Question

Write and test a MIPS assembly language program to compute and display the first prime numbers up to n where n is given. Set n to be 19 but the program should work of any value of n.

For the program to identify primes, the easiest way is to use the algorithm:

for (i = 2; i < x; i++)  
    if ((x % i) == 0) break;   //break out, not prime

where x is the number you are checking to see if prime. The "remu" instruction can do x % i. The suggested algorithm is not an efficient algorithm but easier to code than a more efficient algorithm. (Note for example, the above code does not actually have to iterate from 2 to x to find whether x is prime; stopping at squareroot(x) is sufficient.)

Answer 1

.text
.align 2
.globl main

main:

# compute and display the first prime numbers up to value of  n where n is 19.So #set n to be 19 but the program should work of any value of n. 


li  $v0, 4
la  $a0, prompt
syscall     

li  $v0, 5    # read from keyboard into $v0 (number n is the limit)
syscall       # call operating sys
move    $t0,$v0   # store n i.e 19 in $t0

li  $v0, 4    # display the message to user
la  $a0, message
syscall

      # call operating sys

li  $v0, 4
la  $a0, space
syscall     

# Load variables into registers
lw  $t1, i  # $t1 = i
lw  $t2, k  # $t2 = k
lw  $t3, p  # $t3 = p
lw  $t5, c  # $t5 = c
lw  $t6, d  # $t6 = d



blt $t0,$t1 L2

li  $v0, 1          # print integer function call 1
move    $a0, $t1        # integer to print
syscall
        # call operating sys

li $v0, 4       # print new line
la $a0, space
syscall                 # call operating sys



    #Outer loop 


L2: move $t3, $zero

    # Inner loop


L1: remu $t4, $t1, $t2
bne $t4, $zero, I

move $t3, $t5


I:  add $t2, $t2, $t5   # increment k

blt $t2, $t1 L1

bne $t3, $zero, P

li  $v0, 1          # print integer function call 1
move    $a0, $t1        # integer to print
syscall


li  $v0, 4      # print new line
la  $a0, space
syscall         # call operating sys


P:  add $t1, $t1, $t5   # increment i

move $t2, $t6

bgt  $t1, $t0, E    
j L2


E:  li  $v0,    10  # system call code for exit = 10
    syscall     # call operating sys


end:    jr  $ra

.data

prompt:
.asciiz "Please enter the number you wish to find the prime numbers of :  "

message:
.asciiz "The Prime Numbers are : "



space:  .asciiz  "\n    "

#initialization of registers

i:
.word   2

p:
.word   0

k:
.word   2   

c:
.word   1


d:
.word   2