Merge branch 'master' of git@github.com:costan/pset_writeups

src/6.823/lab1/all.tex

@@ -0,0 +1,101 @@
+\section{Question 1}
+Figure \ref{q1:frequencies} shows the dependencies obtained as suggested in the
+lab handout.
+
+\begin{figure}[htb]
+  \includegraphics[width=6.8in]{6.823/lab1/figs/frequencies.png}
+  \caption{Instruction dependency frequencies for the 11 benchmarks. }
+  \label{q1:frequencies}.
+\end{figure}
+
+The graph is not too helpful, except to tell us that most instructions depend
+on registers written in the past 4-5 instructions. Therefore, we use figure
+\ref{q1:frequencies_zoom} to take a better look at the dependencies at most 5
+instructions apart.
+
+\begin{figure}[htb]
+  \includegraphics[width=6.8in]{6.823/lab1/figs/frequencies_zoom.png}
+  \caption{Instruction dependency frequencies for the 11 benchmarks. }
+  \label{q1:frequencies_zoom}.
+\end{figure}
+
+Given the dependency statistics, it seesms like architecture A would be
+significantly faster than architecture B. In each benchmark, between 40\% -
+80\% of the instructions depend on the previous instruction. In architecture B,
+all instructions with dependencies on the previous instruction would have to be
+stalled for 1 cycle, while the previous instruction writes its registers. This
+means 40\%-80\% pipeline bubbles, which could be avoided by the forwarding
+circuitry.
+
+\section{Question 2}
+
+Figure \ref{q2:reg_frequencies} shows the per-register breakdown for the
+instruction dependency. For each register and instruction distance, we computed
+the proportion of dependencies that are owed to that register. We averaged the
+values for each benchmark. We only plotted registers which contributed a
+dependency of at least 0.005\% on for at least one distance.
+
+\begin{figure}[htb]
+  \includegraphics[width=6.8in]{6.823/lab1/figs/reg_frequencies.png}
+  \caption{Instruction dependency frequencies broken down by register. }
+  \label{q2:reg_frequencies}.
+\end{figure}
+
+The graph suggests that a few registers are responsible for most dependencies.
+This is not very surprising, given the x86 architecture's predilection to use
+the \texttt{eax} register as an accumulator, \texttt{esi} and \texttt{edi}
+as pointers, and the presence of a condition flags register.
+
+The best (but most difficult to implement) suggestion would be to give the
+instruction set a makeover so it looks more like a RISC instruction set. It's
+not cool to have 8 registers, and instructions with limitations on the registers
+they can use. However, as Alpha found out, this strategy might not work
+commercially.\footnote{One could argue that, even though the strategy failed in
+the 1990s, we're living in a different landscape right now, where many servers
+are running some flavor of UNIX/Linux. So, maybe the instruction set will be
+redesigned one day.}
+
+Assuming we're stuck with the ISA, it seems that (limited) forwarding is very
+worth-while. The dependencies seem to taper off after 4 cycles, so it's
+probably not worth forwarding for more than 4 cycles. This is important in
+super-pipelined architectures, like the latest Pentiums and Core processors.
+
+\section{Question 3}
+The trade-off in the analysis is, in a nutshell, simpler code versus more
+accurate results. Ironically, the best way to measure the trade-off is to
+actually get the accurate results, and see the error. Table \ref{q3:mse} shows
+the MSE (mean-square error) for the histograms for each test, as well as the
+differences in the first 3 frequencies (for distance 1 up to distance 3).
+
+\begin{figure}[htb]
+\center
+\input{6.823/lab1/figs/accurate_delta.tex}
+\caption{The MSE and differences in the first 3 frequencies between accurate
+register accounting and approximating x86 8-bit and 16-bit partial registers
+with the full-length register. }
+\label{q3:mse}
+\end{figure}
+
+The tradeoff is not acceptable to me, since I'm a perfectionist, and I'd rather
+write 100 lines of code (mostly obtained by copy-pasting 5 lines) to get
+``perfect'' (exact) numbers.  However, from a technical perspective, the
+trade-off is perfectly acceptable, because the inacurracy introduced (less than
+1\%) should be significantly smaller than the inaccuracy of counting predicated
+instructions (e.g. the \texttt{rep\_\textit{xx}} opcodes) once, instead of
+accurately counting them.
+
+\section{Question 4}
+
+The graphs suggest that architecture B has less general-purpose registers than
+architecture A. Assuming the compiler is decent (gcc3.4 fits the bill) and its
+optimizations are turned on (which would be expected when running benchmarks),
+I would expect that the compiler will try to minimize the dependencies between
+adjacent instructions (it seems like a good idea, no matter what the pipeline
+length is).
+
+In fact, the huge proportion of distance-1 dependencies in architecture B (80\%)
+makes me guess that the architecture either has very few registers, or some
+opcodes force the use of a certain register as an accumulator (for example,
+early Intel x86 processors forced one of the sources and the destination of {\tt
+mul} and {\tt div} to be {\tt \%eax}, the ``accumulator'' register), or the
+opcodes use the 2-register format ($r_t = r_d$).

