| %!PS-Adobe-2.0 |
| %%Creator: dvips 5.528 Copyright 1986, 1994 Radical Eye Software |
| %%Title: evalopt.dvi |
| %%CreationDate: Sun Jul 24 09:42:04 1994 |
| %%Pages: 58 |
| %%PageOrder: Ascend |
| %%BoundingBox: 0 0 612 792 |
| %%EndComments |
| %DVIPSCommandLine: dvips -o evalopt.ps evalopt.dvi |
| %DVIPSParameters: dpi=300, comments removed |
| %DVIPSSource: TeX output 1994.07.24:0931 |
| %%BeginProcSet: tex.pro |
| /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N |
| /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 |
| mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} |
| ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale |
| isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div |
| hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul |
| TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get |
| round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{ |
| statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 |
| 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{/nn 8 dict N nn |
| begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X |
| array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo |
| setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{/sf 1 N /fntrx |
| FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]N df-tail}B /E{ |
| pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get} |
| B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 ch-data dup |
| length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B |
| /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type |
| /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp |
| 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 |
| index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff |
| ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice |
| ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 add]{ |
| ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]}if nn |
| /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 |
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| }B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 |
| moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add |
| .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore showpage |
| userdict /eop-hook known{eop-hook}if}N /@start{userdict /start-hook |
| known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X |
| /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for |
| 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0 |
| 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V |
| {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7 |
| getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false} |
| ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale rulex ruley |
| false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex ruley |
| scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave |
| transform round exch round exch itransform moveto rulex 0 rlineto 0 |
| ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta |
| 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail} |
| B /c{-4 M}B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{ |
| 3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p |
| -1 w}B /q{p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{ |
| 3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end |
| %%EndProcSet |
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| %%Page: 3 4 |
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| 839 y(5.7.1)h(Expressions)25 b Fq(:)20 b(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:) |
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| b Ft(32)158 888 y(5.7.2)h(Lo)q(cal)40 b Fq(:)20 b(:)h(:)f(:)g(:)h(:)f |
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| (:)g(:)g(:)h(:)45 b Ft(32)158 938 y(5.7.3)h(Global)17 |
| b Fq(:)j(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:) |
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| (:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:) |
| h(:)45 b Ft(37)158 1478 y(6.2.2)h(Lo)q(op)13 b(Unswitc)o(hing)36 |
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| g(:)h(:)45 b Ft(41)62 1768 y(7.3)d(Multiplying)12 b(Tw)o(o)h(Induction) |
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| (:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:) |
| h(:)45 b Ft(41)62 1818 y(7.4)d(Irreducible)15 b(Lo)q(ops)20 |
| b Fq(:)g(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:) |
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| (Induction)i(V)m(ariables)24 b Fq(:)c(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g |
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| (:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:) |
| g(:)h(:)f(:)g(:)g(:)h(:)45 b Ft(43)158 2017 y(7.6.2)h(Monotonic)13 |
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| %%Page: 4 5 |
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| Fq(:)i(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f |
| (:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:) |
| g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)45 b Ft(51)62 |
| 938 y(B.13)13 b(T)m(era)29 b Fq(:)20 b(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g |
| (:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:) |
| g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g |
| (:)h(:)f(:)g(:)g(:)h(:)45 b Ft(51)62 988 y(B.14)13 b(T)m(exas)h |
| (Instrumen)o(ts)34 b Fq(:)20 b(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g |
| (:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)f(:) |
| g(:)h(:)f(:)g(:)g(:)h(:)f(:)g(:)h(:)f(:)g(:)g(:)h(:)45 |
| b Ft(51)958 2874 y(iv)p eop |
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| 1 5 bop 0 257 a Fu(Chapter)34 b(1)0 423 y(In)m(tro)s(duction)0 |
| 598 y Ft([1)o(])62 648 y(Man)o(y)13 b(p)q(eople)g(in)o(v)o(en)o(t)g |
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| b(While)12 b(I)h(applaud)f(in)o(v)o(en)o(tion,)g(rein)o(v)o(en-)0 |
| 697 y(tion)h(is)h(less)h(in)o(teresting.)j(I)c(am)e(particularly)h |
| (distressed)j(b)o(y)e(inferior)f(approac)o(hes)i(to)f(w)o(ell-understo) |
| q(o)q(d)g(problems.)62 747 y([5,)9 b(8,)h(6,)g(7])62 |
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| b(and)g(record)h(examples)e(and)h(coun)o(ter-examples)62 |
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| 1412 y Fp(1.2)70 b(Related)20 b(W)-6 b(ork)0 1502 y Ft([25)o(])62 |
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| Ft(Not)d(the)g(same)f(as)h(elimination)d(of)i(unreac)o(hable)i(co)q(de) |
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| (ering)i Ft(elimination)11 b(of)i(redundan)o(t)i(computations)0 |
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| g(understand)j(them)965 2874 y(1)p eop |
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| 2 6 bop 0 91 a Fo(1.3.2)55 b(Other)18 b(P)n(ossibilities)0 |
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| 417 y Fn(\017)21 b Ft(instruction)14 b(selection)62 500 |
| y Fn(\017)21 b Ft(v)o(ectorization)62 583 y Fn(\017)g |
| Ft(cac)o(he)15 b(managemen)o(t)62 666 y Fn(\017)21 b |
| Ft(p)q(oin)o(ter/structure/arra)o(y/alias)14 b(analysis)0 |
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| (feature)h(of)e(a)h(compiler,)e(or)i(ev)o(en)g(the)h(optimizer.)62 |
| 832 y Fn(\017)21 b Ft(correctness)62 915 y Fn(\017)g |
| Ft(e\016ciency)15 b(\(time)d(and)i(space\))h({)f(I)f(wish)h(these)i(w)o |
| (ere)e(rep)q(orted)i(along)c(with)i(SPECmarks.)0 998 |
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| 3 7 bop 0 257 a Fu(Chapter)34 b(2)0 423 y(Exp)s(erimen)m(ts)0 |
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| 906 y(h)p Fw(T)o(yp)q(es)13 b Fm(3e)r Fk(i)104 952 y |
| Fi(3)-150 1033 y Fm(3b)116 b Fl("main.c")p Fk(\021)104 |
