9.4: Bubble Sort

Sorting is the process of arranging data in an ascending or descending order. This example will introduce an algorithm, the Bubble Sort, for sorting integer data in a array. Consider for example the following array containing integer values.

The sort is carried out in two loops. The inner loop passes once through the data comparing elements in the array and swapping them if they are not in the correct order. For example, element 0 (55) is compared to element 1 (27), and they are swapped since 55 > 27

Next element 1 (now 55) is compared with element 2 (13), and they are swapped since 55 > 13.

This process continues until a complete pass has been made through the array. At the end of the inner loop the largest value of the array is at the end of the array, and in its correct position. The array would look as follows.

This process continues until a complete pass has been made through the array. At the end of the inner loop the largest value of the array is at the end of the array, and in its correct position. The array would look as follows.

Repeating this outer loop for all elements results in the array being sorted in ascending order.

Pseudo code for this algorithm follws.

for (int i = 0; i < size-1; i++)
{
    for (int j = 0; j < ((size-1)-i); j++)
    {
        if (data[j] > data[j+1])
        {
            swap(data, j, j+1)
        }
    }    
}

swap(data, i, j)
    int tmp = data[i];
    data[i] = data[j];
    data[j] = tmp;    
}
   

9.3.1 Bubble Sort in MIPS assembly

The following assembly program implements the Bubble Sort matching the pseudo code algorithm in the previous section.

Program 9-4: Bubble Sort

.text
.globl main
main:
    la $a0, array_base
    lw $a1, array_size
    jal PrintIntArray
    
    la $a0, array_base
    lw $a1, array_size
    jal BubbleSort
    
    jal PrintNewLine
    la $a0, array_base
    lw $a1, array_size
    jal PrintIntArray
    
    jal Exit
.data
    array_size: .word 8
    array_base:
        .word 55
        .word 27
        .word 13
        .word 5
        .word 44
        .word 32
        .word 17
        .word 36
.text
# Subproram:    Bubble Sort
# Purpose:      Sort data using a Bubble Sort algorithm
# Input Params: $a0 - array
#               $a1 - array size
# Register conventions:
#               $s0 - array base
#               $s1 - array size
#               $s2 - outer loop counter
#               $s3 - inner loop counter
BubbleSort:
    addi $sp, $sp -20         # save stack information
    sw $ra, 0($sp)
    sw $s0, 4($sp)            # need to keep and restore save registers
    sw $s1, 8($sp)
    sw $s2, 12($sp)
    sw $s3, 16($sp)
    
    move $s0, $a0
    move $s1, $a1
    
    addi $s2, $zero, 0        #outer loop counter
    OuterLoop:
        addi $t1, $s1, -1
        beqz $t0, EndOuterLoop
        
        addi $s3, $zero, 0    #inner loop counter
        InnerLoop:
            addi $t1, $s1, -1
            sub $t1, $t1, $s2
            slt $t0, $s3, $t1
            beqz $t0, EndInnerLoop
            
            sll $t4, $s3, 2   # load data[j]. Note offset is 4 bytes 
            add $t5, $s0, $t4
            lw $t2, 0($t5)
            
            addi $t6, $t5, 4  # load data[j+1]
            lw $t3, 0($t6)
            
            sgt $t0, $t2, $t3
            beqz $t0, NotGreater
                move $a0, $s0
                move $a1, $s3
                addi $t0, $s3, 1
                move $a2, $t0
                jal Swap    # t5 is &data[j], t6 is &data[j=1]
            NotGreater:
            addi $s3, $s3, 1
            b InnerLoop
        EndInnerLoop:
        addi $s2, $s2, 1
        b OuterLoop
    EndOuterLoop:
    
    lw $ra, 0($sp)          #restore stack information
    lw $s0, 4($sp)
    lw $s1, 8($sp)
    lw $s2, 12($sp
    lw $s3, 16($sp)
    addi $sp, $sp 20
    jr $ra

# Subprogram:        swap
# Purpose:           to swap values in an array of integers
#  Input parameters: $a0 - the array containing elements to swap
#                    $a1 - index of element 1
#                    $a2 - index of elelemnt 2
#  Side Effects:           Array is changed to swap element 1 and 2
Swap:
    sll $t0, $a1, 2    # calcualate address of element 1
    add $t0, $a0, $t0
    sll $t1, $a2, 2    # calculate address of element 2
    add $t1, $a0, $t1
    
    lw $t2, 0($t0)     #swap elements
    lw $t3, 0($t1)
    sw $t2, 0($t1)
    sw $t3, 0($t0)
    
    jr $ra

# Subprogram:  PrintIntArray
# Purpose:     print an array of ints
# inputs:      $a0 - the base address of the array 
#              $a1 - the size of the array
#
PrintIntArray:
    addi $sp, $sp, -16    # Stack record
    sw $ra, 0($sp)
    sw $s0, 4($sp)
    sw $s1, 8($sp)    
    sw $s2, 12($sp)

    move $s0, $a0         # save the base of the array to $s0
    
    # initialization for counter loop
    # $s1 is the ending index of the loop
    # $s2 is the loop counter
    move $s1, $a1
    move $s2, $zero
    
    la $a0 open_bracket   # print open bracket
    jal PrintString

loop:
    # check ending condition
    sge $t0, $s2, $s1
    bnez $t0, end_loop
        
        sll $t0, $s2, 2   # Multiply the loop counter by 4 to get offset (each element is 4 big).
        add $t0, $t0, $s0 # address of next array element
        lw $a1, 0($t0)    # Next array element
        la $a0, comma
        jal PrintInt      # print the integer from array

        addi $s2, $s2, 1  #increment $s0
        b loop
end_loop:

    li $v0, 4             # print close bracket
    la $a0, close_bracket
    syscall

    lw $ra, 0($sp)
    lw $s0, 4($sp)
    lw $s1, 8($sp)
    lw $s2, 12($sp)       # restore stack and return
    addi $sp, $sp, 16
    jr $ra

.data
    open_bracket:    .asciiz "[" 
    close_bracket:   .asciiz "]" 
    comma:           .asciiz ","
.include "utils.asm"