Initial Query

Here is the description of a new assembly language: * 8 registers (R1, R2, R3, R4, R5, R6, R7, R8) that can hold integers. * 1 flag that can hold a boolean value (True or False). * 100 memory addresses (0-99) that can hold integers. * 1 instruction pointer that points to the current instruction being executed. Each instruction is of the form OP ARG1 ARG2 ... where ARGn can be either a register (e.g., R1) or a constant (e.g., 10). Labels are written with a lowercase word followed by colon. The assembly language supports the following instructions: * SET Rx C: Assigns the value C to register Rx. * ADD Rx Ry Rz: Adds the values of Ry and Rz and stores the result in Rx. * (similarly for SUB, MUL, DIV, MOD) * EQ Rx Ry: Sets the flag to True if Rx and Ry are equal, False otherwise. * (similarly for NEQ, LT (Rx < Ry), LTE, GT, GTE) * INC/DEC Rx: Increments/Decrements the value of Rx by one. * JMP L: Jumps to label L unconditionally. * JT/JF (jump if true / jump if false) L: Jumps to label L if the is set or not set. * LOAD Rx M: Loads the value at memory address M into register Rx. * STORE Rx M: Stores the value of register Rx into memory address M. * HCF: Stops the program (with pizzazz) Given this assembly language, write a program that puts the first 20 prime numbers in memory cells 0..19

LLM Generation

Query

Output

Here's an assembly program that finds the first 20 prime numbers and stores them in memory locations 0-19:

; R1: current number to test
; R2: counter for found primes
; R3: divisor for primality test
; R4: result of division
; R5: remainder
; R6: temporary comparison
; R7: limit of 20 primes
; R8: temporary calculation

; Initialize
SET R1 2        ; Start testing from 2
SET R2 0        ; Initialize prime counter
SET R7 20       ; We want 20 primes

mainloop:
    ; Test if R1 is prime
    SET R3 2        ; Start dividing by 2
    SET R8 1        ; Assume it's prime until proven otherwise

testprime:
    ; If divisor >= number, it's prime
    GTE R3 R1
    JT isprime
    
    ; Divide and check remainder
    DIV R4 R1 R3    ; R4 = R1 / R3
    MUL R6 R4 R3    ; R6 = R4 * R3
    SUB R5 R1 R6    ; R5 = R1 - R6 (remainder)
    
    ; If remainder is 0, not prime
    EQ R5 0
    JT notprime
    
    ; Try next divisor
    INC R3
    JMP testprime

notprime:
    SET R8 0        ; Mark as not prime

isprime:
    ; If R8 is 0, number wasn't prime
    EQ R8 0
    JT nextnumber
    
    ; Store prime in memory at position R2
    STORE R1 R2
    INC R2
    
    ; Check if we have found 20 primes
    EQ R2 R7
    JT done

nextnumber:
    INC R1
    JMP mainloop

done:
    HCF

This program: 1. Starts testing numbers from 2 2. For each number: - Tries dividing by all numbers from 2 up to itself-1 - If any division has remainder 0, the number isn't prime - If no divisors are found, the number is prime 3. When a prime is found, stores it in memory at the current counter position 4. Continues until 20 primes are found The resulting memory locations 0-19 will contain: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71 The program could be optimized in several ways (like only testing odd numbers after 2, or only testing divisors up to the square root), but this version is more straightforward to understand.

Extract Code

I extracted the following code from that output:

; R1: current number to test
; R2: counter for found primes
; R3: divisor for primality test
; R4: result of division
; R5: remainder
; R6: temporary comparison
; R7: limit of 20 primes
; R8: temporary calculation

; Initialize
SET R1 2        ; Start testing from 2
SET R2 0        ; Initialize prime counter
SET R7 20       ; We want 20 primes

mainloop:
    ; Test if R1 is prime
    SET R3 2        ; Start dividing by 2
    SET R8 1        ; Assume it's prime until proven otherwise

testprime:
    ; If divisor >= number, it's prime
    GTE R3 R1
    JT isprime
    
    ; Divide and check remainder
    DIV R4 R1 R3    ; R4 = R1 / R3
    MUL R6 R4 R3    ; R6 = R4 * R3
    SUB R5 R1 R6    ; R5 = R1 - R6 (remainder)
    
