![Program inputs affect CPI too!
int rand[1000] = {random 0s and 1s }
for(i=0;i<1000;i++)
if(rand[i]) sum -= i;
else sum *= i;
int ones[1000] = {1, 1, ...}
for(i=0;i<1000;i++)
if(ones[i]) sum -= i;
else sum *= i;
• Data-dependent computation
• Data-dependent micro-architectural behavior
–Processors are faster when the computation is
predictable (more later)](https://image.slidesharecdn.com/03performance-150725190230-lva1-app6891/85/03-performance-17-320.jpg)
03 performance
- 1. Evaluating Computers: Bigger, better, faster, more? 1
- 2. What do you want in a computer? 2
- 3. What do you want in a computer? • Low latency -- one unit of work in minimum time • 1/latency = responsiveness • High throughput -- maximum work per time • High bandwidth (BW) • Low cost • Low power -- minimum jules per time • Low energy -- minimum jules per work • Reliability -- Mean time to failure (MTTF) • Derived metrics • responsiveness/dollar • BW/$ • BW/Watt • Work/Jule • Energy * latency -- Energy delay product • MTTF/$ 3
- 4. Latency • This is the simplest kind of performance • How long does it take the computer to perform a task? • The task at hand depends on the situation. • Usually measured in seconds • Also measured in clock cycles • Caution: if you are comparing two different system, you must ensure that the cycle times are the same. 4
- 5. Measuring Latency • Stop watch! • System calls • gettimeofday() • System.currentTimeMillis() • Command line • time <command> 5
- 6. Where latency matters • Application responsiveness • Any time a person is waiting. • GUIs • Games • Internet services (from the users perspective) • “Real-time” applications • Tight constraints enforced by the real world • Anti-lock braking systems • Manufacturing control • Multi-media applications • The cost of poor latency • If you are selling computer time, latency is money. 6
- 7. Latency and Performance • By definition: • Performance = 1/Latency • If Performance(X) > Performance(Y), X is faster. • If Perf(X)/Perf(Y) = S, X is S times faster thanY. • Equivalently: Latency(Y)/Latency(X) = S • When we need to talk about specifically about other kinds of “performance” we must be more specific. 7
- 8. The Performance Equation • We would like to model how architecture impacts performance (latency) • This means we need to quantify performance in terms of architectural parameters. • Instructions -- this is the basic unit of work for a processor • Cycle time -- these two give us a notion of time. • Cycles • The first fundamental theorem of computer architecture: Latency = Instructions * Cycles/Instruction * Seconds/Cycle 8
- 9. The Performance Equation • The units work out! Remember your dimensional analysis! • Cycles/Instruction == CPI • Seconds/Cycle == 1/hz • Example: • 1GHz clock • 1 billion instructions • CPI = 4 • What is the latency? 9 Latency = Instructions * Cycles/Instruction * Seconds/Cycle
- 10. Examples • gcc runs in 100 sec on a 1 GHz machine – How many cycles does it take? • gcc runs in 75 sec on a 600 MHz machine – How many cycles does it take? 100G cycles 45G cycles Latency = Instructions * Cycles/Instruction * Seconds/Cycle
- 11. How can this be? • Different Instruction count? • Different ISAs ? • Different compilers ? • Different CPI? • underlying machine implementation • Microarchitecture • Different cycle time? • New process technology • Microarchitecture 11 Latency = Instructions * Cycles/Instruction * Seconds/Cycle
- 12. Computing Average CPI • Instruction execution time depends on instruction time (we’ll get into why this is so later on) • Integer +, -, <<, |, & -- 1 cycle • Integer *, /, -- 5-10 cycles • Floating point +, - -- 3-4 cycles • Floating point *, /, sqrt() -- 10-30 cycles • Loads/stores -- variable • All theses values depend on the particular implementation, not the ISA • Total CPI depends on the workload’s Instruction mix -- how many of each type of instruction executes • What program is running? • How was it compiled? 12
