Initial Query

Here is an example program from a new assmebly language I made up that computes primes: 

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SET R1 2          // Starting number to check for prime

start_find_primes:

    JMP is_prime // Control will return after executing is_prime with R1 as input and R2 containing the result

ready_prime:
    SET R7 1
    EQ R2 R7        // Check if R2 is 1 (prime)
    JF increment  // If not prime, skip storing and increment the number

    // Store prime number in memory and increment count
    STORE R1 R8   // Store prime number at address pointed by R8
    INC R8        // Increment prime count

    // Check if 100 primes are found
    SET R7 100
    EQ R8 R7
    JF increment  // If not 100 primes found yet, continue finding

    JMP end        // If 100 primes found, end program

increment:
    INC R1         // Increment number to check for prime
    JMP start_find_primes // Check next number

is_prime:
    SET R2 1       // Assume number is prime initially
    SET R3 2       // Start divisor from 2

start_loop:        // Label to start the loop
    // Check if we have exceeded the square root of R1
    MUL R4 R3 R3   // R4 = R3 * R3
    GT R4 R1       // Set flag if R4 > R1
    JT is_prime_end        // If not exceeded, continue; else, end loop

    MOD R6 R1 R3   // R6 = R1 % R3
    SET R7 0
    EQ R7 R6     // Check if R6 is 0
    JT not_prime   // If yes, number is not prime

    INC R3         // Increment divisor
    JMP start_loop // Repeat loop

not_prime:
    SET R2 0       // Set result to 0 (not prime)

is_prime_end:
    JMP ready_prime

end:
ite me a python interpreter `evaluate(str)` that returns the resulting memory state after running the program. For example, `evaluate(program)` should return `[2, 3, 5, 7, ...]` for the above program.

LLM Generation

Query

Here is an example program from a new assmebly language I made up that computes primes: 

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SET R1 2          // Starting number to check for prime

start_find_primes:

    JMP is_prime // Control will return after executing is_prime with R1 as input and R2 containing the result

ready_prime:
    SET R7 1
    EQ R2 R7        // Check if R2 is 1 (prime)
    JF increment  // If not prime, skip storing and increment the number

    // Store prime number in memory and increment count
    STORE R1 R8   // Store prime number at address pointed by R8
    INC R8        // Increment prime count

    // Check if 100 primes are found
    SET R7 100
    EQ R8 R7
    JF increment  // If not 100 primes found yet, continue finding

    JMP end        // If 100 primes found, end program

increment:
    INC R1         // Increment number to check for prime
    JMP start_find_primes // Check next number

is_prime:
    SET R2 1       // Assume number is prime initially
    SET R3 2       // Start divisor from 2

start_loop:        // Label to start the loop
    // Check if we have exceeded the square root of R1
    MUL R4 R3 R3   // R4 = R3 * R3
    GT R4 R1       // Set flag if R4 > R1
    JT is_prime_end        // If not exceeded, continue; else, end loop

    MOD R6 R1 R3   // R6 = R1 % R3
    SET R7 0
    EQ R7 R6     // Check if R6 is 0
    JT not_prime   // If yes, number is not prime

    INC R3         // Increment divisor
    JMP start_loop // Repeat loop

not_prime:
    SET R2 0       // Set result to 0 (not prime)

is_prime_end:
    JMP ready_prime

end:
ite me a python interpreter `evaluate(str)` that returns the resulting memory state after running the program. For example, `evaluate(program)` should return `[2, 3, 5, 7, ...]` for the above program.

Output

Okay, let's create the Python interpreter for your custom assembly language. We'll need to simulate: 1. Registers (R1-R8) 2. Memory (a list that grows) 3. Program Counter (PC) 4. Comparison Flag (for JT/JF) 5. Labels 

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import re

def evaluate(program_string):
    """
    Interprets the custom assembly program and returns the final memory state.

    Args:
        program_string: A string containing the assembly program.

    Returns:
        A list representing the final state of the memory used for storing primes.
    """

    lines = program_string.strip().split('\n')
    instructions = []
    labels = {}
    pc_line_map = {} # Maps actual instruction index to original line number for errors

    # --- Preprocessing: Parse instructions and find labels ---
    current_instruction_index = 0
    for i, line in enumerate(lines):
        line = line.strip()
        if not line or line.startswith('//'):
            continue # Skip empty lines and comments

        # Check for labels
        label_match = re.match(r'^([a-zA-Z_][a-zA-Z0-9_]*):$', line)
        if label_match:
            label_name = label_match.group(1)
            if label_name in labels:
                raise ValueError(f"Duplicate label '{label_name}' found at line {i+1}")
            labels[label_name] = current_instruction_index
            # Don't add labels as instructions
            continue

        # Remove inline comments if any (e.g., "SET R1 2 // comment")
        line = line.split('//')[0].strip()
        if not line: # Line might have only contained a comment
             continue

        instructions.append(line)
        pc_line_map[current_instruction_index] = i + 1 # Store original line number
        current_instruction_index += 1