| 1079 y Fl(#include)16 b("global.h")104 1125 y Fk(h)p |
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| eop |
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| 4 8 bop 0 91 a Ft(compiler)14 b(w)o(as)h(able)g(to)g(optimize)f(the)h |
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| (the)j(size)g(of)f(the)h(sample)e(sets)j(\(the)f(n)o(um)o(b)q(er)f(of)g |
| (times)g(w)o(e)h(ha)o(v)o(e)f(to)g(measure)h(eac)o(h)g(routine\))g(is)f |
| (desirable,)0 307 y(since)h(w)o(e'd)e(lik)o(e)h(the)g(complete)f(set)i |
| (of)e(tests)j(to)d(\014nish)h(is)g(a)g(reasonable)g(time.)j(The)d |
| (assumption)f(of)g(iden)o(tical)g(v)n(ariance)0 357 y(turns)h(out)g |
| (not)f(to)g(matter;)g(that)g(is,)g(under)i(the)f(conditions)f(of)g(our) |
| g(exp)q(erimen)o(t)g(\(t)o(w)o(o)g(sample)g(sets)h(of)f(equal)g |
| (size\),)h(the)0 407 y(test)h(describ)q(ed)h(b)q(elo)o(w)d(is)h(equiv)n |
| (alen)o(t)f(to)h(a)f(v)n(ariance)h(test.)62 457 y(W)m(e)f(b)q(egin)g(b) |
| o(y)f(collecting)h(a)f(sample)g(set)i(for)e(eac)o(h)i(routine)f |
| Fq(x)f Ft(and)h Fq(y)q Ft(,)g(where)i(the)e(n)o(um)o(b)q(er)f(of)g |
| (samples)g(in)h(eac)o(h)g(set)h(is)0 506 y(iden)o(tical)g(and)h(will)e |
| (b)q(e)j(called)e Fq(n)p Ft(.)21 b(\(A)15 b(reasonable)h(n)o(um)o(b)q |
| (er)e(of)g(samples)g(migh)o(t)f(b)q(e)i(10.\))21 b(Compute)14 |
| b(arithmetic)g(means)3 556 y(\026)-24 b Fq(x)14 b Ft(and)i(\026)-24 |
| b Fq(y)16 b Ft(for)d(the)i(sample)e(sets,)h(where)861 |
| 630 y(\026)-24 b Fq(x)12 b Ft(=)942 571 y Ff(P)986 581 |
| y Fe(n)986 614 y(i)p Fv(=1)1049 602 y Fq(x)1073 608 y |
| Fe(i)p 942 621 145 2 v 1002 659 a Fq(n)0 717 y Ft(Compute)h(the)h(v)n |
| (ariance)g Fq(\033)438 723 y Fe(x)473 717 y Ft(and)f |
| Fq(\033)577 723 y Fe(y)611 717 y Ft(for)g(eac)o(h)i(sample)d(set,)j |
| (where)789 837 y Fq(\033)813 843 y Fe(x)845 837 y Ft(=)894 |
| 777 y Ff(P)938 787 y Fe(n)938 821 y(i)p Fv(=1)993 808 |
| y Ft(\()p Fq(x)1033 814 y Fe(i)1056 808 y Fn(\000)d Ft(\026)-23 |
| b Fq(x)p Ft(\))1138 793 y Fv(2)p 894 827 263 2 v 977 |
| 865 a Fq(n)9 b Fn(\000)g Ft(1)0 943 y(Compute)k(an)h(estimate)f(of)g |
| (the)i(p)q(o)q(oled)e(v)n(ariance)j(^)-23 b Fq(\033)q |
| Ft(,)14 b(where)862 1049 y(^)-23 b Fq(\033)13 b Ft(=)946 |
| 1021 y Fq(\033)970 1027 y Fe(x)1000 1021 y Ft(+)c Fq(\033)1065 |
| 1027 y Fe(y)p 946 1040 140 2 v 1005 1078 a Ft(2)0 1152 |
| y(Finally)m(,)i(compute)j(the)g(statistic)g Fq(T)6 b |
| Ft(,)14 b(where)861 1217 y Fq(T)j Ft(=)972 1189 y(\026)-23 |
| b Fq(x)8 b Fn(\000)13 b Ft(\026)-24 b Fq(y)p 951 1207 |
| 134 2 v 951 1216 a Ff(p)p 993 1216 92 2 v 35 x Ft(2)r(^)h |
| Fq(\033)q(=n)0 1324 y Ft(Large)15 b(absolute)f(v)n(alues)h(of)f |
| Fq(T)20 b Ft(suggest)c(that)f(it)f(is)g(unlik)o(ely)g(that)j(\026)-24 |
| b Fq(x)13 b Ft(=)j(\026)-24 b Fq(y)r Ft(.)20 b(Th)o(us,)15 |
| b(if)e Fn(j)p Fq(T)6 b Fn(j)12 b Fq(>)h(t)p Ft(\(2)p |
| Fq(n)d Fn(\000)g Ft(2)p Fq(;)d(p)p Ft(\),)13 b(w)o(e)i(sa)o(y)g(that)i |
| (\026)-24 b Fq(x)0 1374 y Ft(di\013ers)13 b(from)g(\026)-24 |
| b Fq(y)14 b Ft(at)e(the)h Fq(p)f Ft(lev)o(el)g(\(where)h |
| Fq(t)g Ft(is)f(a)f(table)h(of)g(magic)e(v)n(alues)i(copied)h(from)d(a)i |
| (statistics)h(b)q(o)q(ok)f([23)o(,)g(T)m(able)f(A{8]\).)0 |
| 1423 y(F)m(or)i(example,)f(if)g Fq(n)g Ft(=)f(10)i(and)g |
| Fq(T)18 b Ft(=)12 b(2)p Fq(:)p Ft(61,)f(w)o(e)j(can)g(examine)e(the)h |
| (ro)o(w)h(giv)o(en)e(b)o(y)i Fq(t)p Ft(\(18)p Fq(;)7 |
| b Fn(\003)p Ft(\))12 b(in)h(T)m(able)f(2.1)h(and)g(w)o(e)g(see)i(that)0 |
| 1473 y(2)p Fq(:)p Ft(878)10 b Fq(<)i(T)17 b(<)12 b Ft(2)p |
| Fq(:)p Ft(552,)g(leading)h(us)h(to)g(reject)h(the)g(h)o(yp)q(othesis)g |
| (that)h(\026)-24 b Fq(x)12 b Ft(=)i(\026)-23 b Fq(y)q |
| Ft(,)14 b(with)f(less)i(than)f(1\045)f(c)o(hance)i(of)e(error.)0 |
| 1581 y Fs(Cac)o(he)j(P)o(olluti)o(on)0 1658 y Ft(W)m(e)j(use)g(the)h |
| (term)e(\\cac)o(he)i(p)q(ollution")d(to)i(encompass)g(an)g(en)o(tire)g |
| (set)h(of)f(di\016culties)f(in)o(tro)q(duced)i(b)o(y)f(the)g(memory)0 |
| 1708 y(hierarc)o(h)o(y)m(.)g(In)14 b(the)h(w)o(orst)f(case,)h(w)o(e)g |
| (migh)o(t)d(see)j(e\013ects)h(from)d(the)i(data)f(cac)o(he,)g(the)h |
| (instruction)g(cac)o(he,)f(a)g(second-lev)o(el)0 1757 |
| y(cac)o(he,)g(and)g(the)h Fw(TLB)p Ft(.)e(There)i(seem)f(to)f(b)q(e)i |
| (t)o(w)o(o)e(sources)j(of)d(cac)o(he)i(p)q(ollution:)0 |
| 1840 y Fs(self)f(in)o(terference)j Ft(In)11 b(the)g(absence)g(of)f(con) |
| o(text)h(switc)o(hes,)h(w)o(e)e(w)o(ould)g(exp)q(ect)i(that)e(the)h(p)q |
| (ossibilit)o(y)e(of)h(self)g(in)o(terference)104 1890 |
| y(w)o(ould)h(b)q(e)i(minim)o(ized)d(since)j(eac)o(h)g(test)g(is)f |
| (quite)g(small,)e(certainly)i(\014tting)g(in)o(to)g(the)g(I)h(cac)o |
| (he,)g(and)f(only)f(references)p 364 2091 1222 2 v 363 |
| 2137 2 46 v 389 2123 a Fw(Degrees)j(of)p 587 2137 V 430 |
| w(Probabilit)o(y)p 588 2138 998 2 v 363 2182 2 46 v 409 |
| 2169 a(freedom)p 587 2182 V 77 w(0.005)p 738 2182 V 74 |
| w(0.01)p 888 2182 V 72 w(0.025)p 1039 2182 V 74 w(0.05)p |
| 1189 2182 V 92 w(0.1)p 1340 2182 V 92 w(0.15)p 1490 2182 |
| V 66 w Fd(:)6 b(:)g(:)p 364 2184 1222 2 v 363 2260 2 |
| 76 v 471 2213 a Fw(.)471 2229 y(.)471 2246 y(.)p 587 |
| 2260 V 738 2260 V 888 2260 V 1039 2260 V 1189 2260 V |
| 1340 2260 V 1490 2260 V 363 2305 2 46 v 457 2292 a(16)p |
| 587 2305 V 124 w(2.921)p 738 2305 V 64 w(2.583)p 888 |
| 2305 V 63 w(2.120)p 1039 2305 V 64 w(1.746)p 1189 2305 |
| V 63 w(1.363)p 1340 2305 V 64 w(1.071)p 1490 2305 V 363 |
| 2351 V 457 2337 a(17)p 587 2351 V 124 w(2.898)p 738 2351 |
| V 64 w(2.567)p 888 2351 V 63 w(2.110)p 1039 2351 V 64 |
| w(1.740)p 1189 2351 V 63 w(1.333)p 1340 2351 V 64 w(1.069)p |
| 1490 2351 V 363 2397 V 454 2383 a Fc(18)p 587 2397 V |
| 115 w(2.878)p 738 2397 V 50 w(2.552)p 888 2397 V 51 w(2.101)p |
| 1039 2397 V 50 w(1.743)p 1189 2397 V 51 w(1.330)p 1340 |
| 2397 V 50 w(1.067)p 1490 2397 V 363 2442 V 457 2429 a |
| Fw(19)p 587 2442 V 124 w(2.861)p 738 2442 V 64 w(2.539)p |
| 888 2442 V 63 w(2.093)p 1039 2442 V 64 w(1.729)p 1189 |
| 2442 V 63 w(1.328)p 1340 2442 V 64 w(1.066)p 1490 2442 |
| V 363 2488 V 457 2474 a(20)p 587 2488 V 124 w(2.845)p |
| 738 2488 V 64 w(2.528)p 888 2488 V 63 w(2.086)p 1039 |
| 2488 V 64 w(1.725)p 1189 2488 V 63 w(1.325)p 1340 2488 |
| V 64 w(1.064)p 1490 2488 V 363 2564 2 76 v 471 2517 a(.)471 |
| 2534 y(.)471 2550 y(.)p 587 2564 V 738 2564 V 888 2564 |
| V 1039 2564 V 1189 2564 V 1340 2564 V 1490 2564 V 634 |
| 2701 a Fs(T)l(able)15 b(2.1)41 b Ft(Studen)o(t's)15 b |
| Fq(t)f Ft(Distributions)965 2874 y(5)p eop |
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| 6 10 bop 104 91 a Ft(a)12 b(tin)o(y)g(amoun)o(t)f(of)h(data,)g(whic)o |
| (h)h(will)e(easily)h(\014t)h(in)o(to)f(the)h(D)f(cac)o(he.)19 |
| b(A)13 b(single,)f(preliminary)e(run)j(of)f(a)g(test)i(should)104 |
| 141 y(pro)o(v)o(ok)o(e)f(an)o(y)h(initial)e(cac)o(he)i(misses,)f |
| (e\013ectiv)o(ely)i(w)o(arming)d(them)h(up.)104 204 y(Note)j(that)h(a)e |
| (mac)o(hine)g(with)h(a)g(com)o(bined)f(cac)o(he)i(\(v)o(ersus)g |
| (separate)h(I)e(and)g(D)g(cac)o(hes\))h(ma)o(y)d(pro)o(v)o(ok)o(e)i |
| (con\015icts)104 253 y(b)q(et)o(w)o(een)e(instructions)g(and)f(data,)f |
| (particularly)g(in)h(a)f(direct-mapp)q(ed)h(cac)o(he.)19 |
| b(Since)13 b(the)h(con\015ict)f(ma)o(y)e(\(unpred-)104 |
| 303 y(icably\))j(h)o(urt)h(one)g(case)g(without)g(harming)d(another,)j |
| (it)f(w)o(on't)g(really)g(b)q(e)i(p)q(ossible)e(to)h(ensure)h(fair)e |
| (comparisons)104 353 y(on)f(suc)o(h)i(mac)o(hines.)0 |
| 428 y Fs(in)o(terferen)o(ce)e(from)i(other)f(pro)q(cesses)20 |
| b Ft(Besides)13 b(the)e(quan)o(tization)f(errors)i(discussed)h(ab)q(o)o |
| (v)o(e,)e(a)g(con)o(text)g(switc)o(h)h(can)104 478 y(also)h(lea)o(v)o |
| (e)h(the)g(cac)o(he)h(in)e(a)h(non-deterministic)f(state,)h(t)o |
| (ypically)f(pro)o(v)o(oking)f(a)i(string)g(of)f(cac)o(he)i(misses.)104 |
| 541 y(Again,)d(the)i(tactic)g(of)e(using)i(man)o(y)d(runs)j(comes)f(to) |
