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CS 252 Graduate Computer Architecture Lecture 2 - Metrics and Pipelining
Krste Asanovic Electrical Engineering and Computer Sciences University of California at Berkeley CS252 S05
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Review from Last Time Computer Architecture >> instruction sets
Computer Architecture skill sets are different 5 Quantitative principles of design Quantitative approach to design Solid interfaces that really work Technology tracking and anticipation CS 252 to learn new skills, transition to research Computer Science at the crossroads from sequential to parallel computing Salvation requires innovation in many fields, including computer architecture Opportunity for interesting and timely CS 252 projects exploring CS at the crossroads RAMP as experimental platform 8/30 CS252-Fall’07 CS252 S05
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Review (continued) Other fields often borrow ideas from architecture
Quantitative Principles of Design Take Advantage of Parallelism Principle of Locality Focus on the Common Case Amdahl’s Law The Processor Performance Equation Careful, quantitative comparisons Define, quantity, and summarize relative performance Define and quantity relative cost Define and quantity dependability Define and quantity power Culture of anticipating and exploiting advances in technology Culture of well-defined interfaces that are carefully implemented and thoroughly checked 8/30 CS252-Fall’07 CS252 S05
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Metrics used to Compare Designs
Cost Die cost and system cost Execution Time average and worst-case Latency vs. Throughput Energy and Power Also peak power and peak switching current Reliability Resiliency to electrical noise, part failure Robustness to bad software, operator error Maintainability System administration costs Compatibility Software costs dominate 8/30 CS252-Fall’07 CS252 S05
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Architect affects all of these
Cost of Processor Design cost (Non-recurring Engineering Costs, NRE) dominated by engineer-years (~$200K per engineer year) also mask costs (exceeding $1M per spin) Cost of die die area die yield (maturity of manufacturing process, redundancy features) cost/size of wafers die cost ~= f(die area^4) with no redundancy Cost of packaging number of pins (signal + power/ground pins) power dissipation Cost of testing built-in test features? logical complexity of design choice of circuits (minimum clock rates, leakage currents, I/O drivers) Architect affects all of these 8/30 CS252-Fall’07 CS252 S05
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System-Level Cost Impacts
Power supply and cooling Support chipset Off-chip SRAM/DRAM/ROM Off-chip peripherals 8/30 CS252-Fall’07 CS252 S05
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What is Performance? Latency (or response time or execution time)
time to complete one task Bandwidth (or throughput) tasks completed per unit time 8/30 CS252-Fall’07 CS252 S05
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Definition: Performance
Performance is in units of things per sec bigger is better If we are primarily concerned with response time performance(x) = execution_time(x) " X is n times faster than Y" means Performance(X) Execution_time(Y) n = = Performance(Y) Execution_time(X) 8/30 CS252-Fall’07 CS252 S05
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Performance Guarantees
Inputs C B A Execution Rate Average Rate: A > B > C Worst-case Rate: A < B < C 8/30 CS252-Fall’07 CS252 S05
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Types of Benchmark Synthetic Benchmarks Toy Programs Kernels
Designed to have same mix of operations as real workloads, e.g., Dhrystone, Whetstone Toy Programs Small, easy to port. Output often known before program is run, e.g., Nqueens, Bubblesort, Towers of Hanoi Kernels Common subroutines in real programs, e.g., matrix multiply, FFT, sorting, Livermore Loops, Linpack Simplified Applications Extract main computational skeleton of real application to simplify porting, e.g., NAS parallel benchmarks, TPC Real Applications Things people actually use their computers for, e.g., car crash simulations, relational databases, Photoshop, Quake 8/30 CS252-Fall’07 CS252 S05
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Performance: What to measure
Usually rely on benchmarks vs. real workloads To increase predictability, collections of benchmark applications-- benchmark suites -- are popular SPECCPU: popular desktop benchmark suite CPU only, split between integer and floating point programs SPECint2000 has 12 integer, SPECfp2000 has 14 integer pgms SPECCPU2006 to be announced Spring 2006 SPECSFS (NFS file server) and SPECWeb (WebServer) added as server benchmarks Transaction Processing Council measures server performance and cost-performance for databases TPC-C Complex query for Online Transaction Processing TPC-H models ad hoc decision support TPC-W a transactional web benchmark TPC-App application server and web services benchmark 8/30 CS252-Fall’07 CS252 S05
