Advance Computing for Electrical Engineers An Introduction
Virendra SinghAssociate ProfessorComputer Architecture and Dependable Systems LabDepartment of Electrical EngineeringIndian Institute of Technology Bombay http://www.ee.iitb.ac.in/~viren/E-mail: [email protected]
EE717/453:Advance Computing for Electrical Engineers
Lecture0
EE 717/453
• Pre-requisite● Knowledge of programming (Any language C/C+
+/Java, ..)
• Attendance– Not mandatory (except first week)– Submission of assignments (firm deadlines)
• Timing– M Th (Slot 13): 6:30 pm to 8:00 pm– Office Hours: Wed 4 pm to 6 pm
18 July 2013 EE-717/453@IITB 2
Course Outline• Data Structures and Algorithm
– About 6 - 8 classes– Cover basic data structures (Stack, Queue,
Linked List, Tree, Graph, Hashing – Basic Algorithm Design
• Computer Architecture and Compiler Design
– About 2-4 lectures– Basic architectures and compiler design
phases
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Course Outline• Operating System
– About 6-8 classes– Basics of operating system– PintOS– Implementation of basic OS functions
(Threads, user program, virtual memory, file system)
Parallel Programming– About 6 – 8 lectures– Basics of parallel programming– CUDA
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Course Outline• Miscellaneous
– About 1-2 lectures
• Summary
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Books• Data Structures, Algorithms, and its applications in
C++– Sartaj Sahni
• Introduction to Algorithms– Cormen et al.
• Modern Operating Systems– Tanenbaum
• Introduction to parallel programming– Thomas Rauber
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Evaluation
• Mid semester Examination– 15 Marks
• Final Examination– 30 Marks
• Assignments– 40 Marks
• Continuous Evaluation– 15 Marks
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GradesAbsolute• AA: > 94• AB : 85 - 94• BB : 75 - 84• BC : 65 – 74• CC : 55 – 74• CD : 45 – 54• DD : 40 – 45• FR: < 40
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Problem Solving: Main Steps
1. Problem definition
2. Algorithm design/ Algorithm specification
3. Algorithm analysis
4. Implementation
5. Testing
6. [Maintenance]
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Running Program on Processor
Processor Performance = ---------------Time
Program
Architecture --> Implementation --> Realization
Compiler Designer Processor Designer Chip Designer
Instructions
Cycles
Program
Instruction
TimeCycle
(code size)
= X X
(CPI)
(cycle time)
EE-717/453@IITB18 July 2013
10
From Source to Executable
Compiler
main()sub1()data
source program
foo.c
mainsub1data
objectmodules
foo.o
printfscanfgets
fopenexitdata
...
static librarylibc.a
LinkageEditor
mainsub1dataprintfexitdata
loadmodule
a.out
otherprograms
...
mainsub1dataprintfexitdata
other......
kernel
Machine memory
?
(systemcalls)
Loader
(Run Time)
Dynamic library case not shown
“Load time”
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Problem Definition
• What is the task to be accomplished?– Calculate the average of the grades for a
given student – Understand the talks given out by politicians
and translate them in Chinese
What are the time / space / speed performance requirements ?
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Algorithm Design/Specifications• Algorithm: Finite set of instructions that, if followed,
accomplishes a particular task. • Describe: in natural language / pseudo-code / diagrams /
etc • Criteria to follow:
– Input: Zero or more quantities (externally produced) – Output: One or more quantities – Definiteness: Clarity, precision of each instruction – Finiteness: The algorithm has to stop after a finite (may
be very large) number of steps – Effectiveness: Each instruction has to be basic enough
and feasible● Understand speech● Translate to Chinese
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Algorithm Design/Specifications• Algorithm: Finite set of instructions that, if followed,
accomplishes a particular task. • Describe: in natural language / pseudo-code / diagrams /
etc • Criteria to follow:
– Input: Zero or more quantities (externally produced) – Output: One or more quantities – Definiteness: Clarity, precision of each instruction – Finiteness: The algorithm has to stop after a finite (may
be very large) number of steps – Effectiveness: Each instruction has to be basic enough
and feasible● Understand speech● Translate to Chinese
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Implementation, Testing, and Maintenance• Implementation
– Decide on the programming language to use ● C,C++,Lisp,Java,Perl,Prolog,Assembly etc.
– Write clean, well documented code
• Test, test, test
• Integrate feedback from users, fix bugs, ensure compatibility across different versions Maintenance
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Algorithm Analysis
• Space complexity– How much space is required
Time complexity– How much time does it take to run the
algorithm
Often, we deal with estimates!
