ElegantUnifiedPrecisionLedger4.java
package com.xai.float4096;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.util.*;
/**
* High-precision floating-point class with 4096-bit precision.
* Features quaternary DNA logic and a native Turing-complete language (QuatDnaLang).
* Demonstrates functional completeness through subtraction-based logic gates.
*/
public final class Float4096 {
private static final MathContext PRECISION_4096 = new MathContext(4096, RoundingMode.HALF_EVEN);
// Core constants
public static final Float4096 ZERO = new Float4096("0.0");
public static final Float4096 NEG_ZERO = new Float4096("-0.0");
public static final Float4096 ONE = new Float4096("1");
public static final Float4096 TWO = new Float4096("2");
public static final Float4096 PHI = calculateGoldenRatio();
private final BigDecimal value;
// Constructors
public Float4096(String value) {
this.value = new BigDecimal(value, PRECISION_4096);
}
public Float4096(BigDecimal value) {
this.value = Objects.requireNonNull(value).round(PRECISION_4096);
}
public Float4096(double value) {
this.value = new BigDecimal(value, PRECISION_4096);
}
// Core arithmetic operations
public Float4096 add(Float4096 other) {
return new Float4096(this.value.add(other.value, PRECISION_4096));
}
public Float4096 subtract(Float4096 other) {
return new Float4096(this.value.subtract(other.value, PRECISION_4096));
}
public Float4096 multiply(Float4096 other) {
return new Float4096(this.value.multiply(other.value, PRECISION_4096));
}
public Float4096 divide(Float4096 other) {
if (other.value.signum() == 0) {
throw new ArithmeticException("Division by zero");
}
return new Float4096(this.value.divide(other.value, PRECISION_4096));
}
public Float4096 sqrt() {
if (this.value.signum() < 0) {
throw new ArithmeticException("Square root of negative number");
}
BigDecimal x = this.value;
for (int i = 0; i < 100; i++) {
BigDecimal prev = x;
x = x.add(this.value.divide(x, PRECISION_4096)).divide(TWO.value, PRECISION_4096);
if (x.equals(prev)) break;
}
return new Float4096(x);
}
public Float4096 abs() {
return new Float4096(this.value.abs(PRECISION_4096));
}
// Power and logarithm for completeness
public Float4096 pow(Float4096 exponent) {
return exp(exponent.multiply(ln(this)));
}
public static Float4096 exp(Float4096 x) {
BigDecimal bd = x.getValue();
BigDecimal sum = BigDecimal.ONE;
BigDecimal term = BigDecimal.ONE;
BigDecimal n = BigDecimal.ONE;
for (int i = 1; i <= 1000; i++) {
term = term.multiply(bd).divide(n, PRECISION_4096);
BigDecimal newSum = sum.add(term, PRECISION_4096);
if (newSum.equals(sum)) break;
sum = newSum;
n = n.add(BigDecimal.ONE);
}
return new Float4096(sum);
}
public static Float4096 ln(Float4096 x) {
BigDecimal bd = x.getValue();
if (bd.compareTo(BigDecimal.ZERO) <= 0) {
throw new IllegalArgumentException("Natural log of non-positive number");
}
if (bd.compareTo(BigDecimal.ONE) == 0) return ZERO;
// Using continued fraction approximation for ln(x)
BigDecimal y = bd.subtract(BigDecimal.ONE, PRECISION_4096);
BigDecimal ret = new BigDecimal("1001", PRECISION_4096);
for (long i = 1000; i >= 0; i--) {
BigDecimal N = new BigDecimal(i / 2 + 1).pow(2, PRECISION_4096).multiply(y, PRECISION_4096);
ret = N.divide(ret, PRECISION_4096).add(new BigDecimal(i + 1), PRECISION_4096);
}
return new Float4096(y.divide(ret, PRECISION_4096));
}
// Utility methods
public int compareTo(Float4096 other) {
return this.value.compareTo(other.value);
}
public boolean isZero() {
return this.value.signum() == 0;
}
public double toDouble() {
return this.value.doubleValue();
}
public BigDecimal getValue() {
return value;
}
@Override
public String toString() {
return value.toPlainString();
}
@Override
public boolean equals(Object o) {
if (this == o) return true;
if (!(o instanceof Float4096)) return false;
return value.equals(((Float4096) o).value);
}
@Override
public int hashCode() {
return Objects.hash(value);
}
// Logic gates using subtraction (demonstrating functional completeness)
public static Float4096 logicNot(Float4096 input) {
return NEG_ZERO.subtract(input);
}
public static Float4096 logicAnd(Float4096 a, Float4096 b) {
return logicNot(logicOr(logicNot(a), logicNot(b)));
}
public static Float4096 logicOr(Float4096 a, Float4096 b) {
return a.subtract(logicNot(b));
}
public static Float4096 logicXor(Float4096 a, Float4096 b) {
return logicOr(logicAnd(logicNot(a), b), logicAnd(a, logicNot(b)));
}
// Quaternary DNA Logic System
private static final Map<Character, Integer> DNA_TO_QUAT = Map.of(
'A', 0, 'C', 1, 'G', 2, 'T', 3
);
private static final Map<Integer, Character> QUAT_TO_DNA = Map.of(
0, 'A', 1, 'C', 2, 'G', 3, 'T'
);
// Base-4096 alphabet generated deterministically
private static final List<Character> BASE4096_ALPHABET = generateAlphabet();
private static List<Character> generateAlphabet() {
try {
MessageDigest digest = MessageDigest.getInstance("SHA-256");
byte[] hash = digest.digest("Float4096".getBytes("UTF-8"));
Random rand = new Random(new BigInteger(1, hash).longValue());
Set<Character> uniqueChars = new LinkedHashSet<>();
while (uniqueChars.size() < 4096) {
int codePoint = 33 + rand.nextInt(0x10FFFF - 33); // Printable range
if (Character.isValidCodePoint(codePoint) && !Character.isISOControl(codePoint)) {
uniqueChars.add((char) codePoint);
}
}
return new ArrayList<>(uniqueChars);
} catch (Exception e) {
throw new RuntimeException("Failed to generate alphabet", e);
}
}
private static void validateDNA(String dna) {
if (dna == null || dna.isEmpty()) {
throw new IllegalArgumentException("Invalid DNA sequence");
}
for (char c : dna.toCharArray()) {
if (!DNA_TO_QUAT.containsKey(Character.toUpperCase(c))) {
throw new IllegalArgumentException("Invalid DNA base: " + c);
}
}
}
// Quaternary operations
public static int quatMin(int a, int b) {
return Math.min(Math.max(0, Math.min(3, a)), Math.max(0, Math.min(3, b)));
}
public static int quatMax(int a, int b) {
return Math.max(Math.max(0, Math.min(3, a)), Math.max(0, Math.min(3, b)));
}
public static int quatInvert(int a) {
return 3 - Math.max(0, Math.min(3, a));
}
public static int quatSuccessor(int a) {
return (Math.max(0, Math.min(3, a)) + 1) % 4;
}
public static int quatPredecessor(int a) {
return (Math.max(0, Math.min(3, a)) + 3) % 4;
}
// DNA sequence operations
public static String dnaQuatMin(String dna1, String dna2) {
validateDNA(dna1);
validateDNA(dna2);
if (dna1.length() != dna2.length()) {
throw new IllegalArgumentException("DNA sequences must be same length");
}
StringBuilder result = new StringBuilder();
for (int i = 0; i < dna1.length(); i++) {
int a = DNA_TO_QUAT.get(Character.toUpperCase(dna1.charAt(i)));
int b = DNA_TO_QUAT.get(Character.toUpperCase(dna2.charAt(i)));
result.append(QUAT_TO_DNA.get(quatMin(a, b)));
}
return result.toString();
}
public static String dnaQuatMax(String dna1, String dna2) {
validateDNA(dna1);
validateDNA(dna2);
if (dna1.length() != dna2.length()) {
throw new IllegalArgumentException("DNA sequences must be same length");
}
StringBuilder result = new StringBuilder();
for (int i = 0; i < dna1.length(); i++) {
int a = DNA_TO_QUAT.get(Character.toUpperCase(dna1.charAt(i)));
int b = DNA_TO_QUAT.get(Character.toUpperCase(dna2.charAt(i)));
result.append(QUAT_TO_DNA.get(quatMax(a, b)));
}
return result.toString();
}
public static String dnaQuatInvert(String dna) {
validateDNA(dna);
StringBuilder result = new StringBuilder();
for (char c : dna.toCharArray()) {
int val = DNA_TO_QUAT.get(Character.toUpperCase(c));
result.append(QUAT_TO_DNA.get(quatInvert(val)));
}
return result.toString();
}
// Conversion between DNA and numeric representations
public static String dnaQuatAdd(String dna1, String dna2) {
validateDNA(dna1);
validateDNA(dna2);
BigInteger num1 = dnaToBigInteger(dna1);
BigInteger num2 = dnaToBigInteger(dna2);
return bigIntegerToDna(num1.add(num2));
}
private static BigInteger dnaToBigInteger(String dna) {
BigInteger num = BigInteger.ZERO;
BigInteger base = BigInteger.valueOf(4);
for (char c : dna.toUpperCase().toCharArray()) {
int digit = DNA_TO_QUAT.get(c);
num = num.multiply(base).add(BigInteger.valueOf(digit));
}
return num;
}
private static String bigIntegerToDna(BigInteger num) {
if (num.signum() < 0) {
throw new IllegalArgumentException("Negative numbers not supported in DNA representation");
}
if (num.equals(BigInteger.ZERO)) return "A";
StringBuilder dna = new StringBuilder();
BigInteger base = BigInteger.valueOf(4);
while (num.compareTo(BigInteger.ZERO) > 0) {
int remainder = num.mod(base).intValue();
dna.append(QUAT_TO_DNA.get(remainder));
num = num.divide(base);
}
return dna.reverse().toString();
}
// Base-4096 encoding (6 DNA bases = 1 symbol, since 4^6 = 4096)
public static String encodeDnaToBase4096(String dna) {
validateDNA(dna);
String paddedDna = dna.toUpperCase();
int padLength = (6 - (paddedDna.length() % 6)) % 6;
paddedDna += "A".repeat(padLength);
StringBuilder encoded = new StringBuilder();
for (int i = 0; i < paddedDna.length(); i += 6) {
String group = paddedDna.substring(i, i + 6);
BigInteger value = dnaToBigInteger(group);
encoded.append(BASE4096_ALPHABET.get(value.intValueExact()));
}
return encoded.toString();
}
public static String decodeBase4096ToDna(String encoded) {
StringBuilder dna = new StringBuilder();
for (char symbol : encoded.toCharArray()) {
int index = BASE4096_ALPHABET.indexOf(symbol);
if (index == -1) {
throw new IllegalArgumentException("Invalid base-4096 symbol: " + symbol);
}
String groupDna = bigIntegerToDna(BigInteger.valueOf(index));
while (groupDna.length() < 6) {
groupDna = "A" + groupDna;
}
dna.append(groupDna);
}
return dna.toString().replaceAll("A+$", "");
}
// Conversion between Float4096 and DNA
public String toDnaSequence() {
BigInteger intPart = this.value.toBigInteger();
return bigIntegerToDna(intPart);
}
public static Float4096 fromDnaSequence(String dna) {
BigInteger num = dnaToBigInteger(dna);
return new Float4096(new BigDecimal(num, PRECISION_4096));
}
/**
* QuatDnaLang - A minimal Turing-complete language native to Float4096
* Commands are encoded as DNA pairs (2 bases each):
* AA: + (increment quaternary value)
* AC: - (decrement quaternary value)
* AG: > (move right)
* AT: < (move left)
* CA: . (output current cell as DNA base)
* CC: , (input DNA base to current cell)
* CG: [ (loop start if current cell != 0)
* CT: ] (loop end, jump back if current cell != 0)
* GA: I (invert current cell: 3-value)
* GC: M (min with next cell)
* GG: X (max with next cell)
* TT: E (eval: execute subprogram from tape)
*/
public static final class QuatDnaLangInterpreter {
private static final Map<String, Character> COMMANDS = Map.of(
"AA", '+', // Increment (successor in quaternary)
"AC", '-', // Decrement (predecessor in quaternary)
"AG", '>', // Move tape head right
"AT", '<', // Move tape head left
"CA", '.', // Output current cell as DNA base
"CC", ',', // Input DNA base to current cell
"CG", '[', // Loop start
"CT", ']', // Loop end
"GA", 'I', // Invert current cell (3 - value)
"GC", 'M', // Min with next cell
"GG", 'X', // Max with next cell
"TT", 'E' // Eval subprogram from tape
);
public static String execute(String program, String input, int maxSteps) {
validateDNA(program);
if (program.length() % 2 != 0) program += "A"; // Pad if odd length
validateDNA(input);
// Parse program into instructions
List<Character> instructions = new ArrayList<>();
for (int i = 0; i < program.length(); i += 2) {
String pair = program.substring(i, Math.min(i + 2, program.length())).toUpperCase();
Character cmd = COMMANDS.get(pair);
if (cmd != null) instructions.add(cmd);
}
// Build bracket map for loops
Map<Integer, Integer> bracketMap = buildBracketMap(instructions);
// Initialize execution environment
Map<Integer, Integer> tape = new HashMap<>(); // Sparse tape
tape.put(0, 0);
int head = 0;
int inputIndex = 0;
// Convert input to quaternary array
int[] inputArray = input.toUpperCase().chars()
.map(c -> DNA_TO_QUAT.get((char) c))
.toArray();
StringBuilder output = new StringBuilder();
// Execute program
int pc = 0;
int step = 0;
while (pc < instructions.size() && step < maxSteps) {
char cmd = instructions.get(pc);
int current = tape.getOrDefault(head, 0);
switch (cmd) {
case '+' -> tape.put(head, quatSuccessor(current));
case '-' -> tape.put(head, quatPredecessor(current));
case '>' -> head++;
case '<' -> head--;
case '.' -> output.append(QUAT_TO_DNA.get(current));
case ',' -> tape.put(head, inputIndex < inputArray.length ? inputArray[inputIndex++] : 0);
case '[' -> { if (current == 0) pc = bracketMap.get(pc); }
case ']' -> { if (current != 0) pc = bracketMap.get(pc); }
case 'I' -> tape.put(head, quatInvert(current));
case 'M' -> {
int next = tape.getOrDefault(head + 1, 0);
tape.put(head, quatMin(current, next));
}
case 'X' -> {
int next = tape.getOrDefault(head + 1, 0);
tape.put(head, quatMax(current, next));
}
case 'E' -> {
// Extract and execute subprogram from tape
StringBuilder subProgram = extractSubProgram(tape, head + 1);
String subOutput = execute(subProgram.toString(), "", maxSteps - step);
writeSubOutput(tape, head + 1, subOutput);
}
}
pc++;
step++;
}
if (step >= maxSteps) {
throw new RuntimeException("Maximum steps exceeded");
}
return output.toString();
}
private static Map<Integer, Integer> buildBracketMap(List<Character> instructions) {
Map<Integer, Integer> bracketMap = new HashMap<>();
Deque<Integer> stack = new LinkedList<>();
for (int i = 0; i < instructions.size(); i++) {
char cmd = instructions.get(i);
if (cmd == '[') {
stack.push(i);
} else if (cmd == ']') {
if (stack.isEmpty()) {
throw new IllegalArgumentException("Mismatched brackets in program");
}
int open = stack.pop();
bracketMap.put(open, i);
bracketMap.put(i, open);
}
}
if (!stack.isEmpty()) {
throw new IllegalArgumentException("Mismatched brackets in program");
}
return bracketMap;
}
private static StringBuilder extractSubProgram(Map<Integer, Integer> tape, int start) {
StringBuilder subProgram = new StringBuilder();
int pos = start;
while (tape.containsKey(pos) && tape.get(pos) != 0) {
int a = tape.get(pos);
int b = tape.getOrDefault(pos + 1, 0);
if (a == 0 && b == 0) break;
subProgram.append(QUAT_TO_DNA.get(a)).append(QUAT_TO_DNA.get(b));
pos += 2;
}
return subProgram;
}
private static void writeSubOutput(Map<Integer, Integer> tape, int start, String output) {
int pos = start;
// Clear existing data
while (tape.containsKey(pos) && tape.get(pos) != 0) {
tape.remove(pos);
pos++;
}
// Write new output
pos = start;
for (char c : output.toCharArray()) {
tape.put(pos++, DNA_TO_QUAT.get(c));
}
}
}
// Helper method for golden ratio calculation
private static Float4096 calculateGoldenRatio() {
Float4096 five = new Float4096("5");
Float4096 sqrt5 = five.sqrt();
return ONE.add(sqrt5).divide(TWO);
}
}
ElegantUnifiedPrecisionLedger3.java
package com.xai.float4096;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Deque;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Objects;
/**
* High-precision floating-point class with 4096-bit precision, rooted in the golden ratio (φ).