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Summarizing Performance
System Rate (Task 1) Rate (Task 2) A 10 20 B Which system is faster? 8/30 CS252-Fall’07 CS252 S05
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… depends who’s selling
System Rate (Task 1) Rate (Task 2) A 10 20 B Average 15 Average throughput System Rate (Task 1) Rate (Task 2) A 0.50 2.00 B 1.00 Average 1.25 Throughput relative to B System Rate (Task 1) Rate (Task 2) A 1.00 B 2.00 0.50 Average 1.25 Throughput relative to A 8/30 CS252-Fall’07 CS252 S05
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Summarizing Performance over Set of Benchmark Programs
Arithmetic mean of execution times ti (in seconds) 1/n i ti Harmonic mean of execution rates ri (MIPS/MFLOPS) n/ [i (1/ri)] Both equivalent to workload where each program is run the same number of times Can add weighting factors to model other workload distributions 8/30 CS252-Fall’07 CS252 S05
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Normalized Execution Time and Geometric Mean
Measure speedup up relative to reference machine ratio = tRef/tA Average time ratios using geometric mean n(I ratioi ) Insensitive to machine chosen as reference Insensitive to run time of individual benchmarks Used by SPEC89, SPEC92, SPEC95, …, SPEC2006 ….. But beware that choice of reference machine can suggest what is “normal” performance profile: 8/30 CS252-Fall’07 CS252 S05
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Vector/Superscalar Speedup
100 MHz Cray J90 vector machine versus 300MHz Alpha 21164 [LANL Computational Physics Codes, Wasserman, ICS’96] Vector machine peaks on a few codes???? 8/30 CS252-Fall’07 CS252 S05
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Superscalar/Vector Speedup
100 MHz Cray J90 vector machine versus 300MHz Alpha 21164 [LANL Computational Physics Codes, Wasserman, ICS’96] Scalar machine peaks on one code??? 8/30 CS252-Fall’07 CS252 S05
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How to Mislead with Performance Reports
Select pieces of workload that work well on your design, ignore others Use unrealistic data set sizes for application (too big or too small) Report throughput numbers for a latency benchmark Report latency numbers for a throughput benchmark Report performance on a kernel and claim it represents an entire application Use 16-bit fixed-point arithmetic (because it’s fastest on your system) even though application requires 64-bit floating-point arithmetic Use a less efficient algorithm on the competing machine Report speedup for an inefficient algorithm (bubblesort) Compare hand-optimized assembly code with unoptimized C code Compare your design using next year’s technology against competitor’s year old design (1% performance improvement per week) Ignore the relative cost of the systems being compared Report averages and not individual results Report speedup over unspecified base system, not absolute times Report efficiency not absolute times Report MFLOPS not absolute times (use inefficient algorithm) [ David Bailey “Twelve ways to fool the masses when giving performance results for parallel supercomputers” ] 8/30 CS252-Fall’07 CS252 S05
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Benchmarking for Future Machines
Variance in performance for parallel architectures is going to be much worse than for serial processors SPECcpu means only really work across very similar machine configurations What is a good benchmarking methodology? Possible CS252 project Berkeley View Techreport has “Dwarves” as major types of code that must run well ( Can you construct a parallel benchmark methodology from Dwarves? 8/30 CS252-Fall’07 CS252 S05
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Power and Energy Energy to complete operation (Joules)
Corresponds approximately to battery life (Battery energy capacity actually depends on rate of discharge) Peak power dissipation (Watts = Joules/second) Affects packaging (power and ground pins, thermal design) di/dt, peak change in supply current (Amps/second) Affects power supply noise (power and ground pins, decoupling capacitors) 8/30 CS252-Fall’07 CS252 S05
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Peak Power versus Lower Energy
Peak A Peak B Power Integrate power curve to get energy Time System A has higher peak power, but lower total energy System B has lower peak power, but higher total energy 8/30 CS252-Fall’07 CS252 S05
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CS252 Administrivia Instructor: Prof. Krste Asanovic