src/6.823/lab1/code/accurate_delta.rb

@@ -0,0 +1,40 @@
+#!/usr/bin/env ruby
+#
+# Author:: Victor Costan
+# Copyright:: none
+# License:: Public Domain
+
+require 'rubygems'
+require 'gnuplot'
+require '6.823/lab1/code/lab1common.rb'
+
+bench_cases_fix_names 'original'
+bench_cases_fix_names 'accurate'
+cases = bench_cases
+originals = bench_values(bench_cases)
+accurates = bench_values(bench_cases, 'accurate')
+
+def mse(v1, v2)
+  raise "The vectors don't have the same length" unless v1.length == v2.length
+  Math.sqrt((0...v1.length).map { |i| (v1[i] - v2[i]) ** 2 }.
+                            inject(0) { |acc, n| acc + n } / v1.length)
+end
+
+max_distance = 3
+File.open('6.823/lab1/figs/accurate_delta.tex', 'w') do |f|
+  f.write "\\begin{tabular}{lrrrr}\n\\hline\n"
+  f.write "Test & MSE"
+  1.upto(max_distance) { |d| f.write " & Distance #{d}" }
+  f.write " \\\\\n\\hline\n"
+  originals.keys.sort.each do |name|
+    v1, v2 = originals[name], accurates[name]
+    f.write "#{name} & #{'%.3f' % mse(v1, v2)}\\%"
+    0.upto(max_distance - 1) do |d|
+      f.write ' & '
+      f.write('%+.3f' % (v1[d - 1] - v2[d - 1]))
+      f.write "\\%"
+    end
+    f.write " \\\\\n\\hline\n"
+  end
+  f.write "\\end{tabular}\n"
+end

src/6.823/lab1/code/lab1common.rb

@@ -0,0 +1,61 @@
+#!/usr/bin/env ruby
+#
+# Author:: Victor Costan
+# Copyright:: none
+# License:: Public Domain
+
+
+def bench_cases_fix_names(dir_name = 'original')
+  files = Dir.glob("6.823/lab1/data/#{dir_name}/*")
+
+  files.each_with_index do |file, i|
+    ['.out', '.o'].each do |suffix|
+      len = suffix.length
+      next unless file[-len, len] == suffix
+      File.rename file, file[0...-len]
+      files[i] = file[0...-len]
+    end
+  end  
+end
+
+def bench_cases
+  files = Dir.glob('6.823/lab1/data/original/*')  
+
+  names = files.map { |file| File.basename(file) }.
+                map { |file| file[0...file.index('_base')] }
+  Hash[*names.zip(files).flatten]
+end
+
+def bench_values(cases, base_dir = 'original')  
+  {}.tap do |values|
+    cases.each do |name, file|
+      numbers = File.read(file.gsub('/original/', "/#{base_dir}/")).split(',').
+                     select { |token| !token.empty? }.map { |token| token.to_i }
+      sum = numbers.inject(0) { |acc, n| acc + n }.to_f
+      percentages = numbers.map { |n| n / sum }    
+      values[name] = percentages
+    end
+  end
+end
+
+def bench_detailed_values(cases, base_dir = 'detailed')
+  {}.tap do |values|
+    cases.each do |name, file|
+      reg_stats, numbers = nil, nil
+      File.open(file.gsub('/original/', "/#{base_dir}/"), 'r') do |f|
+        nregs = f.gets.to_i
+        reg_stats = (0...nregs).map do
+          f.gets.strip.split(',').select { |token| !token.empty? }.
+                 map { |token| token.to_i }          
+        end
+        numbers = f.gets.split(',').select { |token| !token.empty? }.
+                         map { |token| token.to_i }
+      end
+      reg_stats.each do |stat|
+        stat.each_index { |i| stat[i] /= numbers[i].to_f }
+      end
+
+      values[name] = {:numbers => numbers, :reg_stats => reg_stats}
+    end
+  end
+end