* Provides arithmetic, quaternary DNA logic, and a Turing-complete language (QuatDnaLang).
* Integrates a recursive dimensional framework for derived constants and force modeling.
* Optimized for elegance with sparse tape, cached prime interpolation, and unified field quantities.
*/
public final class Float4096 {
private static final MathContext PRECISION_4096 = new MathContext(4096, RoundingMode.HALF_EVEN);
private static final Float4096 EPSILON = new Float4096("1e-20");
// Core constants
private static final Float4096 FIVE = new Float4096("5");
private static final Float4096 B = new Float4096("10000");
public static final Float4096 ZERO = new Float4096("0.0");
public static final Float4096 NEG_ZERO = new Float4096("-0.0");
public static final Float4096 ONE = new Float4096("1");
public static final Float4096 TWO = new Float4096("2");
public static final Float4096 PHI = calculateGoldenRatio();
public static final Float4096 SQRT5 = FIVE.sqrt();
public static final Float4096 LN_PHI = ln(PHI);
private final BigDecimal value;
// Constructors
public Float4096(String value) {
this.value = new BigDecimal(value, PRECISION_4096);
if (!isFinite()) throw new ArithmeticException("Invalid Float4096 value");
}
public Float4096(BigDecimal value) {
this.value = Objects.requireNonNull(value).round(PRECISION_4096);
if (!isFinite()) throw new ArithmeticException("Invalid Float4096 value");
}
public Float4096(double value) {
this.value = new BigDecimal(value, PRECISION_4096);
if (!isFinite()) throw new ArithmeticException("Invalid Float4096 value");
}
// Arithmetic
public Float4096 add(Float4096 other) {
Float4096 result = new Float4096(this.value.add(other.value, PRECISION_4096));
return result.isFinite() ? result : throwArithmeticException("Addition overflow");
}
public Float4096 subtract(Float4096 other) {
Float4096 result = new Float4096(this.value.subtract(other.value, PRECISION_4096));
return result.isFinite() ? result : throwArithmeticException("Subtraction overflow");
}
public Float4096 multiply(Float4096 other) {
Float4096 result = new Float4096(this.value.multiply(other.value, PRECISION_4096));
return result.isFinite() ? result : throwArithmeticException("Multiplication overflow");
}
public Float4096 divide(Float4096 other) {
if (other.value.signum() == 0) throw new ArithmeticException("Division by zero");
Float4096 result = new Float4096(this.value.divide(other.value, PRECISION_4096));
return result.isFinite() ? result : throwArithmeticException("Division overflow");
}
public Float4096 sqrt() {
if (this.value.signum() < 0) throw new ArithmeticException("Square root of negative number");
BigDecimal x = this.value;
for (int i = 0; i < 100; i++) {
BigDecimal prev = x;
x = x.add(this.value.divide(x, PRECISION_4096)).divide(TWO.value, PRECISION_4096);
if (x.equals(prev)) break;
}
Float4096 result = new Float4096(x);
return result.isFinite() ? result : throwArithmeticException("Square root overflow");
}
public Float4096 abs() {
return new Float4096(this.value.abs(PRECISION_4096));
}
// Exponentiation & log
public Float4096 pow(Float4096 exponent) {
Float4096 result = exp(exponent.multiply(ln(this)));
return result.isFinite() ? result : throwArithmeticException("Power overflow");
}
public static Float4096 exp(Float4096 x) {
BigDecimal bd = x.getValue(), sum = BigDecimal.ONE, term = BigDecimal.ONE, n = BigDecimal.ONE;
for (int i = 1; i <= 2000; i++) {
term = term.multiply(bd).divide(n, PRECISION_4096);
BigDecimal newSum = sum.add(term, PRECISION_4096);
if (newSum.equals(sum)) break;
sum = newSum;
n = n.add(BigDecimal.ONE);
}
Float4096 result = new Float4096(sum);
return result.isFinite() ? result : throwArithmeticException("Exp overflow");
}
public static Float4096 ln(Float4096 x) {
BigDecimal bd = x.getValue();
if (bd.compareTo(BigDecimal.ZERO) <= 0) throw new IllegalArgumentException("ln of non-positive");
if (bd.compareTo(BigDecimal.ONE) == 0) return ZERO;
BigDecimal y = bd.subtract(BigDecimal.ONE, PRECISION_4096), ret = new BigDecimal("2001", PRECISION_4096);
for (long i = 2000; i >= 0; i--) {
BigDecimal N = new BigDecimal(i / 2 + 1).pow(2, PRECISION_4096).multiply(y, PRECISION_4096);
ret = N.divide(ret, PRECISION_4096).add(new BigDecimal(i + 1), PRECISION_4096);
}
Float4096 result = new Float4096(y.divide(ret, PRECISION_4096));
return result.isFinite() ? result : throwArithmeticException("Log overflow");
}
// Utilities
public int compareTo(Float4096 other) { return this.value.compareTo(other.value); }
public boolean isZero() { return this.value.signum() == 0; }
public boolean isFinite() { return this.value.stripTrailingZeros().scale() <= PRECISION_4096.getPrecision() && !this.value.isInfinite() && !this.value.isNaN(); }
public boolean isNaN() { return this.value.isNaN(); }
public double toDouble() { return this.value.doubleValue(); }
public BigDecimal getValue() { return value; }
@Override public String toString() { return value.toPlainString(); }
@Override public boolean equals(Object o) { return this == o || (o instanceof Float4096 f && value.equals(f.value)); }
@Override public int hashCode() { return Objects.hash(value); }
private static Float4096 throwArithmeticException(String message) { throw new ArithmeticException(message); }
// Binary logic
public static Float4096 logicNot(Float4096 input) { return NEG_ZERO.subtract(input); }
public static Float4096 logicAnd(Float4096 a, Float4096 b) { return logicNot(logicOr(logicNot(a), logicNot(b))); }
public static Float4096 logicOr(Float4096 a, Float4096 b) { return a.subtract(logicNot(b)); }
public static Float4096 logicXor(Float4096 a, Float4096 b) { return logicOr(logicAnd(logicNot(a), b), logicAnd(a, logicNot(b))); }
// Quaternary DNA logic
private static final Map<Character, Integer> DNA_TO_QUAT = Map.of('A', 0, 'C', 1, 'G', 2, 'T', 3);
private static final Map<Integer, Character> QUAT_TO_DNA = Map.of(0, 'A', 1, 'C', 2, 'G', 3, 'T');
private static final List<Character> BASE4096_ALPHABET = generateBase4096Alphabet();
private static List<Character> generateBase4096Alphabet() {
List<Character> chars = new ArrayList<>(4096);
Float4096 seed = PHI;
for (int i = 0; i < 4096; i++) {
BigInteger hash = seed.toBigInteger();
int codePoint = hash.mod(BigInteger.valueOf(0x10FFFF + 1)).intValue();
while (!Character.isValidCodePoint(codePoint) || chars.contains((char) codePoint)) {
seed = seed.multiply(PHI).add(new Float4096(i));
hash = seed.toBigInteger();
codePoint = hash.mod(BigInteger.valueOf(0x10FFFF + 1)).intValue();
}
chars.add((char) codePoint);
seed = seed.multiply(PHI).add(new Float4096(i + 1));
}
return chars;
}
private static void validateDNA(String dna) {
if (dna == null || dna.isEmpty()) throw new IllegalArgumentException("Invalid DNA");
for (char c : dna.toCharArray()) if (!DNA_TO_QUAT.containsKey(Character.toUpperCase(c)))
throw new IllegalArgumentException("Invalid DNA base: " + c);
}
public static int quatMin(int a, int b) { return Math.min(Math.max(0, a), 3); }
public static int quatMax(int a, int b) { return Math.max(Math.min(3, a), 0); }
public static int quatInvert(int a) { return 3 - Math.max(0, Math.min(3, a)); }
public static int quatSuccessor(int a) { return (Math.max(0, Math.min(3, a)) + 1) % 4; }
public static int quatPredecessor(int a) { return (Math.max(0, Math.min(3, a)) + 3) % 4; }
public static String dnaQuatMin(String dna1, String dna2) {
validateDNA(dna1); validateDNA(dna2);
if (dna1.length() != dna2.length()) throw new IllegalArgumentException("DNA sequences must be same length");
StringBuilder result = new StringBuilder();
for (int i = 0; i < dna1.length(); i++)
result.append(QUAT_TO_DNA.get(quatMin(DNA_TO_QUAT.get(dna1.charAt(i)), DNA_TO_QUAT.get(dna2.charAt(i)))));
return result.toString();
}
public static String dnaQuatMax(String dna1, String dna2) {
validateDNA(dna1); validateDNA(dna2);
if (dna1.length() != dna2.length()) throw new IllegalArgumentException("DNA sequences must be same length");
StringBuilder result = new StringBuilder();
for (int i = 0; i < dna1.length(); i++)
result.append(QUAT_TO_DNA.get(quatMax(DNA_TO_QUAT.get(dna1.charAt(i)), DNA_TO_QUAT.get(dna2.charAt(i)))));
return result.toString();
}
public static String dnaQuatInvert(String dna) {
validateDNA(dna);
StringBuilder result = new StringBuilder();
for (char c : dna.toCharArray()) result.append(QUAT_TO_DNA.get(quatInvert(DNA_TO_QUAT.get(Character.toUpperCase(c)))));
return result.toString();
}
public static String dnaQuatAdd(String dna1, String dna2) {
validateDNA(dna1); validateDNA(dna2);
return bigIntegerToDna(dnaToBigInteger(dna1).add(dnaToBigInteger(dna2)));
}
public static String encodeDnaToBase4096(String dna) {
validateDNA(dna);
String paddedDna = dna.toUpperCase() + "A".repeat((6 - (dna.length() % 6)) % 6);
StringBuilder encoded = new StringBuilder();
for (int i = 0; i < paddedDna.length(); i += 6)
encoded.append(BASE4096_ALPHABET.get(dnaToBigInteger(paddedDna.substring(i, i + 6)).intValueExact()));
return encoded.toString();
}
public static String decodeBase4096ToDna(String encoded) {
StringBuilder dna = new StringBuilder();
for (char symbol : encoded.toCharArray()) {
int index = BASE4096_ALPHABET.indexOf(symbol);
if (index == -1) throw new IllegalArgumentException("Invalid base-4096 symbol: " + symbol);
String groupDna = bigIntegerToDna(BigInteger.valueOf(index));
while (groupDna.length() < 6) groupDna = "A" + groupDna;
dna.append(groupDna);
}
return dna.toString().replaceAll("A+$", "");
}
public String toDnaSequence() { return bigIntegerToDna(this.value.toBigInteger()); }
public static Float4096 fromDnaSequence(String dna) {
Float4096 result = new Float4096(new BigDecimal(dnaToBigInteger(dna), PRECISION_4096));
return result.isFinite() ? result : throwArithmeticException("DNA conversion overflow");
}
private static BigInteger dnaToBigInteger(String dna) {
BigInteger num = BigInteger.ZERO, base = BigInteger.valueOf(4);
for (char c : dna.toUpperCase().toCharArray()) num = num.multiply(base).add(BigInteger.valueOf(DNA_TO_QUAT.get(c)));
return num;
}
private static String bigIntegerToDna(BigInteger num) {
if (num.signum() < 0) throw new IllegalArgumentException("Negative not supported");
if (num.equals(BigInteger.ZERO)) return "A";
StringBuilder sb = new StringBuilder();
BigInteger base = BigInteger.valueOf(4);
while (num.compareTo(BigInteger.ZERO) > 0) { sb.append(QUAT_TO_DNA.get(num.mod(base).intValue())); num = num.divide(base); }
return sb.reverse().toString();
}
// Dimensional DNA Framework
public static final class DimensionalDnaFramework {
private static final Map<String, float[]> CONSTANTS = Map.of(
"A", new float[]{1.61803398875f, 6.0f, -6.521335f, 0.1f}, // Planck, Ω=φ
"C", new float[]{6.6743e-11f, 10.0f, -0.557388f, 0.5f}, // Gravitational
"G", new float[]{1.380649e-23f, 8.0f, -0.561617f, 0.5f}, // Boltzmann
"T", new float[]{1.66053906660e-27f, 7.0f, -1.063974f, 1.0f}, // Atomic Mass
"L", new float[]{1.0e-5f, 1.0f, -0.283033f, 0.2f} // Cell Length
);
private static final Map<Float, Float4096> FIB_CACHE = new HashMap<>();
private static final Map<Float, Float4096> PRIME_CACHE = new HashMap<>();
private static final int[] PRIMES = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281};
private static final Float4096[] RECURSIVE_INDICES;
private static final Float4096[] PRIME_VALUES;
private static final int CACHE_LIMIT = 10000;
static {
RECURSIVE_INDICES = new Float4096[PRIMES.length];
PRIME_VALUES = new Float4096[PRIMES.length];
for (int i = 0; i < PRIMES.length; i++) {
RECURSIVE_INDICES[i] = ln(new Float4096(i + 2)).divide(LN_PHI);
PRIME_VALUES[i] = new Float4096(PRIMES[i]);
}
}
private static Float4096 fib(Float4096 n) {
float n_float = n.toDouble();
if (n_float > 70) return ZERO;
if (FIB_CACHE.containsKey(n_float)) return FIB_CACHE.get(n_float);
Float4096 phiN = PHI.pow(n), psiN = PHI.negate().pow(n.negate());
Float4096 result = phiN.subtract(psiN).divide(SQRT5);
if (!result.isFinite()) result = ZERO;
if (FIB_CACHE.size() >= CACHE_LIMIT) FIB_CACHE.clear();
FIB_CACHE.put(n_float, result);
return result;
}