Office: 645 Soda Hall, Office Hours: M 1-3PM, 645 Soda Hall T. A.: Rose Liu, Office Hours: W 4-5PM, 751 Soda Hall Lectures: Tu/Th, 9:30-11:00AM McLaughlin Text: Computer Architecture: A Quantitative Approach, 4th Edition (Oct, 2006) Web page: Lectures available online <6:00 AM day of lecture This slide is for the 3-min class administrative matters. Make sure we update Handout #1 so it is consistent with this slide. 8/30 CS252-Fall’07 CS252 S05
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CS252 Updates Prereq quiz will cover:
Finite state machines ISA designs & MIPS assembly code programming (today’s lecture) Simple pipelining (single-issue, in-order, today’s lecture) Simple caches (Tuesday’s lecture) Will try using Bspace this term to manage course private material (readings, assignments) Book order late at book store, will try and get you temporary copies of text This slide is for the 3-min class administrative matters. Make sure we update Handout #1 so it is consistent with this slide. 8/30 CS252-Fall’07 CS252 S05
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A "Typical" RISC ISA 32-bit fixed format instruction (3 formats)
32 32-bit GPR (R0 contains zero, DP take pair) 3-address, reg-reg arithmetic instruction Single address mode for load/store: base + displacement no indirection Simple branch conditions Delayed branch see: SPARC, MIPS, HP PA-Risc, DEC Alpha, IBM PowerPC, CDC 6600, CDC 7600, Cray-1, Cray-2, Cray-3 8/30 CS252-Fall’07 CS252 S05
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Example: MIPS ( MIPS) Register-Register Op Rs1 Rs2 Rd Opx
31 26 25 21 20 16 15 11 10 6 5 Op Rs1 Rs2 Rd Opx Register-Immediate 31 26 25 21 20 16 15 immediate Op Rs1 Rd Branch 31 26 25 21 20 16 15 immediate Op Rs1 Rs2/Opx Jump / Call 31 26 25 target Op 8/30 CS252-Fall’07 CS252 S05
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Datapath vs Control Datapath Controller signals Control Points Datapath: Storage, FU, interconnect sufficient to perform the desired functions Inputs are Control Points Outputs are signals Controller: State machine to orchestrate operation on the data path Based on desired function and signals 8/30 CS252-Fall’07 CS252 S05
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Approaching an ISA Instruction Set Architecture
Defines set of operations, instruction format, hardware supported data types, named storage, addressing modes, sequencing Meaning of each instruction is described by RTL on architected registers and memory Given technology constraints assemble adequate datapath Architected storage mapped to actual storage Function units to do all the required operations Possible additional storage (eg. MAR, MBR, …) Interconnect to move information among regs and FUs Map each instruction to sequence of RTLs Collate sequences into symbolic controller state transition diagram (STD) Lower symbolic STD to control points Implement controller 8/30 CS252-Fall’07 CS252 S05
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5 Steps of MIPS Datapath Figure A.2, Page A-8
Instruction Fetch Instr. Decode Reg. Fetch Execute Addr. Calc Memory Access Write Back Next PC MUX 4 Adder Next SEQ PC Zero? RS1 Reg File Address MUX Memory RS2 ALU Inst Memory Data L M D RD MUX MUX Sign Extend IR <= mem[PC]; PC <= PC + 4 Imm WB Data Reg[IRrd] <= Reg[IRrs] opIRop Reg[IRrt] 8/30 CS252-Fall’07 CS252 S05
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5 Steps of MIPS Datapath Figure A.3, Page A-9
Instruction Fetch Instr. Decode Reg. Fetch Execute Addr. Calc Memory Access Write Back Next PC IF/ID ID/EX MEM/WB EX/MEM MUX Next SEQ PC Next SEQ PC 4 Adder Zero? RS1 Reg File Address Memory MUX RS2 ALU Memory Data MUX MUX IR <= mem[PC]; PC <= PC + 4 Sign Extend Imm WB Data A <= Reg[IRrs]; B <= Reg[IRrt] RD RD RD rslt <= A opIRop B WB <= rslt Reg[IRrd] <= WB 8/30 CS252-Fall’07 CS252 S05
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Inst. Set Processor Controller
IR <= mem[PC]; PC <= PC + 4 Ifetch JSR A <= Reg[IRrs]; B <= Reg[IRrt] opFetch-DCD JR ST PC <= IRjaddr if bop(A,b) PC <= PC+IRim br jmp r <= A + IRim WB <= Mem[r] Reg[IRrd] <= WB LD r <= A opIRop IRim Reg[IRrd] <= WB WB <= r RI RR r <= A opIRop B WB <= r Reg[IRrd] <= WB 8/30 CS252-Fall’07 CS252 S05
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5 Steps of MIPS Datapath Figure A.3, Page A-9
Instruction Fetch Instr. Decode Reg. Fetch Execute Addr. Calc Memory Access Write Back Next PC IF/ID ID/EX MEM/WB EX/MEM MUX Next SEQ PC Next SEQ PC 4 Adder Zero? RS1 Reg File Address Memory MUX RS2 ALU Memory Data MUX MUX Sign Extend Imm WB Data RD RD RD Data stationary control local decode for each instruction phase / pipeline stage 8/30 CS252-Fall’07 CS252 S05
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Visualizing Pipelining Figure A.2, Page A-8
Time (clock cycles) Reg ALU DMem Ifetch Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 6 Cycle 7 Cycle 5 I n s t r. O r d e 8/30 CS252-Fall’07 CS252 S05
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Pipelining is not quite that easy!