- 13. The Compiler’s Role • Compilers affect CPI… • Wise instruction selection • “Strength reduction”: x*2n -> x << n • Use registers to eliminate loads and stores • More compact code -> less waiting for instructions • …and instruction count • Common sub-expression elimination • Use registers to eliminate loads and stores 13
- 14. Stupid Compiler int i, sum = 0; for(i=0;i<10;i++) sum += i; sw 0($sp), $0 #sum = 0 sw 4($sp), $0 #i = 0 loop: lw $1, 4($sp) sub $3, $1, 10 beq $3, $0, end lw $2, 0($sp) add $2, $2, $1 st 0($sp), $2 addi $1, $1, 1 st 4($sp), $1 b loop end: Type CPI Static # dyn # mem 5 6 42 int 1 3 30 br 1 2 20 Total 2.8 11 92 (5*42 + 1*30 + 1*20)/92 = 2.8
- 15. Smart Compiler int i, sum = 0; for(i=0;i<10;i++) sum += i; add $1, $0, $0 # i add $2, $0, $0 # sum loop: sub $3, $1, 10 beq $3, $0, end add $2, $2, $1 addi $1, $1, 1 b loop end: sw 0($sp), $2 Type CPI Static # dyn # mem 5 1 1 int 1 5 32 br 1 2 20 Total 1.01 8 53 (5*1 + 1*32 + 1*20)/53 = 2.8
- 16. Live demo 16
- 17. Program inputs affect CPI too! int rand[1000] = {random 0s and 1s } for(i=0;i<1000;i++) if(rand[i]) sum -= i; else sum *= i; int ones[1000] = {1, 1, ...} for(i=0;i<1000;i++) if(ones[i]) sum -= i; else sum *= i; • Data-dependent computation • Data-dependent micro-architectural behavior –Processors are faster when the computation is predictable (more later)
- 18. Live demo 18
- 19. • Meaningful CPI exists only: • For a particular program with a particular compiler • ....with a particular input. • You MUST consider all 3 to get accurate latency estimations or machine speed comparisons • Instruction Set • Compiler • Implementation of Instruction Set (386 vs Pentium) • Processor Freq (600 Mhz vs 1 GHz) • Same high level program with same input • “wall clock” measurements are always comparable. • If the workloads (app + inputs) are the same 19 Making Meaningful Comparisons Latency = Instructions * Cycles/Instruction * Seconds/Cycle
- 20. The Performance Equation • Clock rate = • Instruction count = • Latency = • Find the CPI! 20 Latency = Instructions * Cycles/Instruction * Seconds/Cycle
- 21. Today • DRAM • Quiz 1 recap • HW 1 recap • Questions about ISAs • More about the project? • Amdahl’s law 21
- 22. Key Points • Amdahl’s law and how to apply it in a variety of situations • It’s role in guiding optimization of a system • It’s role in determining the impact of localized changes on the entire system • 22
- 23. Limits on Speedup: Amdahl’s Law • “The fundamental theorem of performance optimization” • Coined by Gene Amdahl (one of the designers of the IBM 360) • Optimizations do not (generally) uniformly affect the entire program – The more widely applicable a technique is, the more valuable it is – Conversely, limited applicability can (drastically) reduce the impact of an optimization. Always heed Amdahl’s Law!!! It is central to many many optimization problems
- 24. Amdahl’s Law in Action • SuperJPEG-O-Rama2000 ISA extensions ** –Speeds up JPEG decode by 10x!!! –Act now! While Supplies Last! ** Increases processor cost by 45%
- 25. Amdahl’s Law in Action • SuperJPEG-O-Rama2000 in the wild • PictoBench spends 33% of it’s time doing JPEG decode • How much does JOR2k help? JPEG Decodew/o JOR2k w/ JOR2k 30s 21s
- 26. Amdahl’s Law in Action • SuperJPEG-O-Rama2000 in the wild • PictoBench spends 33% of it’s time doing JPEG decode • How much does JOR2k help? JPEG Decodew/o JOR2k w/ JOR2k 30s 21s Performance: 30/21 = 1.4x Speedup != 10x
- 27. Amdahl’s Law in Action • SuperJPEG-O-Rama2000 in the wild • PictoBench spends 33% of it’s time doing JPEG decode • How much does JOR2k help? JPEG Decodew/o JOR2k w/ JOR2k 30s 21s Performance: 30/21 = 1.4x Speedup != 10x Is this worth the 45% increase in cost?