| g(mind.)j(Unfortunately)m(,)d(the)h(errors)g(in)o(tro)q(duced)h(in)e |
| (this)g(case)104 590 y(are)i Fr(not)h Ft(normally)c(distributed.)23 |
| b(Cac)o(he)15 b(misses)g(alw)o(a)o(ys)f(add)h(to)f(the)i(run)f(time;)f |
| (they)i(nev)o(er)g(decrease)h(it.)k(This)104 640 y(suggests)15 |
| b(using)g(the)g(minim)n(um)10 b(time)j(from)g(sev)o(eral)i(runs)g |
| (rather)g(than)g(computing)d(the)j(mean.)k(Unfortunately)m(,)104 |
| 690 y(this)c(notion)f(con\015icts)i(with)f(our)g(earlier)g(approac)o(h) |
| g(to)g(minim)o(i)o(zing)d(the)k(e\013ects)h(of)d(quan)o(tization)g |
| (errors)j(due)e(to)104 740 y(con)o(text)f(switc)o(hes.)0 |
| 807 y(I)h(don't)f(ha)o(v)o(e)h(a)f(comp)q(elling)f(solution)h(to)h(the) |
| g(problems)f(raised)i(here.)22 b(It)15 b(ma)o(y)e(b)q(e)i(a)g(topic)g |
| (for)f(researc)o(h.)23 b(I'll)13 b(ha)o(v)o(e)i(to)0 |
| 857 y(talk)e(to)h(some)f(statistics)i(p)q(eople)f(ab)q(out)g(it.)j |
| (Things)d(that)g(come)f(to)h(mind:)62 924 y Fn(\017)21 |
| b Ft(Ob)o(viously)m(,)12 b(try)i(to)g(get)g(the)h(mac)o(hine)d(in)i |
| (single-user)g(mo)q(de,)e(or)i(at)g(least)g(ligh)o(tly)e(loaded.)62 |
| 999 y Fn(\017)21 b Ft(If)13 b(the)g(standard)h(deviations)f(seem)g |
| (\\to)q(o)g(high")f(\(more)g(than)i(2)f(clo)q(c)o(k)g(tic)o(ks,)g(ma)o |
| (yb)q(e?\),)e(complain)g(that)i(the)h(data)104 1049 y(is)g(to)q(o)f |
| (noisy)h(and)f(ignore)h(the)g(results.)0 1116 y(Is)d(there)g(an)o(y)f |
| (c)o(hance)i(of)d(b)q(ounding,)i(statistically)m(,)e(the)i(c)o(hance)g |
| (for)f(error?)18 b(I'm)9 b(already)h(unsure)h(ab)q(out)f(the)h(com)o |
| (bination)0 1166 y(of)18 b(running)f(for)h(a)g(long)f(time)g(and)h |
| (running)g(man)o(y)e(times.)30 b(Sure,)19 b(the)g(more/longer)e(w)o(e)h |
| (run)g(the)h(thing,)f(the)h(more)0 1216 y(con\014dence)d(w)o(e)e(can)g |
| (ha)o(v)o(e)g(in)f(our)h(conclusion;)f(but)h(what)g(is)g(the)g(real)g |
| (c)o(hance)h(for)f(error?)0 1329 y Fo(2.2.2)55 b(Practice)0 |
| 1405 y Ft(When)15 b(collecting)f(samples,)g(run)h(once,)h(ignoring)d |
| (the)j(result,)f(just)g(to)g(get)g(the)g(Instruction)h(cac)o(he)g |
| (stable.)21 b(Collect)14 b(10)0 1455 y(times)f(from)f(one,)i(then)g(10) |
| g(timings)d(from)i(the)h(other.)62 1505 y(W)m(ork)f(on)h(tests)h(so)f |
| (that)g(the)h(di\013erences)h(are)e(signi\014can)o(t.)-150 |
| 1567 y Fm(6a)114 b Fk(h)p Fw(Include)14 b(\014les)p Fk(i)e(\021)104 |
| 1613 y Fl(#include)k(<math.h>)104 1659 y Fi(3)0 1717 |
| y Fh(See)11 b(3a,)g Fm(3d,)i(9a)p Fh(.)-150 1772 y Fm(6b)116 |
| b Fl("main.c")p Fk(\021)104 1818 y Fl(int)18 b(test\(int)f(ok,)280 |
| 1864 y(FunPar)h(base_case)o(,)280 1910 y(FunPar)g(test_case)o(,)280 |
| 1955 y(int)h(*data,)280 2001 y(int)g(n,)280 2047 y(char)f(*id\))104 |
| 2092 y({)143 2138 y(int)g(ret_val)f(=)j(0;)143 2184 y(printf\(")75 |
| b(\045d\))19 b(\045s)g(-)g(",)g(n,)g(id\);)143 2229 y(if)g(\(1)g(/*)g |
| (always)e(test,)h(for)g(now)g(*/)h(||)g(ok\))g({)182 |
| 2275 y(double)f(base_tim)o(es[)o(SAM)o(PL)o(ES])o(,)e(test_times[)o(SA) |
| o(MPL)o(ES)o(];)182 2321 y(long)i(int)h(iteration)o(s)e(=)i(determine)o |
| (_i)o(ter)o(ati)o(on)o(s\(b)o(as)o(e_c)o(ase)o(,)d(data\);)182 |
| 2366 y(collect_ti)o(min)o(gs)o(\(it)o(era)o(ti)o(ons)o(,)g(test_case,)g |
| (data,)i(test_time)o(s\);)182 2412 y(collect_ti)o(min)o(gs)o(\(it)o |
| (era)o(ti)o(ons)o(,)e(base_case,)g(data,)i(base_time)o(s\);)182 |
| 2458 y Fk(h)p Fw(Analyze)c(timing)h(results)f Fm(7c)r |
| Fk(i)143 2503 y Fl(})143 2549 y(else)k(puts\("skip)o(pi)o(ng")o(\);)143 |
| 2595 y(return)f(ret_val;)104 2640 y(})104 2686 y Fi(3)0 |
| 2743 y Fh(See)11 b Fm(3b)n(c,)j(8c)n(d,)f(9e,)h(10)p |
| Fh(.)965 2874 y Ft(6)p eop |
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| 7 11 bop -150 78 a Fm(7a)114 b Fk(h)p Fw(Constan)o(ts)p |
| Fk(i)11 b(\021)104 124 y Fl(#define)17 b(SAMPLES)g(10)104 |
| 170 y(/*)i(#define)e(CLOCKS_P)o(ER_)o(SEC)f(1000000)134 |
| b(for)19 b(SPARC)e(*/)104 215 y Fi(3)0 273 y Fh(See)11 |
| b(3b,)g Fm(7d)p Fh(.)-150 353 y Fm(7b)116 b Fk(h)p Fw(Protot)o(yp)q(es) |
| p Fk(i)12 b(\021)104 399 y Fl(long)18 b(int)g(determine_)o(ite)o(rat)o |
| (io)o(ns\()o(Fu)o(nPa)o(r)e(base_case,)692 445 y(int)j(*data\);)104 |
| 536 y(void)f(collect_t)o(imi)o(ng)o(s\(l)o(ong)e(int)i(iterations)o(,) |
| 516 582 y(FunPar)f(routine,)516 627 y(int)h(*data,)516 |
| 673 y(double)f(*times\);)104 719 y Fi(3)0 776 y Fh(See)11 |
| b(3b,)g Fm(4,)h(8e,)i(17,)f(25,)g(32b,)h(39,)f(45c)p |
| Fh(.)0 857 y Ft(Note)h(that)g(w)o(e'v)o(e)g(done)g(a)g(little)f |
| (algebraic)g(manipulation,)e(e\013ectiv)o(ely)j(rewriting)g(the)h |
| (computation)d(of)h Fq(T)20 b Ft(as)773 969 y Fq(T)d |
| Ft(=)12 b(\()s(\026)-24 b Fq(x)9 b Fn(\000)k Ft(\026)-24 |
| b Fq(y)r Ft(\))987 914 y Ff(r)p 1028 914 149 2 v 1090 |
| 941 a Fq(n)p 1033 960 140 2 v 1033 998 a(\033)1057 1004 |
| y Fe(x)1087 998 y Ft(+)10 b Fq(\033)1153 1004 y Fe(y)0 |
| 1087 y Ft(whic)o(h)17 b(lo)q(oks)g(a)g(little)f(uglier,)h(but)h(should) |
| f(sa)o(v)o(e)g(some)g(time)f(and)h(precision.)28 b(Additionally)m(,)15 |
| b(w)o(e)j(tak)o(e)f(care)h(to)f(a)o(v)o(oid)0 1137 y(division)d(b)o(y)i |
| (0.)22 b(This)16 b(is)f(a)h(real)f(p)q(ossibilit)o(y)m(,)f(esp)q |
| (ecially)i(with)f(relativ)o(ely)g(slo)o(w)g(clo)q(c)o(ks.)23 |
| b(It)16 b(do)q(esn't)g(imply)d(an)o(y)i(sort)i(of)0 1186 |
| y(problem;)12 b(it)i(only)f(means)g(that)h(all)e(the)j(times)e |
| (measured)h(for)f(eac)o(h)i(w)o(ere)f(iden)o(tical.)-150 |
| 1268 y Fm(7c)116 b Fk(h)p Fw(Analyze)14 b(timing)h(results)p |
| Fk(i)d(\021)104 1314 y Fl({)143 1360 y(double)17 b(base_mean)f(=)k |
| (mean\(base)o(_t)o(ime)o(s\))o(;)143 1406 y(double)d(test_mean)f(=)k |
| (mean\(test)o(_t)o(ime)o(s\))o(;)143 1451 y(double)d(result)h(=)h |
| (test_mean)d(-)j(base_mean;)143 1497 y(double)e(base_varia)o(nce)f(=)j |
| (variance\(b)o(as)o(e_m)o(ean)o(,)d(base_times\))o(;)143 |
| 1543 y(double)h(test_varia)o(nce)f(=)j(variance\(t)o(es)o(t_m)o(ean)o |
| (,)d(test_times\))o(;)143 1588 y(double)h(sum)i(=)g(base_varia)o(nc)o |
| (e)e(+)i(test_vari)o(anc)o(e;)143 1634 y(if)g(\(sum)f(==)h(0.0\))f({) |
| 182 1680 y(if)h(\(result)e(==)i(0.0\))96 b(ret_val)17 |
| b(=)i(1;)182 1725 y(else)f(if)h(\(result)e(<)i(0.0\))f(ret_val)f(=)i |
| (-1;)143 1771 y(})143 1817 y(else)f({)182 1862 y(result)g(=)h(result)e |
| (*)i(sqrt\(SAMPL)o(ES)d(/)j(sum\);)182 1908 y(if)g(\(fabs\(resu)o(lt)o |
| (\))e(<=)i(CUTOFF\))d(ret_val)h(=)j(1;)182 1954 y(else)e(if)h(\(result) |
| e(<)i(0.0\))116 b(ret_val)17 b(=)j(-1;)143 1999 y(})143 |
| 2045 y(if)f(\(ret_val)d(>)k(0\))136 b(puts\("yes")o(\);)143 |
| 2091 y(else)18 b(if)h(\(ret_val)d(==)j(0\))g(puts\("no"\))o(;)143 |
| 2136 y(else)371 b(puts\("bad)16 b(test"\);)143 2182 y |
| Fk(h)p Fw(Chec)o(k)d(for)g(exceptionally)j(noisy)f(data)e |
| Fm(8a)s Fk(i)104 2228 y Fl(})p Fi(3)0 2285 y Fh(See)e(6b.)0 |
| 2362 y Ft(W)m(e'll)18 b(de\014ne)k Fg(CUTOFF)d Ft(to)h(limit)e(ourselv) |
| o(es)j(to)f(a)g(1\045)f(c)o(hance)j(of)d(mistak)o(enly)g(claiming)e(an) |
| j(optimization)e(w)o(as)i(not)0 2412 y(p)q(erformed.)-150 |
| 2493 y Fm(7d)114 b Fk(h)p Fw(Constan)o(ts)p Fk(i)11 b(\021)104 |
| 2540 y Fl(#define)17 b(CUTOFF)g(2.552)104 2585 y Fi(3)0 |
| 2643 y Fh(See)11 b(3b,)g Fm(7a)p Fh(.)965 2874 y Ft(7)p |
| eop |
| %%Page: 8 13 |
| 8 12 bop -150 78 a Fm(8a)114 b Fk(h)p Fw(Chec)o(k)13 |
| b(for)g(exceptionally)j(noisy)f(data)p Fk(i)c(\021)104 |
| 124 y Fl({)143 170 y(int)18 b(n)i(=)f(noisy\(bas)o(e_v)o(ari)o(an)o |
| (ce\))d(||)j(noisy\(tes)o(t_)o(var)o(ia)o(nce)o(\);)143 |
| 215 y(if)g(\(n\))182 261 y(puts\("\\t\(w)o(arn)o(in)o(g)e(--)i(the)f |
| (timings)f(were)h(not)g(very)g(consistent\))o("\))o(;)143 |
| 307 y(if)h(\(1)g(/*)g(always)e(print,)g(for)i(now)f(*/)h(||)g(n)g(||)g |
| (ret_val)e(==)i(-1\))182 352 y Fk(h)p Fw(Prin)o(t)14 |
| b(times)g(and)f(statistical)j(measures)d Fm(8b)r Fk(i)104 |
| 398 y Fl(})p Fi(3)0 455 y Fh(See)e(7c.)0 520 y Ft(I'v)o(e)j(brok)o(en)g |