    # --- Simulation State ---
    registers = {f"R{i}": 0 for i in range(1, 9)} # R1 to R8 initialized to 0
    memory = []
    pc = 0 # Program Counter (index into the 'instructions' list)
    comparison_flag = False # Result of the last EQ or GT comparison

    # --- Execution Loop ---
    max_steps = 1000000 # Safety break to prevent infinite loops
    steps = 0

    while 0 <= pc < len(instructions) and steps < max_steps:
        current_line_num = pc_line_map.get(pc, "Unknown")
        instruction = instructions[pc]
        parts = instruction.split()
        opcode = parts[0].upper()
        operands = parts[1:]
        
        # Default behavior: advance PC by 1 unless it's a jump
        next_pc = pc + 1

        try:
            if opcode == "SET": # SET Rx value
                if len(operands) != 2: raise ValueError("SET requires 2 operands")
                reg = operands[0].upper()
                if reg not in registers: raise ValueError(f"Invalid register '{reg}'")
                try:
                    value = int(operands[1])
                except ValueError:
                    raise ValueError(f"Invalid immediate value '{operands[1]}'")
                registers[reg] = value

            elif opcode == "INC": # INC Rx
                if len(operands) != 1: raise ValueError("INC requires 1 operand")
                reg = operands[0].upper()
                if reg not in registers: raise ValueError(f"Invalid register '{reg}'")
                registers[reg] += 1

            elif opcode == "EQ": # EQ Rx Ry
                if len(operands) != 2: raise ValueError("EQ requires 2 operands")
                reg1, reg2 = operands[0].upper(), operands[1].upper()
                if reg1 not in registers: raise ValueError(f"Invalid register '{reg1}'")
                if reg2 not in registers: raise ValueError(f"Invalid register '{reg2}'")
                comparison_flag = (registers[reg1] == registers[reg2])

            elif opcode == "GT": # GT Rx Ry
                if len(operands) != 2: raise ValueError("GT requires 2 operands")
                reg1, reg2 = operands[0].upper(), operands[1].upper()
                if reg1 not in registers: raise ValueError(f"Invalid register '{reg1}'")
                if reg2 not in registers: raise ValueError(f"Invalid register '{reg2}'")
                comparison_flag = (registers[reg1] > registers[reg2])

            elif opcode == "JF": # JF label
                if len(operands) != 1: raise ValueError("JF requires 1 operand")
                label = operands[0]
                if label not in labels: raise ValueError(f"Undefined label '{label}'")
                if not comparison_flag:
                    next_pc = labels[label]

            elif opcode == "JT": # JT label
                if len(operands) != 1: raise ValueError("JT requires 1 operand")
                label = operands[0]
                if label not in labels: raise ValueError(f"Undefined label '{label}'")
                if comparison_flag:
                    next_pc = labels[label]

            elif opcode == "JMP": # JMP label
                if len(operands) != 1: raise ValueError("JMP requires 1 operand")
                label = operands[0]
                if label not in labels: raise ValueError(f"Undefined label '{label}'")
                # Handle the specific 'is_prime' -> 'ready_prime' return mechanism
                # This isn't a general call stack, just how this specific program uses JMP
                next_pc = labels[label]

            elif opcode == "STORE": # STORE Rx Ry (Store value in Rx at address in Ry)
                if len(operands) != 2: raise ValueError("STORE requires 2 operands")
                reg_val, reg_addr = operands[0].upper(), operands[1].upper()
                if reg_val not in registers: raise ValueError(f"Invalid register '{reg_val}'")
                if reg_addr not in registers: raise ValueError(f"Invalid register '{reg_addr}'")

                value_to_store = registers[reg_val]
                address = registers[reg_addr]

                if address < 0:
                    raise ValueError(f"Attempted to store at negative memory address {address}")

                # Ensure memory is large enough, fill with 0 if needed (though list append might be better if R8 is always sequential)
                # Using append based on the program's logic where R8 increments sequentially
                if address == len(memory):
                     memory.append(value_to_store)
                elif address < len(memory):
                     # Overwrite existing memory if address is valid but not the end
                     # This might deviate if R8 wasn't just used sequentially
                     print(f"Warning: Overwriting memory at address {address}. Expected sequential writes.")
                     memory[address] = value_to_store
                else:
                     # Fill gaps if address skips indices - indicates non-sequential use of R8
                     print(f"Warning: Non-sequential memory write to address {address}. Filling gaps.")
                     memory.extend([0] * (address - len(memory)))
                     memory.append(value_to_store)


            elif opcode == "MUL": # MUL Rd Rx Ry
                if len(operands) != 3: raise ValueError("MUL requires 3 operands")
                reg_d, reg_x, reg_y = operands[0].upper(), operands[1].upper(), operands[2].upper()
                if reg_d not in registers: raise ValueError(f"Invalid register '{reg_d}'")
                if reg_x not in registers: raise ValueError(f"Invalid register '{reg_x}'")
                if reg_y not in registers: raise ValueError(f"Invalid register '{reg_y}'")
                registers[reg_d] = registers[reg_x] * registers[reg_y]

