIELDS (Kept for compatibility and temporary transition)
size_t num_words; // Legacy Count of 64-bit words allocated
int64_t exponent; // Legacy Signed exponent (Base 2)
float base; // Dynamic base (φ-scaled)
int bits_mant; // Actual software-managed bit width (e.g., 4096)
int bits_exp; // Exponent bit width
} Slot4096;
// -----------------------------------------------------------------------------
// GLOBAL HIGH-PRECISION CONSTANT SLOTS
// -----------------------------------------------------------------------------
static Slot4096 APA_CONST_PHI; // Target slot for full precision Golden Ratio
static Slot4096 APA_CONST_PI; // Target slot for full precision Pi
// Forward Declarations for APA Operations
void ap_normalize(Slot4096 *slot);
void ap_free(Slot4096 *slot);
void ap_copy(Slot4096 *dest, const Slot4096 *src);
double ap_to_double(const Slot4096 *slot);
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp);
void ap_shift_right(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount);
// --- Mantissa Magnitude Operations (V4) ---
int apa_mantissa_compare_magnitude(const uint64_t *A, const uint64_t *B, size_t num_words);
uint64_t apa_mantissa_add_magnitude(uint64_t *A, const uint64_t *B, size_t num_words);
void apa_mantissa_subtract_magnitude(uint64_t *A, const uint64_t *B, size_t num_words);
void ap_add(Slot4096 *A, const Slot4096 *B); // Full sign-magnitude V5 implementation
// --- MPI Core Functions (V5 Additions) ---
int mpi_compare_signed(const MPI *A, const MPI *B);
void mpi_update_from_legacy(MPI *m, int64_t value);
void mpi_init(MPI *m, size_t initial_words);
void mpi_free(MPI *m);
void mpi_copy(MPI *dest, const MPI *src);
void mpi_resize(MPI *m, size_t new_words);
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign);
int mpi_compare(const MPI *A, const MPI *B);
void mpi_add(MPI *A, const MPI *B);
void mpi_subtract(MPI *A, const MPI *B);
size_t mpi_get_effective_words(const MPI *m);
// --- V6.0 Comm Layer Functions ---
void comm_layer_init(CommLayerState *c);
void comm_layer_free(CommLayerState *c);
void comm_layer_poll_sync(Slot4096 *slot); // V6.0: The actual decoupling logic
// -----------------------------------------------------------------------------
// MPI FUNCTION IMPLEMENTATIONS (V5 Functional Core)
// -----------------------------------------------------------------------------
void mpi_init(MPI *m, size_t initial_words) {
m->words = calloc(initial_words, sizeof(uint64_t));
m->num_words = initial_words;
m->sign = 0;
}
void mpi_free(MPI *m) {
if (m->words) free(m->words);
m->words = NULL;
m->num_words = 0;
}
void mpi_copy(MPI *dest, const MPI *src) {
mpi_free(dest);
dest->num_words = src->num_words;
dest->words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (src->words && dest->words) {
memcpy(dest->words, src->words, src->num_words * sizeof(uint64_t));
}
dest->sign = src->sign;
}
void mpi_resize(MPI *m, size_t new_words) {
if (new_words == m->num_words) return;
if (new_words == 0) { mpi_free(m); return; }
size_t old_words = m->num_words;
m->words = (uint64_t*)realloc(m->words, new_words * sizeof(uint64_t));
if (new_words > old_words) {
memset(m->words + old_words, 0, (new_words - old_words) * sizeof(uint64_t));
}
m->num_words = new_words;
}
// Helper to update MPI struct from legacy int64_t value (V5: Exponent Sync)
void mpi_update_from_legacy(MPI *m, int64_t value) {
uint8_t sign = 0;
uint64_t magnitude = (uint64_t)value;
if (value < 0) {
sign = 1;
magnitude = (uint64_t)llabs(value);
}
// Ensure we have at least 1 word
if (m->num_words < 1) mpi_resize(m, 1);
m->words[0] = magnitude;
m->sign = sign;
// Zero out higher words if necessary
if (m->num_words > 1) {
memset(m->words + 1, 0, (m->num_words - 1) * sizeof(uint64_t));
}
}
void mpi_set_value(MPI *m, uint64_t value, uint8_t sign) {
if (m->num_words < 1) mpi_resize(m, 1);
m->words[0] = value;
m->sign = sign;
if (m->num_words > 1) {
memset(m->words + 1, 0, (m->num_words - 1) * sizeof(uint64_t));
}
}
size_t mpi_get_effective_words(const MPI *m) {
if (!m->words) return 0;
size_t i = m->num_words;
while (i > 0 && m->words[i - 1] == 0) {
i--;
}
return i;
}
// Magnitude comparison: |A| vs |B|
int mpi_compare(const MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
if (len_A > len_B) return 1;
if (len_A < len_B) return -1;
for (size_t i = len_A; i-- > 0; ) {
if (A->words[i] > B->words[i]) return 1;
if (A->words[i] < B->words[i]) return -1;
}
return 0;
}
// Signed comparison (V5 New): A vs B
int mpi_compare_signed(const MPI *A, const MPI *B) {
if (A->sign != B->sign) {
// POS (sign 0) is greater than NEG (sign 1)
return A->sign == 0 ? 1 : -1;
}
// Signs are the same. Compare magnitudes.