    ; If remainder is 0, not prime
    EQ R5 0
    JT notprime
    
    ; Try next divisor
    INC R3
    JMP testprime

notprime:
    SET R8 0        ; Mark as not prime

isprime:
    ; If R8 is 0, number wasn't prime
    EQ R8 0
    JT nextnumber
    
    ; Store prime in memory at position R2
    STORE R1 R2
    INC R2
    
    ; Check if we have found 20 primes
    EQ R2 R7
    JT done

nextnumber:
    INC R1
    JMP mainloop

done:
    HCF

PyFunc

Resulting in output: False

Initial Query

LLM Generation

Query

Output

Here's a program that finds the first 20 prime numbers and stores them in memory:

# R1: current number we're testing for primeness
# R2: counter for how many primes we've found
# R3: potential divisor when testing primeness
# R4: temporary result for division/mod
# R5: loop limit for prime testing
# R6: used for comparison
# R7: mod result

# Initialize
SET R1 2    # Start with 2 (first prime)
SET R2 0    # Counter for found primes

mainloop:
    # Test if R1 is prime
    SET R3 2        # Start testing divisors from 2
    SET R5 R1       # Set loop limit
    SET R6 1        # For comparison
    
    # If R1 is 2, skip division testing
    EQ R1 2
    JT isprime

primetest:
    # If divisor >= number, it's prime
    GTE R3 R1
    JT isprime
    
    # Test if R3 divides R1 evenly
    MOD R7 R1 R3
    EQ R7 0
    JT notprime
    
    # Try next divisor
    INC R3
    JMP primetest

isprime:
    # Store the prime number
    STORE R1 R2
    INC R2
    
    # Check if we've found 20 primes
    EQ R2 20
    JT done
    
notprime:
    # Try next number
    INC R1
    JMP mainloop

done:
    HCF

This program: 1. Uses R1 to keep track of the current number being tested for primeness 2. Uses R2 as an index/counter for how many primes we've found 3. For each number: - Tests if it's prime by trying to divide it by all numbers from 2 to itself-1 - If no number divides it evenly, it's prime 4. When a prime is found: - Stores it in memory at the index kept in R2 - Increments the counter 5. Continues until 20 primes are found The program will store these primes in memory locations 0-19: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71 Some optimizations could be made (like only testing odd numbers after 2, or only testing divisors up to the square root), but this version is more straightforward to understand.

Extract Code

I extracted the following code from that output:

# R1: current number we're testing for primeness
# R2: counter for how many primes we've found
# R3: potential divisor when testing primeness
# R4: temporary result for division/mod
# R5: loop limit for prime testing
# R6: used for comparison
# R7: mod result

# Initialize
SET R1 2    # Start with 2 (first prime)
SET R2 0    # Counter for found primes

mainloop:
    # Test if R1 is prime
    SET R3 2        # Start testing divisors from 2
    SET R5 R1       # Set loop limit
    SET R6 1        # For comparison
    
    # If R1 is 2, skip division testing
    EQ R1 2
    JT isprime

primetest:
    # If divisor >= number, it's prime
    GTE R3 R1
    JT isprime
    
    # Test if R3 divides R1 evenly
    MOD R7 R1 R3
    EQ R7 0
    JT notprime
    
    # Try next divisor
    INC R3
    JMP primetest

isprime:
    # Store the prime number
    STORE R1 R2
    INC R2
    
    # Check if we've found 20 primes
    EQ R2 20
    JT done
    
notprime:
    # Try next number
    INC R1
    JMP mainloop

done:
    HCF

PyFunc

Resulting in output: False

Initial Query

LLM Generation

Query

Output

Here's a program that finds the first 20 prime numbers and stores them in memory:

# R1: current number to test for primeness
# R2: counter for found primes
# R3: divisor for primality test
# R4: temporary result for division
# R5: remainder from division
# R6: limit for primality testing
# R7: temporary comparison
# R8: constant 1 for comparisons

SET R1 2       # Start with first prime
SET R2 0       # Initialize prime counter
SET R8 1       # Set constant 1

mainloop:
    # Test if R1 is prime
    SET R3 2           # Start dividing by 2
    SET R6 R1         # Set limit to sqrt(R1) [simplified]
    DIV R6 R6 2       # R6 = R1/2