Limits to pipelining: Hazards prevent next instruction from executing during its designated clock cycle Structural hazards: HW cannot support this combination of instructions (single person to fold and put clothes away) Data hazards: Instruction depends on result of prior instruction still in the pipeline (missing sock) Control hazards: Caused by delay between the fetching of instructions and decisions about changes in control flow (branches and jumps). 8/30 CS252-Fall’07 CS252 S05
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One Memory Port/Structural Hazards Figure A.4, Page A-14
Time (clock cycles) Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6 Cycle 7 ALU I n s t r. O r d e Load Ifetch Reg DMem Reg Reg ALU DMem Ifetch Instr 1 Reg ALU DMem Ifetch Instr 2 ALU Instr 3 Ifetch Reg DMem Reg Reg ALU DMem Ifetch Instr 4 8/30 CS252-Fall’07 CS252 S05
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One Memory Port/Structural Hazards (Similar to Figure A.5, Page A-15)
Time (clock cycles) Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6 Cycle 7 ALU I n s t r. O r d e Load Ifetch Reg DMem Reg Reg ALU DMem Ifetch Instr 1 Reg ALU DMem Ifetch Instr 2 Bubble Stall Reg ALU DMem Ifetch Instr 3 How do you “bubble” the pipe? 8/30 CS252-Fall’07 CS252 S05
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Speed Up Equation for Pipelining
For simple RISC pipeline, CPI = 1: 8/30 CS252-Fall’07 CS252 S05
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Example: Dual-port vs. Single-port
Machine A: Dual ported memory (“Harvard Architecture”) Machine B: Single ported memory, but its pipelined implementation has a 1.05 times faster clock rate Ideal CPI = 1 for both Loads are 40% of instructions executed SpeedUpA = Pipeline Depth/(1 + 0) x (clockunpipe/clockpipe) = Pipeline Depth SpeedUpB = Pipeline Depth/( x 1) x (clockunpipe/(clockunpipe / 1.05) = (Pipeline Depth/1.4) x 1.05 = 0.75 x Pipeline Depth SpeedUpA / SpeedUpB = Pipeline Depth/(0.75 x Pipeline Depth) = 1.33 Machine A is 1.33 times faster 8/30 CS252-Fall’07 CS252 S05
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Data Hazard on R1 Figure A.6, Page A-17
Time (clock cycles) IF ID/RF EX MEM WB I n s t r. O r d e add r1,r2,r3 sub r4,r1,r3 and r6,r1,r7 or r8,r1,r9 xor r10,r1,r11 Reg ALU DMem Ifetch 8/30 CS252-Fall’07 CS252 S05
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Three Generic Data Hazards
Read After Write (RAW) InstrJ tries to read operand before InstrI writes it Caused by a “Dependence” (in compiler nomenclature). This hazard results from an actual need for communication. I: add r1,r2,r3 J: sub r4,r1,r3 8/30 CS252-Fall’07 CS252 S05
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Three Generic Data Hazards
Write After Read (WAR) InstrJ writes operand before InstrI reads it Called an “anti-dependence” by compiler writers. This results from reuse of the name “r1”. Can’t happen in MIPS 5 stage pipeline because: All instructions take 5 stages, and Reads are always in stage 2, and Writes are always in stage 5 I: sub r4,r1,r3 J: add r1,r2,r3 K: mul r6,r1,r7 8/30 CS252-Fall’07 CS252 S05
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Three Generic Data Hazards
Write After Write (WAW) InstrJ writes operand before InstrI writes it. Called an “output dependence” by compiler writers This also results from the reuse of name “r1”. Can’t happen in MIPS 5 stage pipeline because: All instructions take 5 stages, and Writes are always in stage 5 Will see WAR and WAW in more complicated pipes I: sub r1,r4,r3 J: add r1,r2,r3 K: mul r6,r1,r7 8/30 CS252-Fall’07 CS252 S05
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Forwarding to Avoid Data Hazard Figure A.7, Page A-19
Time (clock cycles) I n s t r. O r d e add r1,r2,r3 sub r4,r1,r3 and r6,r1,r7 or r8,r1,r9 xor r10,r1,r11 Reg ALU DMem Ifetch 8/30 CS252-Fall’07 CS252 S05