int mag_cmp = mpi_compare(A, B);
if (A->sign == 0) { // Both positive
return mag_cmp;
} else { // Both negative: larger magnitude means smaller (more negative) number
return -mag_cmp;
}
}
void mpi_add(MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
size_t max_len = len_A > len_B ? len_A : len_B;
if (A->num_words < max_len + 1) {
mpi_resize(A, max_len + 1);
}
uint64_t carry = 0;
for (size_t i = 0; i < max_len; ++i) {
uint64_t word_A = (i < len_A) ? A->words[i] : 0ULL;
uint64_t word_B = (i < len_B) ? B->words[i] : 0ULL;
uint64_t sum = word_A + word_B;
uint64_t carry1 = (sum < word_A);
sum += carry;
uint64_t carry2 = (sum < carry);
A->words[i] = sum;
carry = carry1 | carry2;
}
if (carry) {
A->words[max_len] = carry;
} else if (A->num_words > max_len + 1) {
memset(A->words + max_len, 0, (A->num_words - max_len) * sizeof(uint64_t));
}
}
void mpi_subtract(MPI *A, const MPI *B) {
size_t len_A = mpi_get_effective_words(A);
size_t len_B = mpi_get_effective_words(B);
if (len_A < len_B) { return; }
uint64_t borrow = 0;
for (size_t i = 0; i < len_A; ++i) {
uint64_t word_B = (i < len_B) ? B->words[i] : 0ULL;
uint64_t diff = A->words[i] - word_B - borrow;
borrow = (diff > A->words[i]) || (A->words[i] == diff && (word_B | borrow));
A->words[i] = diff;
}
size_t new_len = mpi_get_effective_words(A);
if (new_len < A->num_words) {
// Shrink the array to canonical size (or 1 if it's zero)
mpi_resize(A, new_len > 0 ? new_len : 1);
}
if (new_len == 0) mpi_set_value(A, 0ULL, 0); // Canonical zero
}
// -----------------------------------------------------------------------------
// V6.0: COMMUNICATION LAYER IMPLEMENTATIONS (Exponent Decoupling)
// -----------------------------------------------------------------------------
void comm_layer_init(CommLayerState *c) {
// Initialize the multi-word delta to zero
mpi_init(&c->remote_exponent_delta, MPI_INITIAL_WORDS);
c->status_flags = 0;
c->comm_handle_id = 0; // Start with a clean handle
}
void comm_layer_free(CommLayerState *c) {
mpi_free(&c->remote_exponent_delta);
}
/**
* V6.0 Decoupling Check: Polls the communication layer for remote updates.
* This simulates the non-blocking check for MPI_Isend/MPI_Irecv completion,
* ensuring the core arithmetic logic is decoupled from communication latency.