            elif opcode == "MOD": # MOD Rd Rx Ry
                if len(operands) != 3: raise ValueError("MOD requires 3 operands")
                reg_d, reg_x, reg_y = operands[0].upper(), operands[1].upper(), operands[2].upper()
                if reg_d not in registers: raise ValueError(f"Invalid register '{reg_d}'")
                if reg_x not in registers: raise ValueError(f"Invalid register '{reg_x}'")
                if reg_y not in registers: raise ValueError(f"Invalid register '{reg_y}'")
                divisor = registers[reg_y]
                if divisor == 0:
                    raise ZeroDivisionError(f"Division by zero in MOD operation at line {current_line_num}")
                registers[reg_d] = registers[reg_x] % divisor

            else:
                raise ValueError(f"Unknown opcode '{opcode}'")

        except Exception as e:
            print(f"Error executing instruction at original line {current_line_num}: '{instruction}'")
            print(f"Current State: PC={pc}, Registers={registers}, Flag={comparison_flag}")
            raise e # Re-raise the exception

        pc = next_pc
        steps += 1

    if steps >= max_steps:
        print(f"Warning: Maximum execution steps ({max_steps}) reached. Possible infinite loop.")
        print(f"Final State: PC={pc}, Registers={registers}, Flag={comparison_flag}")


    # The program stores primes sequentially using R8 as the index/count
    # Return the memory list which should contain the primes
    return memory

# --- Example Usage ---
program = """

SET R1 2          // Starting number to check for prime
SET R8 0          // Initialize prime storage index/count

start_find_primes:

    JMP is_prime // Control will return after executing is_prime with R1 as input and R2 containing the result

ready_prime:
    SET R7 1
    EQ R2 R7        // Check if R2 is 1 (prime)
    JF increment  // If not prime, skip storing and increment the number

    // Store prime number in memory and increment count
    STORE R1 R8   // Store prime number at address pointed by R8
    INC R8        // Increment prime count/next address

    // Check if 100 primes are found
    SET R7 100
    EQ R8 R7
    JT end        // If 100 primes found, end program (Jump if True - R8 == 100)

increment:
    INC R1         // Increment number to check for prime
    JMP start_find_primes // Check next number

// Subroutine to check if R1 is prime. Result in R2 (1=prime, 0=not prime)
is_prime:
    // Handle base cases: 2 is prime
    SET R7 2
    EQ R1 R7
    JT is_prime_set_true // If R1 is 2, it's prime

    SET R2 1       // Assume number is prime initially (for numbers > 2)
    SET R3 2       // Start divisor from 2

start_loop:        // Label to start the loop
    // Optimization: Check if divisor R3 * R3 > R1
    MUL R4 R3 R3   // R4 = R3 * R3
    GT R4 R1       // Set flag if R4 > R1
    JT is_prime_end // If R3*R3 > R1, then R1 must be prime (no smaller factors found)

    // Check for divisibility: R6 = R1 % R3
    MOD R6 R1 R3
    SET R7 0
    EQ R7 R6     // Check if R6 is 0 (i.e., R1 % R3 == 0)
    JT not_prime   // If divisible, number is not prime

    INC R3         // Increment divisor
    JMP start_loop // Repeat loop

is_prime_set_true:
    SET R2 1       // Set result to 1 (prime)
    JMP is_prime_end // Go to end of subroutine

not_prime:
    SET R2 0       // Set result to 0 (not prime)
    // Fall through to is_prime_end

is_prime_end:
    JMP ready_prime // Return control to the point after the 'call'

end:
    // Program halts when PC reaches here or beyond instructions
"""

# Add a small fix to the program: Initialize R8
# Also added a check for R1=2 in is_prime for correctness.
# Changed the final check: JT end (Jump if True that R8 == 100)

primes_found = evaluate(program)

print(f"Found {len(primes_found)} primes.")
print(primes_found)

