What makes a good language

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

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.

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

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

Control flow bug

• AT&T 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).

• 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.

Data structure management bug

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 Moore’s Law for software.

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

Algorithms

• Recipes for doing computations

• The underpinnings of programming – Think out your algorithm– Show that it works– Determine it’s efficiency– Write it as a program

What is an algorithm

• Algorithm is a recipe

• Has – Inputs

– Rules

– Evaluation Criteria

– Output

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

Chocolate chip cookies

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

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

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


• 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


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


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

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

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, you’re done

How it works

57

190

219

34

How it works

Find smallest value -- put it first in list

57

190

219

34

34

190

219

57

How it works

Find second smallest value -- put it second

57

190

219

34

34

190

219

57

34

57

219

190

How it works

Finish the sorting

57

190

219

34

34

190

219

57

34

57

219

190

34

57

190

219

A simple method for sorting

• To sort array x = {x[1],x[2], … , x[n]}

For I = 1 to n For J = I+1 to n

If (x[I] > x[J]) Then swap their valuesnext

next

Another sorting algorithm

• Sorting by Merging

• Key idea It’s easy to merge 2 sorted lists

Merging 2 sorted lists

190

219

463

155

255

355


190

219

463

155

255

355

Start at the top of each list


190

219

463

155

255

355

190 is bigger than 155


190

219

463

155

255

355

155

Record 155 and move the arrow


190

219

463

155

255

355

155

190

190 is less than 255


190

219

463

155

255

355

155

190

219



190

219

463

155

255

355

155

190

219

255



190

219

463

155

255

355

155

190

219

255

355

463Finished when at the end of each list

Sorting by Merging

• Key idea It’s easy to merge 2 sorted lists

• Sort larger lists by – Sorting smaller lists– Merging the results

• How do we sort smaller lists?

Sort then merge

157

227

345

134

157

227

345

134

Subdivide

Sort then merge

157

227

345

134

157

227

345

134

157

227

134

345

Subdivide Sort piecesBy merging

Sort then merge

157

227

345

134

157

227

345

134

157

227

134

345

134

157

227

345

Subdivide Sort pieces Merge

SortMerge algorithm

Function SortMerge(x,1,n) -- sort list of n elements xIf n = 1 then

Return -- nothing to sortEnd ifMid = (1+ n)/2 -- midpoint of listSortMerge(x,1, Mid ) -- sort first half of listSortMerge(x, Mid +1, n) -- sort second half of

listMerge(x,1, Mid , Mid +1, n) -- merge sorted halves

End Function

Does it work?

• Have to be careful about stopping

• There are always a lot of things going on

Sort(n) Sort(n/2)

Sort(n/2)

Merge

Sort(n/4)

Sort(n/4)

Merge

Sort(n/2)

Merge

Sort(n/8)

Sort(n/8)

Merge

Sort(n/4)

Merge

Sort(n/2)

Merge

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

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

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

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?

EC coursesPHI 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

Searching for COS 111

Compare to the middle

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

Searching


If smaller search first half

If larger search second 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

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

Repeat


If smaller search first half

If larger search second 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 COS 111

Building indicesPHI 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

AAS

ANT

COS

FRS

GER

HUM

LIN

PHI

PSY

Search indices then dataPHI 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

AAS

ANT

COS

FRS

GER

HUM

LIN

PHI

PSY

COS 111

Documents

What makes a good language