*/
void comm_layer_poll_sync(Slot4096 *slot) {
if (slot->comm_state.status_flags & COMM_FLAG_AWAITING_SYNC) {
// Simulate completion (50% chance per poll)
if (get_normalized_rand() < 0.5) {
slot->comm_state.status_flags &= ~COMM_FLAG_AWAITING_SYNC;
slot->comm_state.status_flags |= COMM_FLAG_SYNC_READY;
// --- Simulate Delta Update from a Remote Rank ---
// In a real system, this delta comes from the MPI layer.
int delta_val = (slot->comm_state.comm_handle_id % 2 == 0) ? 1 : -1;
MPI delta_mpi;
mpi_init(&delta_mpi, 1);
mpi_update_from_legacy(&delta_mpi, (int64_t)delta_val);
// V6.0: Apply the delta to the core APA fields.
slot->exponent += delta_val; // Update legacy exponent
// Update the authoritative MPI exponent based on the delta sign
if (delta_val > 0) mpi_add(&slot->exponent_mpi, &delta_mpi);
else mpi_subtract(&slot->exponent_mpi, &delta_mpi);
mpi_free(&delta_mpi);
// Clear the ready flag after application
slot->comm_state.status_flags &= ~COMM_FLAG_SYNC_READY;
// Uncomment for verbose logging to demonstrate decoupling
// printf("[CommLayer] Slot %d synchronized (Delta: %d).\n", slot->comm_state.comm_handle_id, delta_val);
}
}
}
// -----------------------------------------------------------------------------
// APA UTILITY FUNCTIONS
// -----------------------------------------------------------------------------
// Fixed-width multi-word magnitude comparison
int apa_mantissa_compare_magnitude(const uint64_t *A, const uint64_t *B, size_t num_words) {
for (size_t i = num_words; i-- > 0; ) {
if (A[i] > B[i]) return 1;
if (A[i] < B[i]) return -1;
}
return 0; // Equal
}
// Fixed-width multi-word magnitude addition
uint64_t apa_mantissa_add_magnitude(uint64_t *A, const uint64_t *B, size_t num_words) {
uint64_t carry = 0;
for (size_t i = num_words; i-- > 0; ) {
uint64_t sum = A[i] + B[i];
uint64_t carry1 = (sum < A[i]);
sum += carry;
uint64_t carry2 = (sum < carry);
A[i] = sum;
carry = carry1 | carry2;
}
return carry;
}
// Fixed-width multi-word magnitude subtraction (A = A - B). Assumes |A| >= |B|.
void apa_mantissa_subtract_magnitude(uint64_t *A, const uint64_t *B, size_t num_words) {
uint64_t borrow = 0;
for (size_t i = num_words; i-- > 0; ) {
uint64_t diff = A[i] - B[i] - borrow;
borrow = (diff > A[i]) || (A[i] == diff && B[i] != 0 && borrow);
A[i] = diff;
}
}
// Initialize slot with dynamic precision and APA allocation
Slot4096 slot_init_apa(int bits_mant, int bits_exp) {
Slot4096 slot = {0};
slot.bits_mant = bits_mant;
slot.bits_exp = bits_exp;
slot.num_words = (bits_mant + 63) / 64;
slot.mantissa_words = (uint64_t*)calloc(slot.num_words, sizeof(uint64_t));
// FUTURE-PROOF MPI INITIALIZATION (V3 Functional)
mpi_init(&slot.exponent_mpi, MPI_INITIAL_WORDS);
mpi_init(&slot.num_words_mantissa, MPI_INITIAL_WORDS);
mpi_init(&slot.source_of_infinity, MPI_INITIAL_WORDS);
// V6.0: Comm Layer Initialization
comm_layer_init(&slot.comm_state);
slot.comm_state.comm_handle_id = rand() % 1000; // Assign a random handle ID
slot.comm_state.status_flags |= COMM_FLAG_AWAITING_SYNC; // Simulate remote dependency
if (!slot.mantissa_words) {
fprintf(stderr, "Error: Failed to allocate multi-word mantissa.\n");
return slot;
}
if (slot.num_words > 0) {
slot.mantissa_words[0] = GET_RANDOM_UINT64();
slot.mantissa_words[0] |= MSB_MASK;
}