public static Float4096 estimatePrimeIndex(Float4096 target) {
Float4096 n_beta = new Float4096("5");
for (int i = 0; i < 50; i++) {
Float4096 p = interpolatePrime(n_beta);
Float4096 f_n = fib(n_beta);
Float4096 p_nb = PHI.multiply(f_n).multiply(p);
if (p_nb.abs().subtract(target).abs().compareTo(EPSILON) < 0) break;
Float4096 dp = interpolatePrimeDerivative(n_beta);
Float4096 df = fib(n_beta.add(new Float4096("1e-10"))).subtract(f_n).divide(new Float4096("1e-10"));
Float4096 dp_nb = PHI.multiply(f_n.multiply(dp).add(p.multiply(df)));
n_beta = n_beta.subtract(p_nb.subtract(target).divide(dp_nb));
}
return n_beta.isFinite() ? n_beta : throwArithmeticException("Prime index estimation failed");
}
private static Float4096 interpolatePrime(Float4096 x) {
float x_float = x.toDouble();
if (PRIME_CACHE.containsKey(x_float)) return PRIME_CACHE.get(x_float);
if (x.compareTo(RECURSIVE_INDICES[0]) < 0) return PRIME_VALUES[0];
if (x.compareTo(RECURSIVE_INDICES[PRIMES.length - 1]) > 0) return PRIME_VALUES[PRIMES.length - 1];
int idx = 0;
while (idx < RECURSIVE_INDICES.length - 1 && x.compareTo(RECURSIVE_INDICES[idx + 1]) > 0) idx++;
if (idx >= RECURSIVE_INDICES.length - 3) idx = RECURSIVE_INDICES.length - 4;
Float4096[] x_vals = Arrays.copyOfRange(RECURSIVE_INDICES, idx, idx + 4);
Float4096[] y_vals = Arrays.copyOfRange(PRIME_VALUES, idx, idx + 4);
Float4096 result = cubicInterpolate(x, x_vals, y_vals);
if (PRIME_CACHE.size() >= CACHE_LIMIT) PRIME_CACHE.clear();
PRIME_CACHE.put(x_float, result);
return result;
}
private static Float4096 interpolatePrimeDerivative(Float4096 x) {
if (x.compareTo(RECURSIVE_INDICES[0]) < 0 || x.compareTo(RECURSIVE_INDICES[PRIMES.length - 1]) > 0)
return ONE;
int idx = 0;
while (idx < RECURSIVE_INDICES.length - 1 && x.compareTo(RECURSIVE_INDICES[idx + 1]) > 0) idx++;
if (idx >= RECURSIVE_INDICES.length - 3) idx = RECURSIVE_INDICES.length - 4;
Float4096[] x_vals = Arrays.copyOfRange(RECURSIVE_INDICES, idx, idx + 4);
Float4096[] y_vals = Arrays.copyOfRange(PRIME_VALUES, idx, idx + 4);
Float4096 h = new Float4096("1e-10");
return cubicInterpolate(x.add(h), x_vals, y_vals).subtract(cubicInterpolate(x, x_vals, y_vals)).divide(h);
}
private static Float4096 cubicInterpolate(Float4096 x, Float4096[] x_vals, Float4096[] y_vals) {
Float4096 x0 = x_vals[0], x1 = x_vals[1], x2 = x_vals[2], x3 = x_vals[3];
Float4096 y0 = y_vals[0], y1 = y_vals[1], y2 = y_vals[2], y3 = y_vals[3];
Float4096[] coeffs = new Float4096[4];
coeffs[0] = y0;
Float4096 d1 = y1.subtract(y0).divide(x1.subtract(x0));
Float4096 d2 = y2.subtract(y1).divide(x2.subtract(x1));
Float4096 d3 = y3.subtract(y2).divide(x3.subtract(x2));
coeffs[1] = d1;
coeffs[2] = d2.subtract(d1).divide(x2.subtract(x0));
coeffs[3] = d3.subtract(d2).divide(x3.subtract(x0)).subtract(coeffs[2]).divide(x3.subtract(x1));
Float4096 t = x.subtract(x0);
Float4096 result = coeffs[0].add(coeffs[1].multiply(t))
.add(coeffs[2].multiply(t.multiply(t)))
.add(coeffs[3].multiply(t.multiply(t).multiply(t)));
return result.isFinite() ? result : throwArithmeticException("Interpolation overflow");
}
public static Float4096 computeDomainConstant(Float4096 omega, Float4096 m, Float4096 n, Float4096 beta, Float4096 k, boolean recursive) {
Float4096 n_plus_beta = n.add(beta);
if (recursive && n_plus_beta.toDouble() > 1) {
Float4096 prev = computeDomainConstant(omega, m, n.subtract(ONE), beta, k, true);
Float4096 fn = fib(n_plus_beta);
Float4096 fn_minus_1 = fib(n_plus_beta.subtract(ONE));
if (!fn.isFinite() || !fn_minus_1.isFinite() || fn_minus_1.isZero()) return prev;
Float4096 p_n = interpolatePrime(n_plus_beta);
Float4096 factor = TWO.multiply(p_n).multiply(fn.divide(fn_minus_1)).sqrt();
Float4096 result = prev.multiply(factor);
return result.isFinite() ? result : computeDomainConstant(omega, m, n, beta, k, false);
}
Float4096 f_n = fib(n_plus_beta);
Float4096 result = SQRT5.multiply(omega).multiply(PHI.multiply(f_n))
.multiply(B.pow(m.multiply(n_plus_beta)))
.multiply(PHI.pow(k.multiply(n_plus_beta))).divide(ONE); // r=1
return result.isFinite() ? result : throwArithmeticException("Constant computation overflow");
}
public static Float4096 computeMicrostateForce(Float4096 omega, Float4096 n, Float4096 beta, Float4096 k) {
Float4096 n_plus_beta = n.add(beta);
Float4096 f_n = fib(n_plus_beta);
Float4096 p_n = interpolatePrime(n_plus_beta);
Float4096 result = PHI.multiply(f_n).multiply(p_n).multiply(B.pow(n_plus_beta))
.multiply(PHI.pow(k.multiply(n_plus_beta))).multiply(omega).sqrt().divide(ONE); // r=1
return result.isFinite() ? result : throwArithmeticException("Microstate force overflow");
}
public static Float4096 computeUnifiedForce(Float4096 fieldValue, Float4096 charge, Float4096 mass, Float4096 scale) {
Float4096 result = fieldValue.multiply(mass).multiply(scale).divide(charge.multiply(charge));
return result.isFinite() ? result : throwArithmeticException("Unified force overflow");
}
public static Map<String, Float4096> computeFieldQuantities(Float4096 omega, Float4096 n, Float4096 beta, Float4096 k) {
Float4096 n_plus_beta = n.add(beta);
Float4096 f_n = fib(n_plus_beta);
Float4096 p_n = interpolatePrime(n_plus_beta);
Float4096 d_n = SQRT5.multiply(omega).multiply(PHI.multiply(f_n))
.multiply(B.pow(n_plus_beta)).multiply(PHI.pow(k.multiply(n_plus_beta))).divide(ONE); // r=1
Float4096 t = B.pow(n_plus_beta).divide(PHI.pow(n_plus_beta));
Float4096 field_yield = d_n.sqrt();
Float4096 action = d_n.multiply(t);
Float4096 energy = field_yield;
Float4096 force = field_yield.divide(t);
Float4096 charge = d_n.multiply(p_n).sqrt();
Float4096 voltage = charge.divide(t);
Map<String, Float4096> result = new HashMap<>();
result.put("D_n", d_n.isFinite() ? d_n : ZERO);
result.put("T", t.isFinite() ? t : ZERO);
result.put("field_yield", field_yield.isFinite() ? field_yield : ZERO);
result.put("action", action.isFinite() ? action : ZERO);
result.put("energy", energy.isFinite() ? energy : ZERO);
result.put("force", force.isFinite() ? force : ZERO);
result.put("charge", charge.isFinite() ? charge : ZERO);
result.put("voltage", voltage.isFinite() ? voltage : ZERO);
return result;
}
public static Map<String, Boolean> validateConstants() {
Map<String, float[]> reference = Map.of(
"A", new float[]{6.62607015e-34f, 6.0f, -6.521335f, 0.1f}, // Planck
"C", new float[]{6.6743e-11f, 10.0f, -0.557388f, 0.5f}, // Gravitational
"G", new float[]{1.380649e-23f, 8.0f, -0.561617f, 0.5f}, // Boltzmann
"T", new float[]{1.66053906660e-27f, 7.0f, -1.063974f, 1.0f}, // Atomic Mass
"L", new float[]{1.0e-5f, 1.0f, -0.283033f, 0.2f} // Cell Length
);
Map<String, Boolean> results = new HashMap<>();
for (Map.Entry<String, float[]> entry : reference.entrySet()) {
String key = entry.getKey();
float[] params = entry.getValue();
Float4096 computed = computeDomainConstant(new Float4096(params[0]), new Float4096(params[1]),
new Float4096(params[2]), new Float4096(params[3]),
new Float4096(params[1]), false);
Float4096 expected = new Float4096(params[0]);
boolean valid = computed.abs().subtract(expected).abs().compareTo(EPSILON) < 0;
results.put(key, valid);
}
return results;
}
public static Float4096 getConstant(String type) {
float[] params = CONSTANTS.getOrDefault(type, new float[]{0, 0, 0, 0});
return computeDomainConstant(new Float4096(params[0]), new Float4096(params[1]),
new Float4096(params[2]), new Float4096(params[3]),
new Float4096(params[1]), false);
}
}
// QuatDnaLang Interpreter
public static final class QuatDnaLangInterpreter {
private static final Map<String, Character> COMMANDS = Map.of(
"AA", '+', "AC", '-', "AG", '>', "AT", '<', "CA", '.', "CC", ',', "CG", '[', "CT", ']', "GG", 'F', "TT", 'E');
public static String execute(String program, String input, int maxSteps) {
validateDNA(program); if (program.length() % 2 != 0) program += "A";
validateDNA(input);
List<Character> instr = new ArrayList<>(program.length() / 2);
for (int i = 0; i < program.length(); i += 2)
instr.add(COMMANDS.getOrDefault(program.substring(i, i + 2).toUpperCase(), null));
Map<Integer, Integer> bracketMap = new HashMap<>();
Deque<Integer> stack = new LinkedList<>();
for (int i = 0; i < instr.size(); i++) {
if (instr.get(i) == '[') stack.push(i);
else if (instr.get(i) == ']') {
if (stack.isEmpty()) throw new IllegalArgumentException("Mismatched brackets");
int open = stack.pop();
bracketMap.put(open, i); bracketMap.put(i, open);
}
}
if (!stack.isEmpty()) throw new IllegalArgumentException("Mismatched brackets");
Map<Integer, Integer> tape = new HashMap<>(); tape.put(0, 0);
int head = 0, inputIndex = 0;
int[] inputArray = input.toUpperCase().chars().map(c -> DNA_TO_QUAT.get((char) c)).toArray();
StringBuilder output = new StringBuilder();
int pc = 0, step = 0;
while (pc < instr.size() && step < maxSteps) {
Character cmd = instr.get(pc);
if (cmd == null) { pc++; step++; continue; }
int current = tape.getOrDefault(head, 0);
switch (cmd) {
case '+' -> tape.put(head, quatSuccessor(current));
case '-' -> tape.put(head, quatPredecessor(current));
case '>' -> head++;
case '<' -> head--;
case '.' -> output.append(QUAT_TO_DNA.get(current));
case ',' -> tape.put(head, inputIndex < inputArray.length ? inputArray[inputIndex++] : 0);
case '[' -> { if (current == 0) pc = bracketMap.get(pc); }
case ']' -> { if (current != 0) pc = bracketMap.get(pc); }
case 'E' -> {
int subHead = head + 1;
StringBuilder subProg = new StringBuilder();
while (tape.containsKey(subHead) && tape.get(subHead) != 0) {
int a = tape.get(subHead), b = tape.getOrDefault(subHead + 1, 0);
subProg.append(QUAT_TO_DNA.get(a)).append(QUAT_TO_DNA.get(b));
subHead += 2;
}
String res = execute(subProg.toString(), "", maxSteps - step);
subHead = head + 1;
for (char c : res.toCharArray()) tape.put(subHead++, DNA_TO_QUAT.get(c));
while (tape.containsKey(subHead)) tape.remove(subHead++);
}
case 'F' -> {
int type = tape.getOrDefault(head + 1, 0);
int paramHead = head + 2;
StringBuilder paramDna = new StringBuilder();
while (tape.containsKey(paramHead) && tape.get(paramHead) != 0)
paramDna.append(QUAT_TO_DNA.get(tape.get(paramHead)));
Float4096 result;
if (type == 0) {
result = DimensionalDnaFramework.getConstant(paramDna.toString());
} else if (type == 1) {
result = DimensionalDnaFramework.estimatePrimeIndex(fromDnaSequence(paramDna.toString()));
} else if (type == 2) {
Float4096 x = fromDnaSequence(paramDna.toString());
result = DimensionalDnaFramework.computeDomainConstant(ONE, ONE, x, ZERO, ONE, false);
} else if (type == 3) {
Float4096 x = fromDnaSequence(paramDna.toString());
result = DimensionalDnaFramework.computeMicrostateForce(ONE, x, ZERO, ONE);
} else {
Float4096 x = fromDnaSequence(paramDna.toString());
result = DimensionalDnaFramework.computeFieldQuantities(ONE, x, ZERO, ONE).get("force");
}
String resDna = result.toDnaSequence();
paramHead = head + 1;
for (char c : resDna.toCharArray()) tape.put(paramHead++, DNA_TO_QUAT.get(c));
while (tape.containsKey(paramHead)) tape.remove(paramHead++);
}
}
pc++; step++;
}
if (step >= maxSteps) throw new RuntimeException("Max steps exceeded");
return output.toString();
}
}
private static Float4096 calculateGoldenRatio() { return ONE.add(SQRT5).divide(TWO); }
}
ElegantUnifiedPrecisionLedger2.java
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;
import java.nio.charset.StandardCharsets;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.security.SecureRandom;
import java.time.Instant;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.atomic.AtomicLong;
import java.util.concurrent.locks.ReentrantReadWriteLock;
import java.util.function.Supplier;
import java.util.logging.Logger;
import java.util.stream.Stream;
/**
* Elegant Unified Precision Ledger - The Ultimate Synthesis
*
* Combines mathematical precision, cryptographic security, and elegant design:
* - 4096-bit mathematical precision with holographic DNA signatures
* - Immutable functional architecture with thread-safe operations
* - Git-like branching with comprehensive lineage tracking
* - Advanced analytics and complexity metrics
* - Fluent builder patterns with configuration management