src/6.823/lab1/code/original_plot.rb

@@ -0,0 +1,54 @@
+#!/usr/bin/env ruby
+#
+# Author:: Victor Costan
+# Copyright:: none
+# License:: Public Domain
+
+# This program needs the gnuplot gem to run. Install with the following command:
+# gem install gnuplot
+
+require 'rubygems'
+require 'gnuplot'
+require '6.823/lab1/code/lab1common.rb'
+
+bench_cases_fix_names 'original'
+bench_cases_fix_names 'accurate'
+cases = bench_cases
+originals = bench_values(bench_cases)
+
+
+Gnuplot.open do |gp|
+  Gnuplot::Plot.new gp do |plot|
+    plot.terminal 'png small size 1024,768'
+    plot.output '6.823/lab1/figs/frequencies.png'
+    plot.ylabel '% Instructions'
+    plot.xlabel 'Distance'
+
+    originals.keys.sort.each do |name|
+      data = originals[name]
+      plot.data << Gnuplot::DataSet.new([(1..data.length).to_a, data]) do |ds|
+        ds.title = name
+        ds.with = 'lines'
+        ds.linewidth = 1
+      end
+    end
+  end
+
+  maxpoints = 4
+  Gnuplot::Plot.new gp do |plot|
+    plot.terminal 'png small size 1024,768'
+    plot.output '6.823/lab1/figs/frequencies_zoom.png'
+    plot.ylabel '% Instructions'
+    plot.xlabel 'Distance'
+
+    originals.keys.sort.each do |name|
+      data = originals[name]
+      plot.data << Gnuplot::DataSet.new([(1..maxpoints).to_a,
+                                        data[0, maxpoints]]) do |ds|
+        ds.title = name
+        ds.with = 'lines'
+        ds.linewidth = 1
+      end
+    end
+  end
+end

src/6.823/lab1/code/per_register_plot.rb

@@ -0,0 +1,43 @@
+#!/usr/bin/env ruby
+#
+# Author:: Victor Costan
+# Copyright:: none
+# License:: Public Domain
+
+# This program needs the gnuplot gem to run. Install with the following command:
+# gem install gnuplot
+
+require 'rubygems'
+require 'gnuplot'
+require '6.823/lab1/code/lab1common.rb'
+
+bench_cases_fix_names 'detailed'
+cases = bench_cases
+details = bench_detailed_values bench_cases, 'detailed'
+
+reg_count = details.values.first[:reg_stats].length
+stat_count = details.values.first[:numbers].length
+register_stats = (0...reg_count).map do |reg|
+  (0...stat_count).map do |i|    
+    details.map { |name, detail| detail[:reg_stats][reg][i] }.
+            inject(0) { |acc, n| acc + n} / details.length
+  end
+end
+
+Gnuplot.open do |gp|
+  Gnuplot::Plot.new gp do |plot|
+    plot.terminal 'png small size 1024,768'
+    plot.output '6.823/lab1/figs/reg_frequencies.png'
+    plot.ylabel '% Instructions'
+    plot.xlabel 'Distance'
+
+    register_stats.each_with_index do |stats, i|
+      next if stats.max < 0.005
+      plot.data << Gnuplot::DataSet.new([(1..stat_count).to_a, stats]) do |ds|
+        ds.title = "Reg #{i}"
+        ds.with = 'lines'
+        ds.linewidth = 1
+      end
+    end
+  end
+end