int64_t exp_range = 1LL << bits_exp;
int64_t exp_bias = 1LL << (bits_exp - 1);
slot.exponent = (rand() % exp_range) - exp_bias;
slot.base = PHI + get_normalized_rand() * 0.01;
// Set the target base for future MPI operations
slot.exponent_base = 4096;
// Synchronize Legacy with MPI (V5: Use new helper)
mpi_update_from_legacy(&slot.exponent_mpi, slot.exponent);
mpi_set_value(&slot.num_words_mantissa, (uint64_t)slot.num_words, 0);
return slot;
}
// Helper to free single APA slot's dynamic members
void ap_free(Slot4096 *slot) {
if (slot) {
if (slot->mantissa_words) {
free(slot->mantissa_words);
slot->mantissa_words = NULL;
}
// FUTURE-PROOF MPI CLEANUP
mpi_free(&slot->exponent_mpi);
mpi_free(&slot->num_words_mantissa);
mpi_free(&slot->source_of_infinity);
// V6.0: Comm Layer Cleanup
comm_layer_free(&slot->comm_state);
slot->num_words = 0;
}
}
// Deep copy of APA slot
void ap_copy(Slot4096 *dest, const Slot4096 *src) {
ap_free(dest);
*dest = *src; // Shallow copy of struct members
// Deep copy mantissa
dest->mantissa_words = (uint64_t*)malloc(src->num_words * sizeof(uint64_t));
if (!dest->mantissa_words) {
fprintf(stderr, "Error: Failed deep copy allocation.\n");
dest->num_words = 0;
return;
}
memcpy(dest->mantissa_words, src->mantissa_words, src->num_words * sizeof(uint64_t));
// Deep copy MPI structs
mpi_copy(&dest->exponent_mpi, &src->exponent_mpi);
mpi_copy(&dest->num_words_mantissa, &src->num_words_mantissa);
mpi_copy(&dest->source_of_infinity, &src->source_of_infinity);
// V6.0: Deep copy Comm Layer MPI struct
mpi_copy(&dest->comm_state.remote_exponent_delta, &src->comm_state.remote_exponent_delta);
}
// Converts double to APA slot
Slot4096* ap_from_double(double value, int bits_mant, int bits_exp) {
Slot4096 temp_slot = slot_init_apa(bits_mant, bits_exp);
Slot4096 *slot = (Slot4096*)malloc(sizeof(Slot4096));
if (!slot) { ap_free(&temp_slot); return NULL; }
*slot = temp_slot;
// Clear communication flags for value initialization, as it is a local conversion
slot->comm_state.status_flags = 0;
if (value == 0.0) return slot;
if (value < 0) {
slot->state_flags |= APA_FLAG_SIGN_NEG;
value = -value;
} else {
slot->state_flags &= ~APA_FLAG_SIGN_NEG;
}
int exp_offset;
double mant_val = frexp(value, &exp_offset);
slot->mantissa_words[0] = (uint64_t)(mant_val * (double)UINT64_MAX);
slot->exponent = (int64_t)exp_offset;
// Synchronize Legacy with MPI (V5: Use new helper)
mpi_update_from_legacy(&slot->exponent_mpi, slot->exponent);
return slot;
}
/**
* Multi-word right shift (V4 Logic)
*/
void ap_shift_right(uint64_t *mantissa_words, size_t num_words, int64_t shift_amount) {
if (shift_amount <= 0 || num_words == 0) return;
if (shift_amount >= (int64_t)num_words * 64) {
memset(mantissa_words, 0, num_words * sizeof(uint64_t));
return;
}
int64_t word_shift = shift_amount / 64;
int bit_shift = (int)(shift_amount % 64);
if (word_shift > 0) {
// Shift words right by word_shift positions
memmove(mantissa_words, mantissa_words + word_shift,
(num_words - word_shift) * sizeof(uint64_t));
// Zero out the highest 'word_shift' words
memset(mantissa_words + num_words - word_shift, 0, word_shift * sizeof(uint64_t));
}
if (bit_shift > 0) {
int reverse_shift = 64 - bit_shift;
// Shift bits right, propagating carry (upper bits) down