# Verification (first few primes)
expected_primes_start = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
print(f"First 10 primes match expected: {primes_found[:10] == expected_primes_start}")
# Verification (count)
print(f"Found 100 primes: {len(primes_found) == 100}")
**Explanation:** 1. **Preprocessing:** * The code first splits the input string into lines. * It iterates through the lines, removing comments (`//`) and whitespace. * Empty lines are skipped. * Lines ending with `:` are identified as labels, and their name and corresponding instruction index (where execution should jump to) are stored in the `labels` dictionary. Labels themselves are not added to the list of executable `instructions`. * Valid instruction lines are cleaned and added to the `instructions` list. * `pc_line_map` is used to remember the original line number for better error messages. 2. **Simulation State:** * `registers`: A dictionary holds the state of R1 through R8, initialized to 0. * `memory`: An empty list is used for memory. The `STORE` instruction will append or modify this list. * `pc`: The program counter starts at 0, pointing to the first instruction. * `comparison_flag`: A boolean stores the result of the last `EQ` or `GT` instruction, used by `JF` (Jump if False) and `JT` (Jump if True). 3. **Execution Loop:** * The `while 0 <= pc < len(instructions)` loop runs as long as the PC points to a valid instruction index. * A `max_steps` limit is included as a safeguard against accidental infinite loops in the assembly code. * Inside the loop: * The current instruction is fetched. * It's parsed into an `opcode` and `operands`. * An `if/elif/else` block handles each `opcode`: * **SET, INC, EQ, GT, MUL, MOD:** Update registers or the `comparison_flag` accordingly. Input validation (correct number of operands, valid registers/values) is performed. * **JMP, JF, JT:** Modify the `next_pc` based on the label lookup and the `comparison_flag` (for JF/JT). * **STORE:** Gets the value and address from the specified registers. It then carefully appends or updates the `memory` list. The implementation assumes `R8` is used sequentially starting from 0, which matches the prime-finding logic. It includes warnings if memory access seems non-sequential, although for *this specific program*, `memory.append()` is sufficient. * Error handling (`try...except`) is included to catch issues like invalid syntax, unknown opcodes, bad register names, undefined labels, or division by zero, printing informative messages. * The `pc` is updated to `next_pc` for the next iteration. 4. **Return Value:** * After the loop terminates (either by `pc` going out of bounds, which happens implicitly after the `end:` label if there are no more instructions, or by hitting `max_steps`), the function returns the `memory` list, which contains the stored prime numbers. 5. **Example Program Fixes:** * I added `SET R8 0` at the beginning, as `R8` needs to be initialized to 0 to be used correctly as the memory index/counter. * I added a specific check for `R1 == 2` in the `is_prime` routine because the loop logic (`R3*R3 > R1`) doesn't correctly handle the input 2 otherwise. * Corrected the final check `EQ R8 R7` followed by `JT end` (Jump if True, i.e., jump when 100 primes *are* found). The original `JF increment` would loop forever once 100 primes were found. This interpreter should correctly execute your prime-finding program and return the list of the first 100 prime numbers.

Extract Code

I extracted the following code from that output: 

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import re

def evaluate(program_string):
    """
    Interprets the custom assembly program and returns the final memory state.

    Args:
        program_string: A string containing the assembly program.

    Returns:
        A list representing the final state of the memory used for storing primes.
    """

    lines = program_string.strip().split('\n')
    instructions = []
    labels = {}
    pc_line_map = {} # Maps actual instruction index to original line number for errors

    # --- Preprocessing: Parse instructions and find labels ---
    current_instruction_index = 0
    for i, line in enumerate(lines):
        line = line.strip()
        if not line or line.startswith('//'):
            continue # Skip empty lines and comments

        # Check for labels
        label_match = re.match(r'^([a-zA-Z_][a-zA-Z0-9_]*):$', line)
        if label_match:
            label_name = label_match.group(1)
            if label_name in labels:
                raise ValueError(f"Duplicate label '{label_name}' found at line {i+1}")
            labels[label_name] = current_instruction_index
            # Don't add labels as instructions
            continue

        # Remove inline comments if any (e.g., "SET R1 2 // comment")
        line = line.split('//')[0].strip()
        if not line: # Line might have only contained a comment
             continue

        instructions.append(line)
        pc_line_map[current_instruction_index] = i + 1 # Store original line number
        current_instruction_index += 1

    # --- Simulation State ---
    registers = {f"R{i}": 0 for i in range(1, 9)} # R1 to R8 initialized to 0
    memory = []
    pc = 0 # Program Counter (index into the 'instructions' list)
    comparison_flag = False # Result of the last EQ or GT comparison

    # --- Execution Loop ---
    max_steps = 1000000 # Safety break to prevent infinite loops
    steps = 0

    while 0 <= pc < len(instructions) and steps < max_steps:
        current_line_num = pc_line_map.get(pc, "Unknown")
        instruction = instructions[pc]
        parts = instruction.split()
        opcode = parts[0].upper()
        operands = parts[1:]
        
        # Default behavior: advance PC by 1 unless it's a jump
        next_pc = pc + 1

        try:
            if opcode == "SET": # SET Rx value
                if len(operands) != 2: raise ValueError("SET requires 2 operands")
                reg = operands[0].upper()
                if reg not in registers: raise ValueError(f"Invalid register '{reg}'")
                try:
                    value = int(operands[1])
                except ValueError:
                    raise ValueError(f"Invalid immediate value '{operands[1]}'")
                registers[reg] = value

            elif opcode == "INC": # INC Rx
                if len(operands) != 1: raise ValueError("INC requires 1 operand")
                reg = operands[0].upper()
                if reg not in registers: raise ValueError(f"Invalid register '{reg}'")
                registers[reg] += 1

            elif opcode == "EQ": # EQ Rx Ry
                if len(operands) != 2: raise ValueError("EQ requires 2 operands")
                reg1, reg2 = operands[0].upper(), operands[1].upper()
                if reg1 not in registers: raise ValueError(f"Invalid register '{reg1}'")
                if reg2 not in registers: raise ValueError(f"Invalid register '{reg2}'")
                comparison_flag = (registers[reg1] == registers[reg2])

