Hope there's no bug...

README.md

@@ -0,0 +1,20 @@
+# lab-1
+Here are three different version...
+
+1. [recursion](lab-1/): Use `make` command to check the answer
+2. [iteration](lab-1i/): Use `make` command to check the answer
+3. [c-code](lab-1-c/): Translate arm code to c, and use `gprof` to analyze. You can use `make` to run the `gprof` script, the results will show in `analysis.txt`. After arranging the data, you can see the example in [result.txt](lab-1-c/result.txt). Finally, I use the [script](lab-1-c/gplot_cmd.txt) and the [result](lab-1-c/efficiency.png) shows as following...
+```sh
+gnuplot
+> plot "analysis-result.txt"
+> set style data lines                                           # connect each dots
+> set grid                                                       # set background as grid
+> set title "fib efficiency"                                     # add title
+> replot
+> plot "analysis-result.txt" using 1:2 title 'Recursion', \
+       "analysis-result.txt" using 1:3 title 'Tail-Recursion', \    
+       "analysis-result.txt" using 1:4 title 'Iteration'         # plot three data at the same time
+> set logscale y; replot                                         # data in y-axis is large, use logscale
+> set output "efficiency.png" ; set term png ; replot
+```
+![picture alt](lab-1-c/efficiency.png)

lab-1-c/Makefile

@@ -0,0 +1,19 @@
+
+default: fib
+
+fib: fib.o
+	gcc -Wall -pg fib.c -o fib
+
+fib.o: fib.c
+
+qemu: fib
+	@num=1 ; while [ $$num -le 10 ] ; do \
+		echo "go to $$num" ; \
+		echo "\ngo to $$num \n" >> analysis.txt ; \
+		./fib $$num ; \
+		gprof fib gmon.out -p -b >> analysis.txt ; \
+		num=`expr $$num + 1` ; \
+	done
+
+clean: 
+	rm fib fib.o gmon.out analysis.txt

lab-1-c/fib.c

@@ -0,0 +1,22 @@
+#include <stdio.h>
+#define TIMES 1000000
+
+int recursive(int n){ return n<3 ? 1 : recursive(n-1)+recursive(n-2); }
+
+int tail_rec(int n,int a,int b){ return n==0 ? b : tail_rec(n-1,a+b,a); }
+
+int iterative(int n){
+	int i1=0, i2=1, res;
+	for(;n;--n){ res=i2; i2+=i1; i1=res; }
+	return res;
+}
+
+int main(int argc, char* argv[]){
+	int n=atoi(argv[1]),i;
+	for(i=0;i<TIMES;++i){
+		recursive(n);
+		tail_rec(n,1,0);
+		iterative(n);
+	}
+}
+

lab-1-c/fib_iterative.c

@@ -0,0 +1,8 @@
+#include <stdio.h>
+
+int main(void){
+	int i1=0, i2=1, n, res;
+	scanf("%d",&n);
+	for(;n;--n){ res=i2; i2+=i1; i1=res; }
+	printf("%d\n",res);
+}

lab-1-c/fib_recursive.c

@@ -0,0 +1,9 @@
+#include <stdio.h>
+
+int fib(int n){ return n<3 ? 1 : fib(n-1)+fib(n-2); }
+
+int main(void){
+	int n;
+	scanf("%d",&n);
+	printf("%d\n",fib(n));
+}

lab-1-c/fib_tail_recursive.c

@@ -0,0 +1,12 @@
+#include <stdio.h>
+#define times 10000000
+
+int fib(int n,int a,int b){ return n==0 ? b : fib(n-1,a+b,a); }
+
+int main(void){
+	int n,i;
+	scanf("%d",&n);
+	for(i=0;i<times;++i) fib(n,1,0);
+//	printf("%d\n",fib(n,1,0));
+}
+

lab-1-c/gplot_cmd.txt

@@ -0,0 +1,11 @@
+gnuplot
+> plot "analysis-result.txt"
+> set style data lines            # 設定成連線模式
+> set grid                        # 模擬方格紙效果
+> set title "fib efficiency"      # 加上標題。
+> replot                          # 重畫一遍
+> plot "analysis-result.txt" using 1:2 title 'Recursion', \
+       "analysis-result.txt" using 1:3 title 'Tail-Recursion', \    
+       "analysis-result.txt" using 1:4 title 'Iteration'     #  同時畫三圖 
+> set logscale y; replot          # y軸差異太大, 用 logscale
+> set output "efficiency.png" ; set term png ; replot

