In this post we will look at how to convert java code into DLX code. We will create two functions Perrin and gensum .
The function P(n) computes the nth Perrin number. Perrin numbers are defined by the recursive rules:
P(0) = 3
P(1) = 0
P(2) = 2
P(n) = P(n-2) + P(n-3) for n > 2
So for example: -
The gensum function will return the sum of Perrin numbers from P(a) to P(b) using an increment of step.
The range of the parameters are as follows:
- 0 <= a <= b
- step >=1
For example:
- gensum(0, 5, 1) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) = 3 + 0 + 2 + 3 + 2 + 5 = 15
- gensum(2, 11, 2) = P(2) + P(4) + P(6) + P(8) + P(10) = 2 + 2 + 5 + 10 + 17 = 36
- gensum(5, 2, 1) = -1
- gensum(2, 10, -1) = -1
1: public class Perrin {
2: private static int P(int n) {
3: int a = 3, b = 0, c = 2; // the first three P(n)
4: if (n==0)
5: {
6: return a;
7: }
8: else if (n==1){
9: return b;
10: }
11: else if (n==2){
12: return c;
13: }
14: else{
15: int m = 0; //r2
16: while (n > 2) {
17: // System.out.println(n+" a"+a+" b"+b+" c"+c);
18: m = a + b; //r2=r3+r4
19: a = b;//r3=r4
20: b = c;//r4=r5
21: c = m;//r5=r2
22: n=n-1;//r1=r1-1
23: // System.out.println(n+" a"+a+" b"+b+" c"+c);
24: }
25: return m;
26: }
27: }
28: private static int gensum(int a,int b,int step)
29: {
30: int sum=0;
31: int p=0;
32: for(int i=a;i<=b;i=i+step)
33: {
34: p=P(i);
35: sum=sum+p;
36: System.out.print(" i"+i+" p"+p+" "+sum+" ");
37: }
38: return sum;
39: }
40: public static void main(String[] args) {
41: for (int i = 0; i < 21; i++)
42: System.out.println("p(" + i + ")=" + P(i));
43: System.out.println(gensum(0, 7, 1) );
44: }
45: }
DLX code Main DLX code
1: lights .equ 16#FFFFFFF8
2: switches .equ 16#FFFFFFFC
3: .start main
4: main:
5: add r1,r0,r0 ;a=0
6: addi r3,r0,1 ;c=1
7: lw r2,switches ;b=switches input
8: jal gensum ;gensum(a,b,c)
9: sw lights,r1 ;lights=result
10: halt
1: P: ;P(x)
2: sw r2backup,r2 ;result
4: sw r3backup,r3 ;a
5: sw r4backup,r4 ;b
6: sw r5backup,r5 ;c
7: sw r6backup,r6 ;If Result
8: ;Backup Registers End
9: sequi r6,r1,0 ;x==0?
10: bt r6,case0 ;if x=0 case0
11: sequi r6,r1,1 ;x==1?
12: bt r6,case1 ;if x=1 case1
13: sequi r6,r1,2 ;x==2?
14: bt r6,case2 ;if x=2 case2
15: addi r2,r0,0 ;if x>2 result=0
16: addi r3,r0,3 ;a=3
17: addi r4,r0,0 ;b=0
18: addi r5,r0,2 ;c=2
19: while sgti r6,r1,2 ;while(x>2)
20: bf r6,case3 ;if while not true case3
21: add r2,r3,r4 ;y = a + b
22: add r3,r4,r0 ;a = b
23: add r4,r5,r0 ;b = c
24: add r5,r2,r0 ;c = y
25: subi r1,r1,1 ;x=x-1
26: j while ;continue while loop
27: case3
28: addi r1,r2,0 ;result=y
29: j endp
30: case0
31: addi r1,r0,3 ;r1=result=3
32: j endp
33: case1
34: addi r1,r0,0 ;r1=result=0
35: j endp
36: case2
37: addi r1,r0,2 ;r1=result=2
38: j endp
39: endp ;end of P Subroutine
40: ;Restore Registers Start
41: lw r2,r2backup
42: lw r3,r3backup
43: lw r4,r4backup
44: lw r5,r5backup
45: lw r6,r6backup
46: ;Restore Registers End
47: jr r31 ; end P
48: r2backup .word 1000
49: r3backup .word 1004
50: r4backup .word 1008
51: r5backup .word 1012
52: r6backup .word 1016
1: gensum: ;gensum(a,b,c)
2: ;Backup Registers Start
3: sw r2backupG,r2 ;b
4: sw r3backupG,r3 ;c
5: sw r4backupG,r4 ;result of IF
6: sw r5backupG,r5 ;sum
7: sw r6backupG,r6 ;result of P Subroutine
8: sw r7backupG,r7 ;i
9: sw r8backupG,r8 ;backup r31 register
10: ;Backup Registers End
11: slt r4,r1,r0 ;a<0?
12: bt r4,errorcase ;if true,errorcase
13: slt r4,r2,r0 ;b<0?
14: bt r4,errorcase ;if true,errorcase
15: slti r4,r3,1 ;step<1?
16: bt r4,errorcase ;if true,errorcase
17: sle r4,r2,r1 ;a<b?
18: bt r4,errorcase ;if true,errorcase
19: addi r5,r0,0 ;sum=0
20: addi r6,r0,0 ;result of P=0
21: add r7,r0,r1 ;i=a
22: for slt r4,r2,r7 ;i<b for (i=a;i<b;i=i+step)
23: bt r4,endfor ;end for loop
24: add r1,r0,r7 ;a=i
25: add r8,r31,r0 ;backup r31 register
26: jal P ;P(i)
27: add r31,r8,r0 ;restore r31 register
28: add r5,r5,r1 ;sum=sum+P(i)
29: add r7,r7,r3 ;i=i+step
30: j for
31: endfor
32: add r1,r5,r0 ;a=sum
33: sw result,r1 ;result=sum
34: j endgensum
35: errorcase
36: addi r1,r0,-1 ;a=-1
37: j endgensum
38: endgensum
39: ;Restore Registers Start
40: lw r2,r2backupG
41: lw r3,r3backupG
42: lw r4,r4backupG
43: lw r5,r5backupG
44: lw r6,r6backupG
45: lw r7,r7backupG
46: lw r8,r8backupG
47: ;Restore Registers End
48: jr r31 ;end gensum()
49: r2backupG .word 2000
50: r3backupG .word 2004
51: r4backupG .word 2008
52: r5backupG .word 2012
53: r6backupG .word 2016
54: r7backupG .word 2020
55: r8backupG .word 2024
56: result .word 2028