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Space Complexity (1/3)• Space complexity = The amount of
memory required by an algorithm to run to completion
– [Core dumps = the most often encountered cause is “memory leaks” – the amount of memory required larger than the memory available on a given system]
Some algorithms may be more efficient if data completely loaded into memory
– Need to look also at system limitations– E.g. Classify 10 GB of text in various categories
[politics, tourism, sport, natural disasters, etc.] – can I afford to load the entire collection? 18 July 2013 EE-717/453@IITB 17
Space complexity (2/3 )• Fixed part: The size required to store
certain data/variables, that is independent of the size of the problem:
– e.g. name of the data collection – same size for classifying 2GB or 1MB of texts
• Variable part: Space needed by variables, whose size is dependent on the size of the problem:
– e.g. actual text– load 2GB of text VS. load 1MB of text
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Space Complexity (3/3)
• S(P) = c + S(instance characteristics)• Example: void float sum (float* a, int n){
float s = 0;
for (int i = 0; I < n; i++){
s += a[i]
}
return s;
}
• Space? One word for n, one for a [passed by reference], one for i Constant space
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Time Complexity
• Often more important than space complexity
– space available (for computer programs!) tends to be larger and larger
– time is still a problem for all of us
3-4 GHz multi-core processors are in the market
– still researchers estimate that the computation of various transformations for 1 single DNA chain for one single protein on 10 GHz computer would take about 1 year to run to completion
Algorithms running time is an important issue
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Running Time• Problem: Prefix average
– Given an array X – Compute the array A such that A[i] is the average of
elements X[0] ... X[i], for i=0..n-1
Solution 1:– At each step i, compute the element X[i] by
traversing the array A and determining the sum of its elements, respectively the average
Solution 2:– At each step i update a sum of the elements in the
array A – Compute the element X[i] as sum/I
Big question: Which solution to choose?18 July 2013 EE-717/453@IITB 21
Running Time
• Suppose the program includes an if-then statement that may execute or not variable running time
• Typically algorithms are measured by their worst case
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Worst case
Best case
Average case
Experimental Approach
• Write a program that implements the algorithm
• Run the program with data sets of varying size.
• Determine the actual running time using a system call to measure time (e.g. system (date) );
• Problems?
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Experimental Approach
• It is necessary to implement and test the algorithm in order to determine its running time
• Experiments can be done only on a limited set of inputs, and may not be indicative of the running time of the other inputs
• The same hardware and software should be used in order to compare two algorithms – condition very hard to achieve!
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Theoretical Approach
• Based on high-level description of the algorithms, rather than language dependent implementation
• Makes possible an evaluation of the algorithms that is independent of the hardware and software environment
Generality
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Algorithm Description• How to describe algorithms independent of a programming
language• Pseudo-Code = a description of an algorithm that
– more structured than usual prose but– less formal than a programming language
• (Or diagram)• Example: find the maximum element of an array
Algorithm ArrayMax (A, n):
Input: An array A storing n intergers
Output: The maximum element in A
currentMax A[0]
for I 1 to n-1 do
if currentMax < A[i] then currentMax A[i]
return currentMax18 July 2013 EE-717/453@IITB 26
Pseudo Code• Expression: use standard mathematical symbols
– use for assignment– use = for the equality relationship
• Method declarations: Algorithm name (parameters)• Programming constructs:
– Decision structures: if … then … [else ..]– While-loop: while .. Do– Repeat-loops: repeat … until …– For-loop: for … do– Array indexing: A[i]
• Methods– Calls: object methods (arguments) ; - return: return value
• Use comments• Instructions have to be basic enough and feasible
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Low Level Algorithm Analysis• Based on primitive operations (low-level
computations independent from the programming language)
• For example:– Make an addition = 1 operation– Calling a method or returning from a method = 1
operation– Index in an array = 1 operation– Comparison = 1 operation etc.
• Method: Inspect the pseudo-code and count the number of primitive operations executed by the algorithm
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Example
• Algorithm ArrayMax (A, n):Input: An array A storing n intergers
Output: The maximum element in A
currentMax A[0]
for I 1 to n-1 do
if currentMax < A[i] then currentMax A[i]
return currentMax
• How many operations ?
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Asymptotic Notation
• Need to abstract further• Give an idea of how the algorithm
performs• n steps vs. n+5 steps• n steps vs. n2 steps
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