import math
import hashlib

# -------------------------------
# φ-only Turing-Complete BTC VM (Log-Safe, Finite Loops)
# -------------------------------
PHI = 1.6180339887
INV_PHI = PHI - 1

def DNA_n_log(n):
    """Return log(DNA_n) to prevent overflow"""
    if n == 0:
        return math.log(PHI)
    return math.log(PHI) + DNA_n_log(n - 1)

class PHI_Covenant_VM:
    def __init__(self, slots=32):
        self.slots = {}
        self.bits = {}
        self.stack = []
        self.slots_count = slots

    # Initialize slots with log-space DNA values
    def provision_lattice(self):
        for n in range(1, self.slots_count + 1):
            val_log = DNA_n_log(n)
            self.slots[n] = val_log
            self.bits[n] = self.discretize(val_log)

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

    # Stack-safe pop
    def safe_pop(self):
        if self.stack:
            return self.stack.pop()
        else:
            return 0.0  # log(1) in log-space

    # Execute φ-only program
    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 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)  # log-space multiplication

            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())  # finite loop count
                loop_stack.append((ip, count))
                if count <= 0:
                    # skip to ENDLOOP
                    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  # repeat loop
                    # else exit loop naturally

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

    # Report current slots, stack, and covenant fingerprint
    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 Utilized Finite φ-only Covenant Program
# -------------------------------
if __name__ == "__main__":
    vm = PHI_Covenant_VM()
    vm.provision_lattice()

    program = [
        # Push first DNA values and combine
        "DNA1", "DNA2", "ADD",
        "DNA3", "MUL",
        "DNA4", "ADD",
        "DNA5", "MUL",
        # Loop using finite counter
        5, "LOOP",  # repeat 5 times
            "DNA6", "MUL",
            "DNA7", "ADD",
        "ENDLOOP",
        # Additional operations
        "DNA8", "MUL",
        "DNA9", "ADD",
        "DNA10", "MUL",
        # Generate deterministic covenant ID
        "SHA256"
    ]

    vm.execute_stream(program)
    vm.report()
