Some examples based on speedup and Amdahl's law

Here are some of the examples based on speedup and Amdahl's law. The purpose of these examples is to understand the concepts by applying them in given situations.

Example 1:

A computer spends 80 percent of time executing a particular type of instruction. Engineers claim to improve that instruction execution by the factor of 10. What is the resultant speedup obtained?

Sol:

We need to apply Amdahl's law here.

Example 2:

A computer program to be executed by a given processor has the following characteristic:

S.No	Instruction type	% of time	CPI
1	Integer-type	40	1
2	Branch	20	4
3	Load	30	2
4	Store	10	3

The processor is clocked at 2GHz.

Calculate the speedup obtained in each of the cases

1. Branch instruction CPI is changed from 4 to 3

2. Clock frequency is changed from 2GHz to 2.3GHz

3. Store instruction CPI is changed from 3 to 2.

Sol.

     Let us discuss each case one by one.

Case1:  Branch instruction CPI is changed from 4 to 3



Here Frac_used=0.2 (from table given in the table)
Speedup_used= 4/3=1.33

Frac_unused= 1-  Frac_used= 0.8

Case2:  Clock frequency is changed from 2GHz to 2.3GHz




execution time is inversely proportional to the frequency with which the processor is operating.

Case3: Store instruction CPI is changed from 3 to 2

Frac_used=0.1 (from the table given in the question)
speedup_used= 3/2=1.5

Frac_unused= 1- Frac_used=0.9

Iron law

Iron law is a law or principle which is indisputable and unavoidable. It can be derived by using logic, without the knowledge of any arduous subject. 
In computer architecture and organisation, Iron law is given by

Execution time= (number of instructions executed) * (cycles per instruction (CPI)) * (clock cycle time)

Example 1:

A program executes 3 billion instructions in a processor. The processor spends 2 cycles on each instruction and is working at 3GHz. 

Sol. 

Example2:

A program contains 50 billion instruction whose composition is as follows:

• 10 billion branch instructions, CPI=4
• 15 billion load instructions, CPI=2
• 5 billion store instructions, CPI=3
• 20 billion integer-type instructions, CPI=1

Evaluate the execution time for above program.

Sol.