*/
public final class ElegantUnifiedPrecisionLedger {
private static final Logger LOGGER = Logger.getLogger(ElegantUnifiedPrecisionLedger.class.getName());
private static final MathContext PRECISION_4096 = new MathContext(4096, RoundingMode.HALF_EVEN);
private static final BigDecimal PHI = calculateGoldenRatio();
// Core immutable state
private final Configuration config;
private final AtomicLong operationCounter;
private final ConcurrentHashMap<BranchId, ImmutableBranch> branches;
private final LineageTree lineageTree;
private final MathEngine mathEngine;
private final CryptoEngine cryptoEngine;
private final HolographicEncoder holographicEncoder;
private final ReentrantReadWriteLock lock;
private ElegantUnifiedPrecisionLedger(Configuration config) {
this.config = Objects.requireNonNull(config);
this.operationCounter = new AtomicLong(0);
this.branches = new ConcurrentHashMap<>();
this.lineageTree = LineageTree.empty();
this.mathEngine = new MathEngine(config);
this.cryptoEngine = new CryptoEngine();
this.holographicEncoder = new HolographicEncoder();
this.lock = new ReentrantReadWriteLock();
// Initialize main branch
BranchId mainBranchId = BranchId.create("main", BranchType.MAIN);
branches.put(mainBranchId, ImmutableBranch.create(mainBranchId));
LOGGER.info("Initialized Elegant Unified Precision Ledger: " + config);
}
// ===== Configuration =====
public record Configuration(
int precisionBits,
int checkpointInterval,
boolean enableMathematicalSignatures,
boolean enableHolographicEncoding,
boolean enableAnalytics,
boolean enableVerboseLogging
) {
public Configuration {
if (precisionBits <= 0) throw new IllegalArgumentException("Precision bits must be positive");
if (checkpointInterval <= 0) throw new IllegalArgumentException("Checkpoint interval must be positive");
}
public static Configuration defaultConfig() {
return new Configuration(4096, 10, true, true, true, false);
}
public Configuration withPrecision(int bits) {
return new Configuration(bits, checkpointInterval, enableMathematicalSignatures,
enableHolographicEncoding, enableAnalytics, enableVerboseLogging);
}
public Configuration withAnalytics(boolean enabled) {
return new Configuration(precisionBits, checkpointInterval, enableMathematicalSignatures,
enableHolographicEncoding, enabled, enableVerboseLogging);
}
}
// ===== Builder Pattern =====
public static final class Builder {
private Configuration config = Configuration.defaultConfig();
public Builder withConfig(Configuration config) {
this.config = Objects.requireNonNull(config);
return this;
}
public Builder withPrecision(int bits) {
this.config = config.withPrecision(bits);
return this;
}
public Builder withAnalytics(boolean enabled) {
this.config = config.withAnalytics(enabled);
return this;
}
public ElegantUnifiedPrecisionLedger build() {
return new ElegantUnifiedPrecisionLedger(config);
}
}
public static Builder builder() { return new Builder(); }
public static ElegantUnifiedPrecisionLedger create() { return builder().build(); }
// ===== Core Data Structures =====
/**
* Ultra-high precision floating point with 4096-bit accuracy
*/
public static final class Float4096 {
private final BigDecimal value;
public Float4096(String value) {
this.value = new BigDecimal(value, PRECISION_4096);
}
public Float4096(BigDecimal value) {
this.value = value.round(PRECISION_4096);
}
public Float4096 add(Float4096 other) {
return new Float4096(this.value.add(other.value, PRECISION_4096));
}
public Float4096 multiply(Float4096 other) {
return new Float4096(this.value.multiply(other.value, PRECISION_4096));
}
public BigDecimal getValue() { return value; }
@Override
public String toString() {
return value.toPlainString();
}
@Override
public boolean equals(Object o) {
return this == o || (o instanceof Float4096 that && value.equals(that.value));
}
@Override
public int hashCode() {
return Objects.hash(value);
}
}
/**
* Mathematical signature with golden ratio resonance
*/
public record MathematicalSignature(
Float4096 goldenPhase,
Float4096 primeInterpolation,
Float4096 complexityMetric,
String holographicGlyph
) {
public static MathematicalSignature create(long operationId, String data, MathEngine engine) {
Float4096 n = new Float4096(String.valueOf(operationId));
Float4096 goldenPhase = computeGoldenPhase(n);
Float4096 primeInterpolation = engine.interpolatePrime(n);
Float4096 complexity = goldenPhase.multiply(primeInterpolation);
String glyph = generateHolographicGlyph(operationId, data);
return new MathematicalSignature(goldenPhase, primeInterpolation, complexity, glyph);
}
private static Float4096 computeGoldenPhase(Float4096 n) {
Float4096 phase = n.multiply(new Float4096(PHI.toString()));
return new Float4096(phase.getValue().remainder(new BigDecimal("6.283185307179586")));
}
private static String generateHolographicGlyph(long operationId, String data) {
double phase = (operationId * PHI.doubleValue()) % (2 * Math.PI);
char projectedChar = (char) (0x2100 + (int)((Math.sin(phase) * 0.5 + 0.5) * 256));
return projectedChar + ":" + Integer.toHexString(data.hashCode());
}
public boolean isHighComplexity() {
return complexityMetric.getValue().compareTo(new BigDecimal("1.0")) > 0;
}
public double getComplexityValue() {
return complexityMetric.getValue().doubleValue();
}
}
/**
* DNA signature with entropy and golden ratio resonance
*/
public record DNASignature(
String sequence,
String hash,
double entropy,
double gcContent,
double phiResonance,
double complexity
) {
public static DNASignature create(String data, String salt, CryptoEngine crypto, long operationId) {
String hash = crypto.computeHash(data + salt);
String sequence = generateDNASequence(hash);
double entropy = calculateEntropy(sequence);
double gcContent = calculateGCContent(sequence);
double phiResonance = Math.abs(Math.sin(operationId * PHI.doubleValue()));
double complexity = entropy * gcContent * phiResonance;
return new DNASignature(sequence, hash, entropy, gcContent, phiResonance, complexity);
}
private static String generateDNASequence(String hash) {
char[] dnaMap = {'A', 'G', 'T', 'C'};
StringBuilder sequence = new StringBuilder();
for (int i = 0; i < Math.min(64, hash.length()); i++) {
int idx = Math.abs(hash.charAt(i)) % dnaMap.length;
sequence.append(dnaMap[idx]);
}
return sequence.toString();
}
private static double calculateEntropy(String seq) {
Map<Character, Long> counts = seq.chars()
.mapToObj(c -> (char) c)
.collect(HashMap::new, (map, c) -> map.merge(c, 1L, Long::sum),
(m1, m2) -> { m2.forEach((k, v) -> m1.merge(k, v, Long::sum)); return m1; });
double entropy = 0.0;
int total = seq.length();
for (long count : counts.values()) {
if (count > 0) {
double probability = (double) count / total;
entropy -= probability * (Math.log(probability) / Math.log(2));
}
}
return entropy;
}
private static double calculateGCContent(String seq) {
long gcCount = seq.chars().filter(c -> c == 'G' || c == 'C').count();
return (double) gcCount / seq.length();
}
public boolean isHighComplexity() { return complexity > 0.75; }
public boolean isBalanced() { return Math.abs(gcContent - 0.5) < 0.1; }
}
/**
* Immutable ledger entry with comprehensive signatures
*/
public record LedgerEntry(
UUID id,
String key,
String value,
long operationId,
long timestamp,
String salt,
BigInteger cryptoHash,
MathematicalSignature mathSignature,
DNASignature dnaSignature
) {
public static LedgerEntry create(String key, String value, long operationId,
CryptoEngine crypto, MathEngine mathEngine) {
UUID id = UUID.randomUUID();
long timestamp = System.currentTimeMillis();
String salt = crypto.generateSalt();
BigInteger cryptoHash = crypto.computeBigIntegerHash(key + ":" + value + ":" + salt);
MathematicalSignature mathSig = MathematicalSignature.create(operationId, value, mathEngine);
DNASignature dnaSig = DNASignature.create(value, salt, crypto, operationId);
return new LedgerEntry(id, key, value, operationId, timestamp, salt, cryptoHash, mathSig, dnaSig);
}
public long ageInMillis() { return System.currentTimeMillis() - timestamp; }
public String getShortId() { return id.toString().substring(0, 8); }
public String getSummary() {
return String.format("Entry[%s] %s->%s complexity=%.3f glyph=%s",
getShortId(), key, value, mathSignature.getComplexityValue(), mathSignature.holographicGlyph());
}
}
/**
* Branch identification
*/
public record BranchId(UUID id, String name, BranchType type) {
public static BranchId create(String name, BranchType type) {
return new BranchId(UUID.randomUUID(), name, type);
}
}
public enum BranchType { MAIN, FEATURE, EXPERIMENTAL, RELEASE }
/**
* Immutable branch with lineage tracking
*/
public static final class ImmutableBranch {
private final BranchId branchId;
private final List<LedgerEntry> entries;
private final List<Checkpoint> checkpoints;
private final Optional<BranchId> parentId;
private final long creationTime;
private ImmutableBranch(BranchId branchId, List<LedgerEntry> entries,
List<Checkpoint> checkpoints, Optional<BranchId> parentId, long creationTime) {
this.branchId = Objects.requireNonNull(branchId);
this.entries = List.copyOf(entries);
this.checkpoints = List.copyOf(checkpoints);
this.parentId = parentId;
this.creationTime = creationTime;
}
public static ImmutableBranch create(BranchId branchId) {
return new ImmutableBranch(branchId, List.of(), List.of(), Optional.empty(), System.currentTimeMillis());
}
public static ImmutableBranch createFrom(BranchId branchId, BranchId parentId) {
return new ImmutableBranch(branchId, List.of(), List.of(), Optional.of(parentId), System.currentTimeMillis());
}
public ImmutableBranch addEntry(LedgerEntry entry) {
List<LedgerEntry> newEntries = Stream.concat(entries.stream(), Stream.of(entry)).toList();
return new ImmutableBranch(branchId, newEntries, checkpoints, parentId, creationTime);
}
public ImmutableBranch addCheckpoint(Checkpoint checkpoint) {
List<Checkpoint> newCheckpoints = Stream.concat(checkpoints.stream(), Stream.of(checkpoint)).toList();
return new ImmutableBranch(branchId, entries, newCheckpoints, parentId, creationTime);
}
// Getters
public BranchId getBranchId() { return branchId; }
public List<LedgerEntry> getEntries() { return entries; }
public List<Checkpoint> getCheckpoints() { return checkpoints; }
public Optional<BranchId> getParentId() { return parentId; }
public long getCreationTime() { return creationTime; }
public double getAverageComplexity() {
return entries.stream()
.mapToDouble(entry -> entry.mathSignature().getComplexityValue())
.average()
.orElse(0.0);
}
public Stream<LedgerEntry> streamEntries() { return entries.stream(); }
@Override
public String toString() {
return String.format("Branch[%s] entries=%d checkpoints=%d complexity=%.3f",
branchId.name(), entries.size(), checkpoints.size(), getAverageComplexity());
}
}
/**
* Checkpoint for state snapshots
*/
public record Checkpoint(UUID id, String merkleRoot, List<UUID> entryIds, long operationId, long timestamp) {
public static Checkpoint create(String merkleRoot, List<UUID> entryIds, long operationId) {
return new Checkpoint(UUID.randomUUID(), merkleRoot, entryIds, operationId, System.currentTimeMillis());
}
public long ageInMillis() { return System.currentTimeMillis() - timestamp; }
}
/**
* Lineage tracking for branch relationships
*/
public static final class LineageTree {
private final Map<BranchId, BranchLineage> lineages;
private LineageTree(Map<BranchId, BranchLineage> lineages) {
this.lineages = Map.copyOf(lineages);
}
public static LineageTree empty() {
return new LineageTree(Map.of());
}
public LineageTree withLineage(BranchId branchId, BranchLineage lineage) {
Map<BranchId, BranchLineage> newLineages = new HashMap<>(lineages);
newLineages.put(branchId, lineage);
return new LineageTree(newLineages);
}
public Optional<BranchLineage> getLineage(BranchId branchId) {
return Optional.ofNullable(lineages.get(branchId));
}
public Map<BranchId, BranchLineage> getAllLineages() { return lineages; }
}
/**
* Branch lineage information
*/
public record BranchLineage(Optional<BranchId> parentId, String creator, Instant createdAt) {
