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The Insertion sort is another sorting algorithm where each iteration of the "main" loop extends the size of the sorted part by one element. The idea is to extend the sorted part by inserting the first unsorted element into the correct spot in the sorted part. In the below example, 35 should be inserted between 30 and 40 in the sorted part. To do this, you must find the correct spot to insert 35 and shift larger elements (40 and 50) to the right one location to make room for 35. The following algorithm calls a subprogram Insert which combines finding the insertion spot and shifting larger elements as follows:

i) Copy the first unsorted element into a temporary variable named "elementToInsert"

ii) Scan the sorted part of the array from right-to-left. As you scan, shift larger sorted elements to the right one location to make room for the elementToInsert. Stop scanning when you reach the front of the array or you encounter a sorted element that is less-than-or-equal-to the elementToInsert.

iii) Insert the elementToInsert into the array

The following example show these steps:

Reg. #	APCS Name	APCS Role
R0	a1	Argument 1/integer result/scratch reg	Caller-saved registers - subprogram can use them as scratch registers, but it must also save any needed values before calling another subprogram.
R1	a2	Argument 2/scratch register
R2	a3	Argument 3/scratch register
R3	a4	Argument 4/scratch register
R4	v1	Register variable 1	Callee-saved registers - subprogram must save them if it wishes to use these registers, but it can rely on an subprogram it calls not to change them.
R5	v2	Register variable 2
R6	v3	Register variable 3
R7	v4	Register variable 4
R8	v5	Register variable 5
R9	v6/sb	Register variable 6	Used for reentrant code
R10	v7/sl	Register variable 7	Stack limit register used to check for stack overflow
R11	fp	Frame pointer
R12	ip	Scratch register / new static base in inter-link-unit calls
R13	sp	stack pointer	Points to "top" of current call-frame
R14	lr	link register/scratch register	Receives return addr. on BL
R15	pc	program counter	Points to next instruction to execute

Implement the following two Insertion sort subprograms (i.e., InsertionSort and Insert) using the ARM APCS calling convensions. Include all assembly language directives (EXTERN, AREA, EXPORT, END, etc.) to make each a complete subprogram. For each subprogram, include comments indicating what argument or local variable each register is holding.

(Note: "length" argument to InsertionSort is a count of elements in the array "numbers")

InsertionSort(numbers - address to integer array, length - integer) 
    integer firstUnsortedIndex

    for firstUnsortedIndex = 1 to (length-1) do 
        Insert(numbers, numbers[firstUnsortedIndex], firstUnsortedIndex-1); 

    end for 
end InsertionSort


Insert(numbers - address to integer array, elementToInsert - integer,                 firstSortedIndex - integer) { 
    integer testIndex;

    testIndex = firstSortedIndex; 
    while (testIndex >=0) AND (numbers[testIndex] > elementToInsert ) do 
        numbers[ testIndex + 1 ] = numbers[ testIndex ]; 
    testIndex = testIndex - 1; 
    end while 
    numbers[ testIndex + 1 ] = elementToInsert;
end Insert

You are encouraged to work in small groups (2-4) on this pencil-and-paper exercise. Each group should turn in ONE copy of their answer to my mailbox in the CS office (Wright 219).

List all the names of students in your group: ____________________________________

___________________________________________________________________________

Start your code on this page and include additional sheets of paper as necessary. There is a stapler in the CS office (Wright 219).