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HW Change for Forwarding Figure A.23, Page A-37
ID/EX EX/MEM MEM/WR NextPC mux Registers ALU Data Memory mux mux Immediate What circuit detects and resolves this hazard? 8/30 CS252-Fall’07 CS252 S05
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Forwarding to Avoid LW-SW Data Hazard Figure A.8, Page A-20
Time (clock cycles) I n s t r. O r d e add r1,r2,r3 lw r4, 0(r1) sw r4,12(r1) or r8,r6,r9 xor r10,r9,r11 Reg ALU DMem Ifetch 8/30 CS252-Fall’07 CS252 S05
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Data Hazard Even with Forwarding Figure A.9, Page A-21
Time (clock cycles) Reg ALU DMem Ifetch I n s t r. O r d e lw r1, 0(r2) sub r4,r1,r6 and r6,r1,r7 or r8,r1,r9 MIPS actutally didn’t interlecok: MPU without Interlocked Pipelined Stages 8/30 CS252-Fall’07 CS252 S05
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Data Hazard Even with Forwarding (Similar to Figure A.10, Page A-21)
Time (clock cycles) I n s t r. O r d e Reg ALU DMem Ifetch lw r1, 0(r2) Reg Ifetch ALU DMem Bubble sub r4,r1,r6 Ifetch ALU DMem Reg Bubble and r6,r1,r7 Bubble Ifetch Reg ALU DMem or r8,r1,r9 How is this detected? 8/30 CS252-Fall’07 CS252 S05
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Software Scheduling to Avoid Load Hazards
Try producing fast code for a = b + c; d = e – f; assuming a, b, c, d ,e, and f in memory. Slow code: LW Rb,b LW Rc,c ADD Ra,Rb,Rc SW a,Ra LW Re,e LW Rf,f SUB Rd,Re,Rf SW d,Rd Fast code: LW Rb,b LW Rc,c LW Re,e ADD Ra,Rb,Rc LW Rf,f SW a,Ra SUB Rd,Re,Rf SW d,Rd Compiler optimizes for performance. Hardware checks for safety. 8/30 CS252-Fall’07 CS252 S05
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Control Hazard on Branches Three Stage Stall
Reg ALU DMem Ifetch 10: beq r1,r3,36 14: and r2,r3,r5 18: or r6,r1,r7 22: add r8,r1,r9 36: xor r10,r1,r11 What do you do with the 3 instructions in between? How do you do it? Where is the “commit”? 8/30 CS252-Fall’07 CS252 S05
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Branch Stall Impact If CPI = 1, 30% branch, Stall 3 cycles => new CPI = 1.9! Two part solution: Determine branch taken or not sooner, AND Compute taken branch address earlier MIPS branch tests if register = 0 or 0 MIPS Solution: Move Zero test to ID/RF stage Adder to calculate new PC in ID/RF stage 1 clock cycle penalty for branch versus 3 8/30 CS252-Fall’07 CS252 S05
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Pipelined MIPS Datapath Figure A.24, page A-38
Instruction Fetch Instr. Decode Reg. Fetch Execute Addr. Calc Memory Access Write Back Next PC Next SEQ PC ID/EX EX/MEM MEM/WB MUX 4 Adder IF/ID Adder Zero? RS1 Address Reg File Memory RS2 ALU Memory Data MUX MUX Sign Extend Imm WB Data RD RD RD Interplay of instruction set design and cycle time. 8/30 CS252-Fall’07 CS252 S05
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Four Branch Hazard Alternatives
#1: Stall until branch direction is clear #2: Predict Branch Not Taken Execute successor instructions in sequence “Squash” instructions in pipeline if branch actually taken Advantage of late pipeline state update 47% MIPS branches not taken on average PC+4 already calculated, so use it to get next instruction #3: Predict Branch Taken 53% MIPS branches taken on average But haven’t calculated branch target address in MIPS MIPS still incurs 1 cycle branch penalty Other machines: branch target known before outcome 8/30 CS252-Fall’07 CS252 S05
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Four Branch Hazard Alternatives
#4: Delayed Branch Define branch to take place AFTER a following instruction branch instruction sequential successor1 sequential successor sequential successorn branch target if taken 1 slot delay allows proper decision and branch target address in 5 stage pipeline MIPS uses this Branch delay of length n 8/30 CS252-Fall’07 CS252 S05