    # Inner loop to test divisibility
testprime:
    MOD R5 R1 R3      # R5 = R1 % R3
    EQ R5 R0          # Check if remainder is 0
    JT notprime       # If divisible, not prime
    
    INC R3            # Try next divisor
    GT R3 R6          # Check if we've tested enough
    JF testprime      # If not, continue testing

    # If we get here, number is prime
    STORE R1 R2       # Store prime in memory at position R2
    INC R2            # Increment prime counter
    
    # Check if we have found 20 primes
    SET R7 20
    EQ R2 R7
    JT done

notprime:
    INC R1            # Try next number
    JMP mainloop

done:
    HCF

This program works by: 1. Starting with 2 (the first prime) 2. For each number: - Tests if it's prime by checking divisibility by all numbers up to its half - If prime, stores it in memory and increments counter - If not prime, moves to next number 3. Continues until 20 primes are found The first 20 prime numbers (which will be stored in memory locations 0-19) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71 Note: This implementation uses a simplified primality test. A more efficient version could: - Only test odd numbers after 2 - Only test up to square root of the number - Only test against previously found primes But this version is more straightforward to understand and implement in this assembly language.

Extract Code

I extracted the following code from that output:

# R1: current number to test for primeness
# R2: counter for found primes
# R3: divisor for primality test
# R4: temporary result for division
# R5: remainder from division
# R6: limit for primality testing
# R7: temporary comparison
# R8: constant 1 for comparisons

SET R1 2       # Start with first prime
SET R2 0       # Initialize prime counter
SET R8 1       # Set constant 1

mainloop:
    # Test if R1 is prime
    SET R3 2           # Start dividing by 2
    SET R6 R1         # Set limit to sqrt(R1) [simplified]
    DIV R6 R6 2       # R6 = R1/2

    # Inner loop to test divisibility
testprime:
    MOD R5 R1 R3      # R5 = R1 % R3
    EQ R5 R0          # Check if remainder is 0
    JT notprime       # If divisible, not prime
    
    INC R3            # Try next divisor
    GT R3 R6          # Check if we've tested enough
    JF testprime      # If not, continue testing

    # If we get here, number is prime
    STORE R1 R2       # Store prime in memory at position R2
    INC R2            # Increment prime counter
    
    # Check if we have found 20 primes
    SET R7 20
    EQ R2 R7
    JT done

notprime:
    INC R1            # Try next number
    JMP mainloop

done:
    HCF

PyFunc

'R0' Resulting in output: False

Initial Query

LLM Generation

Query

Output

Here's a program that finds and stores the first 20 prime numbers in memory:

SET R1 2      ; Current number to test for primeness
SET R2 0      ; Counter for found primes
SET R3 20     ; Target number of primes

start:
    SET R4 2      ; Divisor to test with
    SET R8 1      ; Flag for prime (1=prime, 0=not prime)

test_prime:
    ; If divisor >= number, it's prime
    GTE R4 R1
    JT is_prime
    
    ; Test if R1 is divisible by R4
    MOD R5 R1 R4
    EQ R5 0
    JT not_prime
    
    INC R4
    JMP test_prime

not_prime:
    SET R8 0
    JMP check_result

is_prime:
    SET R8 1

check_result:
    EQ R8 1
    JF next_number
    
    ; Store prime number in memory at position R2
    STORE R1 R2
    INC R2
    
    ; Check if we found enough primes
    EQ R2 R3
    JT done

next_number:
    INC R1
    JMP start

done:
    HCF

This program works as follows: 1. R1 holds the current number being tested 2. R2 counts how many primes we've found 3. R3 holds our target (20) 4. R4 is used as the divisor when testing primality 5. R5 is used for temporary calculations 6. R8 is used as a flag to indicate if the current number is prime For each number (starting at 2): 1. We try dividing it by all numbers from 2 up to itself-1 2. If any division has remainder 0, the number isn't prime 3. If we reach the number itself without finding any divisors, it's prime 4. When we find a prime, we store it in memory at the position indicated by our counter 5. We continue until we've found 20 primes The program will store these values in memory locations 0-19: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71 This is a basic implementation that works but isn't optimized. We could make it more efficient by: - Only testing odd numbers after 2 - Only testing divisors up to the square root - Only testing division by known primes But this version is more straightforward to understand.

