What makes a good language

1
What makes a good language

• Does the task you want
• Keeps you from making mistakes
• Supports debugging when you need it
• Has a strong tool kit

2
Big number bug
On June 4, 1996 an unmanned Ariane 5 rocket
launched by the European Space Agency exploded
just forty seconds after its lift-off from
Kourou, French Guiana. The rocket was on its
first voyage, after a decade of development
costing 7 billion. The destroyed rocket and its
cargo were valued at 500 million. A board of
inquiry investigated the causes of the explosion
and in two weeks issued a report. It turned out
that the cause of the failure was a software
error in the inertial reference system.
Specifically, a 64 bit floating point number
relating to the horizontal velocity of the rocket
with respect to the platform was converted to a
16 bit signed integer. The number was larger than
32,768, the largest integer that could be stored
in a 16 bit signed integer, and so the conversion
failed.
3
Pentium II bug

• Software bug encoded in hardware
• Division algorithm uses a lookup table of 1066
  entries
• Only 1061 of the entries are downloaded to the
  PLA (programmed logic array from which the data
  are used)
• Intel had to recall all versions of the chip

4
Syntax typo bugs

• NASA Mariner 1 , Venus probe (1992)
• Intended to be the first US spacecraft to visit
  another planet, it was destroyed by a range
  officer on 22 July 1962 when it behaved
  erratically four minutes after launch.
• Essentially a period instead of a comma in a
  FORTRAN DO-Loop

5
Control flow bug

• ATT long distance service fails for nine
  hours(Wrong BREAK statement in C code)
• January 15, 1990
• 70 million of 138 million long distance customers
  in the US lost long distance service.
• Cost to ATT was between 75 Million and 100
  Million (plus the loss of good will).

6
Data structure management bug

• E-mail buffer overflow (1998)
• Several E-mail systems suffer from a "buffer
  overflow error", when extremely long e-mail
  addresses are received.  The internal buffers
  receiving the addresses do not check for length
  and allow their buffers to overflow causing the
  applications to crash.  Hostile hackers use this
  fault to trick the computer into running a
  malicious program in its place.

7
Summary

• Programming is difficult
• Have to thoroughly understand the task
• Have to anticipate all possibilities
• Code is written at a fairly primitive level
• Impossible to anticipate what users might do
• Programming languages allow the user to use tools
  to build code
• But everything still has bugs
• The cost of a bug can be very large
• There is no Moores Law for software.

8
The big picture

• We built a computer
• We talked about languages and compilers to make
  programming the computer easier
• Next we talk about algorithms, which are
  implemented by programs

9
Algorithms

• Recipes for doing computations
• The underpinnings of programming
• Think out your algorithm
• Show that it works
• Determine its efficiency
• Write it as a program

10
What is an algorithm

• Algorithm is a recipe
• Has
• Inputs
• Rules
• Evaluation Criteria
• Output

11
When Do We Use Algorithms

• When we have a problem to solve
• Examples of problems
• Baking cookies
• Putting things in alphabetical order
• Searching the Web

12
Chocolate chip cookies
13
Chocolate chip cookies

• Input
• flour (2 ¼ c)
• baking soda (1t)
• salt (1t)
• butter (1c)
• granulated sugar (3/4 c)
• brown sugar(3/4c)
• vanilla(1t)
• eggs (2)
• chocolate chip morsels (2c)
• chopped nuts (1c)
• Output
• 5 dozen cookies

14
Chocolate chip cookies Steps

• Combine flour, baking soda, and salt in small
  bowl.
• Beat butter, granulated sugar, brown sugar and
  vanilla in large bowl
• Add eggs one at a time Beating after adding each
  egg
• Gradually beat in flour mixture
• Stir in morsels and nuts
• Drop by rounded tablespoons onto ungreased baking
  sheets
• Bake 9-11 minutes
• Let stand for 2 minutes

15
Chocolate chip cookie algorithm

• Primitives
• Inputs
• Flour, baking soda, salt, butter, brown sugar,
  granulated sugar, vanilla, egg, morsels, nuts
• Alternatively, chocolate chip cookie mix
• Alternatively, wheat, sugar cane,
• Operators
• Combine, Beat, Gradually beat, Stir, Drop, Bake,
  Let stand

16
Chocolate chip cookie algorithm

• Execution
• First 2 steps can be done in parallel?
• Parbegin (Combine(),Beat()) Parend
• Machine dependencies
• Ovens vary (Bake 9-11 minutes)
• Ingredients vary and so need to be handled
  differently

17
Chocolate chip cookie algorithm

• Algorithm testing
• Proof of the pudding is in the eating
• How do we mechanize this?