public static BranchLineage create(Optional<BranchId> parentId, String creator) {
return new BranchLineage(parentId, creator, Instant.now());
}
}
// ===== Result Types =====
public record BranchResult<T>(boolean success, T value, BranchId branchId, String message) {
public static <T> BranchResult<T> success(T value, BranchId branchId) {
return new BranchResult<>(true, value, branchId, "Success");
}
public static <T> BranchResult<T> failure(String message) {
return new BranchResult<>(false, null, null, message);
}
}
public record MergeResult<T>(boolean success, T value, String message) {
public static <T> MergeResult<T> success(T value) {
return new MergeResult<>(true, value, "Merge successful");
}
public static <T> MergeResult<T> failure(String message) {
return new MergeResult<>(false, null, message);
}
}
// ===== Statistics =====
public record LedgerStats(
int branchCount,
int entryCount,
int checkpointCount,
long operationCount,
double averageComplexity
) {
@Override
public String toString() {
return String.format("Stats{branches=%d, entries=%d, checkpoints=%d, ops=%d, avgComplexity=%.3f}",
branchCount, entryCount, checkpointCount, operationCount, averageComplexity);
}
}
// ===== Engine Classes =====
private static final class MathEngine {
private final Configuration config;
private final List<Integer> primes;
public MathEngine(Configuration config) {
this.config = config;
this.primes = generatePrimes(1000);
}
public Float4096 interpolatePrime(Float4096 n) {
double nValue = n.getValue().doubleValue();
int index = (int) (Math.abs(nValue) % primes.size());
return new Float4096(String.valueOf(primes.get(index)));
}
private List<Integer> generatePrimes(int count) {
List<Integer> primes = new ArrayList<>();
int candidate = 2;
while (primes.size() < count) {
if (isPrime(candidate)) {
primes.add(candidate);
}
candidate++;
}
return primes;
}
private boolean isPrime(int n) {
if (n < 2) return false;
if (n == 2) return true;
if (n % 2 == 0) return false;
for (int i = 3; i * i <= n; i += 2) {
if (n % i == 0) return false;
}
return true;
}
}
private static final class CryptoEngine {
private final SecureRandom secureRandom;
private final ThreadLocal<MessageDigest> threadDigest;
public CryptoEngine() {
this.secureRandom = new SecureRandom();
this.threadDigest = ThreadLocal.withInitial(() -> {
try {
return MessageDigest.getInstance("SHA-256");
} catch (NoSuchAlgorithmException e) {
throw new RuntimeException("SHA-256 not available", e);
}
});
}
public String generateSalt() {
byte[] saltBytes = new byte[16];
secureRandom.nextBytes(saltBytes);
return HexFormat.of().formatHex(saltBytes);
}
public String computeHash(String input) {
MessageDigest digest = threadDigest.get();
digest.reset();
return HexFormat.of().formatHex(digest.digest(input.getBytes(StandardCharsets.UTF_8)));
}
public BigInteger computeBigIntegerHash(String input) {
return new BigInteger(1, threadDigest.get().digest(input.getBytes(StandardCharsets.UTF_8)));
}
}
private static final class HolographicEncoder {
public String base4096Encode(String input) {
Objects.requireNonNull(input, "Input cannot be null");
StringBuilder encoded = new StringBuilder();
for (byte b : input.getBytes(StandardCharsets.UTF_8)) {
encoded.append((char) (0x2800 + (b & 0xFF)));
}
return encoded.toString();
}
}
// ===== Core Operations =====
public LedgerEntry addEntry(String branchName, String key, String value) {
Objects.requireNonNull(branchName, "Branch name cannot be null");
Objects.requireNonNull(key, "Key cannot be null");
Objects.requireNonNull(value, "Value cannot be null");
return withWriteLock(() -> {
BranchId branchId = findBranchId(branchName);
ImmutableBranch branch = branches.get(branchId);
if (branch == null) {
throw new IllegalArgumentException("Branch not found: " + branchName);
}
long operationId = operationCounter.incrementAndGet();
LedgerEntry entry = LedgerEntry.create(key, value, operationId, cryptoEngine, mathEngine);
ImmutableBranch newBranch = branch.addEntry(entry);
// Create checkpoint if needed
if (newBranch.getEntries().size() % config.checkpointInterval() == 0) {
String merkleRoot = "merkle_" + operationId;
List<UUID> entryIds = newBranch.getEntries().stream().map(LedgerEntry::id).toList();
Checkpoint checkpoint = Checkpoint.create(merkleRoot, entryIds, operationId);
newBranch = newBranch.addCheckpoint(checkpoint);
}
branches.put(branchId, newBranch);
if (config.enableVerboseLogging()) {
LOGGER.info("Added to " + branchName + ": " + entry.getSummary());
}
return entry;
});
}
public BranchResult<ElegantUnifiedPrecisionLedger> createBranch(String name, String parentName) {
Objects.requireNonNull(name, "Branch name cannot be null");
return withWriteLock(() -> {
if (findBranchIdByName(name).isPresent()) {
return BranchResult.failure("Branch already exists: " + name);
}
BranchId newBranchId = BranchId.create(name, BranchType.FEATURE);
ImmutableBranch newBranch;
if (parentName != null) {
BranchId parentId = findBranchId(parentName);
newBranch = ImmutableBranch.createFrom(newBranchId, parentId);
} else {
newBranch = ImmutableBranch.create(newBranchId);
}
Map<BranchId, ImmutableBranch> newBranches = new HashMap<>(branches);
newBranches.put(newBranchId, newBranch);
// Update this ledger's branches
branches.put(newBranchId, newBranch);
LOGGER.info("Created branch: " + name + (parentName != null ? " from " + parentName : ""));
return BranchResult.success(this, newBranchId);
});
}
// ===== Query Operations =====
public Optional<LedgerEntry> findEntry(String branchName, String key) {
return withReadLock(() -> {
Optional<BranchId> branchId = findBranchIdByName(branchName);
if (branchId.isEmpty()) return Optional.empty();
ImmutableBranch branch = branches.get(branchId.get());
return branch.getEntries().stream()
.filter(entry -> entry.key().equals(key))
.findFirst();
});
}
public List<LedgerEntry> findHighComplexityEntries(double threshold) {
return withReadLock(() ->
branches.values().stream()
.flatMap(ImmutableBranch::streamEntries)
.filter(entry -> entry.mathSignature().isHighComplexity() ||
entry.dnaSignature().isHighComplexity())
.toList()
);
}
public double getAverageComplexity() {
return withReadLock(() ->
branches.values().stream()
.flatMap(ImmutableBranch::streamEntries)
.mapToDouble(entry -> entry.mathSignature().getComplexityValue())
.average()
.orElse(0.0)
);
}
public Map<String, Integer> getBranchSizes() {
return withReadLock(() -> {
Map<String, Integer> sizes = new HashMap<>();
branches.forEach((branchId, branch) -> sizes.put(branchId.name(), branch.getEntries().size()));
return sizes;
});
}
public Stream<LedgerEntry> streamAllEntries() {
return withReadLock(() ->
branches.values().stream().flatMap(ImmutableBranch::streamEntries)
);
}
// ===== Statistics =====
public LedgerStats getStatistics() {
return withReadLock(() -> {
int totalEntries = branches.values().stream()
.mapToInt(branch -> branch.getEntries().size())
.sum();
int totalCheckpoints = branches.values().stream()
.mapToInt(branch -> branch.getCheckpoints().size())
.sum();
double avgComplexity = getAverageComplexity();
return new LedgerStats(
branches.size(),
totalEntries,
totalCheckpoints,
operationCounter.get(),
avgComplexity
);
});
}
// ===== Verification =====
public boolean verifyBranchIntegrity(String branchName) {
return withReadLock(() -> {
Optional<BranchId> branchId = findBranchIdByName(branchName);
if (branchId.isEmpty()) return false;
ImmutableBranch branch = branches.get(branchId.get());
boolean valid = branch.getEntries().stream().allMatch(entry -> {
String expectedHash = cryptoEngine.computeHash(
entry.key() + ":" + entry.value() + ":" + entry.salt());
return expectedHash.equals(entry.dnaSignature().hash());
});
if (config.enableVerboseLogging()) {
LOGGER.info("Branch '" + branchName + "' integrity: " + (valid ? "VALID" : "INVALID"));
}
return valid;
});
}
// ===== Holographic Operations =====
public String getEncodedSummary() {
String summary = getStatistics().toString();
return holographicEncoder.base4096Encode(summary);
}
// ===== Utility Methods =====
private BranchId findBranchId(String branchName) {
return findBranchIdByName(branchName)
.orElseThrow(() -> new IllegalArgumentException("Branch not found: " + branchName));
}
private Optional<BranchId> findBranchIdByName(String branchName) {
return branches.keySet().stream()
.filter(id -> id.name().equals(branchName))
.findFirst();
}
private <T> T withReadLock(Supplier<T> operation) {
lock.readLock().lock();
try {
return operation.get();
} finally {
lock.readLock().unlock();
}
}
private <T> T withWriteLock(Supplier<T> operation) {
lock.writeLock().lock();
try {
return operation.get();
} finally {
lock.writeLock().unlock();
}
}
// ===== Mathematical Utilities =====
private static BigDecimal calculateGoldenRatio() {
// φ = (1 + √5) / 2
BigDecimal five = new BigDecimal("5", PRECISION_4096);
BigDecimal sqrt5 = sqrt(five);
BigDecimal one = new BigDecimal("1", PRECISION_4096);
BigDecimal two = new BigDecimal("2", PRECISION_4096);
return one.add(sqrt5).divide(two, PRECISION_4096);
}
private static BigDecimal sqrt(BigDecimal value) {
BigDecimal x = value;
BigDecimal previous;
BigDecimal two = new BigDecimal("2");
for (int i = 0; i < 100; i++) {
previous = x;
x = x.add(value.divide(x, PRECISION_4096)).divide(two, PRECISION_4096);
if (x.subtract(previous).abs().compareTo(new BigDecimal("1E-2000")) <= 0) break;
}
return x;
}
// ===== Display & Summary =====
public void printSummary() {
System.out.println("=== Elegant Unified Precision Ledger Summary ===");
LedgerStats stats = getStatistics();
System.out.println("Statistics: " + stats);
System.out.println("Configuration: " + config);
System.out.println();
branches.forEach((branchId, branch) -> {
System.out.println(branch);
// Show top 3 entries per branch
branch.getEntries().stream()
.limit(3)
.forEach(entry -> {
System.out.println(" " + entry.getSummary());
if (config.enableAnalytics()) {
System.out.println(" Math: " + entry.mathSignature());
System.out.println(" DNA: " + entry.dnaSignature());
}
});
if (branch.getEntries().size() > 3) {
System.out.println(" ... and " + (branch.getEntries().size() - 3) + " more entries");
}
System.out.println();
});
}
// ===== Configuration Access =====
public Configuration getConfiguration() { return config; }
public LineageTree getLineageTree() { return lineageTree; }
// ===== Comprehensive Demo =====
public static void main(String[] args) {
System.out.println("=== Elegant Unified Precision Ledger Demo ===\n");
// Create ledger with configuration
ElegantUnifiedPrecisionLedger ledger = ElegantUnifiedPrecisionLedger.builder()
.withPrecision(4096)
.withAnalytics(true)
.build();
System.out.println("1. Adding mathematically rich entries...");
ledger.addEntry("main", "quantum_state", "Superposition analysis");
ledger.addEntry("main", "golden_spiral", "Fibonacci convergence");
ledger.addEntry("main", "prime_theory", "Distribution patterns");
ledger.addEntry("main", "field_equations", "Galois structures");
System.out.println("\n2. Creating feature branches...");
var mathResult = ledger.createBranch("mathematics", "main");
if (mathResult.success()) {
ledger.addEntry("mathematics", "euler_identity", "e^(iπ) + 1 = 0");
ledger.addEntry("mathematics", "zeta_function", "Critical line analysis");
}
var cryptoResult = ledger.createBranch("cryptography", "main");
if (cryptoResult.success()) {
ledger.addEntry("cryptography", "elliptic_curves", "ECDSA schemes");
ledger.addEntry("cryptography", "lattice_crypto", "Post-quantum security");
}
System.out.println("\n3. High-complexity analysis...");
List<LedgerEntry> highComplexity = ledger.findHighComplexityEntries(0.5);
System.out.printf("Found %d high-complexity entries:\n", highComplexity.size());
highComplexity.forEach(entry -> System.out.println(" " + entry.getSummary()));
System.out.println("\n4. Branch verification...");
boolean mainValid = ledger.verifyBranchIntegrity("main");
boolean mathValid = ledger.verifyBranchIntegrity("mathematics");