for (size_t i = num_words; i-- > 0; ) {
uint64_t upper_carry = 0;
if (i > 0) {
// Carry from the word below (higher index) in memory, which is higher magnitude
upper_carry = mantissa_words[i - 1] << reverse_shift;
}
mantissa_words[i] = (mantissa_words[i] >> bit_shift) | upper_carry;
}
}
}
// -----------------------------------------------------------------------------
// APA CORE ARITHMETIC FUNCTIONS (V6.0: Decoupling Implementation)
// -----------------------------------------------------------------------------
// Performs multi-word normalization to maintain canonical range [0.5, 1.0)
void ap_normalize(Slot4096 *slot) {
if (slot->num_words == 0) return;
// --- Check for Zero Mantissa ---
int is_zero = 1;
for (size_t i = 0; i < slot->num_words; i++) {
if (slot->mantissa_words[i] != 0) {
is_zero = 0;
break;
}
}
if (is_zero) {
slot->exponent = 0;
slot->state_flags &= ~APA_FLAG_SIGN_NEG; // Canonical zero is positive
mpi_update_from_legacy(&slot->exponent_mpi, slot->exponent); // V5: Sync MPI
return;
}
// --- Shift Left (Underflow Correction: Mantissa < 0.5) ---
while (!(slot->mantissa_words[0] & MSB_MASK)) {
if (slot->exponent <= -(1LL << (slot->bits_exp - 1))) {
slot->state_flags |= APA_FLAG_GUZ;
break;
}
uint64_t carry = 0;
for (size_t i = slot->num_words; i-- > 0; ) {
uint64_t next_carry = (slot->mantissa_words[i] & MSB_MASK) ? 1 : 0;
slot->mantissa_words[i] = (slot->mantissa_words[i] << 1) | carry;
carry = next_carry;
}
slot->exponent--;
}
// V5: Synchronize MPI after all shifting is complete
mpi_update_from_legacy(&slot->exponent_mpi, slot->exponent);
}
// Full APA addition with sign-magnitude handling (V6.0)
void ap_add(Slot4096 *A, const Slot4096 *B) {
if (A->num_words != B->num_words) {
fprintf(stderr, "Error: APA addition failed due to unaligned word counts.\n");
return;
}
Slot4096 B_aligned;
ap_copy(&B_aligned, B);
// --- V6.0: Communication Layer Synchronization Point ---
// Enforce decoupling: If the exponent is dependent on a remote operation, poll for completion
comm_layer_poll_sync(A);
comm_layer_poll_sync(&B_aligned);
// After this point, the core logic relies on the now-synchronized MPI exponents.
// --- 1. Exponent Alignment (V5/V6.0: Use MPI comparison for decision) ---
// Determine which MPI exponent is larger (signed comparison)
int exp_cmp = mpi_compare_signed(&A->exponent_mpi, &B_aligned.exponent_mpi);
int64_t exp_diff = A->exponent - B_aligned.exponent; // Use legacy field for the shift amount calculation
if (exp_cmp > 0) { // A.exp > B.exp (A is larger/more positive)
// Shift B right. Shift amount is the difference (A.exp - B.exp).
int64_t shift_amount = exp_diff;
ap_shift_right(B_aligned.mantissa_words, B_aligned.num_words, shift_amount);
// Update B_aligned's exponent to match A's
B_aligned.exponent = A->exponent;
mpi_copy(&B_aligned.exponent_mpi, &A->exponent_mpi); // V5: Sync B's MPI
} else if (exp_cmp < 0) { // B.exp > A.exp (B is larger/more positive)
// Shift A right. Shift amount is the difference (B.exp - A.exp).
int64_t shift_amount = -exp_diff;
ap_shift_right(A->mantissa_words, A->num_words, shift_amount);
// Update A's exponent to match B's
A->exponent = B_aligned.exponent;
mpi_copy(&A->exponent_mpi, &B_aligned.exponent_mpi); // V5: Sync A's MPI
}
// If exp_cmp == 0, exponents are already aligned.