src/6.823/lab1/data/accurate/applu_base.none_______applu.in

@@ -0,0 +1 @@
+1047108636,252165086,122681484,60136336,111417706,29735778,20414680,48328895,2929923,22280847,969630,4502499,5518819,5597508,5373531,5289723,2992835,1842674,3303019,8141786,2340449,2011381,808271,421024,8591190,533186,338627,3426036,2242165,1212897,3141629,1185065,3019531,1071335,200345,2855576,91893,548276,17557,25717,432974,190469,270029,795646,3913931,464219,947773,526049,156737,107774,856405,589752,907977,8349,5828,19224,100985,1082205,312223,271020,219217,3088243,6846,5233,11663,65382,105916,48104,155000,100508,314612,6099,12062,465649,67238,80753,574981,104630,5783,505184,5477,666922,5403,501715,4355,173814,454992,612018,6755,3876,4026,6136,5372,2675,5255,3808,18520,65020,4099,3215,

src/6.823/lab1/data/accurate/art_base.none___-scanfile___c756hel.in___-trainfile1___a10.img___-stride___2___-startx___134___-starty___220___-endx___139___-endy___225___-objects___1

@@ -0,0 +1 @@
+6758147487,801586904,687232152,15177101,63418426,66219749,354942,5256529,460726,240631,14675443,52249675,25565851,81910,29578342,33304065,11827736,14692804,5090722,359495,11801978,20131665,7888,15313762,27212565,34446255,10213221,14517311,10203861,5110857,180863,5136326,132041,28484026,81063,14149131,5100760,2570612,2541183,5082708,14439193,9853627,5269386,3748514,15598919,2570656,28487293,28951071,5110200,35154,139574,3894560,4705583,2580362,2498829,11326022,1105676,1428115,85869,4145524,17054656,30650,30725,1074376,2549948,16980422,3963858,1118346,1078170,6194652,1422539,1516707,4036781,84715,451,12479395,590,2325,2528651,76158,14690,4242381,2586056,3598,1217775,1087608,2560357,5080576,6531863,1118891,4717841,2159624,1452575,8417971,2945473,89275,1432530,84998,940,30456,

src/6.823/lab1/data/accurate/bzip2_base.x86_linux___input.random___2

@@ -0,0 +1 @@
+4349320624,971428644,887447585,896575489,388201344,280640188,263465006,1283264280,206093193,202730348,322783342,52288372,29139878,29846050,44635284,18154233,67344881,17674364,46753242,40814025,41965613,25233926,13862056,25935100,26866454,14500241,21655249,10893933,18940247,23257898,7614827,15939075,10297264,5311606,2666980,4759805,895830,1121430,1061289,2531807,524890,4091322,9613951,5393736,5359605,6894338,1114355,7807430,2492408,3614488,1743780,1353617,232224,946723,333934,6209357,524414,4356901,715745,519385,2259403,1308745,3085482,4685527,4319920,6403613,2641296,2265548,2099495,1758309,105022,1040010,646687,2627837,6332018,6348205,7354904,6720568,4443859,7792785,3673066,2324632,6631777,2843766,3773060,3832242,2474094,2451063,2910366,4057450,3527456,3876840,1967323,3183026,2512868,3773890,4107077,2210772,2850921,2569145,