System.out.printf("Integrity: main=%s, mathematics=%s\n", mainValid, mathValid);
System.out.println("\n5. Statistical analysis...");
Map<String, Integer> branchSizes = ledger.getBranchSizes();
branchSizes.forEach((name, size) ->
System.out.printf(" %s: %d entries\n", name, size));
System.out.println("\nAverage complexity: " +
String.format("%.6f", ledger.getAverageComplexity()));
System.out.println("\n6. Holographic encoding demonstration...");
String encoded = ledger.getEncodedSummary();
System.out.println("Encoded summary: " + encoded.substring(0, Math.min(50, encoded.length())) + "...");
System.out.println("\n7. Full ledger summary:");
ledger.printSummary();
System.out.println("\n=== Demo completed successfully! ===");
System.out.println("\nKey features demonstrated:");
System.out.println("✓ Mathematical precision with 4096-bit arithmetic");
System.out.println("✓ Holographic DNA signatures with golden ratio resonance");
System.out.println("✓ Immutable functional architecture");
System.out.println("✓ Thread-safe concurrent operations");
System.out.println("✓ Comprehensive cryptographic verification");
System.out.println("✓ Advanced analytics and complexity metrics");
System.out.println("✓ Git-like branching with lineage tracking");
System.out.println("✓ Elegant builder patterns and fluent APIs");
}
}
ElegantUnifiedPrecisionLedger.java
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;
import java.nio.charset.StandardCharsets;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.security.SecureRandom;
import java.time.Instant;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.atomic.AtomicLong;
import java.util.concurrent.locks.ReentrantReadWriteLock;
import java.util.function.Supplier;
import java.util.logging.Logger;
import java.util.stream.Stream;
/**
* Elegant Unified Precision Ledger - The Ultimate Synthesis
*
* Combines mathematical precision, cryptographic security, and elegant design:
* - 4096-bit mathematical precision with holographic DNA signatures
* - Immutable functional architecture with thread-safe operations
* - Git-like branching with comprehensive lineage tracking
* - Advanced analytics and complexity metrics
* - Fluent builder patterns with configuration management
*/
public final class ElegantUnifiedPrecisionLedger {
private static final Logger LOGGER = Logger.getLogger(ElegantUnifiedPrecisionLedger.class.getName());
private static final MathContext PRECISION_4096 = new MathContext(4096, RoundingMode.HALF_EVEN);
private static final BigDecimal PHI = calculateGoldenRatio();
// Core immutable state
private final Configuration config;
private final AtomicLong operationCounter;
private final ConcurrentHashMap<BranchId, ImmutableBranch> branches;
private final LineageTree lineageTree;
private final MathEngine mathEngine;
private final CryptoEngine cryptoEngine;
private final HolographicEncoder holographicEncoder;
private final ReentrantReadWriteLock lock;
private ElegantUnifiedPrecisionLedger(Configuration config) {
this.config = Objects.requireNonNull(config);
this.operationCounter = new AtomicLong(0);
this.branches = new ConcurrentHashMap<>();
this.lineageTree = LineageTree.empty();
this.mathEngine = new MathEngine(config);
this.cryptoEngine = new CryptoEngine();
this.holographicEncoder = new HolographicEncoder();
this.lock = new ReentrantReadWriteLock();
// Initialize main branch
BranchId mainBranchId = BranchId.create("main", BranchType.MAIN);
branches.put(mainBranchId, ImmutableBranch.create(mainBranchId));
LOGGER.info("Initialized Elegant Unified Precision Ledger: " + config);
}
// ===== Configuration =====
public record Configuration(
int precisionBits,
int checkpointInterval,
boolean enableMathematicalSignatures,
boolean enableHolographicEncoding,
boolean enableAnalytics,
boolean enableVerboseLogging
) {
public Configuration {
if (precisionBits <= 0) throw new IllegalArgumentException("Precision bits must be positive");
if (checkpointInterval <= 0) throw new IllegalArgumentException("Checkpoint interval must be positive");
}
public static Configuration defaultConfig() {
return new Configuration(4096, 10, true, true, true, false);
}
public Configuration withPrecision(int bits) {
return new Configuration(bits, checkpointInterval, enableMathematicalSignatures,
enableHolographicEncoding, enableAnalytics, enableVerboseLogging);
}
public Configuration withAnalytics(boolean enabled) {
return new Configuration(precisionBits, checkpointInterval, enableMathematicalSignatures,
enableHolographicEncoding, enabled, enableVerboseLogging);
}
}
// ===== Builder Pattern =====
public static final class Builder {
private Configuration config = Configuration.defaultConfig();
public Builder withConfig(Configuration config) {
this.config = Objects.requireNonNull(config);
return this;
}
public Builder withPrecision(int bits) {
this.config = config.withPrecision(bits);
return this;
}
public Builder withAnalytics(boolean enabled) {
this.config = config.withAnalytics(enabled);
return this;
}
public ElegantUnifiedPrecisionLedger build() {
return new ElegantUnifiedPrecisionLedger(config);
}
}
public static Builder builder() { return new Builder(); }
public static ElegantUnifiedPrecisionLedger create() { return builder().build(); }
// ===== Core Data Structures =====
/**
* Ultra-high precision floating point with 4096-bit accuracy
*/
public static final class Float4096 {
private final BigDecimal value;
public Float4096(String value) {
this.value = new BigDecimal(value, PRECISION_4096);
}
public Float4096(BigDecimal value) {
this.value = value.round(PRECISION_4096);
}
public Float4096 add(Float4096 other) {
return new Float4096(this.value.add(other.value, PRECISION_4096));
}
public Float4096 multiply(Float4096 other) {
return new Float4096(this.value.multiply(other.value, PRECISION_4096));
}
public BigDecimal getValue() { return value; }
@Override
public String toString() {
return value.toPlainString();
}
@Override
public boolean equals(Object o) {
return this == o || (o instanceof Float4096 that && value.equals(that.value));
}
@Override
public int hashCode() {
return Objects.hash(value);
}
}
/**
* Mathematical signature with golden ratio resonance
*/
public record MathematicalSignature(
Float4096 goldenPhase,
Float4096 primeInterpolation,
Float4096 complexityMetric,
String holographicGlyph
) {
public static MathematicalSignature create(long operationId, String data, MathEngine engine) {
Float4096 n = new Float4096(String.valueOf(operationId));
Float4096 goldenPhase = computeGoldenPhase(n);
Float4096 primeInterpolation = engine.interpolatePrime(n);
Float4096 complexity = goldenPhase.multiply(primeInterpolation);
String glyph = generateHolographicGlyph(operationId, data);
return new MathematicalSignature(goldenPhase, primeInterpolation, complexity, glyph);
}
private static Float4096 computeGoldenPhase(Float4096 n) {
Float4096 phase = n.multiply(new Float4096(PHI.toString()));
return new Float4096(phase.getValue().remainder(new BigDecimal("6.283185307179586")));
}
private static String generateHolographicGlyph(long operationId, String data) {
double phase = (operationId * PHI.doubleValue()) % (2 * Math.PI);
char projectedChar = (char) (0x2100 + (int)((Math.sin(phase) * 0.5 + 0.5) * 256));
return projectedChar + ":" + Integer.toHexString(data.hashCode());
}
public boolean isHighComplexity() {
return complexityMetric.getValue().compareTo(new BigDecimal("1.0")) > 0;
}
public double getComplexityValue() {
return complexityMetric.getValue().doubleValue();
}
}
/**
* DNA signature with entropy and golden ratio resonance
*/
public record DNASignature(
String sequence,
String hash,
double entropy,
double gcContent,
double phiResonance,
double complexity
) {
public static DNASignature create(String data, String salt, CryptoEngine crypto, long operationId) {
String hash = crypto.computeHash(data + salt);
String sequence = generateDNASequence(hash);
double entropy = calculateEntropy(sequence);
double gcContent = calculateGCContent(sequence);
double phiResonance = Math.abs(Math.sin(operationId * PHI.doubleValue()));
double complexity = entropy * gcContent * phiResonance;
return new DNASignature(sequence, hash, entropy, gcContent, phiResonance, complexity);
}
private static String generateDNASequence(String hash) {
char[] dnaMap = {'A', 'G', 'T', 'C'};
StringBuilder sequence = new StringBuilder();
for (int i = 0; i < Math.min(64, hash.length()); i++) {
int idx = Math.abs(hash.charAt(i)) % dnaMap.length;
sequence.append(dnaMap[idx]);
}
return sequence.toString();
}
private static double calculateEntropy(String seq) {
Map<Character, Long> counts = seq.chars()
.mapToObj(c -> (char) c)
.collect(HashMap::new, (map, c) -> map.merge(c, 1L, Long::sum),
(m1, m2) -> { m2.forEach((k, v) -> m1.merge(k, v, Long::sum)); return m1; });
double entropy = 0.0;
int total = seq.length();
for (long count : counts.values()) {
if (count > 0) {
double probability = (double) count / total;
entropy -= probability * (Math.log(probability) / Math.log(2));
}
}
return entropy;
}
private static double calculateGCContent(String seq) {
long gcCount = seq.chars().filter(c -> c == 'G' || c == 'C').count();
return (double) gcCount / seq.length();
}
public boolean isHighComplexity() { return complexity > 0.75; }
public boolean isBalanced() { return Math.abs(gcContent - 0.5) < 0.1; }
}
/**
* Immutable ledger entry with comprehensive signatures
*/
public record LedgerEntry(
UUID id,
String key,
String value,
long operationId,
long timestamp,
String salt,
BigInteger cryptoHash,
MathematicalSignature mathSignature,
DNASignature dnaSignature
) {
public static LedgerEntry create(String key, String value, long operationId,
CryptoEngine crypto, MathEngine mathEngine) {
UUID id = UUID.randomUUID();
long timestamp = System.currentTimeMillis();
String salt = crypto.generateSalt();
BigInteger cryptoHash = crypto.computeBigIntegerHash(key + ":" + value + ":" + salt);
MathematicalSignature mathSig = MathematicalSignature.create(operationId, value, mathEngine);
DNASignature dnaSig = DNASignature.create(value, salt, crypto, operationId);
return new LedgerEntry(id, key, value, operationId, timestamp, salt, cryptoHash, mathSig, dnaSig);
}
public long ageInMillis() { return System.currentTimeMillis() - timestamp; }
public String getShortId() { return id.toString().substring(0, 8); }
public String getSummary() {
return String.format("Entry[%s] %s->%s complexity=%.3f glyph=%s",
getShortId(), key, value, mathSignature.getComplexityValue(), mathSignature.holographicGlyph());
}
}
/**
* Branch identification
*/
public record BranchId(UUID id, String name, BranchType type) {
public static BranchId create(String name, BranchType type) {
return new BranchId(UUID.randomUUID(), name, type);
}
}
public enum BranchType { MAIN, FEATURE, EXPERIMENTAL, RELEASE }
/**
* Immutable branch with lineage tracking
*/
public static final class ImmutableBranch {
private final BranchId branchId;
private final List<LedgerEntry> entries;
private final List<Checkpoint> checkpoints;
private final Optional<BranchId> parentId;
private final long creationTime;
private ImmutableBranch(BranchId branchId, List<LedgerEntry> entries,
List<Checkpoint> checkpoints, Optional<BranchId> parentId, long creationTime) {
this.branchId = Objects.requireNonNull(branchId);
this.entries = List.copyOf(entries);
this.checkpoints = List.copyOf(checkpoints);
this.parentId = parentId;
this.creationTime = creationTime;
}
public static ImmutableBranch create(BranchId branchId) {
return new ImmutableBranch(branchId, List.of(), List.of(), Optional.empty(), System.currentTimeMillis());
}
public static ImmutableBranch createFrom(BranchId branchId, BranchId parentId) {
return new ImmutableBranch(branchId, List.of(), List.of(), Optional.of(parentId), System.currentTimeMillis());
}
public ImmutableBranch addEntry(LedgerEntry entry) {
List<LedgerEntry> newEntries = Stream.concat(entries.stream(), Stream.of(entry)).toList();
return new ImmutableBranch(branchId, newEntries, checkpoints, parentId, creationTime);
}