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Scheduling Branch Delay Slots (Fig A.14)
A. From before branch B. From branch target C. From fall through add $1,$2,$3 if $2=0 then add $1,$2,$3 if $1=0 then sub $4,$5,$6 delay slot delay slot add $1,$2,$3 if $1=0 then delay slot sub $4,$5,$6 becomes becomes becomes if $2=0 then add $1,$2,$3 add $1,$2,$3 if $1=0 then sub $4,$5,$6 add $1,$2,$3 if $1=0 then sub $4,$5,$6 Limitations on delayed-branch scheduling come from 1) restrictions on the instructions that can be moved/copied into the delay slot and 2) limited ability to predict at compile time whether a branch is likely to be taken or not. In B and C, the use of $1 prevents the add instruction from being moved to the delay slot In B the sub may need to be copied because it could be reached by another path. B is preferred when the branch is taken with high probability (such as loop branches A is the best choice, fills delay slot & reduces instruction count (IC) In B, the sub instruction may need to be copied, increasing IC In B and C, must be okay to execute sub when branch fails 8/30 CS252-Fall’07 CS252 S05
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Delayed Branch Compiler effectiveness for single branch delay slot:
Fills about 60% of branch delay slots About 80% of instructions executed in branch delay slots useful in computation About 50% (60% x 80%) of slots usefully filled Delayed Branch downside: As processor go to deeper pipelines and multiple issue, the branch delay grows and need more than one delay slot Delayed branching has lost popularity compared to more expensive but more flexible dynamic approaches Growth in available transistors has made dynamic approaches relatively cheaper 8/30 CS252-Fall’07 CS252 S05
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Evaluating Branch Alternatives
Assume 4% unconditional branch, 6% conditional branch- untaken, 10% conditional branch-taken Scheduling Branch CPI speedup v. speedup v. scheme penalty unpipelined stall Stall pipeline Predict taken Predict not taken Delayed branch 8/30 CS252-Fall’07 CS252 S05
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Problems with Pipelining
Exception: An unusual event happens to an instruction during its execution Examples: divide by zero, undefined opcode Interrupt: Hardware signal to switch the processor to a new instruction stream Example: a sound card interrupts when it needs more audio output samples (an audio “click” happens if it is left waiting) Problem: It must appear that the exception or interrupt must appear between 2 instructions (Ii and Ii+1) The effect of all instructions up to and including Ii is totalling complete No effect of any instruction after Ii can take place The interrupt (exception) handler either aborts program or restarts at instruction Ii+1 8/30 CS252-Fall’07 CS252 S05
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Precise Exceptions In-Order Pipelines
Key observation: architected state only change in memory and register write stages. CS252 S05
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Summary: Metrics and Pipelining
Machines compared over many metrics Cost, performance, power, reliability, compatibility, … Difficult to compare widely differing machines on benchmark suite Control VIA State Machines and Microprogramming Just overlap tasks; easy if tasks are independent Speed Up Pipeline Depth; if ideal CPI is 1, then: Hazards limit performance on computers: Structural: need more HW resources Data (RAW,WAR,WAW): need forwarding, compiler scheduling Control: delayed branch, prediction Exceptions, Interrupts add complexity Next time: Read Appendix C! 8/30 CS252-Fall’07 CS252 S05
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