18
Chocolate chip cookie algorithm

• Comparing different algorithms
• Quality of results
• User time
• Machine (oven) time

19
Putting things in alphabetical order

• Data set sizes
• Course list for COS 111 10-15 students
• PU directory assistance 10,000 people
• Manhattan phone book 1 million people
• Social Security database 1 billion records
• Long distance call billing records 100
  billion/year
• Different methods for different tasks
• Fast for large
• Simple for small

20
A simple method for sorting

• Find smallest value -- put it first in list
• Find second smallest value -- put it second
• Find next smallest value put it next
• When no more values, youre done

21
How it works
57
190
219
34
22
How it works
57
190
219
34
34
190
219
57
Find smallest value -- put it first in list
23
How it works
57
190
219
34
34
190
219
57
34
57
219
190
Find second smallest value -- put it second
24
How it works
57
190
219
34
34
190
219
57
34
57
219
190
34
57
190
219
Finish the sorting
25
A simple method for sorting

• To sort array x x1,x2, , xn
• For I 1 to n
• For J I1 to n
• If (xI gt xJ) Then swap their values
• next
• next

26
Another sorting algorithm

• Sorting by Merging
• Key idea ? Its easy to merge 2 sorted lists

27
Merging 2 sorted lists
190
219
463
155
255
355
28
Merging 2 sorted lists
190
219
463
155
255
355






Start at the top of each list
29
Merging 2 sorted lists
190
219
463
155
255
355






190 is bigger than 155
30
Merging 2 sorted lists
190
219
463
155
255
355
155





Record 155 and move the arrow
31
Merging 2 sorted lists
190
219
463
155
255
355
155
190




190 is less than 255
32
Merging 2 sorted lists
190
219
463
155
255
355
155
190
219



219 is less than 255
33
Merging 2 sorted lists
190
219
463
155
255
355
155
190
219
255


255 is less than 463
34
Merging 2 sorted lists
190
219
463
155
255
355
155
190
219
255
355
463
Finished when at the end of each list
35
Sorting by Merging

• Key idea ? Its easy to merge 2 sorted lists
• Sort larger lists by
• Sorting smaller lists
• Merging the results
• How do we sort smaller lists?

36
Sort then merge
157
227
157
227
345
134
345
134
Subdivide
37
Sort then merge
157
227
157
227
157
227
345
134
345
134
134
345
Sort pieces By merging
Subdivide
38
Sort then merge
157
227
157
227
157
227
345
134
134
157
227
345
345
134
134
345
Sort pieces
Merge
Subdivide
39
SortMerge algorithm

• Function SortMerge(x,1,n) -- sort list of n
  elements x
• If n 1 then
• Return -- nothing to sort
• End if
• Mid (1 n)/2 -- midpoint of list
• SortMerge(x,1, Mid ) -- sort first half of list
• SortMerge(x, Mid 1, n) -- sort second half of
  list
• Merge(x,1, Mid , Mid 1, n) -- merge sorted
  halves
• End Function

40
Does it work?

• Have to be careful about stopping
• There are always a lot of things going on

Sort(n/8)
Sort(n/8)
Merge
Sort(n/4)
Merge
Sort(n/2)
Merge
Sort(n)
Sort(n/2)
Sort(n/2)
Merge
Sort(n/4)
Sort(n/4)
Merge
Sort(n/2)
Merge
41
Divide and conquer

• Use recursion
• reduce solving for problem of size n to solving
  two problems of size n/2
• then combine the solutions

• S(n) 2 S(n/2) M(n/2,n/2)
• Solving a sorting problem of size n requires
  solving 2 sorting problems of size n/2 and doing
  a merge of 2 sets of size n/2

42
Comparing running times
N Insertion (ms) SortMerge(ms)
100 1 0
200 2 0
1000 58 1
10,000 5841 11
100,000 626943 162
1,000,000 70626916 3421


43
Comparing running times
N Insertion (ms) SortMerge(ms)
100 1 0
200 2 0
1000 58 1
10,000 5841 11
100,000 626943 162
1,000,000 70626916 3421


Reducing 20 hours to 3 seconds
44
Searching

• Once a list is in alphabetical order, how do you
  find things in it?
• For example, is COS 111 on the list of courses
  that satisfy the (EC) Epistemology and Cognition
  requirement?

45
EC courses
PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI
321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY
316
AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER
306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI
200
46
Searching for COS 111
AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER
306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI
200
PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI
321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY
316
COS 111
Compare to the middle
47
Searching
AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER
306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI
200
PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI
321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY
316
If larger search second half
If smaller search first half
COS 111
Compare to the middle
48
Repeat
If smaller search first half
AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER
306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI
200
If larger search second half
COS 111
Compare to the middle
49
Building indices
PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI
321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY
316
AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER
306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI
200
50
Search indices then data
PHI 201 PHI 204 PHI 301 PHI 304 PHI 312 PHI
321 PHI 333 PHI 338 PSY 255 PSY 306 PSY 307 PSY
316
AAS 391 ANT 201 COS 302 FRS 135 FRS 137 GER
306 HUM 365 LIN 213 LIN 302 LIN 306 LIN 315 PHI
200
COS 111