| (this)g(out)f(as)h(a)g(separate)h(scrap)g(so)f(I)g(can)g(use)g(it)g |
| (con)o(v)o(enien)o(tly)g(during)f(dev)o(elopmen)o(t)g(of)h(the)g |
| (tests.)-150 593 y Fm(8b)116 b Fk(h)p Fw(Prin)o(t)14 |
| b(times)f(and)h(statistical)h(measures)p Fk(i)d(\021)104 |
| 639 y Fl({)143 685 y(int)18 b(i;)143 730 y(puts\("\\nTi)o(mi)o(ngs)o |
| (\\n)o(\\tb)o(ase)o(-c)o(ase)o(\\t)o(tes)o(t-)o(cas)o(e"\))o(;)143 |
| 776 y(for)g(\(i=0;)g(i<SAMPLES;)e(i++\))182 822 y(printf\("\\t)o |
| (\045-9)o(.3)o(f\\t)o(\045-9)o(.3)o(f\\n)o(",)g(base_times)o([i)o(],)g |
| (test_times)o([i])o(\);)143 867 y(printf\("me)o(an)o(s\\t)o(\045-)o |
| (9.3)o(f\\t)o(\045-)o(9.3)o(f\\)o(n",)g(base_mean)o(,)h(test_mean)o |
| (\);)143 913 y(printf\("va)o(rs)o(\\t\045)o(-9)o(.6f)o(\\t\045)o(-9)o |
| (.6f)o(\\n)o(",)f(base_varia)o(nce)o(,)g(test_varian)o(ce)o(\);)143 |
| 959 y(printf\("sd)o(s\\)o(t\045-)o(9.)o(6f\\)o(t\045-)o(9.)o(6f\\)o(n") |
| o(,)h(sqrt\(base)o(_v)o(ari)o(an)o(ce\))o(,)g(sqrt\(tes)o(t_v)o(ari)o |
| (an)o(ce\))o(\);)143 1004 y(printf\("re)o(su)o(lt\\)o(t\045)o(-9.)o |
| (6f\\)o(n\\)o(n",)f(result\);)104 1050 y(})p Fi(3)0 1107 |
| y Fh(See)11 b(8a.)0 1172 y Ft(W)m(e'll)h(assume)i(the)g(data)g(w)o(as)f |
| (noisy)h(if)f(the)h(standard)h(deviation)e(is)g(more)g(than)h(2)g(tic)o |
| (ks.)-150 1240 y Fm(8c)116 b Fl("main.c")p Fk(\021)104 |
| 1286 y Fl(int)18 b(noisy\(doub)o(le)e(variance\))104 |
| 1332 y({)143 1377 y(double)h(std_dev)g(=)i(sqrt\(varian)o(ce)o(\);)143 |
| 1423 y(return)e(std_dev)g(>)i(2.0)g(/)g(ticks_per_)o(se)o(c;)104 |
| 1468 y(})104 1514 y Fi(3)0 1572 y Fh(See)11 b Fm(3b)n(c,)j(6b,)f(8d,)g |
| (9e,)g(10)p Fh(.)-150 1638 y Fm(8d)114 b Fl("main.c")p |
| Fk(\021)104 1684 y Fl(double)17 b(mean\(doubl)o(e)f(*times\))104 |
| 1729 y({)143 1775 y(int)i(i;)143 1821 y(double)f(sum)i(=)g(0.0;)143 |
| 1866 y(for)f(\(i=0;)g(i<SAMPLES;)e(i++\))182 1912 y(sum)j(+=)g |
| (times[i])o(;)143 1958 y(return)e(sum)i(/)g(SAMPLES;)104 |
| 2003 y(})104 2049 y Fi(3)1003 1684 y Fl(double)e(variance\(d)o(ou)o |
| (ble)f(mean,)i(double)f(*times\))1003 1729 y({)1042 1775 |
| y(int)i(i;)1042 1821 y(double)e(sum)i(=)g(0.0;)1042 1866 |
| y(for)g(\(i=0;)e(i<SAMPLES;)f(i++\))i({)1081 1912 y(double)g(diff)g(=)h |
| (mean)f(-)h(times[i];)1081 1958 y(sum)g(+=)g(diff)f(*)h(diff;)1042 |
| 2003 y(})1042 2049 y(return)e(sum)i(/)g(\(SAMPLES)e(-)i(1\);)1003 |
| 2095 y(})1003 2140 y Fi(3)0 2198 y Fh(See)11 b Fm(3b)n(c,)j(6b,)f(8c,)g |
| (9e,)h(10)p Fh(.)-150 2269 y Fm(8e)116 b Fk(h)p Fw(Protot)o(yp)q(es)p |
| Fk(i)12 b(\021)104 2315 y Fl(double)17 b(mean\(doubl)o(e)f(*times\);) |
| 104 2361 y(double)h(variance\(d)o(ou)o(ble)f(mean,)i(double)f |
| (*times\);)104 2406 y Fi(3)0 2464 y Fh(See)11 b(3b,)g |
| Fm(4,)h(7b,)i(17,)f(25,)g(32b,)h(39,)f(45c)p Fh(.)0 2565 |
| y Fo(2.2.3)55 b(Timing)17 b(Routines)0 2642 y Ft(In)k(the)g(bad)g(old)f |
| (da)o(ys,)h(timing)e(routines)i(w)o(ere)g(fairly)f(mac)o(hine)f(dep)q |
| (enden)o(t)k(and)d(programs)g(lik)o(e)g(this)g(had)h(to)f(b)q(e)0 |
| 2692 y(customized)14 b(for)f(eac)o(h)i(mac)o(hine.)h(F)m(ortunately)m |
| (,)d(there's)i(no)o(w)f(some)f(standardization)g(in)h(the)g(area)g(and) |
| g(w)o(e)g(are)g(able)g(to)0 2742 y(use)h(routines)f(from)e |
| Fw(ANSI)i Ft(C's)g(standard)g(run)o(time)f(library)g(to)h(a)o(v)o(oid)e |
| (some)h(of)g(this)h(p)q(orting)g(e\013ort.)965 2874 y(8)p |
| eop |
| %%Page: 9 14 |
| 9 13 bop -150 78 a Fm(9a)114 b Fk(h)p Fw(Include)14 b(\014les)p |
| Fk(i)e(\021)104 124 y Fl(#include)k(<time.h>)104 170 |
| y Fi(3)0 227 y Fh(See)11 b(3a,)g Fm(3d,)i(6a)p Fh(.)0 |
| 308 y Ft(One)k(migh)o(t)d(think)i(that)h(the)g(v)n(alue)e(of)h |
| Fg(CLOCKS_PER_SEC)d Ft(w)o(ould)j(indicate)g(the)h(n)o(um)o(b)q(er)f |
| (of)f(timer)h(tic)o(ks)g(p)q(er)h(second,)0 358 y(allo)o(wing)12 |
| b(con)o(v)o(enien)o(t)i(determination)f(of)g(the)h(timer)f(resolution.) |
| 18 b(Unfortunately)m(,)13 b(this)h(isn't)f(the)i(case.)k(Some)13 |
| b(systems)0 408 y(de\014ne)i Fg(CLOCKS_PER_SEC)c Ft(to)j(b)q(e)g(a)g(v) |
| o(ery)g(large)f(v)n(alue,)g(despite)i(a)f(fairly)e(coarse)j(timer.)-150 |
| 490 y Fm(9b)116 b Fk(h)p Fw(V)m(ariables)p Fk(i)12 b(\021)104 |
| 536 y Fl(clock_t)17 b(ticks_per)o(_s)o(ec)f(=)k(0;)104 |
| 581 y Fi(3)0 639 y Fh(See)11 b(3b.)-150 713 y Fm(9c)116 |
| b Fk(h)p Fw(Initialize)p Fk(i)14 b(\021)104 759 y Fl({)143 |
| 804 y(clock_t)j(start,)g(diff;)143 850 y Fk(h)p Fw(Mak)o(e)c(sure)h |
| Fl(clock\(\))c Fw(w)o(orks)j(on)g(this)h(system)g Fm(9d)s |
| Fk(i)143 896 y Fl(start)k(=)h(clock\(\);)143 941 y(diff)f(=)h |
| (clock\(\))e(-)i(start;)143 987 y(while)f(\(diff)f(==)i(0\))182 |
| 1033 y(diff)f(=)i(clock\(\))c(-)k(start;)143 1078 y(ticks_per_)o(se)o |
| (c)d(=)38 b(CLOCKS_PER_)o(SE)o(C)17 b(/)i(diff;)143 1124 |
| y(printf\("Ti)o(me)o(r)e(seems)g(to)i(run)g(at)f(\045d)h(ticks/seco)o |
| (nd\\)o(n")o(,)e(ticks_per)o(_s)o(ec\))o(;)104 1170 y(})p |
| Fi(3)0 1227 y Fh(See)11 b(3c.)0 1301 y Ft(Though)16 b |
| Fg(clock)g Ft(is)h(a)g(standard)g(routine,)g(systems)g(are)h(not)e |
| (required)i(to)f(supp)q(ort)g(it;)h(as)f(an)g(alternativ)o(e,)g(they)g |
| (ma)o(y)0 1351 y(return)g Fg(-1)p Ft(.)25 b(On)17 b(suc)o(h)g(systems,) |
| f(an)g(alternativ)o(e)g(approac)o(h)g(will)f(b)q(e)i(required)g(\()p |
| Fr(i.e.,)e Ft(w)o(e're)i(bac)o(k)f(to)g(customizing)f(the)0 |
| 1401 y(co)q(de)g(for)e(ev)o(ery)i(mac)o(hine\).)-150 |
| 1485 y Fm(9d)114 b Fk(h)p Fw(Mak)o(e)13 b(sure)h Fl(clock\(\))c |
| Fw(w)o(orks)j(on)g(this)h(system)p Fk(i)d(\021)104 1531 |
| y Fl({)143 1577 y(if)19 b(\(clock\(\))d(==)j(-1\))g({)182 |
| 1623 y(fputs\("\\nT)o(he)d(routine)h('clock')g(is)i(not)f(supported\\)o |
| (n",)e(stderr\);)182 1668 y(exit\(-1\);)143 1714 y(})104 |
| 1760 y(})p Fi(3)0 1817 y Fh(See)11 b(9c.)-150 1885 y |
| Fm(9e)116 b Fl("main.c")p Fk(\021)104 1931 y Fl(long)18 |
| b(int)g(determine_)o(ite)o(rat)o(io)o(ns\()o(Fu)o(nPa)o(r)e(base_case,) |
| 692 1977 y(int)j(*data\))104 2023 y({)143 2068 y(long)f(int)h(iteratio) |
| o(ns)d(=)k(1;)143 2114 y(base_case\()o(da)o(ta\))o(;)36 |
| b(/*)19 b(an)g(initial,)d(untimed)h(invocation)f(*/)143 |
| 2160 y(while)i(\(1\))g({)182 2205 y(long)g(int)h(i;)182 |
| 2251 y(clock_t)e(start)h(=)h(clock\(\);)182 2297 y(for)g(\(i=0;)e |
| (i<iteration)o(s;)f(i++\))221 2342 y(base_case\(d)o(at)o(a\);)182 |
| 2388 y(if)j(\(\(\(double\))d(clock\(\))h(-)i(start\))e(/)i(CLOCKS_PER_) |
| o(SE)o(C)e(>)i(100.0)f(/)h(ticks_per)o(_se)o(c\))221 |
| 2434 y(return)f(iteration)o(s;)182 2479 y(iterations)e(+=)j(iteration)o |
| (s;)143 2525 y(})104 2571 y(})104 2616 y Fi(3)0 2674 |
| y Fh(See)11 b Fm(3b)n(c,)j(6b,)f(8c)n(d,)h(10)p Fh(.)965 |
| 2874 y Ft(9)p eop |
| %%Page: 10 15 |
| 10 14 bop -150 73 a Fm(10)114 b Fl("main.c")p Fk(\021)104 |
| 119 y Fl(void)18 b(collect_t)o(imi)o(ng)o(s\(l)o(ong)e(int)i |
| (iterations)o(,)516 164 y(FunPar)f(routine,)516 210 y(int)h(*data,)516 |
| 256 y(double)f(*times\))104 301 y({)143 347 y(int)h(i;)143 |
| 393 y(routine\(da)o(ta)o(\);)36 b(/*)19 b(an)g(initial,)d(untimed)h |
| (invocatio)o(n)g(*/)143 438 y(for)h(\(i=0;)g(i<SAMPLES;)e(i++\))i({)182 |
| 484 y(long)g(int)h(j;)182 530 y(clock_t)e(start)h(=)h(clock\(\);)182 |
| 575 y(for)g(\(j=0;)e(j<iteration)o(s;)f(j++\))221 621 |
| y(routine\(dat)o(a\))o(;)182 667 y(times[i])h(=)i(\(\(double\))d |
| (\(clock\(\))h(-)i(start\)\))e(/)i(CLOCKS_PER)o(_S)o(EC;)143 |
| 712 y(})104 758 y(})104 804 y Fi(3)0 861 y Fh(See)11 |
| b Fm(3b)n(c,)j(6b,)f(8c)n(d,)h(9e)p Fh(.)954 2874 y Ft(10)p |
| eop |
| %%Page: 11 16 |
| 11 15 bop 0 257 a Fu(Chapter)34 b(3)0 423 y(Dead)f(Co)s(de)i |
| (Elimination)0 598 y Ft(b)q(est)15 b(approac)o(h)f(is)g(based)g(on)g |
| (use-def)h(c)o(hains)e([15,)c(16,)h(17)o(])62 648 y(using)k(liv)o |
| (eness)g(analysis)f(is)h(inferior)f([9])62 697 y(ref-coun)o(ting)h(is)g |
| (inferior)62 747 y(SSA-based)h(v)o(ersion)f(of)f(use-def)i(c)o(hains)f |
| (is)g(c)o(heap)q(er)h([13)o(,)e(Section)i(7.1])62 797 |