lab-1-c/result.txt

@@ -0,0 +1,46 @@
+1	1.52	     3.03     2.02
+2	3.03         1.01     6.06
+3	7.58        13.13     5.05
+4	9.09         9.09     5.05
+5	29.80       20.20     7.07
+6	50.52       16.16     6.06
+7	30.31       21.21    10.10
+8	95.98       22.22    28.28
+9	121.24      25.25    15.15
+10	298.04      29.29    44.44
+11	272.78      40.40    35.35
+12	722.37      30.30    26.26
+13	914.33      43.43    31.31
+14	1400        43.43    40.40
+15	2550        52.53    46.46
+16	3030        49.49    35.35
+17	10100       56.57    58.59
+18	9090        63.64    65.66
+19	15150       68.69    49.49
+20	23740       64.65    67.68
+21	48490       98.99    62.63
+22	60110       72.73    78.79
+23	111640      78.79    66.67
+24	183880      87.88    77.78
+25	293490      85.86    84.85
+26	606190      90.91    79.80
+27	1210000     97.98    81.82
+28	1520000     96.97    90.91
+29	2170000    124.24    84.85
+30	3740000    130.30    74.75
+31	5250000    121.21    78.79
+32	9500000    104.04    90.91
+33	13490000   146.46    94.95
+34	22530000   111.11   118.18
+35	46520000   119.19   109.09
+36	65670000   120.20    98.99
+37	70720000   151.52   101.01
+38	141440000  129.29   123.23
+39	227320000  153.54   117.17
+40	434430000  132.32   135.35
+41	676910000  161.62   122.22
+42	1120000000 137.37   143.43
+43	1720000000 200.00   130.30
+44	3120000000 155.56   115.15
+45	4600000000 157.58   128.28
+45	8660000000 159.60   145.45

lab-1/Makefile

@@ -1,34 +1 @@
-CC	= arm-linux-gnueabihf-gcc
-CFLAGS	= -O1 -Wall
-LDFLAGS = -fno-stack-protector
-
-objects	= fibseq.o fib.o
-
-default: fibseq
-
-.PHONY: default clean qemu
-
-fibseq: $(objects)
-	$(CC) $(LDFLAGS) -o $@ $^
-
-fib.o: fib.s
-fibseq.o: fibseq.c
-
-%.o: %.c
-	$(CC) -c $(CFLAGS) -o $@ $<
-
-%.o: %.s
-	$(CC) -c $(CFLAGS) -o $@ $<
-
-clean:
-	rm -f $(objects) fibseq
-
-QEMU_CMD = qemu-arm -L /usr/arm-linux-gnueabihf ./fibseq &
-CMD = yes 9 | $(call QEMU_CMD) && sleep 1
-qemu: fibseq
-	@yes 5 | $(call QEMU_CMD)
-	@sleep 1
-	@yes 6 | $(call QEMU_CMD)
-	@sleep 1
-	@yes 7 | $(call QEMU_CMD)
-	@sleep 1
+include ../make_fib.mk

lab-1/fib.s

@@ -11,33 +11,25 @@
 fibonacci:
 	@ ADD/MODIFY CODE BELOW
 	@ PROLOG
-	push {r3, r4, r5, lr}
+	push {r4, r5, lr}
 
-	@ R4 = R0 - 0 (update flags)
-	@ if(R0 <= 0) goto .L3 (which returns 0)
+	subs r4, r0, #0 	@ R4 = R0 - 0 (update flags)
+	beq .L4  			@ If R4 == 0 goto .L4 (which returns second)
 
-	@ Compare R4 wtih 1
-	@ If R4 == 1 goto .L4 (which returns 1)
+	sub r5, r1, #0 		@ R5 = first
 
-	@ R0 = R4 - 1
-	@ Recursive call to fibonacci with R4 - 1 as parameter
+	sub r0, r4, #1 		@ R0 = R4 - 1
+	add r1, r5, r2 		@ R1 = first+second
+	mov r2, r5     		@ R2 = first
+	bl fibonacci 		@ Recursive call to fibonacci 
 
-	@ R5 = R0
-	@ R0 = R4 - 2
-	@ Recursive call to fibonacci with R4 - 2 as parameter
-
-	@ R0 = R5 + R0 (update flags)
-
-	pop {r3, r4, r5, pc}		@EPILOG
+	pop {r4, r5, pc}		@EPILOG
 
 	@ END CODE MODIFICATION
-.L3:
-	mov r0, #0			@ R0 = 0
-	pop {r3, r4, r5, pc}		@ EPILOG
 
 .L4:
-	mov r0, #1			@ R0 = 1
-	pop {r3, r4, r5, pc}		@ EPILOG
+	sub r0, r2, #0				@ R0 = second
+	pop {r4, r5, pc}			@ EPILOG
 
 	.size fibonacci, .-fibonacci
 	.end

lab-1/fibseq.c

@@ -1,14 +1,21 @@
+/* * The fibonacci function call here,
+   * there are three arguments:  fibonacci(int x, int y, int z)
+   * 	x: request for the xth Fibonacci number
+   *    y: the last Fibonacci number we've known (fib 1 = 1)
+   *    z: the second last Fibonacci number (fib0 = 0)
+   */
+
 #include <stdio.h>
 