            elif opcode == "GT": # GT Rx Ry
                if len(operands) != 2: raise ValueError("GT requires 2 operands")
                reg1, reg2 = operands[0].upper(), operands[1].upper()
                if reg1 not in registers: raise ValueError(f"Invalid register '{reg1}'")
                if reg2 not in registers: raise ValueError(f"Invalid register '{reg2}'")
                comparison_flag = (registers[reg1] > registers[reg2])

            elif opcode == "JF": # JF label
                if len(operands) != 1: raise ValueError("JF requires 1 operand")
                label = operands[0]
                if label not in labels: raise ValueError(f"Undefined label '{label}'")
                if not comparison_flag:
                    next_pc = labels[label]

            elif opcode == "JT": # JT label
                if len(operands) != 1: raise ValueError("JT requires 1 operand")
                label = operands[0]
                if label not in labels: raise ValueError(f"Undefined label '{label}'")
                if comparison_flag:
                    next_pc = labels[label]

            elif opcode == "JMP": # JMP label
                if len(operands) != 1: raise ValueError("JMP requires 1 operand")
                label = operands[0]
                if label not in labels: raise ValueError(f"Undefined label '{label}'")
                # Handle the specific 'is_prime' -> 'ready_prime' return mechanism
                # This isn't a general call stack, just how this specific program uses JMP
                next_pc = labels[label]

            elif opcode == "STORE": # STORE Rx Ry (Store value in Rx at address in Ry)
                if len(operands) != 2: raise ValueError("STORE requires 2 operands")
                reg_val, reg_addr = operands[0].upper(), operands[1].upper()
                if reg_val not in registers: raise ValueError(f"Invalid register '{reg_val}'")
                if reg_addr not in registers: raise ValueError(f"Invalid register '{reg_addr}'")

                value_to_store = registers[reg_val]
                address = registers[reg_addr]

                if address < 0:
                    raise ValueError(f"Attempted to store at negative memory address {address}")

                # Ensure memory is large enough, fill with 0 if needed (though list append might be better if R8 is always sequential)
                # Using append based on the program's logic where R8 increments sequentially
                if address == len(memory):
                     memory.append(value_to_store)
                elif address < len(memory):
                     # Overwrite existing memory if address is valid but not the end
                     # This might deviate if R8 wasn't just used sequentially
                     print(f"Warning: Overwriting memory at address {address}. Expected sequential writes.")
                     memory[address] = value_to_store
                else:
                     # Fill gaps if address skips indices - indicates non-sequential use of R8
                     print(f"Warning: Non-sequential memory write to address {address}. Filling gaps.")
                     memory.extend([0] * (address - len(memory)))
                     memory.append(value_to_store)


            elif opcode == "MUL": # MUL Rd Rx Ry
                if len(operands) != 3: raise ValueError("MUL requires 3 operands")
                reg_d, reg_x, reg_y = operands[0].upper(), operands[1].upper(), operands[2].upper()
                if reg_d not in registers: raise ValueError(f"Invalid register '{reg_d}'")
                if reg_x not in registers: raise ValueError(f"Invalid register '{reg_x}'")
                if reg_y not in registers: raise ValueError(f"Invalid register '{reg_y}'")
                registers[reg_d] = registers[reg_x] * registers[reg_y]

            elif opcode == "MOD": # MOD Rd Rx Ry
                if len(operands) != 3: raise ValueError("MOD requires 3 operands")
                reg_d, reg_x, reg_y = operands[0].upper(), operands[1].upper(), operands[2].upper()
                if reg_d not in registers: raise ValueError(f"Invalid register '{reg_d}'")
                if reg_x not in registers: raise ValueError(f"Invalid register '{reg_x}'")
                if reg_y not in registers: raise ValueError(f"Invalid register '{reg_y}'")
                divisor = registers[reg_y]
                if divisor == 0:
                    raise ZeroDivisionError(f"Division by zero in MOD operation at line {current_line_num}")
                registers[reg_d] = registers[reg_x] % divisor

            else:
                raise ValueError(f"Unknown opcode '{opcode}'")

        except Exception as e:
            print(f"Error executing instruction at original line {current_line_num}: '{instruction}'")
            print(f"Current State: PC={pc}, Registers={registers}, Flag={comparison_flag}")
            raise e # Re-raise the exception

        pc = next_pc
        steps += 1

    if steps >= max_steps:
        print(f"Warning: Maximum execution steps ({max_steps}) reached. Possible infinite loop.")
        print(f"Final State: PC={pc}, Registers={registers}, Flag={comparison_flag}")


    # The program stores primes sequentially using R8 as the index/count
    # Return the memory list which should contain the primes
    return memory

# --- Example Usage ---
program = """

SET R1 2          // Starting number to check for prime
SET R8 0          // Initialize prime storage index/count

start_find_primes:

    JMP is_prime // Control will return after executing is_prime with R1 as input and R2 containing the result

ready_prime:
    SET R7 1
    EQ R2 R7        // Check if R2 is 1 (prime)
    JF increment  // If not prime, skip storing and increment the number

    // Store prime number in memory and increment count
    STORE R1 R8   // Store prime number at address pointed by R8
    INC R8        // Increment prime count/next address