| y(Allo)o(ws)e(remo)o(v)n(al)f(of)h(useless)j(con)o(trol)d(\015o)o(w,)g |
| (and)h(therefore)h(more)e(useless)j(expressions)62 847 |
| y(partially)d(dead)h(co)q(de)62 897 y(within)f(blo)q(c)o(k,)g(across)i |
| (blo)q(c)o(ks,)f(simple)e(lo)q(op,)h(complex)f(lo)q(op)h(case,)i(dead)f |
| (con)o(trol)g(\015o)o(w)f(\(if)g(and)h(lo)q(op\))-150 |
| 981 y Fm(11a)96 b Fk(h)p Fw(Ev)n(aluation)16 b(driv)o(ers)p |
| Fk(i)c(\021)104 1027 y Fl({)143 1073 y(int)18 b(ok;)143 |
| 1118 y(puts\("Dead)e(code)i(eliminati)o(on")o(\);)143 |
| 1164 y Fk(h)p Fw(Dead)c(co)q(de)f(eliminatio)q(n)j Fm(11c,)d |
| Fj(:)6 b(:)g(:)f Fk(i)104 1210 y Fl(})p Fi(3)0 1267 y |
| Fh(See)11 b(3c,)g Fm(18a,)i(26a,)g(33a,)h(40a)p Fh(.)0 |
| 1381 y Fp(3.1)70 b(Lo)r(cal)0 1481 y Fo(3.1.1)55 b(The)19 |
| b(Easiest)e(Case)0 1557 y Ft(This)e(illustrates)h(one)g(of)f(the)h |
| (easiest)g(p)q(ossible)g(cases.)24 b(The)16 b(initialization)d(of)i |
| Fg(j)g Ft(is)h(useless,)h(so)e(the)h(add)g(and)f(the)h(\014rst)0 |
| 1607 y(t)o(w)o(o)d(references)k(to)d Fg(data)f Ft(ma)o(y)f(b)q(e)i |
| (remo)o(v)o(ed,)f(as)h(sho)o(wn)g(in)f(the)i(result)f(case.)-150 |
| 1684 y Fm(11b)98 b Fl("dead.c")p Fk(\021)104 1730 y Fl(void)18 |
| b(dead_test)o(1\(i)o(nt)e(*data\))104 1776 y({)143 1821 |
| y(int)i(j)i(=)f(data[0])e(+)i(data[1];)143 1867 y(j)g(=)g(data[2];)143 |
| 1913 y(data[j])e(=)i(2;)104 1958 y(})104 2004 y Fi(3)1297 |
| 1730 y Fl(void)f(dead_resul)o(t1)o(\(in)o(t)f(*data\))1297 |
| 1776 y({)1336 1821 y(int)i(j;)1336 1867 y(j)g(=)h(data[2];)1336 |
| 1913 y(data[j])d(=)i(2;)1297 1958 y(})1297 2004 y Fi(3)0 |
| 2061 y Fh(See)11 b Fm(12ac,)i(13ac,)h(14ac,)g(15ac,)g(16ac)p |
| Fh(.)0 2142 y Ft(This)g(bit)g(of)g(co)q(de)h(is)g(t)o(ypical)e(of)h |
| (the)h(w)o(a)o(y)f(w)o(e'll)f(in)o(v)o(ok)o(e)g Fg(test)p |
| Ft(.)19 b(W)m(e)14 b(initialize)f(a)h(small)e(arra)o(y)i(of)g(data,)g |
| (then)h(call)e Fg(test)p Ft(,)0 2192 y(passing)f(in)g(the)h(test)g |
| (data)f(and)g(the)h(t)o(w)o(o)e(routines)i(to)f(b)q(e)h(compared.)k |
| (The)12 b(\014rst)h(parameter)f(is)g(simply)e(a)i(\015ag)g(indicating)0 |
| 2242 y(the)j(test)g(is)e(to)h(b)q(e)h(p)q(erformed)e(\(in)h(other)g |
| (cases,)h(w)o(e'll)e(pass)h(in)g(a)g(v)n(ariable)e(con)o(trolling)h |
| (whether)i(the)g(comparison)d(is)i(to)0 2291 y(b)q(e)h(p)q(erformed)e |
| (or)h(skipp)q(ed\).)19 b(The)14 b(last)g(t)o(w)o(o)f(parameters)h(are)g |
| (used)h(to)f(iden)o(tify)f(the)h(test.)-150 2376 y Fm(11c)98 |
| b Fk(h)p Fw(Dead)14 b(co)q(de)f(eliminatio)q(n)p Fk(i)h(\021)104 |
| 2422 y Fl({)143 2467 y(int)k(data[3])f(=)j({)f(0,)g(1,)g(2)g(};)143 |
| 2513 y(ok)g(=)g(test\(1,)e(dead_resul)o(t1)o(,)g(dead_tes)o(t1,)f |
| (data,)i(1,)g("basic)g(block"\);)104 2559 y(})p Fi(3)0 |
| 2616 y Fh(See)11 b(11a,)f Fm(12b)n(d,)k(13b)n(d,)g(14b)n(d,)g(15b)n(d,) |
| g(16b)n(d)p Fh(.)954 2874 y Ft(11)p eop |
| %%Page: 12 17 |
| 12 16 bop 0 91 a Fo(3.1.2)55 b(Sligh)n(tly)18 b(More)g(Complex)-150 |
| 155 y Fm(12a)96 b Fl("dead.c")p Fk(\021)104 201 y Fl(void)18 |
| b(dead_test)o(2\(i)o(nt)e(*data\))104 247 y({)143 292 |
| y(int)i(j)i(=)f(data[0])e(+)i(data[1];)143 338 y(int)f(k)i(=)f(j)g(+)g |
| (data[2];)143 384 y(int)f(m)i(=)f(k)g(+)g(data[3];)143 |
| 429 y(int)f(n)i(=)f(m)g(+)g(data[4];)143 475 y(j)g(=)g(data[2];)143 |
| 521 y(data[j])e(=)i(2;)104 566 y(})104 612 y Fi(3)1297 |
| 201 y Fl(void)f(dead_resul)o(t2)o(\(in)o(t)f(*data\))1297 |
| 247 y({)1336 292 y(int)i(j;)1336 338 y(j)g(=)h(data[2];)1336 |
| 384 y(data[j])d(=)i(2;)1297 429 y(})1297 475 y Fi(3)0 |
| 669 y Fh(See)11 b Fm(11b,)i(12c,)h(13ac,)g(14ac,)f(15ac,)h(16ac)p |
| Fh(.)-150 750 y Fm(12b)98 b Fk(h)p Fw(Dead)14 b(co)q(de)f(eliminatio)q |
| (n)p Fk(i)h(\021)104 796 y Fl({)143 841 y(int)k(data[5])f(=)j({)f(0,)g |
| (1,)g(2,)f(3,)h(4)g(};)143 887 y(ok)g(=)g(test\(ok,)e(dead_resu)o(lt)o |
| (2,)f(dead_test2)o(,)h(data,)g(2,)i("basic)e(block"\);)104 |
| 933 y(})p Fi(3)0 990 y Fh(See)11 b(11a,)f Fm(11c,)k(12d,)f(13b)n(d,)h |
| (14b)n(d,)g(15b)n(d,)g(16b)n(d)p Fh(.)0 1105 y Fp(3.2)70 |
| b(Global)0 1204 y Fo(3.2.1)55 b(Across)19 b(Basic)g(Blo)r(c)n(ks)0 |
| 1281 y Fs(Easy)-150 1343 y Fm(12c)98 b Fl("dead.c")p |
| Fk(\021)104 1389 y Fl(void)18 b(dead_test)o(3\(i)o(nt)e(*data\))104 |
| 1435 y({)143 1480 y(int)i(k)i(=)f(0;)143 1526 y(int)f(j)i(=)f(data[1];) |
| 143 1571 y(if)g(\(j\))f({)182 1617 y(k++;)182 1663 y(j)h(=)h(k)f(+)g |
| (data[0])e(*)i(j;)143 1708 y(})143 1754 y(else)182 1800 |
| y(k--;)143 1845 y(j)g(=)g(data[2];)143 1891 y(data[j])e(=)i(2;)143 |
| 1937 y(data[3])e(=)i(k;)104 1982 y(})104 2028 y Fi(3)1297 |
| 1389 y Fl(void)f(dead_resul)o(t3)o(\(in)o(t)f(*data\))1297 |
| 1435 y({)1336 1480 y(int)i(k)g(=)g(0;)1336 1526 y(int)g(j)g(=)g |
| (data[1];)1336 1571 y(if)g(\(j\))1375 1617 y(k++;)1336 |
| 1663 y(else)1375 1708 y(k--;)1336 1754 y(j)g(=)h(data[2];)1336 |
| 1800 y(data[j])d(=)i(2;)1336 1845 y(data[3])e(=)i(k;)1297 |
| 1891 y(})1297 1937 y Fi(3)0 2086 y Fh(See)11 b Fm(11b,)i(12a,)h(13ac,)f |
| (14ac,)h(15ac,)g(16ac)p Fh(.)-150 2166 y Fm(12d)96 b |
| Fk(h)p Fw(Dead)14 b(co)q(de)f(eliminatio)q(n)p Fk(i)h(\021)104 |
| 2212 y Fl({)143 2258 y(int)k(data[4])f(=)j({)f(0,)g(1,)g(2)g(};)143 |
| 2303 y(ok)g(=)g(test\(ok,)e(dead_resu)o(lt)o(3,)f(dead_test3)o(,)h |
| (data,)g(3,)i("across)e(basic)h(blocks"\);)104 2349 y(})p |
| Fi(3)0 2406 y Fh(See)11 b(11a,)f Fm(11c,)k(12b,)f(13b)n(d,)h(14b)n(d,)g |
| (15b)n(d,)g(16b)n(d)p Fh(.)954 2874 y Ft(12)p eop |
| %%Page: 13 18 |
| 13 17 bop 0 91 a Fs(More)16 b(In)o(terestin)o(g)-150 |
| 153 y Fm(13a)96 b Fl("dead.c")p Fk(\021)104 199 y Fl(void)18 |
| b(dead_test)o(4\(i)o(nt)e(*data\))104 245 y({)143 291 |
| y(int)i(k)i(=)f(0;)143 336 y(int)f(j)i(=)f(data[1];)143 |
| 382 y(if)g(\(j\))f({)182 428 y(k++;)182 473 y(j)h(=)h(k)f(+)g(j)g(*)h |
| (data[0];)143 519 y(})143 565 y(else)182 610 y(k--;)143 |
| 656 y(if)f(\(data[4])d(&)k(1\))182 702 y(k++;)143 747 |
| y(else)e({)182 793 y(k--;)182 839 y(j++;)143 884 y(})143 |
| 930 y(j)h(=)g(data[2];)143 976 y(data[j])e(=)i(2;)143 |
| 1021 y(data[3])e(=)i(k;)104 1067 y(})104 1113 y Fi(3)1297 |
| 199 y Fl(void)f(dead_resul)o(t4)o(\(in)o(t)f(*data\))1297 |
| 245 y({)1336 291 y(int)i(k)g(=)g(0;)1336 336 y(int)g(j)g(=)g(data[1];) |
| 1336 382 y(if)g(\(j\))1375 428 y(k++;)1336 473 y(else)1375 |
| 519 y(k--;)1336 565 y(if)g(\(data[4])e(&)i(1\))1375 610 |
| y(k++;)1336 656 y(else)1375 702 y(k--;)1336 747 y(j)g(=)h(data[2];)1336 |
| 793 y(data[j])d(=)i(2;)1336 839 y(data[3])e(=)i(k;)1297 |
| 884 y(})1297 930 y Fi(3)0 1170 y Fh(See)11 b Fm(11b,)i(12ac,)h(13c,)g |
| (14ac,)f(15ac,)h(16ac)p Fh(.)-150 1250 y Fm(13b)98 b |
| Fk(h)p Fw(Dead)14 b(co)q(de)f(eliminatio)q(n)p Fk(i)h(\021)104 |
| 1296 y Fl({)143 1342 y(int)k(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3,)h(4)g |
| (};)143 1388 y(ok)g(=)g(test\(ok,)e(dead_resu)o(lt)o(4,)f(dead_test4)o |
| (,)h(data,)g(4,)i("across)e(basic)h(blocks"\);)104 1433 |
| y(})p Fi(3)0 1491 y Fh(See)11 b(11a,)f Fm(11c,)k(12b)n(d,)g(13d,)f(14b) |
| n(d,)h(15b)n(d,)g(16b)n(d)p Fh(.)0 1594 y Fo(3.2.2)55 |
| b(Around)20 b(Lo)r(ops)0 1671 y Fs(Simple)-150 1733 y |
| Fm(13c)98 b Fl("dead.c")p Fk(\021)104 1779 y Fl(void)18 |
| b(dead_test)o(5\(i)o(nt)e(*data\))104 1825 y({)143 1870 |
| y(int)i(i,)h(j;)143 1916 y(int)f(k)i(=)f(0;)143 1962 |
| y(int)f(stop)h(=)g(data[0];)143 2007 y(for)f(\(i=0;)g(i<stop;)f(i++\))h |
| ({)182 2053 y(k)h(=)h(k)f(*)g(data[1];)182 2099 y(j)g(=)h(data[2];)182 |
| 2144 y(data[j])d(=)i(2;)143 2190 y(})104 2236 y(})104 |
| 2281 y Fi(3)1297 1779 y Fl(void)f(dead_resul)o(t5)o(\(in)o(t)f(*data\)) |
| 1297 1825 y({)1336 1870 y(int)i(i,)g(j;)1336 1916 y(int)g(stop)f(=)h |
| (data[0];)1336 1962 y(for)g(\(i=0;)e(i<stop;)g(i++\))h({)1375 |
| 2007 y(j)i(=)f(data[2];)1375 2053 y(data[j])e(=)j(2;)1336 |
| 2099 y(})1297 2144 y(})1297 2190 y Fi(3)0 2339 y Fh(See)11 |
| b Fm(11b,)i(12ac,)h(13a,)f(14ac,)h(15ac,)g(16ac)p Fh(.)-150 |