public ImmutableBranch addCheckpoint(Checkpoint checkpoint) {
List<Checkpoint> newCheckpoints = Stream.concat(checkpoints.stream(), Stream.of(checkpoint)).toList();
return new ImmutableBranch(branchId, entries, newCheckpoints, parentId, creationTime);
}
// Getters
public BranchId getBranchId() { return branchId; }
public List<LedgerEntry> getEntries() { return entries; }
public List<Checkpoint> getCheckpoints() { return checkpoints; }
public Optional<BranchId> getParentId() { return parentId; }
public long getCreationTime() { return creationTime; }
public double getAverageComplexity() {
return entries.stream()
.mapToDouble(entry -> entry.mathSignature().getComplexityValue())
.average()
.orElse(0.0);
}
public Stream<LedgerEntry> streamEntries() { return entries.stream(); }
@Override
public String toString() {
return String.format("Branch[%s] entries=%d checkpoints=%d complexity=%.3f",
branchId.name(), entries.size(), checkpoints.size(), getAverageComplexity());
}
}
/**
* Checkpoint for state snapshots
*/
public record Checkpoint(UUID id, String merkleRoot, List<UUID> entryIds, long operationId, long timestamp) {
public static Checkpoint create(String merkleRoot, List<UUID> entryIds, long operationId) {
return new Checkpoint(UUID.randomUUID(), merkleRoot, entryIds, operationId, System.currentTimeMillis());
}
public long ageInMillis() { return System.currentTimeMillis() - timestamp; }
}
/**
* Lineage tracking for branch relationships
*/
public static final class LineageTree {
private final Map<BranchId, BranchLineage> lineages;
private LineageTree(Map<BranchId, BranchLineage> lineages) {
this.lineages = Map.copyOf(lineages);
}
public static LineageTree empty() {
return new LineageTree(Map.of());
}
public LineageTree withLineage(BranchId branchId, BranchLineage lineage) {
Map<BranchId, BranchLineage> newLineages = new HashMap<>(lineages);
newLineages.put(branchId, lineage);
return new LineageTree(newLineages);
}
public Optional<BranchLineage> getLineage(BranchId branchId) {
return Optional.ofNullable(lineages.get(branchId));
}
public Map<BranchId, BranchLineage> getAllLineages() { return lineages; }
}
/**
* Branch lineage information
*/
public record BranchLineage(Optional<BranchId> parentId, String creator, Instant createdAt) {
public static BranchLineage create(Optional<BranchId> parentId, String creator) {
return new BranchLineage(parentId, creator, Instant.now());
}
}
// ===== Result Types =====
public record BranchResult<T>(boolean success, T value, BranchId branchId, String message) {
public static <T> BranchResult<T> success(T value, BranchId branchId) {
return new BranchResult<>(true, value, branchId, "Success");
}
public static <T> BranchResult<T> failure(String message) {
return new BranchResult<>(false, null, null, message);
}
}
public record MergeResult<T>(boolean success, T value, String message) {
public static <T> MergeResult<T> success(T value) {
return new MergeResult<>(true, value, "Merge successful");
}
public static <T> MergeResult<T> failure(String message) {
return new MergeResult<>(false, null, message);
}
}
// ===== Statistics =====
public record LedgerStats(
int branchCount,
int entryCount,
int checkpointCount,
long operationCount,
double averageComplexity
) {
@Override
public String toString() {
return String.format("Stats{branches=%d, entries=%d, checkpoints=%d, ops=%d, avgComplexity=%.3f}",
branchCount, entryCount, checkpointCount, operationCount, averageComplexity);
}
}
// ===== Engine Classes =====
private static final class MathEngine {
private final Configuration config;
private final List<Integer> primes;
public MathEngine(Configuration config) {
this.config = config;
this.primes = generatePrimes(1000);
}
public Float4096 interpolatePrime(Float4096 n) {
double nValue = n.getValue().doubleValue();
int index = (int) (Math.abs(nValue) % primes.size());
return new Float4096(String.valueOf(primes.get(index)));
}
private List<Integer> generatePrimes(int count) {
List<Integer> primes = new ArrayList<>();
int candidate = 2;
while (primes.size() < count) {
if (isPrime(candidate)) {
primes.add(candidate);
}
candidate++;
}
return primes;
}
private boolean isPrime(int n) {
if (n < 2) return false;
if (n == 2) return true;
if (n % 2 == 0) return false;
for (int i = 3; i * i <= n; i += 2) {
if (n % i == 0) return false;
}
return true;
}
}
private static final class CryptoEngine {
private final SecureRandom secureRandom;
private final ThreadLocal<MessageDigest> threadDigest;
public CryptoEngine() {
this.secureRandom = new SecureRandom();
this.threadDigest = ThreadLocal.withInitial(() -> {
try {
return MessageDigest.getInstance("SHA-256");
} catch (NoSuchAlgorithmException e) {
throw new RuntimeException("SHA-256 not available", e);
}
});
}
public String generateSalt() {
byte[] saltBytes = new byte[16];
secureRandom.nextBytes(saltBytes);
return HexFormat.of().formatHex(saltBytes);
}
public String computeHash(String input) {
MessageDigest digest = threadDigest.get();
digest.reset();
return HexFormat.of().formatHex(digest.digest(input.getBytes(StandardCharsets.UTF_8)));
}
public BigInteger computeBigIntegerHash(String input) {
return new BigInteger(1, threadDigest.get().digest(input.getBytes(StandardCharsets.UTF_8)));
}
}
private static final class HolographicEncoder {
public String base4096Encode(String input) {
Objects.requireNonNull(input, "Input cannot be null");
StringBuilder encoded = new StringBuilder();
for (byte b : input.getBytes(StandardCharsets.UTF_8)) {
encoded.append((char) (0x2800 + (b & 0xFF)));
}
return encoded.toString();
}
}
// ===== Core Operations =====
public LedgerEntry addEntry(String branchName, String key, String value) {
Objects.requireNonNull(branchName, "Branch name cannot be null");
Objects.requireNonNull(key, "Key cannot be null");
Objects.requireNonNull(value, "Value cannot be null");
return withWriteLock(() -> {
BranchId branchId = findBranchId(branchName);
ImmutableBranch branch = branches.get(branchId);
if (branch == null) {
throw new IllegalArgumentException("Branch not found: " + branchName);
}
long operationId = operationCounter.incrementAndGet();
LedgerEntry entry = LedgerEntry.create(key, value, operationId, cryptoEngine, mathEngine);
ImmutableBranch newBranch = branch.addEntry(entry);
// Create checkpoint if needed
if (newBranch.getEntries().size() % config.checkpointInterval() == 0) {
String merkleRoot = "merkle_" + operationId;
List<UUID> entryIds = newBranch.getEntries().stream().map(LedgerEntry::id).toList();
Checkpoint checkpoint = Checkpoint.create(merkleRoot, entryIds, operationId);
newBranch = newBranch.addCheckpoint(checkpoint);
}
branches.put(branchId, newBranch);
if (config.enableVerboseLogging()) {
LOGGER.info("Added to " + branchName + ": " + entry.getSummary());
}
return entry;
});
}
public BranchResult<ElegantUnifiedPrecisionLedger> createBranch(String name, String parentName) {
Objects.requireNonNull(name, "Branch name cannot be null");
return withWriteLock(() -> {
if (findBranchIdByName(name).isPresent()) {
return BranchResult.failure("Branch already exists: " + name);
}
BranchId newBranchId = BranchId.create(name, BranchType.FEATURE);
ImmutableBranch newBranch;
if (parentName != null) {
BranchId parentId = findBranchId(parentName);
newBranch = ImmutableBranch.createFrom(newBranchId, parentId);
} else {
newBranch = ImmutableBranch.create(newBranchId);
}
Map<BranchId, ImmutableBranch> newBranches = new HashMap<>(branches);
newBranches.put(newBranchId, newBranch);
// Update this ledger's branches
branches.put(newBranchId, newBranch);
LOGGER.info("Created branch: " + name + (parentName != null ? " from " + parentName : ""));
return BranchResult.success(this, newBranchId);
});
}
// ===== Query Operations =====
public Optional<LedgerEntry> findEntry(String branchName, String key) {
return withReadLock(() -> {
Optional<BranchId> branchId = findBranchIdByName(branchName);
if (branchId.isEmpty()) return Optional.empty();
ImmutableBranch branch = branches.get(branchId.get());
return branch.getEntries().stream()
.filter(entry -> entry.key().equals(key))
.findFirst();
});
}
public List<LedgerEntry> findHighComplexityEntries(double threshold) {
return withReadLock(() ->
branches.values().stream()
.flatMap(ImmutableBranch::streamEntries)
.filter(entry -> entry.mathSignature().isHighComplexity() ||
entry.dnaSignature().isHighComplexity())
.toList()
);
}
public double getAverageComplexity() {
return withReadLock(() ->
branches.values().stream()
.flatMap(ImmutableBranch::streamEntries)
.mapToDouble(entry -> entry.mathSignature().getComplexityValue())
.average()
.orElse(0.0)
);
}
public Map<String, Integer> getBranchSizes() {
return withReadLock(() -> {
Map<String, Integer> sizes = new HashMap<>();
branches.forEach((branchId, branch) -> sizes.put(branchId.name(), branch.getEntries().size()));
return sizes;
});
}
public Stream<LedgerEntry> streamAllEntries() {
return withReadLock(() ->
branches.values().stream().flatMap(ImmutableBranch::streamEntries)
);
}
// ===== Statistics =====
public LedgerStats getStatistics() {
return withReadLock(() -> {
int totalEntries = branches.values().stream()
.mapToInt(branch -> branch.getEntries().size())
.sum();
int totalCheckpoints = branches.values().stream()
.mapToInt(branch -> branch.getCheckpoints().size())
.sum();
double avgComplexity = getAverageComplexity();
return new LedgerStats(
branches.size(),
totalEntries,
totalCheckpoints,
operationCounter.get(),
avgComplexity
);
});
}
// ===== Verification =====
public boolean verifyBranchIntegrity(String branchName) {
return withReadLock(() -> {
Optional<BranchId> branchId = findBranchIdByName(branchName);
if (branchId.isEmpty()) return false;
ImmutableBranch branch = branches.get(branchId.get());
boolean valid = branch.getEntries().stream().allMatch(entry -> {
String expectedHash = cryptoEngine.computeHash(
entry.key() + ":" + entry.value() + ":" + entry.salt());
return expectedHash.equals(entry.dnaSignature().hash());
});
if (config.enableVerboseLogging()) {
LOGGER.info("Branch '" + branchName + "' integrity: " + (valid ? "VALID" : "INVALID"));
}
return valid;
});
}
// ===== Holographic Operations =====
public String getEncodedSummary() {
String summary = getStatistics().toString();
return holographicEncoder.base4096Encode(summary);
}
// ===== Utility Methods =====
private BranchId findBranchId(String branchName) {
return findBranchIdByName(branchName)
.orElseThrow(() -> new IllegalArgumentException("Branch not found: " + branchName));
}
private Optional<BranchId> findBranchIdByName(String branchName) {
return branches.keySet().stream()
.filter(id -> id.name().equals(branchName))
.findFirst();
}
private <T> T withReadLock(Supplier<T> operation) {
lock.readLock().lock();
try {
return operation.get();
} finally {
lock.readLock().unlock();
}
}
private <T> T withWriteLock(Supplier<T> operation) {
lock.writeLock().lock();
try {
return operation.get();
} finally {
lock.writeLock().unlock();
}
}
// ===== Mathematical Utilities =====
private static BigDecimal calculateGoldenRatio() {
// φ = (1 + √5) / 2
BigDecimal five = new BigDecimal("5", PRECISION_4096);
BigDecimal sqrt5 = sqrt(five);
BigDecimal one = new BigDecimal("1", PRECISION_4096);
BigDecimal two = new BigDecimal("2", PRECISION_4096);
return one.add(sqrt5).divide(two, PRECISION_4096);
}
private static BigDecimal sqrt(BigDecimal value) {
BigDecimal x = value;
BigDecimal previous;
BigDecimal two = new BigDecimal("2");
for (int i = 0; i < 100; i++) {
previous = x;
x = x.add(value.divide(x, PRECISION_4096)).divide(new BigDecimal("2"), PRECISION_4096);
if (x.equals(previous)) break;
}
return x;
}
}
ElegantUnifiedPrecisionLedgerCombined.java
package com.xai.float4096;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;
import java.security.MessageDigest;
import java.util.*;
/**
* Elegant high-precision floating-point class with 4096-bit precision.
* Features quaternary DNA logic, golden ratio foundation, and Turing-complete QuatDnaLang.
* Demonstrates functional completeness through subtraction-based logic gates.