// --- 2. Sign-Magnitude Decision (V4 Core Logic) ---
int sign_A = (A->state_flags & APA_FLAG_SIGN_NEG) ? 1 : 0;
int sign_B = (B_aligned.state_flags & APA_FLAG_SIGN_NEG) ? 1 : 0;
uint64_t final_carry = 0;
if (sign_A == sign_B) {
// Case 1: Same Signs -> Add Magnitudes
final_carry = apa_mantissa_add_magnitude(A->mantissa_words, B_aligned.mantissa_words, A->num_words);
} else {
// Case 2: Different Signs -> Subtract Magnitudes
int cmp_result = apa_mantissa_compare_magnitude(A->mantissa_words, B_aligned.mantissa_words, A->num_words);
if (cmp_result >= 0) {
// |A| >= |B|. Result sign is A's sign. (A = A - B)
apa_mantissa_subtract_magnitude(A->mantissa_words, B_aligned.mantissa_words, A->num_words);
} else {
// |A| < |B|. Result sign is B's sign. (A = B - A)
uint64_t *temp_words = (uint64_t*)malloc(A->num_words * sizeof(uint64_t));
memcpy(temp_words, B_aligned.mantissa_words, A->num_words * sizeof(uint64_t));
apa_mantissa_subtract_magnitude(temp_words, A->mantissa_words, A->num_words);
memcpy(A->mantissa_words, temp_words, A->num_words * sizeof(uint64_t));
free(temp_words);
// Set A's sign to B's sign
if (sign_B) A->state_flags |= APA_FLAG_SIGN_NEG;
else A->state_flags &= ~APA_FLAG_SIGN_NEG;
}
}
// --- 3. Final Carry Handling (Only for magnitude addition) ---
if (final_carry) {
// Overflow due to addition (result >= 2.0 * 2^exp). Renormalize.
if (A->exponent >= (1LL << (A->bits_exp - 1))) {
A->state_flags |= APA_FLAG_GOI;
} else {
A->exponent += 1; // Increment legacy exponent
// Right shift all words by 1 bit, propagating carry down
uint64_t next_carry = final_carry << 63;
for (size_t i = 0; i < A->num_words; i++) {
uint64_t current_carry_bit = A->mantissa_words[i] & 1;
A->mantissa_words[i] = (A->mantissa_words[i] >> 1) | next_carry;
next_carry = current_carry_bit << 63;
}
}
// V5: Sync A's MPI exponent after carry update
mpi_update_from_legacy(&A->exponent_mpi, A->exponent);
}
// --- 4. Final Normalization and Sync ---
ap_normalize(A);
ap_free(&B_aligned);
}
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
// HDGL Lattice (Unchanged from V4/V5)
// ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
typedef struct {
Slot4096 *slots;
size_t allocated;
} HDGLChunk;
typedef struct {
HDGLChunk **chunks;
int num_chunks;
int num_instances;
int slots_per_instance;
double omega;
double time;
} HDGLLattice;
// Initialize lattice
HDGLLattice* lattice_init(int num_instances, int slots_per_instance) {
HDGLLattice *lat = malloc(sizeof(HDGLLattice));
if (!lat) return NULL;
lat->num_instances = num_instances;
lat->slots_per_instance = slots_per_instance;
lat->omega = 0.0;
lat->time = 0.0;
int total_slots = num_instances * slots_per_instance;
lat->num_chunks = (total_slots + CHUNK_SIZE - 1) / CHUNK_SIZE;
lat->chunks = calloc(lat->num_chunks, sizeof(HDGLChunk*));
if (!lat->chunks) { free(lat); return NULL; }
return lat;
}
// Get chunk, allocate if needed
HDGLChunk* lattice_get_chunk(HDGLLattice *lat, int chunk_idx) {
if (chunk_idx >= lat->num_chunks) return NULL;
if (!lat->chunks[chunk_idx]) {
HDGLChunk *chunk = malloc(sizeof(HDGLChunk));
if (!chunk) return NULL;
chunk->allocated = CHUNK_SIZE;
chunk->slots = (Slot4096*)malloc(CHUNK_SIZE * sizeof(Slot4096));
if (!chunk->slots) { free(chunk); return NULL; }
for (int i = 0; i < CHUNK_SIZE; i++) {
// Dynamic precision allocation: 4096 bits minimum, up to 4576 bits
int bits_mant = 4096 + (i % 8) * 64;
int bits_exp = 16 + (i % 8) * 2;
chunk->slots[i] = slot_init_apa(bits_mant, bits_exp);
}
lat->chunks[chunk_idx] = chunk;
}
return lat->chunks[chunk_idx];
}