src/6.823/lab1/data/accurate/cc1_base.x86_linux___cccp.i___-o___foo

@@ -0,0 +1 @@
+1057145592,235129639,164096770,107005600,81726717,61044318,52223733,42326516,38400880,40919828,28167252,28323446,24440731,17912725,17650310,16878103,13869750,14592789,13317316,11518041,9538504,11502915,8302636,8970440,7624872,7902799,7512973,7254577,6540812,6070650,6175028,4488082,5420195,4537693,3931123,4599335,3899888,3994311,3691171,3918689,4105546,3658000,3138308,2994494,3139518,2718928,2648182,2637298,2151047,1819945,2010288,2164976,1969453,2341430,1874643,1726134,1996265,1794677,1760226,1643142,1611822,1777720,1272701,1295618,1135999,1159825,1159926,1436524,1169731,1207982,969052,1033102,1289916,1040663,937388,862202,1086969,984824,1184942,846939,1114715,827793,803580,691294,750841,806260,834905,688904,840322,738072,754941,675360,486066,548117,719253,590739,748691,592480,613482,607873,

src/6.823/lab1/data/accurate/crafty_base.x86_linux_______crafty.in

@@ -0,0 +1 @@
+4214905136,953933376,584178057,267761334,252848100,108936758,115050063,145879598,79065665,84603724,58727725,89563821,65227853,61050117,60173995,42387409,74713567,60242271,91364883,71686548,73898555,51435741,53659792,41032426,35746627,34182778,35296859,26865945,29428838,33330354,31789307,32500485,29243672,24973540,31529082,33253240,36642116,29755033,33532206,34830389,22189841,25623068,25790692,27511449,25042200,26671559,27603684,33126882,17129881,30205826,23882245,30253123,26894837,34878485,23618409,23829962,26258419,20985966,24306018,19338695,26444087,20436637,15743750,17187486,20807341,22726529,16505708,22302802,21401768,11112484,17627940,15493690,14749793,13823170,13767594,13008208,12878509,11681767,9891715,15683586,12185469,14085056,12295184,15749957,11141818,13009005,12358816,14080537,12669092,13909405,7971506,10956665,13240849,11709425,11108805,11222514,13996867,11566087,11146423,11160238,

src/6.823/lab1/data/accurate/equake_base.none_______inp.in

@@ -0,0 +1 @@
+1752305273,244693639,115173681,75309215,33136602,26183871,31109137,13866605,16583025,12947847,14019898,15582533,17290071,13804907,6022456,15180178,20070806,9561669,9898170,5774490,7872041,7792926,12452771,7953722,934023,10349781,2963685,2187852,5570636,2282926,1670478,3753673,4248030,3377548,2776086,3908091,5005038,3861268,3113310,2136771,3221178,4173497,488208,509106,1566890,1700722,1507096,779660,1349587,2334942,1015311,2089701,1003550,1769242,796766,7802606,1300316,471876,782860,5020711,1261734,1135758,1480060,2021668,630006,513038,713608,767307,753894,1040595,241591,1585138,727161,745703,427480,1335202,1536198,520328,664674,797791,1455298,709726,184397,685492,751603,902247,153589,429824,717140,201551,1638495,262696,1330448,672015,412492,759359,414070,959693,182039,1589405,

src/6.823/lab1/data/accurate/gap_base.x86_linux___-l___input___-q___-m___64M_______test.in

@@ -0,0 +1 @@
+637164513,142093954,87732309,71402717,45966650,44896393,47638471,24462950,21734864,21053316,13410777,12952929,9824035,9909490,8638980,8347952,5332097,5817408,6141256,4992309,8498858,4130178,5251507,5209901,3225440,4023789,3465722,3820539,2487734,2769803,2741300,2453934,2738866,2236524,1912082,2278884,1700746,947455,1989921,1507625,1331954,975472,998956,886451,945781,1142307,1026577,691791,537292,532956,440278,1150783,337645,904950,669212,1153189,351590,377606,833471,380138,448224,1163491,539992,365405,405560,320607,677383,321480,495783,515991,439267,592670,1278592,341018,292613,437299,1041190,335670,308504,407577,417713,519783,303545,318149,571188,246188,225490,224028,317268,260206,204925,159887,323551,306321,276976,140766,131628,283662,207979,192183,