Extract Code

I extracted the following code from that output:

SET R1 2      ; Current number to test for primeness
SET R2 0      ; Counter for found primes
SET R3 20     ; Target number of primes

start:
    SET R4 2      ; Divisor to test with
    SET R8 1      ; Flag for prime (1=prime, 0=not prime)

test_prime:
    ; If divisor >= number, it's prime
    GTE R4 R1
    JT is_prime
    
    ; Test if R1 is divisible by R4
    MOD R5 R1 R4
    EQ R5 0
    JT not_prime
    
    INC R4
    JMP test_prime

not_prime:
    SET R8 0
    JMP check_result

is_prime:
    SET R8 1

check_result:
    EQ R8 1
    JF next_number
    
    ; Store prime number in memory at position R2
    STORE R1 R2
    INC R2
    
    ; Check if we found enough primes
    EQ R2 R3
    JT done

next_number:
    INC R1
    JMP start

done:
    HCF

PyFunc

Resulting in output: False

Initial Query

LLM Generation

Query

Output

Here's an assembly program that computes and stores the first 20 prime numbers:

; R1: current number to test
; R2: counter for found primes
; R3: divisor for primality test
; R4: remainder from division
; R5: temp register for comparisons
; R6: limit of found primes (20)
; R7: temp for division calculation

SET R1 2      ; Start with first prime
SET R2 0      ; Initialize prime counter
SET R6 20     ; We want 20 primes

mainloop:
    SET R3 2          ; Start divisor at 2
    
    ; Store R1 in memory at position R2 if prime
    ; First assume it's prime
    SET R5 1          ; R5 = 1 means prime

testprime:
    ; If divisor >= number, number is prime
    GTE R3 R1
    JT isprime
    
    ; Test if R1 is divisible by R3
    MOD R4 R1 R3     ; R4 = R1 % R3
    SET R5 0         ; Assume not prime
    EQ R4 0          ; Check if remainder is 0
    JT notprime      ; If divisible, not prime
    
    INC R3           ; Try next divisor
    JMP testprime

isprime:
    ; Store prime number in memory
    STORE R1 R2      ; Store at position R2
    INC R2           ; Increment prime counter
    
    ; Check if we have found all primes
    EQ R2 R6
    JT done

notprime:
    INC R1           ; Try next number
    JMP mainloop

done:
    HCF

This program works as follows: 1. We start testing numbers from 2 (stored in R1) 2. For each number, we test if it's prime by: - Trying to divide it by all numbers from 2 up to itself - If any number divides evenly (remainder 0), it's not prime - If no number divides evenly, it's prime 3. When we find a prime, we store it in memory at the position tracked by R2 4. We continue until we've found 20 primes The program will store the following values in memory positions 0-19: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71 Each memory position corresponds to the index of the prime in the sequence (e.g., memory[0] = 2, memory[1] = 3, etc.). The program uses a straightforward primality test. While not the most efficient algorithm possible, it's relatively simple to implement in assembly and gets the job done for small numbers.

Extract Code

I extracted the following code from that output:

; R1: current number to test
; R2: counter for found primes
; R3: divisor for primality test
; R4: remainder from division
; R5: temp register for comparisons
; R6: limit of found primes (20)
; R7: temp for division calculation

SET R1 2      ; Start with first prime
SET R2 0      ; Initialize prime counter
SET R6 20     ; We want 20 primes

mainloop:
    SET R3 2          ; Start divisor at 2
    
    ; Store R1 in memory at position R2 if prime
    ; First assume it's prime
    SET R5 1          ; R5 = 1 means prime

testprime:
    ; If divisor >= number, number is prime
    GTE R3 R1
    JT isprime
    
    ; Test if R1 is divisible by R3
    MOD R4 R1 R3     ; R4 = R1 % R3
    SET R5 0         ; Assume not prime
    EQ R4 0          ; Check if remainder is 0
    JT notprime      ; If divisible, not prime
    
    INC R3           ; Try next divisor
    JMP testprime

isprime:
    ; Store prime number in memory
    STORE R1 R2      ; Store at position R2
    INC R2           ; Increment prime counter
    
    ; Check if we have found all primes
    EQ R2 R6
    JT done

notprime:
    INC R1           ; Try next number
    JMP mainloop

done:
    HCF

PyFunc

Resulting in output: False