- 28. Amdahl’s Law in Action • SuperJPEG-O-Rama2000 in the wild • PictoBench spends 33% of it’s time doing JPEG decode • How much does JOR2k help? JPEG Decodew/o JOR2k w/ JOR2k 30s 21s Performance: 30/21 = 1.4x Speedup != 10x Is this worth the 45% increase in cost? Amdahl ate our Speedup!
- 29. Amdahl’s Law • The second fundamental theorem of computer architecture. • If we can speed up X of the program by S times • Amdahl’s Law gives the total speed up, Stot Stot = 1 . (x/S + (1-x))
- 30. Amdahl’s Law • The second fundamental theorem of computer architecture. • If we can speed up X of the program by S times • Amdahl’s Law gives the total speed up, Stot Stot = 1 . (x/S + (1-x)) x =1 => Stot = 1 = 1 = S (1/S + (1-1)) 1/S Sanity check:
- 31. Amdahl’s Corollary #1 • Maximum possible speedup, Smax Smax = 1 (1-x) S = infinity
- 32. Amdahl’s Law Practice • Protein String Matching Code –200 hours to run on current machine, spends 20% of time doing integer instructions –How much faster must you make the integer unit to make the code run 10 hours faster? –How much faster must you make the integer unit to make the code run 50 hours faster? A)1.1 B)1.25 C)1.75 D)1.33 E) 10.0 F) 50.0 G) 1 million times H) Other
- 33. Amdahl’s Law Practice • Protein String Matching Code –4 days ET on current machine • 20% of time doing integer instructions • 35% percent of time doing I/O –Which is the better economic tradeoff? • Compiler optimization that reduces number of integer instructions by 25% (assume each integer inst takes the same amount of time) • Hardware optimization that makes I/O run 20% faster?
- 34. Amdahl’s Law Applies All Over 30 • SSDs use 10x less power than HDs • But they only save you ~50% overall.
- 35. Amdahl’s Law in Memory 31 Memory Device Rowdecoder Column decoder Sense Amps High order bits Low order bits Storage array DataAddress • Storage array 90% of area • Row decoder 4% • Column decode 2% • Sense amps 4% • What’s the benefit of reducing bit size by 10%? • Reducing column decoder size by 90%?
- 36. Amdahl’s Corollary #2 • Make the common case fast (i.e., x should be large)! –Common == “most time consuming” not necessarily “most frequent” –The uncommon case doesn’t make much difference –Be sure of what the common case is –The common case changes. • Repeat… –With optimization, the common becomes uncommon and vice versa.
- 37. Amdahl’s Corollary #2: Example Common case
- 38. Amdahl’s Corollary #2: Example Common case 7x => 1.4x
- 39. Amdahl’s Corollary #2: Example Common case 7x => 1.4x 4x => 1.3x
- 40. Amdahl’s Corollary #2: Example Common case 7x => 1.4x 4x => 1.3x 1.3x => 1.1x Total = 20/10 = 2x
- 41. Amdahl’s Corollary #2: Example Common case 7x => 1.4x 4x => 1.3x 1.3x => 1.1x Total = 20/10 = 2x • In the end, there is no common case! • Options: – Global optimizations (faster clock, better compiler) – Find something common to work on (i.e. memory latency) – War of attrition – Total redesign (You are probably well-prepared for this)
- 42. Amdahl’s Corollary #3 • Benefits of parallel processing • p processors • x% is p-way parallizable • maximum speedup, Spar Spar = 1 . (x/p + (1-x))
- 43. Amdahl’s Corollary #3 • Benefits of parallel processing • p processors • x% is p-way parallizable • maximum speedup, Spar Spar = 1 . (x/p + (1-x)) x is pretty small for desktop applications, even for p = 2
- 44. Amdahl’s Corollary #3 • Benefits of parallel processing • p processors • x% is p-way parallizable • maximum speedup, Spar Spar = 1 . (x/p + (1-x)) x is pretty small for desktop applications, even for p = 2 Does Intel’s 80-core processor make much sense?