| 2419 y Fm(13d)96 b Fk(h)p Fw(Dead)14 b(co)q(de)f(eliminatio)q(n)p |
| Fk(i)h(\021)104 2465 y Fl({)143 2511 y(int)k(data[3])f(=)j({)f(2,)g(1,) |
| g(2)g(};)143 2556 y(ok)g(=)g(test\(ok,)e(dead_resu)o(lt)o(5,)f |
| (dead_test5)o(,)h(data,)g(5,)i("around)e(loops"\);)104 |
| 2602 y(})p Fi(3)0 2660 y Fh(See)11 b(11a,)f Fm(11c,)k(12b)n(d,)g(13b,)f |
| (14b)n(d,)h(15b)n(d,)g(16b)n(d)p Fh(.)954 2874 y Ft(13)p |
| eop |
| %%Page: 14 19 |
| 14 18 bop 0 91 a Fs(In)o(terestin)o(g)-150 153 y Fm(14a)96 |
| b Fl("dead.c")p Fk(\021)104 199 y Fl(void)18 b(dead_test)o(6\(i)o(nt)e |
| (*data\))104 245 y({)143 291 y(int)i(i;)143 336 y(int)g(k)i(=)f(0;)143 |
| 382 y(int)f(m)i(=)f(0;)143 428 y(int)f(n)i(=)f(0;)143 |
| 473 y(int)f(stop)h(=)g(data[0];)143 519 y(for)f(\(i=0;)g(i<stop;)f |
| (i++\))h({)182 565 y(int)h(j)g(=)g(data[1];)182 610 y(if)g(\(j\))g({) |
| 221 656 y(n)h(=)f(j)g(*)g(stop)f(+)i(m;)221 702 y(k++;)182 |
| 747 y(})182 793 y(else)e({)221 839 y(m)i(=)f(n)g(*)g(stop)f(+)i(k;)221 |
| 884 y(k--;)182 930 y(})182 976 y(j)f(=)h(data[2];)182 |
| 1021 y(data[j])d(=)i(2;)143 1067 y(})143 1113 y(data[3])e(=)i(k;)104 |
| 1158 y(})104 1204 y Fi(3)1297 199 y Fl(void)f(dead_resul)o(t6)o(\(in)o |
| (t)f(*data\))1297 245 y({)1336 291 y(int)i(i;)1336 336 |
| y(int)g(k)g(=)g(0;)1336 382 y(int)g(m)g(=)g(0;)1336 428 |
| y(int)g(n)g(=)g(0;)1336 473 y(int)g(stop)f(=)h(data[0];)1336 |
| 519 y(for)g(\(i=0;)e(i<stop;)g(i++\))h({)1375 565 y(int)h(j)g(=)g |
| (data[1];)1375 610 y(if)g(\(j\))1415 656 y(k++;)1375 |
| 702 y(else)1415 747 y(k--;)1375 793 y(j)h(=)f(data[2];)1375 |
| 839 y(data[j])e(=)j(2;)1336 884 y(})1336 930 y(data[3])d(=)i(k;)1297 |
| 976 y(})1297 1021 y Fi(3)0 1261 y Fh(See)11 b Fm(11b,)i(12ac,)h(13ac,)g |
| (14c,)f(15ac,)h(16ac)p Fh(.)-150 1342 y Fm(14b)98 b Fk(h)p |
| Fw(Dead)14 b(co)q(de)f(eliminatio)q(n)p Fk(i)h(\021)104 |
| 1388 y Fl({)143 1433 y(int)k(data[4])f(=)j({)f(2,)g(1,)g(2)g(};)143 |
| 1479 y(ok)g(=)g(test\(ok,)e(dead_resu)o(lt)o(6,)f(dead_test6)o(,)h |
| (data,)g(6,)i("around)e(loops"\);)104 1525 y(})p Fi(3)0 |
| 1582 y Fh(See)11 b(11a,)f Fm(11c,)k(12b)n(d,)g(13b)n(d,)g(14d,)f(15b)n |
| (d,)h(16b)n(d)p Fh(.)0 1697 y Fp(3.3)70 b(Dead)22 b(Con)n(trol)h(Flo)n |
| (w)0 1796 y Fo(3.3.1)55 b(Conditionals)0 1873 y Fs(Simple)-150 |
| 1935 y Fm(14c)98 b Fl("dead.c")p Fk(\021)104 1981 y Fl(void)18 |
| b(dead_test)o(7\(i)o(nt)e(*data\))104 2026 y({)143 2072 |
| y(int)i(k)i(=)f(0;)143 2118 y(int)f(j)i(=)f(data[2];)143 |
| 2163 y(data[j])e(=)i(2;)143 2209 y(if)g(\(j\))f(k++;)143 |
| 2255 y(else)g(k--;)104 2300 y(})104 2346 y Fi(3)1297 |
| 1981 y Fl(void)g(dead_resul)o(t7)o(\(in)o(t)f(*data\))1297 |
| 2026 y({)1336 2072 y(int)i(j)g(=)g(data[2];)1336 2118 |
| y(data[j])e(=)i(2;)1297 2163 y(})1297 2209 y Fi(3)0 2404 |
| y Fh(See)11 b Fm(11b,)i(12ac,)h(13ac,)g(14a,)f(15ac,)h(16ac)p |
| Fh(.)-150 2484 y Fm(14d)96 b Fk(h)p Fw(Dead)14 b(co)q(de)f(eliminatio)q |
| (n)p Fk(i)h(\021)104 2530 y Fl({)143 2576 y(int)k(data[3])f(=)j({)f(0,) |
| g(1,)g(2)g(};)143 2621 y(ok)g(=)g(test\(1,)e(dead_resul)o(t7)o(,)g |
| (dead_tes)o(t7,)f(data,)i(7,)g("useless)f(conditiona)o(ls)o("\);)104 |
| 2667 y(})p Fi(3)0 2724 y Fh(See)11 b(11a,)f Fm(11c,)k(12b)n(d,)g(13b)n |
| (d,)g(14b,)f(15b)n(d,)h(16b)n(d)p Fh(.)954 2874 y Ft(14)p |
| eop |
| %%Page: 15 20 |
| 15 19 bop 0 91 a Fs(In)o(terestin)o(g)-150 153 y Fm(15a)96 |
| b Fl("dead.c")p Fk(\021)104 199 y Fl(void)18 b(dead_test)o(8\(i)o(nt)e |
| (*data\))104 245 y({)143 291 y(int)i(i;)143 336 y(int)g(k)i(=)f(0;)143 |
| 382 y(int)f(stop)h(=)g(data[0];)143 428 y(for)f(\(i=0;)g(i<stop;)f |
| (i++\))h({)182 473 y(int)h(j)g(=)g(data[1])e(+)i(k;)182 |
| 519 y(if)g(\(j\))g(k++;)182 565 y(else)f(k--;)182 610 |
| y(j)h(=)h(data[2];)182 656 y(data[j])d(=)i(2;)143 702 |
| y(})104 747 y(})104 793 y Fi(3)1297 199 y Fl(void)f(dead_resul)o(t8)o |
| (\(in)o(t)f(*data\))1297 245 y({)1336 291 y(int)i(i;)1336 |
| 382 y(int)g(stop)f(=)h(data[0];)1336 428 y(for)g(\(i=0;)e(i<stop;)g |
| (i++\))h({)1375 473 y(int)h(j;)1375 519 y(j)h(=)f(data[2];)1375 |
| 565 y(data[j])e(=)j(2;)1336 610 y(})1297 656 y(})1297 |
| 702 y Fi(3)0 850 y Fh(See)11 b Fm(11b,)i(12ac,)h(13ac,)g(14ac,)f(15c,)h |
| (16ac)p Fh(.)-150 931 y Fm(15b)98 b Fk(h)p Fw(Dead)14 |
| b(co)q(de)f(eliminatio)q(n)p Fk(i)h(\021)104 977 y Fl({)143 |
| 1022 y(int)k(data[3])f(=)j({)f(2,)g(1,)g(2)g(};)143 1068 |
| y(ok)g(=)g(test\(ok,)e(dead_resu)o(lt)o(8,)f(dead_test8)o(,)h(data,)g |
| (8,)i("useless)e(condition)o(al)o(s"\))o(;)104 1114 y(})p |
| Fi(3)0 1171 y Fh(See)11 b(11a,)f Fm(11c,)k(12b)n(d,)g(13b)n(d,)g(14b)n |
| (d,)f(15d,)h(16b)n(d)p Fh(.)0 1274 y Fo(3.3.2)55 b(Lo)r(ops)0 |
| 1351 y Fs(Conserv)m(ativ)o(e)-150 1405 y Fm(15c)98 b |
| Fl("dead.c")p Fk(\021)104 1451 y Fl(void)18 b(dead_test)o(9\(i)o(nt)e |
| (*data\))104 1496 y({)143 1542 y(int)i(k)i(=)f(0;)143 |
| 1588 y(int)f(j;)143 1633 y(for)g(\(j=0;)g(j<5;)g(j++\))g(k++;)143 |
| 1679 y(j)h(=)g(data[2];)143 1725 y(data[j])e(=)i(2;)104 |
| 1770 y(})104 1816 y Fi(3)1297 1451 y Fl(void)f(dead_resul)o(t9)o(\(in)o |
| (t)f(*data\))1297 1496 y({)1336 1542 y(int)i(j;)1336 |
| 1588 y(j)g(=)h(data[2];)1336 1633 y(data[j])d(=)i(2;)1297 |
| 1679 y(})1297 1725 y Fi(3)0 1874 y Fh(See)11 b Fm(11b,)i(12ac,)h(13ac,) |
| g(14ac,)f(15a,)h(16ac)p Fh(.)-150 1954 y Fm(15d)96 b |
| Fk(h)p Fw(Dead)14 b(co)q(de)f(eliminatio)q(n)p Fk(i)h(\021)104 |
| 2000 y Fl({)143 2046 y(int)k(data[3])f(=)j({)f(0,)g(1,)g(2)g(};)143 |
| 2091 y(ok)g(=)g(test\(1,)e(dead_resul)o(t9)o(,)g(dead_tes)o(t9,)f |
| (data,)i(9,)g("useless)f(loops)h(\(conserva)o(ti)o(ve\))o("\))o(;)104 |
| 2137 y(})p Fi(3)0 2194 y Fh(See)11 b(11a,)f Fm(11c,)k(12b)n(d,)g(13b)n |
| (d,)g(14b)n(d,)f(15b,)h(16b)n(d)p Fh(.)0 2292 y Fs(Aggressiv)o(e)0 |
| 2369 y Ft(Remo)o(ving)h(a)h(lo)q(op)h(with)g(unkno)o(wn)f(b)q(ounds)i |
| (\(a)f(p)q(oten)o(tially)f(in\014nite)h(lo)q(op\))f(ma)o(y)g(c)o(hange) |
| h(the)h(b)q(eha)o(viour)f(of)f(a)h(non-)0 2418 y(terminating)12 |
| b(program.)954 2874 y(15)p eop |
| %%Page: 16 21 |
| 16 20 bop -150 73 a Fm(16a)96 b Fl("dead.c")p Fk(\021)104 |
| 119 y Fl(void)18 b(dead_test)o(10\()o(in)o(t)f(*data\))104 |
| 164 y({)143 210 y(int)h(k)i(=)f(0;)143 256 y(int)f(j;)143 |
| 301 y(for)g(\(j=0;)g(j<data[0];)e(j++\))i(k++;)143 347 |
| y(j)h(=)g(data[2];)143 393 y(data[j])e(=)i(2;)104 438 |
| y(})104 484 y Fi(3)1277 119 y Fl(void)f(dead_result)o(10)o(\(in)o(t)f |
| (*data\))1277 164 y({)1317 210 y(int)h(j;)1317 256 y(j)h(=)g(data[2];) |
| 1317 301 y(data[j])e(=)i(2;)1277 347 y(})1277 393 y Fi(3)0 |
| 542 y Fh(See)11 b Fm(11b,)i(12ac,)h(13ac,)g(14ac,)f(15ac,)h(16c)p |
| Fh(.)-150 622 y Fm(16b)98 b Fk(h)p Fw(Dead)14 b(co)q(de)f(eliminatio)q |
| (n)p Fk(i)h(\021)104 668 y Fl({)143 714 y(int)k(data[3])f(=)j({)f(2,)g |
| (1,)g(2)g(};)143 759 y(\(void\))e(test\(ok,)g(dead_resu)o(lt1)o(0,)f |
| (dead_test1)o(0,)g(data,)i(10,)g("useless)f(loops)g(\(aggressiv)o(e\)") |
| o(\);)104 805 y(})p Fi(3)0 862 y Fh(See)11 b(11a,)f Fm(11c,)k(12b)n(d,) |
| g(13b)n(d,)g(14b)n(d,)f(15b)n(d,)h(16d)p Fh(.)0 977 y |
| Fp(3.4)70 b(P)n(artially)21 b(Dead)i(Co)r(de)0 1068 y |
| Ft(Remo)o(v)n(al)7 b(of)i(partially-dead)f(co)q(de)i(is)g(actually)f |
| (an)g(unrelated)i(optimization;)c(it's)j(closer)g(in)f(spirit)h(to)f |
| (partial)g(redundancy)0 1118 y(elimination.)15 b(2)f(pap)q(ers)g(in)g |
| (PLDI)g('94.)j(This)c(case)i(can)f(b)q(e)h(done)f(b)o(y)g(a)f(simple)g |
| (forw)o(ard)g(propagation.)-150 1194 y Fm(16c)98 b Fl("dead.c")p |
| Fk(\021)104 1241 y Fl(void)18 b(dead_test)o(11\()o(in)o(t)f(*data\))104 |
| 1286 y({)143 1332 y(int)h(i)i(=)f(data[0];)143 1378 y(int)f(j)i(=)f |
| (data[1];)143 1423 y(int)f(k)i(=)f(i)g(*)g(j;)143 1469 |
| y(if)g(\(i)g(&)g(j\))182 1515 y(data[0])e(=)i(k;)143 |
| 1560 y(j)g(=)g(data[2];)143 1606 y(data[j])e(=)i(2;)104 |
| 1652 y(})104 1697 y Fi(3)1277 1241 y Fl(void)f(dead_result)o(11)o(\(in) |
