Computer Architecture Formulas 1. CPU time = Instruction count ! Clock cycles per instruction ! Clock cycle time 2. X is n times faster than Y: n = Execution time Y / Execution time X = Performance X / Performance Y 1 Execution time old 3. Amdahl’s Law: Speedupoverall = ------------------------------------------- = -------------------------------------------------------------------------------------------Fraction enhanced Execution time new (#1 – Fraction ) + ----------------------------------enhanced Speedup enhanced 2 4. Energydynamic 1 / 2 ! Capacitive load ! Voltage 5. Power dynamic 1 / 2 ! Capacitive load ! Voltage ! Frequency switched 6. Power static 2 Current static ! Voltage 7. Availability = Mean time to fail / (Mean time to fail + Mean time to repair) 8. Die yield = Wafer yield ! 1 / ( 1 + Defects per unit area ! Die area ) N where Wafer yield accounts for wafers that are so bad they need not be tested and N is a parameter called the process-complexity factor, a measure of manufacturing difficulty. N ranges from 11.5 to 15.5 in 2011. 9. Means—arithmetic (AM), weighted arithmetic (WAM), and geometric (GM): 1 AM = --n n n n Time i WAM = i =1 n Time i Weight i ! Time i GM = i =1 i=1 where Timei is the execution time for the ith program of a total of n in the workload, Weighti 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: 2index = Cache size / (Block size ! Set associativity) Total Facility Power 13. Power Utilization Effectiveness (PUE) of a Warehouse Scale Computer = -------------------------------------------------IT Equipment Power 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 improvement 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 setassociative 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. 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 architecture, 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 students 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 computer 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 window 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 architects 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 promising approaches and prophesies a rebirth in computer architecture. Lik

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