import math
import hashlib

# -------------------------------
# Constants
# -------------------------------
PHI = 1.6180339887
INV_PHI = PHI - 1

# -------------------------------
# Helper Functions
# -------------------------------
def DNA_n_log(n):
    """Return log(DNA_n) recursively to avoid overflow"""
    if n == 0:
        return math.log(PHI)
    return math.log(PHI) + DNA_n_log(n - 1)

def log_fib(n):
    """Log-space Fibonacci using Binet's formula"""
    phi = PHI
    psi = -1 / PHI
    val = (phi ** n - psi ** n) / math.sqrt(5)
    return math.log(abs(val) + 1e-12)  # avoid log(0)

def log_prime(n):
    """Approximate log(n-th prime)"""
    if n < 2:
        return 0
    return math.log(n * math.log(n))

# -------------------------------
# PHI-only Turing-Complete Covenant VM
# -------------------------------
class PHI_Covenant_VM:
    def __init__(self, slots=32):
        self.slots = {}
        self.bits = {}
        self.stack = []
        self.slots_count = slots

    def discretize(self, value, threshold=math.log(PHI)):
        return 1 if value >= threshold else 0

    def safe_pop(self):
        return self.stack.pop() if self.stack else 0.0

    # Provision all slots with DNA, Fibonacci, primes, and combined values
    def provision_lattice(self):
        for n in range(1, self.slots_count):
            if n <= 5:
                val = DNA_n_log(n)
            elif n <= 10:
                val = log_fib(n)
            elif n <= 15:
                val = log_prime(n)
            else:
                # Combined log-space operator
                val = DNA_n_log(n - 10) + log_fib(n - 10) + log_prime(n - 10)
            self.slots[n] = val
            self.bits[n] = self.discretize(val)
        self.slots[32] = 0
        self.bits[32] = 0

    def execute_stream(self, program):
        ip = 0
        loop_stack = []

        while ip < len(program):
            instr = program[ip]

            if isinstance(instr, (int, float)):
                self.stack.append(math.log(abs(instr) + 1))
            elif isinstance(instr, str) and instr.startswith("DNA"):
                k = int(instr[3:])
                self.stack.append(DNA_n_log(k))
            elif isinstance(instr, str) and instr.startswith("FIB"):
                k = int(instr[3:])
                self.stack.append(log_fib(k))
            elif isinstance(instr, str) and instr.startswith("PRIME"):
                k = int(instr[5:])
                self.stack.append(log_prime(k))
            elif instr == "ADD":
                b, a = self.safe_pop(), self.safe_pop()
                self.stack.append(math.log(math.exp(a) + math.exp(b)))
            elif instr == "MUL":
                b, a = self.safe_pop(), self.safe_pop()
                self.stack.append(a + b)
            elif instr == "SIN":
                a = self.safe_pop()
                self.stack.append(math.sin(math.exp(a)))
            elif instr == "COS":
                a = self.safe_pop()
                self.stack.append(math.cos(math.exp(a)))
            elif instr == "LOOP":
                count = int(self.safe_pop())
                loop_stack.append((ip, count))
                if count <= 0:
                    # Skip loop if zero
                    depth = 1
                    while depth > 0:
                        ip += 1
                        if program[ip] == "LOOP":
                            depth += 1
                        elif program[ip] == "ENDLOOP":
                            depth -= 1
            elif instr == "ENDLOOP":
                if loop_stack:
                    start_ip, count = loop_stack.pop()
                    count -= 1
                    if count > 0:
                        loop_stack.append((start_ip, count))
                        ip = start_ip
            elif instr == "IF":
                threshold = math.exp(self.safe_pop())
                cond = math.exp(self.safe_pop())
                if cond >= threshold:
                    # execute true branch
                    pass
                else:
                    # skip to ELSE or ENDIF
                    depth = 1
                    while depth > 0:
                        ip += 1
                        if program[ip] == "IF":
                            depth += 1
                        elif program[ip] in ("ELSE", "ENDIF"):
                            depth -= 1
            elif instr == "ELSE":
                # skip to ENDIF
                depth = 1
                while depth > 0:
                    ip += 1
                    if program[ip] == "IF":
                        depth += 1
                    elif program[ip] == "ENDIF":
                        depth -= 1
            elif instr == "ENDIF":
                pass
            elif instr == "SHA256":
                bitstring = ''.join(str(self.discretize(v)) for v in self.slots.values())
                h = hashlib.sha256(bitstring.encode()).hexdigest()
                self.slots[32] = int(h[:8], 16)
            else:
                raise ValueError(f"Unknown instruction: {instr}")

            ip += 1

        # Update bits
        for n, val in self.slots.items():
            self.bits[n] = self.discretize(val)

    def report(self):
        print("\n[Final Slots State]")
        for n, val in sorted(self.slots.items()):
            print(f"D_{n}(log) = {val:.6e} → {self.bits.get(n,0)}")
        bitstring = ''.join(str(self.bits.get(n,0)) for n in sorted(self.slots.keys(), reverse=True))
        print("Binary:", bitstring)
        print("Hex   :", hex(int(bitstring, 2)) if bitstring else "0x0")
        print("Stack :", self.stack)
        print("Covenant ID (slot 32):", hex(self.slots.get(32, 0)))

# -------------------------------
# Fully Expressive Covenant Program
# -------------------------------
if __name__ == "__main__":
    vm = PHI_Covenant_VM()
    vm.provision_lattice()

    program = [
        # Combine DNA slots
        "DNA1", "DNA2", "ADD",
        "DNA3", "MUL",
        "DNA4", "ADD",
        "DNA5", "MUL",
        # Finite loop with DNA/FIB/PRIME
        5, "LOOP",
            "DNA6", "MUL",
            "FIB7", "ADD",
            "PRIME8", "MUL",
        "ENDLOOP",
        # Conditional branching example
        "DNA9", 2.0, "IF",
            "DNA10", "ADD",
        "ELSE",
            "DNA11", "MUL",
        "ENDIF",
        # Additional Fibonacci and prime braids
        "FIB12", "MUL",
        "PRIME13", "ADD",
        # Final deterministic covenant ID
        "SHA256"
    ]

    vm.execute_stream(program)
    vm.report()