src/6.823/lab1/data/accurate/gzip_base.x86_linux___input.compressed___2

@@ -0,0 +1 @@
+1443493370,328816052,303074799,127123686,149124309,98769574,103732742,26770252,41597523,100644908,31956310,30555925,68000293,23709146,7272735,30967080,4711309,21898880,19925152,15830717,19735923,8831257,17197836,11041789,14095040,29446469,7897247,11613014,8614914,7849031,9140884,3033245,9320359,794061,15120425,10014175,8367753,6572826,14151609,7123246,3183697,5099362,3749745,5447274,2391286,693890,918555,2322228,185147,2167291,1978936,831483,5450751,1346907,5583071,340375,4037128,4009154,92365,878680,627449,1335337,681129,120126,411226,496091,474477,173077,218115,267711,241614,444166,109925,188404,293602,122877,153809,132407,246549,186249,72282,105572,80104,147331,59626,192894,110810,156015,66797,100477,49536,77190,59856,66963,15723,68655,119067,116321,54066,38857,

src/6.823/lab1/data/accurate/mesa_base.none___-frames___10___-meshfile___mesa.in

@@ -0,0 +1 @@
+2012614036,597652299,297926314,219103920,157692810,175723969,164888012,130049991,105403434,71337011,83455200,55627694,61269417,62117427,78066849,30517364,47170727,52377426,27463922,29808877,27480920,33013745,16494964,20073674,28377202,16150778,21923627,21174489,16857483,11778939,14036220,24414049,18680352,14712382,24682916,21701770,6004408,21341776,10713823,11327217,22132897,22019930,11006497,10462516,11258883,12714318,8451667,15331039,13801464,8278684,7576997,17917688,8608361,20167659,20446239,15911445,15470182,4270049,5529064,11773818,6604988,7593217,7917858,3632136,2919961,2656999,10162673,6505206,46972,3945015,1357495,1345947,3955876,28855,3705496,8674424,35103,10852536,46721,5277218,3937399,40103,3967283,6572315,30210,6612199,3608798,14088091,9191984,8851794,7882961,7894622,12784016,3608785,10491045,14111254,3597165,8846841,3603981,3632060,

src/6.823/lab1/data/accurate/parser_base.x86_linux___2.1.dict___-batch_______test.in

@@ -0,0 +1 @@
+2701225550,669887518,421525485,478195162,267275648,175591064,266038996,132519783,105858561,89708772,59474473,46419325,49552088,51366197,31367332,23711043,22346959,26375392,36225939,26321183,13821868,10796693,13147200,17426132,21359526,14686592,17067891,10675837,5792956,3568538,2804089,4554867,2957986,3431430,4942828,4323798,4158625,6266574,5734683,3063459,5906439,6161416,5756628,2780123,4681496,3869578,3730615,3724639,2117755,2642923,2631204,850937,1219781,1259999,1078262,1026711,944134,1409931,1597784,1263946,823815,476448,774500,623919,926993,913595,1156957,1533315,518274,1188092,728976,397962,341793,300364,461988,293152,383352,214621,367123,292870,230572,192091,187601,607244,135005,467976,183096,455637,368800,274335,224291,156214,495431,225666,215143,217354,176710,216648,123633,298530,

src/6.823/lab1/data/accurate/swim_base.none_______swim.in

@@ -0,0 +1 @@
+867515455,85612267,14672425,52018933,22896587,11064485,14981785,1336460,6053813,539929,8139735,3421649,285346,7130,1061233,5253861,6345,8918720,4199029,5774086,2888582,528601,2623214,6298962,3977,2623588,9316,3148808,5244805,2891379,265192,2623858,3676,8362,270282,1402,2623578,264152,1421,2622870,1192,1537,1783,2617425,2623056,2626924,729,1107,904,666,787,5181,2357358,840,837,6170,910,263929,1081,667,773,866,1097,578,4896,1298,743,1118,766,679,466,676,654,812,1012,585,364,461,358,411,360,712,319,510,666,803,366,407,679,456,265,817,539,263,258,581,478,518,630,431,