| o(t)f(*data\))1277 1286 y({)1317 1332 y(int)h(i)h(=)h(data[0];)1317 |
| 1378 y(int)e(j)h(=)h(data[1];)1317 1423 y(if)e(\(i)h(&)h(j\))1356 |
| 1469 y(data[0])d(=)i(i)g(*)g(j;)1317 1515 y(j)g(=)g(data[2];)1317 |
| 1560 y(data[j])e(=)i(2;)1277 1606 y(})1277 1652 y Fi(3)0 |
| 1755 y Fh(See)11 b Fm(11b,)i(12ac,)h(13ac,)g(14ac,)f(15ac,)h(16a)p |
| Fh(.)-150 1835 y Fm(16d)96 b Fk(h)p Fw(Dead)14 b(co)q(de)f(eliminatio)q |
| (n)p Fk(i)h(\021)104 1881 y Fl({)143 1927 y(int)k(data[3])f(=)j({)f(0,) |
| g(1,)g(2)g(};)143 1972 y(\(void\))e(test\(1,)g(dead_resul)o(t11)o(,)f |
| (dead_test11)o(,)g(data,)i(11,)h("partial)o(ly)d(dead"\);)104 |
| 2018 y(})p Fi(3)0 2076 y Fh(See)11 b(11a,)f Fm(11c,)k(12b)n(d,)g(13b)n |
| (d,)g(14b)n(d,)f(15b)n(d,)h(16b)p Fh(.)954 2874 y Ft(16)p |
| eop |
| %%Page: 17 22 |
| 17 21 bop 0 91 a Fp(3.5)70 b(Protot)n(yp)r(es)-150 176 |
| y Fm(17)114 b Fk(h)p Fw(Protot)o(yp)q(es)p Fk(i)12 b(\021)104 |
| 222 y Fl(extern)17 b(void)h(dead_test1)o(\(in)o(t)e(*data\);)104 |
| 268 y(extern)h(void)h(dead_test2)o(\(in)o(t)e(*data\);)104 |
| 314 y(extern)h(void)h(dead_test3)o(\(in)o(t)e(*data\);)104 |
| 359 y(extern)h(void)h(dead_test4)o(\(in)o(t)e(*data\);)104 |
| 405 y(extern)h(void)h(dead_test5)o(\(in)o(t)e(*data\);)104 |
| 451 y(extern)h(void)h(dead_test6)o(\(in)o(t)e(*data\);)104 |
| 496 y(extern)h(void)h(dead_test7)o(\(in)o(t)e(*data\);)104 |
| 542 y(extern)h(void)h(dead_test8)o(\(in)o(t)e(*data\);)104 |
| 588 y(extern)h(void)h(dead_test9)o(\(in)o(t)e(*data\);)104 |
| 633 y(extern)h(void)h(dead_test1)o(0\(i)o(nt)e(*data\);)104 |
| 679 y(extern)h(void)h(dead_test1)o(1\(i)o(nt)e(*data\);)104 |
| 725 y Fi(3)1121 222 y Fl(extern)h(void)h(dead_resu)o(lt1)o(\(i)o(nt)e |
| (*data\);)1121 268 y(extern)h(void)h(dead_resu)o(lt2)o(\(i)o(nt)e |
| (*data\);)1121 314 y(extern)h(void)h(dead_resu)o(lt3)o(\(i)o(nt)e |
| (*data\);)1121 359 y(extern)h(void)h(dead_resu)o(lt4)o(\(i)o(nt)e |
| (*data\);)1121 405 y(extern)h(void)h(dead_resu)o(lt5)o(\(i)o(nt)e |
| (*data\);)1121 451 y(extern)h(void)h(dead_resu)o(lt6)o(\(i)o(nt)e |
| (*data\);)1121 496 y(extern)h(void)h(dead_resu)o(lt7)o(\(i)o(nt)e |
| (*data\);)1121 542 y(extern)h(void)h(dead_resu)o(lt8)o(\(i)o(nt)e |
| (*data\);)1121 588 y(extern)h(void)h(dead_resu)o(lt9)o(\(i)o(nt)e |
| (*data\);)1121 633 y(extern)h(void)h(dead_resu)o(lt1)o(0\()o(int)e |
| (*data\);)1121 679 y(extern)h(void)h(dead_resu)o(lt1)o(1\()o(int)e |
| (*data\);)1121 725 y Fi(3)0 782 y Fh(See)11 b(3b,)g Fm(4,)h(7b,)i(8e,)f |
| (25,)g(32b,)h(39,)f(45c)p Fh(.)954 2874 y Ft(17)p eop |
| %%Page: 18 23 |
| 18 22 bop 0 257 a Fu(Chapter)34 b(4)0 423 y(Constan)m(t)h(Propagation)0 |
| 598 y Ft(Best)15 b(is)f([21)o(,)c(22)o(])62 648 y(com)o(bines)j |
| (constan)o(t)i(prop)f(with)f(elimination)e(of)i(unreac)o(hable)i(co)q |
| (de)62 697 y(ideal)e(time)g(to)h(con)o(v)o(ert)g(m)o(ultiplies)e(in)o |
| (to)h(shifts,)g(adds,)h(and)g(subtracts)h([7])62 747 |
| y(can)f(tak)o(e)g(further)h(adv)n(an)o(tage)e(of)g(conditionals)g |
| (\(assertion)i(stu\013)s(\))62 797 y(basic)h(blo)q(c)o(k,)e(extended)j |
| (basic)e(blo)q(c)o(k,)g(dominance,)f(global)f(\(p)q(essimistic\),)i |
| (global)f(\(optimistic\),)f(conditional)h(con-)0 847 |
| y(stan)o(t,)g(reasso)q(ciation,)f(through)h(\015oats,)g(in)o(trinsics)g |
| (\(but)g(this)g(is)g(C\))62 897 y(ma)o(yb)q(e)f(c)o(hec)o(k)i(for)e(o)o |
| (v)o(er\015o)o(ws)-150 978 y Fm(18a)96 b Fk(h)p Fw(Ev)n(aluation)16 |
| b(driv)o(ers)p Fk(i)c(\021)104 1025 y Fl({)143 1070 y(int)18 |
| b(ok;)143 1116 y(puts\("Cons)o(ta)o(nt)e(propagatio)o(n"\))o(;)143 |
| 1162 y Fk(h)p Fw(Constan)o(t)d(propagation)j Fm(18c,)d |
| Fj(:)6 b(:)g(:)f Fk(i)104 1207 y Fl(})p Fi(3)0 1264 y |
| Fh(See)11 b(3c,)g Fm(11a,)i(26a,)g(33a,)h(40a)p Fh(.)0 |
| 1379 y Fp(4.1)70 b(Lo)r(cal)0 1478 y Fo(4.1.1)55 b(Constan)n(t)20 |
| b(F)-5 b(olding)-150 1542 y Fm(18b)98 b Fl("cprop.c")p |
| Fk(\021)104 1588 y Fl(void)18 b(cprop_tes)o(t1\()o(in)o(t)f(*data\))104 |
| 1634 y({)143 1679 y(int)h(j)i(=)f(1)g(+)g(2)h(*)f(4;)143 |
| 1725 y(data[0])e(=)i(j;)104 1771 y(})104 1816 y Fi(3)1277 |
| 1588 y Fl(void)f(cprop_resul)o(t1)o(\(in)o(t)f(*data\))1277 |
| 1634 y({)1317 1679 y(int)h(j)h(=)h(9;)1317 1725 y(data[0])d(=)i(j;)1277 |
| 1771 y(})1277 1816 y Fi(3)0 1874 y Fh(See)11 b Fm(19ac)n(e,)j(20b)n(d,) |
| g(21ac,)g(22ac)n(e,)g(23b)n(d,)g(24a)p Fh(.)-150 1954 |
| y Fm(18c)98 b Fk(h)p Fw(Constan)o(t)13 b(propagation)p |
| Fk(i)h(\021)104 2000 y Fl({)143 2046 y(int)k(data[1];)143 |
| 2092 y(ok)h(=)g(test\(1,)e(cprop_resu)o(lt)o(1,)f(cprop_test)o(1,)g |
| (data,)i(1,)h("folding")o(\);)104 2137 y(})p Fi(3)0 2195 |
| y Fh(See)11 b(18a,)f Fm(19b)n(d,)k(20ac)n(e,)g(21b)n(d,)g(22b)n(d,)g |
| (23ac)n(e,)h(24b)p Fh(.)954 2874 y Ft(18)p eop |
| %%Page: 19 24 |
| 19 23 bop 0 91 a Fo(4.1.2)55 b(Propagating)19 b(through)g(Expressions) |
| -150 155 y Fm(19a)96 b Fl("cprop.c")p Fk(\021)104 201 |
| y Fl(void)18 b(cprop_tes)o(t2\()o(in)o(t)f(*data\))104 |
| 247 y({)143 292 y(int)h(j)i(=)f(1;)143 338 y(int)f(k)i(=)f(2;)143 |
| 384 y(int)f(m)i(=)f(4;)143 429 y(int)f(n)i(=)f(k)g(*)g(m;)143 |
| 475 y(j)g(=)g(n)h(+)f(j;)143 521 y(data[0])e(=)i(j;)104 |
| 566 y(})104 612 y Fi(3)1277 201 y Fl(void)f(cprop_resul)o(t2)o(\(in)o |
| (t)f(*data\))1277 247 y({)1317 292 y(int)h(j;)1317 338 |
| y(j)h(=)g(9;)1317 384 y(data[0])e(=)i(j;)1277 429 y(})1277 |
| 475 y Fi(3)0 669 y Fh(See)11 b Fm(18b,)i(19c)n(e,)h(20b)n(d,)g(21ac,)g |
| (22ac)n(e,)g(23b)n(d,)g(24a)p Fh(.)-150 750 y Fm(19b)98 |
| b Fk(h)p Fw(Constan)o(t)13 b(propagation)p Fk(i)h(\021)104 |
| 796 y Fl({)143 841 y(int)k(data[1];)143 887 y(ok)h(=)g(test\(ok,)e |
| (cprop_res)o(ul)o(t2,)f(cprop_tes)o(t2,)g(data,)h(2,)i("basic)f |
| (block"\);)104 933 y(})p Fi(3)0 990 y Fh(See)11 b(18a,)f |
| Fm(18c,)k(19d,)f(20ac)n(e,)h(21b)n(d,)g(22b)n(d,)g(23ac)n(e,)h(24b)p |
| Fh(.)0 1105 y Fp(4.2)70 b(Global)0 1204 y Fo(4.2.1)55 |
| b(Extended)18 b(Basic)g(Blo)r(c)n(ks)-150 1258 y Fm(19c)98 |
| b Fl("cprop.c")p Fk(\021)104 1304 y Fl(void)18 b(cprop_tes)o(t3\()o(in) |
| o(t)f(*data\))104 1350 y({)143 1395 y(int)h(j)i(=)f(12345;)143 |
| 1441 y(if)g(\(data[0]\))182 1487 y(data[1])e(=)i(1)h(+)f(j)g(-)g(1234;) |
| 143 1532 y(else)182 1578 y(data[2])e(=)i(123)g(+)g(j)g(+)h(10;)104 |
| 1624 y(})104 1669 y Fi(3)1277 1304 y Fl(void)e(cprop_resul)o(t3)o(\(in) |
| o(t)f(*data\))1277 1350 y({)1317 1395 y(if)h(\(data[0]\))1356 |
| 1441 y(data[1])f(=)i(11112;)1317 1487 y(else)1356 1532 |
| y(data[2])e(=)i(12478;)1277 1578 y(})1277 1624 y Fi(3)0 |
| 1727 y Fh(See)11 b Fm(18b,)i(19ae,)h(20b)n(d,)g(21ac,)g(22ac)n(e,)g |
| (23b)n(d,)g(24a)p Fh(.)-150 1807 y Fm(19d)96 b Fk(h)p |
| Fw(Constan)o(t)13 b(propagation)p Fk(i)h(\021)104 1853 |
| y Fl({)143 1899 y(int)k(data[3])f(=)j({)f(1)g(};)143 |
| 1945 y(ok)g(=)g(test\(ok,)e(cprop_res)o(ul)o(t3,)f(cprop_tes)o(t3,)g |
| (data,)h(3,)i("extended)d(basic)i(blocks"\);)104 1990 |
| y(})p Fi(3)0 2048 y Fh(See)11 b(18a,)f Fm(18c,)k(19b,)f(20ac)n(e,)i |
| (21b)n(d,)e(22b)n(d,)h(23ac)n(e,)h(24b)p Fh(.)0 2131 |
| y Ft(This)f(one)g(exp)q(oses)h(a)f(problem)e(I)i(stum)o(bled)f(across)i |
| (in)e(gcc)i(\(ok)f(with)f Fg(-O2)p Ft(\).)-150 2210 y |
| Fm(19e)98 b Fl("cprop.c")p Fk(\021)104 2256 y Fl(void)18 |
| b(cprop_tes)o(t4\()o(in)o(t)f(*data\))104 2302 y({)143 |
| 2347 y(int)h(j)i(=)f(12345;)143 2393 y(if)g(\(data[0]\))182 |
| 2439 y(data[1])e(=)i(1)h(+)f(j)g(-)g(1234;)143 2484 y(else)182 |
| 2530 y(data[2])e(=)i(123)g(-)g(j)g(+)h(10;)104 2576 y(})104 |
| 2621 y Fi(3)1277 2256 y Fl(void)e(cprop_resul)o(t4)o(\(in)o(t)f |
| (*data\))1277 2302 y({)1317 2393 y(if)h(\(data[0]\))1356 |
| 2439 y(data[1])f(=)i(11112;)1317 2484 y(else)1356 2530 |
| y(data[2])e(=)i(-12212;)1277 2576 y(})1277 2621 y Fi(3)0 |
| 2679 y Fh(See)11 b Fm(18b,)i(19ac,)h(20b)n(d,)g(21ac,)g(22ac)n(e,)g |
| (23b)n(d,)g(24a)p Fh(.)954 2874 y Ft(19)p eop |
| %%Page: 20 25 |