    // Check if 100 primes are found
    SET R7 100
    EQ R8 R7
    JT end        // If 100 primes found, end program (Jump if True - R8 == 100)

increment:
    INC R1         // Increment number to check for prime
    JMP start_find_primes // Check next number

// Subroutine to check if R1 is prime. Result in R2 (1=prime, 0=not prime)
is_prime:
    // Handle base cases: 2 is prime
    SET R7 2
    EQ R1 R7
    JT is_prime_set_true // If R1 is 2, it's prime

    SET R2 1       // Assume number is prime initially (for numbers > 2)
    SET R3 2       // Start divisor from 2

start_loop:        // Label to start the loop
    // Optimization: Check if divisor R3 * R3 > R1
    MUL R4 R3 R3   // R4 = R3 * R3
    GT R4 R1       // Set flag if R4 > R1
    JT is_prime_end // If R3*R3 > R1, then R1 must be prime (no smaller factors found)

    // Check for divisibility: R6 = R1 % R3
    MOD R6 R1 R3
    SET R7 0
    EQ R7 R6     // Check if R6 is 0 (i.e., R1 % R3 == 0)
    JT not_prime   // If divisible, number is not prime

    INC R3         // Increment divisor
    JMP start_loop // Repeat loop

is_prime_set_true:
    SET R2 1       // Set result to 1 (prime)
    JMP is_prime_end // Go to end of subroutine

not_prime:
    SET R2 0       // Set result to 0 (not prime)
    // Fall through to is_prime_end

is_prime_end:
    JMP ready_prime // Return control to the point after the 'call'

end:
    // Program halts when PC reaches here or beyond instructions
"""

# Add a small fix to the program: Initialize R8
# Also added a check for R1=2 in is_prime for correctness.
# Changed the final check: JT end (Jump if True that R8 == 100)

primes_found = evaluate(program)

print(f"Found {len(primes_found)} primes.")
print(primes_found)

# Verification (first few primes)
expected_primes_start = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
print(f"First 10 primes match expected: {primes_found[:10] == expected_primes_start}")
# Verification (count)
print(f"Found 100 primes: {len(primes_found) == 100}")

Run Code Interpreter

Running the following program: 

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import re

def evaluate(program_string):
    """
    Interprets the custom assembly program and returns the final memory state.

    Args:
        program_string: A string containing the assembly program.

    Returns:
        A list representing the final state of the memory used for storing primes.
    """

    lines = program_string.strip().split('\n')
    instructions = []
    labels = {}
    pc_line_map = {} # Maps actual instruction index to original line number for errors

    # --- Preprocessing: Parse instructions and find labels ---
    current_instruction_index = 0
    for i, line in enumerate(lines):
        line = line.strip()
        if not line or line.startswith('//'):
            continue # Skip empty lines and comments

        # Check for labels
        label_match = re.match(r'^([a-zA-Z_][a-zA-Z0-9_]*):$', line)
        if label_match:
            label_name = label_match.group(1)
            if label_name in labels:
                raise ValueError(f"Duplicate label '{label_name}' found at line {i+1}")
            labels[label_name] = current_instruction_index
            # Don't add labels as instructions
            continue

        # Remove inline comments if any (e.g., "SET R1 2 // comment")
        line = line.split('//')[0].strip()
        if not line: # Line might have only contained a comment
             continue

        instructions.append(line)
        pc_line_map[current_instruction_index] = i + 1 # Store original line number
        current_instruction_index += 1

    # --- Simulation State ---
    registers = {f"R{i}": 0 for i in range(1, 9)} # R1 to R8 initialized to 0
    memory = []
    pc = 0 # Program Counter (index into the 'instructions' list)
    comparison_flag = False # Result of the last EQ or GT comparison

    # --- Execution Loop ---
    max_steps = 1000000 # Safety break to prevent infinite loops
    steps = 0

    while 0 <= pc < len(instructions) and steps < max_steps:
        current_line_num = pc_line_map.get(pc, "Unknown")
        instruction = instructions[pc]
        parts = instruction.split()
        opcode = parts[0].upper()
        operands = parts[1:]
        
        # Default behavior: advance PC by 1 unless it's a jump
        next_pc = pc + 1

        try:
            if opcode == "SET": # SET Rx value
                if len(operands) != 2: raise ValueError("SET requires 2 operands")
                reg = operands[0].upper()
                if reg not in registers: raise ValueError(f"Invalid register '{reg}'")
                try:
                    value = int(operands[1])
                except ValueError:
                    raise ValueError(f"Invalid immediate value '{operands[1]}'")
                registers[reg] = value

            elif opcode == "INC": # INC Rx
                if len(operands) != 1: raise ValueError("INC requires 1 operand")
                reg = operands[0].upper()
                if reg not in registers: raise ValueError(f"Invalid register '{reg}'")
                registers[reg] += 1