-extern int fibonacci(int x);
+extern int fibonacci(int x, int y, int z);
 
 int main(int argc, char **argv)
 {
   int number=0;
   int result=0;
 
   scanf("%d",&number);
-  result = fibonacci(number);   
+  result = fibonacci(number,1,0);   
   printf("The fibonacci sequence at %d is: %d\n", number, result);
 }
 

lab-1i/Makefile

@@ -1,34 +1 @@
-CC	= arm-linux-gnueabihf-gcc
-CFLAGS	= -O1 -Wall
-LDFLAGS = -fno-stack-protector
-
-objects	= fibseq.o fib.o
-
-default: fibseq
-
-.PHONY: default clean qemu
-
-fibseq: $(objects)
-	$(CC) $(LDFLAGS) -o $@ $^
-
-fib.o: fib.s
-fibseq.o: fibseq.c
-
-%.o: %.c
-	$(CC) -c $(CFLAGS) -o $@ $<
-
-%.o: %.s
-	$(CC) -c $(CFLAGS) -o $@ $<
-
-clean:
-	rm -f $(objects) fibseq
-
-QEMU_CMD = qemu-arm -L /usr/arm-linux-gnueabihf ./fibseq &
-CMD = yes 9 | $(call QEMU_CMD) && sleep 1
-qemu: fibseq
-	@yes 5 | $(call QEMU_CMD)
-	@sleep 1
-	@yes 6 | $(call QEMU_CMD)
-	@sleep 1
-	@yes 7 | $(call QEMU_CMD)
-	@sleep 1
+include ../make_fib.mk

lab-1i/fib.s

@@ -11,33 +11,22 @@
 fibonacci:
 	@ ADD/MODIFY CODE BELOW
 	@ PROLOG
-	push {r3, r4, r5, lr}
+	push {r4, r5, r6, lr}
 
-	@ R4 = R0 - 0 (update flags)
-	@ if(R0 <= 0) goto .L3 (which returns 0)
+	sub r4, r0, #0 	@ R4 = R0 - 0 (update flags)
 
-	@ Compare R4 wtih 1
-	@ If R4 == 1 goto .L4 (which returns 1)
+	mov r5, #0		@ init fib(0) = 0
+	mov r6, #1		@ init fib(1) = 1
+.Loop:
+	mov r0, r6		@ R0 = R6 and also the result
+	add r6, r5, r6	@ R6 += R5
+	mov r5, r0		@ R5 = R0   (exchange R5, R6)
+	subs r4, r4, #1 	@ R4 = R4 - 1
+	bne .Loop
 
-	@ R0 = R4 - 1
-	@ Recursive call to fibonacci with R4 - 1 as parameter
-
-	@ R5 = R0
-	@ R0 = R4 - 2
-	@ Recursive call to fibonacci with R4 - 2 as parameter
-
-	@ R0 = R5 + R0 (update flags)
-
-	pop {r3, r4, r5, pc}		@EPILOG
+	pop {r4, r5, r6, pc}		@EPILOG
 
 	@ END CODE MODIFICATION
-.L3:
-	mov r0, #0			@ R0 = 0
-	pop {r3, r4, r5, pc}		@ EPILOG
-
-.L4:
-	mov r0, #1			@ R0 = 1
-	pop {r3, r4, r5, pc}		@ EPILOG
 
 	.size fibonacci, .-fibonacci
 	.end

make_fib.mk

@@ -0,0 +1,48 @@
+CC	= arm-linux-gnueabihf-gcc
+CFLAGS	= -O1 -Wall
+LDFLAGS = -fno-stack-protector
+
+objects	= fibseq.o fib.o
+
+default: fibseq
+
+.PHONY: default clean qemu
+
+fibseq: $(objects)
+	$(CC) $(LDFLAGS) -o $@ $^
+
+fib.o: fib.s
+fibseq.o: fibseq.c
+
+%.o: %.c
+	$(CC) -c $(CFLAGS) -o $@ $<
+
+%.o: %.s
+	$(CC) -c $(CFLAGS) -o $@ $<
+
+clean:
+	rm -f $(objects) fibseq
+
+QEMU_CMD = qemu-arm -L /usr/arm-linux-gnueabihf ./fibseq &
+CMD = yes 9 | $(call QEMU_CMD) && sleep 1
+qemu: fibseq
+	@num=1 ; i1=0 ; i2=1 ; \
+	while [ $$num -le 50 ] ; do \
+		# save output answer \
+		ans=`yes $$num | $(call QEMU_CMD)` ; \
+		sleep 0.5 ; \
+		# echo output \
+		echo $$ans ; \
+		# split output string && save answer \
+		ans=`echo $$ans | cut -d ' ' -f 7` ;  \
+		# calculate the correct answer \
+		i3=$$i2 ;  i2=`expr $$i1 + $$i2` ; i1=$$i3 ; \
+		# check if it is right \
+		if [ "$$i1" -eq "$$ans" ] ; then \
+			echo " -> correct" ; \
+		else \
+			echo " -> wrong, the ans is $$i1" ; \
+		fi ; \
+		num=`expr $$num + 1` ; \
+	done
+