// Get slot pointer
Slot4096* lattice_get_slot(HDGLLattice *lat, int idx) {
int chunk_idx = idx / CHUNK_SIZE;
int local_idx = idx % CHUNK_SIZE;
HDGLChunk *chunk = lattice_get_chunk(lat, chunk_idx);
if (!chunk) return NULL;
return &chunk->slots[local_idx];
}
// Prismatic recursion function (MUST use lossy double for calculation input)
double prismatic_recursion(HDGLLattice *lat, int idx, double val) {
double phi_harm = pow(PHI, (double)(idx % 16));
double fib_harm = fib_table[idx % fib_len];
double dyadic = (double)(1 << (idx % 16));
double prime_harm = prime_table[idx % prime_len];
double omega_val = 0.5 + 0.5 * sin(lat->time + idx * 0.01);
double r_dim = pow(val, (double)((idx % 7) + 1));
return sqrt(phi_harm * fib_harm * dyadic * prime_harm * omega_val) * r_dim;
}
// Converts APA to double (Lossy, for display/recursion input)
double ap_to_double(const Slot4096 *slot) {
if (!slot || slot->num_words == 0 || !slot->mantissa_words) return 0.0;
double mantissa_double = (double)slot->mantissa_words[0] / (double)UINT64_MAX;
double result = mantissa_double * pow(2.0, (double)slot->exponent);
if (slot->state_flags & APA_FLAG_SIGN_NEG) {
result *= -1.0;
}
return result;
}
// CPU step with APA processing
void lattice_step_cpu(HDGLLattice *lat, double tick) {
int total_slots = lat->num_instances * lat->slots_per_instance;
for (int i = 0; i < total_slots; i++) {
Slot4096 *slot = lattice_get_slot(lat, i);
if (!slot) continue;
// Check for Implied Precision State
if (slot->state_flags & (APA_FLAG_GOI | APA_FLAG_IS_NAN)) {
// Skip computation if state is implied infinity or NaN
continue;
}
double val = ap_to_double(slot);
double r = prismatic_recursion(lat, i, fabs(val));
// Ensure increment value can be negative to test sign-magnitude arithmetic
double increment_value = (pow(slot->base, (double)slot->exponent) * tick + 0.05 * r) * (i % 2 == 0 ? 1.0 : -1.0);
Slot4096 *increment_apa = ap_from_double(
increment_value, slot->bits_mant, slot->bits_exp
);
if (!increment_apa) continue;
ap_add(slot, increment_apa);
ap_free(increment_apa);
free(increment_apa);
}
lat->omega += 0.01 * tick;
lat->time += tick;
}
// Prismatic folding: double instance count
void lattice_fold(HDGLLattice *lat) {
int old_instances = lat->num_instances;
int new_instances = old_instances * 2;
if (new_instances > MAX_INSTANCES) return;
int old_total = old_instances * lat->slots_per_instance;
int new_total = new_instances * lat->slots_per_instance;
int old_chunks = lat->num_chunks;
int new_chunks = (new_total + CHUNK_SIZE - 1) / CHUNK_SIZE;
HDGLChunk **new_chunks_ptr = realloc(lat->chunks, new_chunks * sizeof(HDGLChunk*));
if (!new_chunks_ptr) {
fprintf(stderr, "Failed to allocate memory for folding\n");
return;
}
lat->chunks = new_chunks_ptr;
for (int i = old_chunks; i < new_chunks; i++) {
lat->chunks[i] = NULL;
}
for (int i = 0; i < old_total; i++) {
Slot4096 *old_slot = lattice_get_slot(lat, i);
Slot4096 *new_slot = lattice_get_slot(lat, old_total + i);
if (old_slot && new_slot) {
ap_copy(new_slot, old_slot);
double perturbation = fib_table[i % fib_len] * 0.01;
Slot4096 *pert_apa = ap_from_double(perturbation, new_slot->bits_mant, new_slot->bits_exp);
if (pert_apa) {
ap_add(new_slot, pert_apa);
ap_free(pert_apa);
free(pert_apa);
}
new_slot->base += get_normalized_rand() * 0.001;
}
}
lat->num_instances = new_instances;
lat->num_chunks = new_chunks;
}
// Free lattice: MUST handle freeing multi-word mantissa in every slot
void lattice_free(HDGLLattice *lat) {
if (!lat) return;
for (int i = 0; i < lat->num_chunks; i++) {
if (lat->chunks[i])
