From: Dana Dahlstrom <dana+15L@cs.ucsd.edu>
To: cse15L@ucsd.edu
Subject: notes X ddahlstr mpartner

Dana Dahlstrom and Mysterious Partner
Notes X (eXample)

$ javac Example.java
$ java Example
Usage: java Example max
$ java Example 0
Maximum prime to look for must be 2 or greater
$ java Example 1
Maximum prime to look for must be 2 or greater
$ java Example 2
2
$ java Example 3
2
3
$ java Example 4
2
3
4

----

failure: 4 is not prime
began walking through code for max=4
max is passed to PrimeFinder.getPrimes
PrimeFinder.getPrimes appears to implement sieve of Eratosthenes
no apparent defects in PrimeFinder.getPrimes; FixedSizedBitSet may be at fault

----

$ java Example 8
2
3
4
5
6
7
8
$ java Example 16
2
3
5
7
11
13
$ java Example 12
2
3
5
7
9
11
$ java Example 10
2
3
5
7
9
$ java Example 9
2
3
5
7
9

----

...intriguing

returned to inspecting code
FixedSizedBitSet unary constructor looks OK; add and contain methods are used
FixedSizedBitSet.remove is never used
the IllegalArgumentExceptions have no detail strings
add and contains use a private method, mask
the program uses a lot of bitwise operators

began walking through the code again, comparing max=9 to max=8
noticed the cast to int on line 59:
    int stop = (int)Math.sqrt(max);
considered adding 1, taking the ceiling instead of the floor
noticed the loop termination condition on line 63 contradicts a comment:

    for(int i=2;i<stop;i++){

the comment above the stop variable reads:

    /* All composite numbers less than or equal to max
    will have at least one factor less than or equal to
    stop. */

this suggests a hypothesis

----

$ java Example 15
2
3
5
7
9
11
13
15

----

changed line 63 from

    for(int i=2;i<stop;i++){

to

    for(int i=2;i<=stop;i++){

saved Example.java, and...

----

$ javac Example.java
$ java Example 4
2
3
$ java Example 8
2
3
5
7
$ java Example 9
2
3
5
7
$ java Example 15
2
3
5
7
11
13
$ java Example 16
2
3
5
7
11
13
$ java Example 32
2
3
5
7
11
13
17
19
23
29
31
$ java Example 64
5
11
17
29
37
43
49
61
$ java Example 63
5
11
17
29
37
43
49
61
$ java Example 62
5
11
17
29
31
37
43
49
61
$ java Example 33
2
3
5
7
11
13
17
19
23
29
31
$ java Example 34
3
5
7
11
13
17
19
23
29
31

$ diff -u <(java Example 33) <(java Example 34)
--- /dev/fd/63  2009-03-25 16:09:02.996470878 -0700
+++ /dev/fd/62  2009-03-25 16:09:02.997470801 -0700
@@ -1,4 +1,3 @@
-2
 3
 5
 7
$ diff -u <(java Example 34) <(java Example 35)
--- /dev/fd/63  2009-03-25 16:09:08.362055132 -0700
+++ /dev/fd/62  2009-03-25 16:09:08.363055054 -0700
@@ -1,4 +1,3 @@
-3
 5
 7
 11
$ diff -u <(java Example 35) <(java Example 36)
$ diff -u <(java Example 36) <(java Example 37)
--- /dev/fd/63  2009-03-25 16:09:17.565342028 -0700
+++ /dev/fd/62  2009-03-25 16:09:17.566341950 -0700
@@ -7,3 +7,4 @@
 23
 29
 31
+37
$ diff -u <(java Example 37) <(java Example 38)
$ diff -u <(java Example 38) <(java Example 39)
--- /dev/fd/63  2009-03-25 16:09:26.604641634 -0700
+++ /dev/fd/62  2009-03-25 16:09:26.604641634 -0700
@@ -1,5 +1,4 @@
 5
-7
 11
 13
 17

----

so at 34 we lose 2, at 35 we lose 3, and at 39 we lose 7
34-32=2, 35-32=3, and 39-32=7
we lose 5 at 37, but 37 is a prime
32 is the size of an int, but most of the code uses 64-bit longs
line 129 (in FixedSizedBitSet.mask) left-shifts an int literal up to 63 bits

----

$ diff -u <(java Example 42) <(java Example 43)
--- /dev/fd/63  2009-03-25 22:43:30.962816769 -0700
+++ /dev/fd/62  2009-03-25 22:43:30.963816693 -0700
@@ -7,3 +7,4 @@
 29
 31
 37
+43
$ diff -u <(java Example 44) <(java Example 45)
--- /dev/fd/63  2009-03-25 22:42:46.083295104 -0700
+++ /dev/fd/62  2009-03-25 22:42:46.084295027 -0700
@@ -1,6 +1,5 @@
 5
 11
-13
 17
 19
 23

----

changed line 129 from

    return 1 << (elem %64);

to

    return (long)1 << (elem %64);

saved Example.java, and...

----

$ javac Example.java
$ java Example 34
2
3
5
7
11
13
17
19
23
29
31
$ java Example 64
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
$ java Example 128
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
101
103
107
109
113
127

----

OK, we had to look those up on Wikipedia; they're right