            elif opcode == "EQ": # EQ Rx Ry
                if len(operands) != 2: raise ValueError("EQ requires 2 operands")
                reg1, reg2 = operands[0].upper(), operands[1].upper()
                if reg1 not in registers: raise ValueError(f"Invalid register '{reg1}'")
                if reg2 not in registers: raise ValueError(f"Invalid register '{reg2}'")
                comparison_flag = (registers[reg1] == registers[reg2])

            elif opcode == "GT": # GT Rx Ry
                if len(operands) != 2: raise ValueError("GT requires 2 operands")
                reg1, reg2 = operands[0].upper(), operands[1].upper()
                if reg1 not in registers: raise ValueError(f"Invalid register '{reg1}'")
                if reg2 not in registers: raise ValueError(f"Invalid register '{reg2}'")
                comparison_flag = (registers[reg1] > registers[reg2])

            elif opcode == "JF": # JF label
                if len(operands) != 1: raise ValueError("JF requires 1 operand")
                label = operands[0]
                if label not in labels: raise ValueError(f"Undefined label '{label}'")
                if not comparison_flag:
                    next_pc = labels[label]

            elif opcode == "JT": # JT label
                if len(operands) != 1: raise ValueError("JT requires 1 operand")
                label = operands[0]
                if label not in labels: raise ValueError(f"Undefined label '{label}'")
                if comparison_flag:
                    next_pc = labels[label]

            elif opcode == "JMP": # JMP label
                if len(operands) != 1: raise ValueError("JMP requires 1 operand")
                label = operands[0]
                if label not in labels: raise ValueError(f"Undefined label '{label}'")
                # Handle the specific 'is_prime' -> 'ready_prime' return mechanism
                # This isn't a general call stack, just how this specific program uses JMP
                next_pc = labels[label]

            elif opcode == "STORE": # STORE Rx Ry (Store value in Rx at address in Ry)
                if len(operands) != 2: raise ValueError("STORE requires 2 operands")
                reg_val, reg_addr = operands[0].upper(), operands[1].upper()
                if reg_val not in registers: raise ValueError(f"Invalid register '{reg_val}'")
                if reg_addr not in registers: raise ValueError(f"Invalid register '{reg_addr}'")

                value_to_store = registers[reg_val]
                address = registers[reg_addr]

                if address < 0:
                    raise ValueError(f"Attempted to store at negative memory address {address}")

                # Ensure memory is large enough, fill with 0 if needed (though list append might be better if R8 is always sequential)
                # Using append based on the program's logic where R8 increments sequentially
                if address == len(memory):
                     memory.append(value_to_store)
                elif address < len(memory):
                     # Overwrite existing memory if address is valid but not the end
                     # This might deviate if R8 wasn't just used sequentially
                     print(f"Warning: Overwriting memory at address {address}. Expected sequential writes.")
                     memory[address] = value_to_store
                else:
                     # Fill gaps if address skips indices - indicates non-sequential use of R8
                     print(f"Warning: Non-sequential memory write to address {address}. Filling gaps.")
                     memory.extend([0] * (address - len(memory)))
                     memory.append(value_to_store)


            elif opcode == "MUL": # MUL Rd Rx Ry
                if len(operands) != 3: raise ValueError("MUL requires 3 operands")
                reg_d, reg_x, reg_y = operands[0].upper(), operands[1].upper(), operands[2].upper()
                if reg_d not in registers: raise ValueError(f"Invalid register '{reg_d}'")
                if reg_x not in registers: raise ValueError(f"Invalid register '{reg_x}'")
                if reg_y not in registers: raise ValueError(f"Invalid register '{reg_y}'")
                registers[reg_d] = registers[reg_x] * registers[reg_y]

            elif opcode == "MOD": # MOD Rd Rx Ry
                if len(operands) != 3: raise ValueError("MOD requires 3 operands")
                reg_d, reg_x, reg_y = operands[0].upper(), operands[1].upper(), operands[2].upper()
                if reg_d not in registers: raise ValueError(f"Invalid register '{reg_d}'")
                if reg_x not in registers: raise ValueError(f"Invalid register '{reg_x}'")
                if reg_y not in registers: raise ValueError(f"Invalid register '{reg_y}'")
                divisor = registers[reg_y]
                if divisor == 0:
                    raise ZeroDivisionError(f"Division by zero in MOD operation at line {current_line_num}")
                registers[reg_d] = registers[reg_x] % divisor

            else:
                raise ValueError(f"Unknown opcode '{opcode}'")

        except Exception as e:
            print(f"Error executing instruction at original line {current_line_num}: '{instruction}'")
            print(f"Current State: PC={pc}, Registers={registers}, Flag={comparison_flag}")
            raise e # Re-raise the exception

        pc = next_pc
        steps += 1

    if steps >= max_steps:
        print(f"Warning: Maximum execution steps ({max_steps}) reached. Possible infinite loop.")
        print(f"Final State: PC={pc}, Registers={registers}, Flag={comparison_flag}")


    # The program stores primes sequentially using R8 as the index/count
    # Return the memory list which should contain the primes
    return memory

# --- Example Usage ---
program = """

SET R1 2          // Starting number to check for prime
SET R8 0          // Initialize prime storage index/count

start_find_primes:

    JMP is_prime // Control will return after executing is_prime with R1 as input and R2 containing the result

ready_prime:
    SET R7 1
    EQ R2 R7        // Check if R2 is 1 (prime)
    JF increment  // If not prime, skip storing and increment the number

    // Store prime number in memory and increment count
    STORE R1 R8   // Store prime number at address pointed by R8
    INC R8        // Increment prime count/next address

    // Check if 100 primes are found
    SET R7 100
    EQ R8 R7
    JT end        // If 100 primes found, end program (Jump if True - R8 == 100)

increment:
    INC R1         // Increment number to check for prime
    JMP start_find_primes // Check next number

// Subroutine to check if R1 is prime. Result in R2 (1=prime, 0=not prime)
is_prime:
    // Handle base cases: 2 is prime
    SET R7 2
    EQ R1 R7
    JT is_prime_set_true // If R1 is 2, it's prime

    SET R2 1       // Assume number is prime initially (for numbers > 2)
    SET R3 2       // Start divisor from 2

start_loop:        // Label to start the loop
    // Optimization: Check if divisor R3 * R3 > R1
    MUL R4 R3 R3   // R4 = R3 * R3
    GT R4 R1       // Set flag if R4 > R1
    JT is_prime_end // If R3*R3 > R1, then R1 must be prime (no smaller factors found)

    // Check for divisibility: R6 = R1 % R3
    MOD R6 R1 R3
    SET R7 0
    EQ R7 R6     // Check if R6 is 0 (i.e., R1 % R3 == 0)
    JT not_prime   // If divisible, number is not prime

    INC R3         // Increment divisor
    JMP start_loop // Repeat loop

is_prime_set_true:
    SET R2 1       // Set result to 1 (prime)
    JMP is_prime_end // Go to end of subroutine

not_prime:
    SET R2 0       // Set result to 0 (not prime)
    // Fall through to is_prime_end

is_prime_end:
    JMP ready_prime // Return control to the point after the 'call'

end:
    // Program halts when PC reaches here or beyond instructions
"""

# Add a small fix to the program: Initialize R8
# Also added a check for R1=2 in is_prime for correctness.
# Changed the final check: JT end (Jump if True that R8 == 100)

primes_found = evaluate(program)

print(f"Found {len(primes_found)} primes.")
print(primes_found)

# Verification (first few primes)
expected_primes_start = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
print(f"First 10 primes match expected: {primes_found[:10] == expected_primes_start}")
# Verification (count)
print(f"Found 100 primes: {len(primes_found) == 100}")





answer = evaluate("""
    SET R1 0
    SET R2 1
loop:
    MUL R3 R2 R2
    STORE R3 R1
    INC R1
    INC R2
    SET R3 20
    EQ R1 R3
    JF loop
""")[:10]
expected = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'

answer = evaluate("""

SET R1 2          // Starting number to check for prime

start_find_primes:

    JMP is_prime // Control will return after executing is_prime with R1 as input and R2 containing the result

ready_prime:
    SET R7 1
    EQ R2 R7        // Check if R2 is 1 (prime)
    JF increment  // If not prime, skip storing and increment the number

    // Store prime number in memory and increment count
    STORE R1 R8   // Store prime number at address pointed by R8
    INC R8        // Increment prime count

    // Check if 100 primes are found
    SET R7 100
    EQ R8 R7
    JF increment  // If not 100 primes found yet, continue finding

    JMP end        // If 100 primes found, end program

increment:
    INC R1         // Increment number to check for prime
    JMP start_find_primes // Check next number

is_prime:
    SET R2 1       // Assume number is prime initially
    SET R3 2       // Start divisor from 2

start_loop:        // Label to start the loop
    // Check if we have exceeded the square root of R1
    MUL R4 R3 R3   // R4 = R3 * R3
    GT R4 R1       // Set flag if R4 > R1
    JT is_prime_end        // If not exceeded, continue; else, end loop

    MOD R6 R1 R3   // R6 = R1 % R3
    SET R7 0
    EQ R7 R6     // Check if R6 is 0
    JT not_prime   // If yes, number is not prime

    INC R3         // Increment divisor
    JMP start_loop // Repeat loop

not_prime:
    SET R2 0       // Set result to 0 (not prime)

is_prime_end:
    JMP ready_prime

end:
""")[:10]
expected = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: Error executing instruction at original line 36: 'start_loop:' Current State: PC=18, Registers={'R1': 3, 'R2': 1, 'R3': 2, 'R4': 0, 'R5': 0, 'R6': 0, 'R7': 2, 'R8': 1}, Flag=False Traceback (most recent call last): File "/usr/src/app/main.py", line 258, in <module> primes_found = evaluate(program) ^^^^^^^^^^^^^^^^^ File "/usr/src/app/main.py", line 172, in evaluate raise e # Re-raise the exception ^^^^^^^ File "/usr/src/app/main.py", line 167, in evaluate raise ValueError(f"Unknown opcode '{opcode}'") ValueError: Unknown opcode 'START_LOOP:'

Substring Evaluation

Testing if the previous output contains the string All tests passed: False