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Computer Architecture Formulas
1. CPU time = Instruction count
!
Clock cycles per instruction
!
Clock cycle time
2. X is n times faster than Y: n =
3. Amdahl’s Law: Speedup
overall
= =
4.
5.
6.
7. Availability = Mean time to fail / (Mean time to fail + Mean time to repair)
8.
where Wafer yield accounts for wafers that are so bad they need not be tested and
is a parameter called
the process-complexity factor, a measure of manufacturing difficulty.
ranges from 11.5 to 15.5 in 2011.
9. Means—arithmetic (AM), weighted arithmetic (WAM), and geometric (GM):
AM =
WAM =
GM =
where Time
i
is the execution time for the ith program of a total of n in the workload, Weight
i
is the
weighting of the ith program in the workload.
10. Average memory-access time = Hit time + Miss rate
!
Miss penalty
11. Misses per instruction = Miss rate
!
Memory access per instruction
12. Cache index size: 2
index
= Cache size
/
(Block size
!
Set associativity)
13. Power Utilization Effectiveness (PUE) of a Warehouse Scale Computer =
Rules of Thumb
1. Amdahl/Case Rule: A balanced computer system needs about 1 MB of main memory capacity and 1
megabit per second of I/O bandwidth per MIPS of CPU performance.
2. 90/10 Locality Rule: A program executes about 90% of its instructions in 10% of its code.
3. Bandwidth Rule: Bandwidth grows by at least the square of the i
mprovement in latency.
4. 2:1 Cache Rule: The miss rate of a direct-mapped cache of size N is about the same as a two-way set-
associative cache of size N/2.
5. Dependability Rule: Design with no single point of failure.
6. Watt-Year Rule: The fully burdened cost of a Watt per year in a Warehouse Scale Computer in North
America in 2011, including the cost of amortizing the power and cooling infrastructure, is about $2.
Execution time
Y
Execution time
X
/
Performance
X
Performance
Y
/=
Execution time
old
Execution time
new
-------------------------------------------
1
1Fraction
enhanced
–#)
Fraction
enhanced
Speedup
enhanced
------------------------------------+
---------------------------------------------------------------------------------------------
Energy
dynamic
12
/
Capacitive load Voltage
2
!!
Power
dynamic
12
/
Capacitive load
!
Voltage
2
Frequency switched
! !
Power
static
Current
static
Voltage
!
Die yield Wafer yield 1 1 Defects per unit area Die area
!
+ )(
/
N
!
=
1
n
---Time
i
i
1=
n
Weight
i
Time
i
!
i
1=
n
n
Time
i
i
1=
n
Total Facility Power
IT Equipment Power
--------------------------------------------------
(
N
N
In Praise of Computer Architecture: A Quantitative Approach
Sixth Edition
“Although important concepts of architecture are timeless, this edition has been
thoroughly updated with the latest technology developments, costs, examples,
and references. Keeping pace with recent developments in open-sourced architec-
ture, the instruction set architecture used in the book has been updated to use the
RISC-V ISA.”
—from the foreword by Norman P. Jouppi, Google
“Computer Architecture: A Quantitative Approach is a classic that, like fine wine,
just keeps getting better. I bought my first copy as I finished up my undergraduate
degree and it remains one of my most frequently referenced texts today.”
—James Hamilton, Amazon Web Service
“Hennessy and Patterson wrote the first edition of this book when graduate stu-
dents built computers with 50,000 transistors. Today, warehouse-size computers
contain that many servers, each consisting of dozens of independent processors
and billions of transistors. The evolution of compu ter architecture has been rapid
and relentless, but Computer Architecture: A Quantitative Approach has kept pace,
with each edition accurately explaining and analyzing the important emerging
ideas that make this field so exciting.”
—James Larus, Microsoft Research
“Another timely and relevant update to a classic, once again also serving as a win-
dow into the relentless and exciting evolution of computer architecture! The new
discussions in this edition on the slowing of Moore's law and implications for
future systems are must-reads for both computer architects and practitioners
working on broader systems.”
—Parthasarathy (Partha) Ranganathan, Google
“I love the ‘Quantitative Approach’ books because they are written by engineers,
for engineers. John Hennessy and Dave Patterson show the limits imposed by
mathematics and the possibilities enabled by materials science. Then they teach
through real-world examples how architect s analyze, measure, and compromise
to build working systems. This sixth edition comes at a critical time: Moore’s
Law is fading just as deep learning demands unprecedented compute cycles.
The new chapter on domain-specific architectures documents a number of prom-
ising approaches and prophesies a rebirth in computer architecture. Like the
scholars of the European Renaissance, computer architects must understand our
own history, and then combine the lessons of that history with new techniques
to remake the world.”
—Cliff Young, Google
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Computer Architecture
A Quantitative Approach
Sixth Edition
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