- 45. Amdahl’s Corollary #4 • Amdahl’s law for latency (L) Lnew = Lbase *1/Speedup Lnew = Lbase *(x/S + (1-x)) Lnew = (Lbase /S)*x + ETbase*(1-x) • If you can speed up y% of the remaining (1-x), you can apply Amdahl’s law recursively Lnew = (Lbase /S1)*x + (Sbase*(1-x)/S2*y + Lbase*(1-x)*(1-y)) • This is how we will analyze memory system performance
- 46. Amdahl’s Non-Corollary • Amdahl’s law does not bound slowdown Lnew = (Lbase /S)*x + Lbase*(1-x) • Lnew is linear in 1/S • Example: x = 0.01 of execution, Lbase = 1 –S = 0.001; • Enew = 1000*Lbase *0.01 + Lbase *(0.99) ~ 10*Lbase –S = 0.00001; • Enew = 100000*Lbase *0.01 + Lbase *(0.99) ~ 1000*Lbase • Things can only get so fast, but they can get arbitrarily slow. –Do not hurt the non-common case too much!
- 47. Benchmarks: Standard Candles for Performance • It’s hard to convince manufacturers to run your program (unless you’re a BIG customer) • A benchmark is a set of programs that are representative of a class of problems. • To increase predictability, collections of benchmark applications, called benchmark suites, are popular – “Easy” to set up – Portable – Well-understood – Stand-alone – Standardized conditions – These are all things that real software is not.
- 48. Classes of benchmarks • Microbenchmark – measure one feature of system – e.g. memory accesses or communication speed • Kernels – most compute-intensive part of applications – e.g. Linpack and NAS kernel b’marks (for supercomputers) • Full application: – SpecInt / SpecFP (int and float) (for Unix workstations) – Other suites for databases, web servers, graphics,...
- 49. Bandwidth • The amount of work (or data) per time • MB/s, GB/s -- network BW, disk BW, etc. • Frames per second -- Games, video transcoding • (why are games under both latency and BW?) • Also called “throughput” 39
- 50. Measuring Bandwidth • Measure how much work is done • Measure latency • Divide 40
- 51. Latency-BW Trade-offs • Often, increasing latency for one task and increase BW for many tasks. • Think of waiting in line for one of 4 bank tellers • If the line is empty, your response time is minimized, but throughput is low because utilization is low. • If there is always a line, you wait longer (your latency goes up), but there is always work available for tellers. • Much of computer performance is about scheduling work onto resources • Network links. • Memory ports. • Processors, functional units, etc. • IO channels. • Increasing contention for these resources generally increases throughput but hurts latency. 41
- 52. Stationwagon Digression • IPv6 Internet 2: 272,400 terabit-meters per second –585GB in 30 minutes over 30,000 Km –9.08 Gb/s • Subaru outback wagon – Max load = 408Kg – 21Mpg • MHX2 BT 300 Laptop drive – 300GB/Drive – 0.135Kg • 906TB • Legal speed: 75MPH (33.3 m/s) • BW = 8.2 Gb/s • Latency = 10 days • 241,535 terabit-meters per second
- 53. Prius Digression • IPv6 Internet 2: 272,400 terabit-meters per second –585GB in 30 minutes over 30,000 Km –9.08 Gb/s • My Toyota Prius – Max load = 374Kg – 44Mpg (2x power efficiency) • MHX2 BT 300 – 300GB/Drive – 0.135Kg • 831TB • Legal speed: 75MPH (33.3 m/s) • BW = 7.5 Gb/s • Latency = 10 days • 221,407 terabit-meters per second (13% performance hit)