*/
public final class Float4096 {
private static final MathContext PRECISION = new MathContext(4096, RoundingMode.HALF_EVEN);
private static final Float4096 EPSILON = new Float4096("1e-4095");
// Core constants rooted in golden ratio
public static final Float4096 ZERO = new Float4096("0");
public static final Float4096 ONE = new Float4096("1");
public static final Float4096 TWO = new Float4096("2");
public static final Float4096 FIVE = new Float4096("5");
public static final Float4096 PHI = calculateGoldenRatio();
public static final Float4096 LN_PHI = ln(PHI);
private final BigDecimal value;
// Constructors with validation
public Float4096(String value) {
this.value = new BigDecimal(value, PRECISION);
validateFinite();
}
public Float4096(BigDecimal value) {
this.value = Objects.requireNonNull(value).round(PRECISION);
validateFinite();
}
public Float4096(double value) {
this.value = new BigDecimal(String.valueOf(value), PRECISION);
validateFinite();
}
private void validateFinite() {
if (value.scale() > PRECISION.getPrecision() || !isRealNumber(value)) {
throw new ArithmeticException("Invalid Float4096 value: " + value);
}
}
private static boolean isRealNumber(BigDecimal bd) {
try { bd.doubleValue(); return true; } catch (Exception e) { return false; }
}
// Arithmetic operations with overflow protection
public Float4096 add(Float4096 other) {
return new Float4096(this.value.add(other.value, PRECISION));
}
public Float4096 subtract(Float4096 other) {
return new Float4096(this.value.subtract(other.value, PRECISION));
}
public Float4096 multiply(Float4096 other) {
return new Float4096(this.value.multiply(other.value, PRECISION));
}
public Float4096 divide(Float4096 other) {
if (other.isZero()) throw new ArithmeticException("Division by zero");
return new Float4096(this.value.divide(other.value, PRECISION));
}
public Float4096 sqrt() {
if (value.signum() < 0) throw new ArithmeticException("Square root of negative number");
BigDecimal x = value, two = TWO.value;
for (int i = 0; i < 200 && !x.equals(value.divide(x, PRECISION).add(x).divide(two, PRECISION)); i++) {
x = value.divide(x, PRECISION).add(x).divide(two, PRECISION);
}
return new Float4096(x);
}
public Float4096 abs() {
return new Float4096(value.abs(PRECISION));
}
public Float4096 pow(Float4096 exponent) {
return exp(exponent.multiply(ln(this)));
}
// Advanced mathematical functions
public static Float4096 exp(Float4096 x) {
BigDecimal bd = x.value, sum = BigDecimal.ONE, term = BigDecimal.ONE;
for (int i = 1; i <= 1000; i++) {
term = term.multiply(bd).divide(BigDecimal.valueOf(i), PRECISION);
BigDecimal newSum = sum.add(term, PRECISION);
if (newSum.equals(sum)) break;
sum = newSum;
}
return new Float4096(sum);
}
public static Float4096 ln(Float4096 x) {
if (x.value.signum() <= 0) throw new IllegalArgumentException("ln of non-positive number");
if (x.equals(ONE)) return ZERO;
BigDecimal bd = x.value, y = bd.subtract(BigDecimal.ONE, PRECISION);
BigDecimal ret = new BigDecimal("1001", PRECISION);
for (long i = 1000; i >= 0; i--) {
BigDecimal n = BigDecimal.valueOf(i / 2 + 1).pow(2, PRECISION).multiply(y, PRECISION);
ret = n.divide(ret, PRECISION).add(BigDecimal.valueOf(i + 1), PRECISION);
}
return new Float4096(y.divide(ret, PRECISION));
}
// Utility methods
public int compareTo(Float4096 other) { return value.compareTo(other.value); }
public boolean isZero() { return value.signum() == 0; }
public boolean isFinite() { return isRealNumber(value); }
public double toDouble() { return value.doubleValue(); }
public BigDecimal getValue() { return value; }
public BigInteger toBigInteger() { return value.toBigInteger(); }
@Override public String toString() { return value.toPlainString(); }
@Override public boolean equals(Object o) {
return this == o || (o instanceof Float4096 f && value.equals(f.value));
}
@Override public int hashCode() { return Objects.hash(value); }
// Functional complete logic via subtraction
public static Float4096 not(Float4096 x) { return ZERO.subtract(x); }
public static Float4096 and(Float4096 a, Float4096 b) { return not(or(not(a), not(b))); }
public static Float4096 or(Float4096 a, Float4096 b) { return a.subtract(not(b)); }
public static Float4096 xor(Float4096 a, Float4096 b) {
return or(and(not(a), b), and(a, not(b)));
}
// Quaternary DNA system
private static final Map<Character, Integer> DNA_TO_QUAT =
Map.of('A', 0, 'C', 1, 'G', 2, 'T', 3);
private static final Map<Integer, Character> QUAT_TO_DNA =
Map.of(0, 'A', 1, 'C', 2, 'G', 3, 'T');
// Base-4096 alphabet (deterministically generated from PHI)
private static final List<Character> BASE4096_ALPHABET = generateAlphabet();
private static List<Character> generateAlphabet() {
try {
MessageDigest md = MessageDigest.getInstance("SHA-256");
byte[] seed = md.digest(PHI.toString().getBytes());
Random rand = new Random(new BigInteger(1, seed).longValue());
Set<Character> chars = new LinkedHashSet<>();
while (chars.size() < 4096) {
int cp = 33 + rand.nextInt(0x10FFFF - 33);
if (Character.isValidCodePoint(cp) && !Character.isISOControl(cp)) {
chars.add((char) cp);
}
}
return new ArrayList<>(chars);
} catch (Exception e) {
throw new RuntimeException("Alphabet generation failed", e);
}
}
// DNA validation and quaternary operations
private static void validateDNA(String dna) {
if (dna == null || dna.isEmpty())
throw new IllegalArgumentException("Invalid DNA sequence");
for (char c : dna.toCharArray()) {
if (!DNA_TO_QUAT.containsKey(Character.toUpperCase(c))) {
throw new IllegalArgumentException("Invalid DNA base: " + c);
}
}
}
public static int quatMin(int a, int b) { return Math.min(clamp(a), clamp(b)); }
public static int quatMax(int a, int b) { return Math.max(clamp(a), clamp(b)); }
public static int quatInvert(int a) { return 3 - clamp(a); }
public static int quatSuccessor(int a) { return (clamp(a) + 1) % 4; }
public static int quatPredecessor(int a) { return (clamp(a) + 3) % 4; }
private static int clamp(int x) { return Math.max(0, Math.min(3, x)); }
// DNA sequence operations
public static String dnaMin(String dna1, String dna2) {
validateDNA(dna1); validateDNA(dna2);
if (dna1.length() != dna2.length())
throw new IllegalArgumentException("DNA sequences must be same length");
StringBuilder result = new StringBuilder(dna1.length());
for (int i = 0; i < dna1.length(); i++) {
int a = DNA_TO_QUAT.get(Character.toUpperCase(dna1.charAt(i)));
int b = DNA_TO_QUAT.get(Character.toUpperCase(dna2.charAt(i)));
result.append(QUAT_TO_DNA.get(quatMin(a, b)));
}
return result.toString();
}
public static String dnaMax(String dna1, String dna2) {
validateDNA(dna1); validateDNA(dna2);
if (dna1.length() != dna2.length())
throw new IllegalArgumentException("DNA sequences must be same length");
StringBuilder result = new StringBuilder(dna1.length());
for (int i = 0; i < dna1.length(); i++) {
int a = DNA_TO_QUAT.get(Character.toUpperCase(dna1.charAt(i)));
int b = DNA_TO_QUAT.get(Character.toUpperCase(dna2.charAt(i)));
result.append(QUAT_TO_DNA.get(quatMax(a, b)));
}
return result.toString();
}
public static String dnaInvert(String dna) {
validateDNA(dna);
StringBuilder result = new StringBuilder(dna.length());
for (char c : dna.toCharArray()) {
result.append(QUAT_TO_DNA.get(quatInvert(DNA_TO_QUAT.get(Character.toUpperCase(c)))));
}
return result.toString();
}
// Numeric conversions
public static String dnaAdd(String dna1, String dna2) {
validateDNA(dna1); validateDNA(dna2);
return bigIntToDna(dnaToBigInt(dna1).add(dnaToBigInt(dna2)));
}
private static BigInteger dnaToBigInt(String dna) {
BigInteger result = BigInteger.ZERO, base = BigInteger.valueOf(4);
for (char c : dna.toUpperCase().toCharArray()) {
result = result.multiply(base).add(BigInteger.valueOf(DNA_TO_QUAT.get(c)));
}
return result;
}
private static String bigIntToDna(BigInteger num) {
if (num.signum() < 0) throw new IllegalArgumentException("Negative numbers not supported");
if (num.equals(BigInteger.ZERO)) return "A";
StringBuilder dna = new StringBuilder();
BigInteger base = BigInteger.valueOf(4);
while (num.signum() > 0) {
dna.append(QUAT_TO_DNA.get(num.remainder(base).intValue()));
num = num.divide(base);
}
return dna.reverse().toString();
}
// Base-4096 encoding (6 DNA bases = 1 symbol, 4^6 = 4096)
public static String encodeToBase4096(String dna) {
validateDNA(dna);
String padded = dna.toUpperCase() + "A".repeat((6 - dna.length() % 6) % 6);
StringBuilder encoded = new StringBuilder();
for (int i = 0; i < padded.length(); i += 6) {
String group = padded.substring(i, i + 6);
encoded.append(BASE4096_ALPHABET.get(dnaToBigInt(group).intValueExact()));
}
return encoded.toString();
}
public static String decodeFromBase4096(String encoded) {
StringBuilder dna = new StringBuilder();
for (char symbol : encoded.toCharArray()) {
int index = BASE4096_ALPHABET.indexOf(symbol);
if (index == -1) throw new IllegalArgumentException("Invalid base-4096 symbol: " + symbol);
String group = bigIntToDna(BigInteger.valueOf(index));
dna.append("A".repeat(6 - group.length())).append(group);
}
return dna.toString().replaceAll("A+$", "");
}
// Float4096 ↔ DNA conversion
public String toDnaSequence() { return bigIntToDna(toBigInteger()); }
public static Float4096 fromDnaSequence(String dna) {
return new Float4096(new BigDecimal(dnaToBigInt(dna), PRECISION));
}
/**
* QuatDnaLang - Turing-complete language native to Float4096
* Commands encoded as DNA pairs:
* AA(+), AC(-), AG(>), AT(<), CA(.), CC(,), CG([), CT(]), GA(I), GC(M), GG(X), TT(E)
*/
public static final class QuatDnaLang {
private static final Map<String, Character> COMMANDS = Map.of(
"AA", '+', "AC", '-', "AG", '>', "AT", '<', "CA", '.', "CC", ',',
"CG", '[', "CT", ']', "GA", 'I', "GC", 'M', "GG", 'X', "TT", 'E'
);
public static String execute(String program, String input, int maxSteps) {
validateDNA(program); validateDNA(input);
if (program.length() % 2 != 0) program += "A";
// Parse instructions
List<Character> instructions = new ArrayList<>();
for (int i = 0; i < program.length(); i += 2) {
String pair = program.substring(i, i + 2).toUpperCase();
Character cmd = COMMANDS.get(pair);
if (cmd != null) instructions.add(cmd);
}
// Build bracket map
Map<Integer, Integer> bracketMap = new HashMap<>();
Deque<Integer> stack = new LinkedList<>();
for (int i = 0; i < instructions.size(); i++) {
char cmd = instructions.get(i);
if (cmd == '[') {
stack.push(i);
} else if (cmd == ']') {
if (stack.isEmpty()) throw new IllegalArgumentException("Mismatched brackets");
int open = stack.pop();
bracketMap.put(open, i);
bracketMap.put(i, open);
}
}
if (!stack.isEmpty()) throw new IllegalArgumentException("Mismatched brackets");
// Execute
Map<Integer, Integer> tape = new HashMap<>(); // Sparse tape
int head = 0, inputIndex = 0, pc = 0, steps = 0;
int[] inputArray = input.toUpperCase().chars()
.map(c -> DNA_TO_QUAT.get((char) c)).toArray();
StringBuilder output = new StringBuilder();
while (pc < instructions.size() && steps < maxSteps) {
char cmd = instructions.get(pc);
int current = tape.getOrDefault(head, 0);
switch (cmd) {
case '+' -> tape.put(head, quatSuccessor(current));
case '-' -> tape.put(head, quatPredecessor(current));
case '>' -> head++;
case '<' -> head--;
case '.' -> output.append(QUAT_TO_DNA.get(current));
case ',' -> tape.put(head, inputIndex < inputArray.length ? inputArray[inputIndex++] : 0);
case '[' -> { if (current == 0) pc = bracketMap.get(pc); }
case ']' -> { if (current != 0) pc = bracketMap.get(pc); }
case 'I' -> tape.put(head, quatInvert(current));
case 'M' -> tape.put(head, quatMin(current, tape.getOrDefault(head + 1, 0)));
case 'X' -> tape.put(head, quatMax(current, tape.getOrDefault(head + 1, 0)));
case 'E' -> {
// Extract and execute subprogram
StringBuilder subProg = new StringBuilder();
int pos = head + 1;
while (tape.containsKey(pos) && tape.get(pos) != 0) {
int a = tape.get(pos), b = tape.getOrDefault(pos + 1, 0);
if (a == 0 && b == 0) break;
subProg.append(QUAT_TO_DNA.get(a)).append(QUAT_TO_DNA.get(b));
pos += 2;
}
String result = execute(subProg.toString(), "", maxSteps - steps);
// Write result back
pos = head + 1;
for (char c : result.toCharArray()) {
tape.put(pos++, DNA_TO_QUAT.get(c));
}
while (tape.containsKey(pos)) tape.remove(pos++);
}
}
pc++; steps++;
}
if (steps >= maxSteps) throw new RuntimeException("Maximum steps exceeded");
return output.toString();
}
}
// Helper method for golden ratio
private static Float4096 calculateGoldenRatio() {
return ONE.add(FIVE.sqrt()).divide(TWO);
}
}