| 20 24 bop -150 78 a Fm(20a)96 b Fk(h)p Fw(Constan)o(t)13 |
| b(propagation)p Fk(i)h(\021)104 124 y Fl({)143 170 y(int)k(data[3])f(=) |
| j({)f(1)g(};)143 215 y(\(void\))e(test\(ok,)g(cprop_res)o(ult)o(4,)f |
| (cprop_test)o(4,)g(data,)i(4,)h("extende)o(d)e(basic)g(blocks"\);)104 |
| 261 y(})p Fi(3)0 319 y Fh(See)11 b(18a,)f Fm(18c,)k(19b)n(d,)g(20c)n |
| (e,)g(21b)n(d,)g(22b)n(d,)g(23ac)n(e,)g(24b)p Fh(.)0 |
| 422 y Fo(4.2.2)55 b(Dominators)-150 476 y Fm(20b)98 b |
| Fl("cprop.c")p Fk(\021)104 522 y Fl(void)18 b(cprop_tes)o(t5\()o(in)o |
| (t)f(*data\))104 568 y({)143 613 y(int)h(j)i(=)f(5;)143 |
| 659 y(if)g(\(data[0]\))182 705 y(data[1])e(=)i(10;)143 |
| 750 y(else)182 796 y(data[2])e(=)i(15;)143 842 y(data[3])e(=)i(j)g(+)h |
| (21;)104 887 y(})104 933 y Fi(3)1277 522 y Fl(void)e(cprop_resul)o(t5)o |
| (\(in)o(t)f(*data\))1277 568 y({)1317 613 y(if)h(\(data[0]\))1356 |
| 659 y(data[1])f(=)i(10;)1317 705 y(else)1356 750 y(data[2])e(=)i(15;) |
| 1317 796 y(data[3])e(=)i(26;)1277 842 y(})1277 887 y |
| Fi(3)0 990 y Fh(See)11 b Fm(18b,)i(19ac)n(e,)i(20d,)e(21ac,)h(22ac)n |
| (e,)g(23b)n(d,)g(24a)p Fh(.)-150 1071 y Fm(20c)98 b Fk(h)p |
| Fw(Constan)o(t)13 b(propagation)p Fk(i)h(\021)104 1117 |
| y Fl({)143 1162 y(int)k(data[4])f(=)j({)f(1)g(};)143 |
| 1208 y(ok)g(=)g(test\(ok,)e(cprop_res)o(ul)o(t5,)f(cprop_tes)o(t5,)g |
| (data,)h(5,)i("dominator)o(s"\))o(;)104 1254 y(})p Fi(3)0 |
| 1311 y Fh(See)11 b(18a,)f Fm(18c,)k(19b)n(d,)g(20ae,)f(21b)n(d,)h(22b)n |
| (d,)g(23ac)n(e,)h(24b)p Fh(.)0 1392 y Ft(Still)f(more)g(o)q(dd)h |
| (problems)f(with)h(gcc.)22 b(The)15 b(m)o(ultiplies)e(don't)h(seem)h |
| (to)g(pro)o(v)o(ok)o(e)g(the)h(problem;)d(it)i(also)f(app)q(ears)i |
| (with)0 1442 y(simple)c(adds.)-150 1519 y Fm(20d)96 b |
| Fl("cprop.c")p Fk(\021)104 1565 y Fl(void)18 b(cprop_tes)o(t6\()o(in)o |
| (t)f(*data\))104 1611 y({)143 1656 y(int)h(j)i(=)f(5;)143 |
| 1702 y(if)g(\(data[0]\))182 1748 y(data[1])e(=)i(j)h(*)f(10;)143 |
| 1793 y(else)182 1839 y(data[2])e(=)i(j)h(*)f(15;)143 |
| 1885 y(data[3])e(=)i(j)g(*)h(21;)104 1930 y(})104 1976 |
| y Fi(3)1277 1565 y Fl(void)e(cprop_resul)o(t6)o(\(in)o(t)f(*data\))1277 |
| 1611 y({)1317 1656 y(if)h(\(data[0]\))1356 1702 y(data[1])f(=)i(50;) |
| 1317 1748 y(else)1356 1793 y(data[2])e(=)i(75;)1317 1839 |
| y(data[3])e(=)i(105;)1277 1885 y(})1277 1930 y Fi(3)0 |
| 2034 y Fh(See)11 b Fm(18b,)i(19ac)n(e,)i(20b,)e(21ac,)h(22ac)n(e,)g |
| (23b)n(d,)g(24a)p Fh(.)-150 2114 y Fm(20e)98 b Fk(h)p |
| Fw(Constan)o(t)13 b(propagation)p Fk(i)h(\021)104 2160 |
| y Fl({)143 2205 y(int)k(data[4])f(=)j({)f(1)g(};)143 |
| 2251 y(\(void\))e(test\(ok,)g(cprop_res)o(ult)o(6,)f(cprop_test)o(6,)g |
| (data,)i(6,)h("dominat)o(ors)o("\);)104 2297 y(})p Fi(3)0 |
| 2354 y Fh(See)11 b(18a,)f Fm(18c,)k(19b)n(d,)g(20ac,)f(21b)n(d,)h(22b)n |
| (d,)g(23ac)n(e,)h(24b)p Fh(.)954 2874 y Ft(20)p eop |
| %%Page: 21 26 |
| 21 25 bop 0 91 a Fo(4.2.3)55 b(D)n(A)n(Gs)-150 145 y |
| Fm(21a)96 b Fl("cprop.c")p Fk(\021)104 191 y Fl(void)18 |
| b(cprop_tes)o(t7\()o(in)o(t)f(*data\))104 237 y({)143 |
| 283 y(int)h(j;)143 328 y(if)h(\(data[0]\))d({)182 374 |
| y(j)j(=)h(5;)182 420 y(data[1])d(=)i(10;)143 465 y(})143 |
| 511 y(else)f({)182 557 y(data[2])f(=)i(15;)182 602 y(j)g(=)h(5;)143 |
| 648 y(})143 694 y(data[3])d(=)i(j)g(+)h(21;)104 739 y(})104 |
| 785 y Fi(3)1277 191 y Fl(void)e(cprop_resul)o(t7)o(\(in)o(t)f(*data\)) |
| 1277 237 y({)1317 283 y(if)h(\(data[0]\))1356 328 y(data[1])f(=)i(10;) |
| 1317 374 y(else)1356 420 y(data[2])e(=)i(15;)1317 465 |
| y(data[3])e(=)i(26;)1277 511 y(})1277 557 y Fi(3)0 842 |
| y Fh(See)11 b Fm(18b,)i(19ac)n(e,)i(20b)n(d,)e(21c,)h(22ac)n(e,)g(23b)n |
| (d,)g(24a)p Fh(.)-150 923 y Fm(21b)98 b Fk(h)p Fw(Constan)o(t)13 |
| b(propagation)p Fk(i)h(\021)104 969 y Fl({)143 1014 y(int)k(data[4])f |
| (=)j({)f(1)g(};)143 1060 y(ok)g(=)g(test\(ok,)e(cprop_res)o(ul)o(t7,)f |
| (cprop_tes)o(t7,)g(data,)h(7,)i("dags"\);)104 1106 y(})p |
| Fi(3)0 1163 y Fh(See)11 b(18a,)f Fm(18c,)k(19b)n(d,)g(20ac)n(e,)g(21d,) |
| f(22b)n(d,)h(23ac)n(e,)h(24b)p Fh(.)0 1244 y Ft(Here's)h(a)e(similar)e |
| (lo)q(oking)h(case)i(that)g(I)f(don't)g(exp)q(ect)i(an)o(y)o(one)e(to)h |
| (get,)f(though)g(it)h(could)f(b)q(e)h(handled)f(b)o(y)h(\014rst)g |
| (cloning)0 1294 y(the)f(blo)q(c)o(k)g(con)o(taining)f(the)h(assignmen)o |
| (t)f(to)h Fg(data[3])p Ft(.)-150 1371 y Fm(21c)98 b Fl("cprop.c")p |
| Fk(\021)104 1417 y Fl(void)18 b(cprop_tes)o(t8\()o(in)o(t)f(*data\))104 |
| 1462 y({)143 1508 y(int)h(j,)h(k;)143 1554 y(if)g(\(data[0]\))d({)182 |
| 1599 y(j)j(=)h(4;)182 1645 y(k)f(=)h(6;)182 1691 y(data[1])d(=)i(j;)143 |
| 1736 y(})143 1782 y(else)f({)182 1828 y(j)h(=)h(7;)182 |
| 1873 y(k)f(=)h(3;)182 1919 y(data[2])d(=)i(k;)143 1965 |
| y(})143 2010 y(data[3])e(=)i(\(j)g(+)g(k\))g(*)g(21;)104 |
| 2056 y(})104 2102 y Fi(3)1277 1417 y Fl(void)f(cprop_resul)o(t8)o(\(in) |
| o(t)f(*data\))1277 1462 y({)1317 1508 y(if)h(\(data[0]\))1356 |
| 1554 y(data[1])f(=)i(4;)1317 1599 y(else)1356 1645 y(data[2])e(=)i(3;) |
| 1317 1691 y(data[3])e(=)i(210;)1277 1736 y(})1277 1782 |
| y Fi(3)0 2159 y Fh(See)11 b Fm(18b,)i(19ac)n(e,)i(20b)n(d,)e(21a,)h |
| (22ac)n(e,)g(23b)n(d,)g(24a)p Fh(.)-150 2239 y Fm(21d)96 |
| b Fk(h)p Fw(Constan)o(t)13 b(propagation)p Fk(i)h(\021)104 |
| 2286 y Fl({)143 2331 y(int)k(data[4])f(=)j({)f(1)g(};)143 |
| 2377 y(\(void\))e(test\(ok,)g(cprop_res)o(ult)o(8,)f(cprop_test)o(8,)g |
| (data,)i(8,)h("dags)e(\(hard\)"\);)104 2423 y(})p Fi(3)0 |
| 2480 y Fh(See)11 b(18a,)f Fm(18c,)k(19b)n(d,)g(20ac)n(e,)g(21b,)f(22b)n |
| (d,)h(23ac)n(e,)h(24b)p Fh(.)954 2874 y Ft(21)p eop |
| %%Page: 22 27 |
| 22 26 bop 0 91 a Fo(4.2.4)55 b(Lo)r(ops)-150 155 y Fm(22a)96 |
| b Fl("cprop.c")p Fk(\021)104 201 y Fl(void)18 b(cprop_tes)o(t9\()o(in)o |
| (t)f(*data\))104 247 y({)143 292 y(int)h(i;)143 338 y(int)g(stop)h(=)g |
| (data[0];)143 384 y(int)f(j)i(=)f(21;)143 429 y(for)f(\(i=1;)g(i<stop;) |
| f(i++\))182 475 y(j)i(=)h(\(j)f(-)g(20\))f(*)h(21;)143 |
| 521 y(data[1])e(=)i(j;)143 566 y(data[2])e(=)i(i;)104 |
| 612 y(})104 658 y Fi(3)1277 201 y Fl(void)f(cprop_resul)o(t9)o(\(in)o |
| (t)f(*data\))1277 247 y({)1317 292 y(int)h(i;)1317 338 |
| y(int)g(stop)g(=)h(data[0];)1317 384 y(for)f(\(i=1;)g(i<stop;)f(i++\)) |
| 1356 429 y(;)1317 475 y(data[1])g(=)i(21;)1317 521 y(data[2])e(=)i(i;) |
| 1277 566 y(})1277 612 y Fi(3)0 715 y Fh(See)11 b Fm(18b,)i(19ac)n(e,)i |
| (20b)n(d,)e(21ac,)h(22c)n(e,)g(23b)n(d,)g(24a)p Fh(.)-150 |
| 786 y Fm(22b)98 b Fk(h)p Fw(Constan)o(t)13 b(propagation)p |
| Fk(i)h(\021)104 833 y Fl({)143 878 y(int)k(data[3])f(=)j({)f(2)g(};)143 |
| 924 y(ok)g(=)g(test\(ok,)e(cprop_res)o(ul)o(t9,)f(cprop_tes)o(t9,)g |
| (data,)h(9,)i("loops"\);)104 970 y(})p Fi(3)0 1027 y |
| Fh(See)11 b(18a,)f Fm(18c,)k(19b)n(d,)g(20ac)n(e,)g(21b)n(d,)g(22d,)f |
| (23ac)n(e,)i(24b)p Fh(.)0 1140 y Fp(4.3)70 b(Conditional)21 |
| b(Constan)n(ts)-150 1208 y Fm(22c)98 b Fl("cprop.c")p |
| Fk(\021)104 1255 y Fl(void)18 b(cprop_tes)o(t10)o(\(i)o(nt)e(*data\)) |
| 104 1300 y({)143 1346 y(int)i(j)i(=)f(1;)143 1391 y(if)g(\(j\))f(j)i(=) |
| f(10;)143 1437 y(else)57 b(j)20 b(=)f(data[0];)143 1483 |
| y(data[0])e(=)i(j)g(*)h(21)e(+)i(data[1];)104 1528 y(})104 |
| 1574 y Fi(3)1258 1255 y Fl(void)e(cprop_res)o(ult)o(10)o(\(in)o(t)f |
| (*data\))1258 1300 y({)1297 1346 y(data[0])g(=)i(210)g(+)g(data[1];) |
| 1258 1391 y(})1258 1437 y Fi(3)0 1632 y Fh(See)11 b Fm(18b,)i(19ac)n |
| (e,)i(20b)n(d,)e(21ac,)h(22ae,)g(23b)n(d,)g(24a)p Fh(.)-150 |
| 1703 y Fm(22d)96 b Fk(h)p Fw(Constan)o(t)13 b(propagation)p |
| Fk(i)h(\021)104 1749 y Fl({)143 1795 y(int)k(data[2])f(=)j({)f(1,)g(2)g |
| (};)143 1840 y(ok)g(=)g(test\(1,)e(cprop_resu)o(lt)o(10,)f(cprop_tes)o |
| (t10)o(,)g(data,)i(10,)h("conditi)o(ona)o(l)e(constant)o(s"\))o(;)104 |
| 1886 y(})p Fi(3)0 1944 y Fh(See)11 b(18a,)f Fm(18c,)k(19b)n(d,)g(20ac)n |
| (e,)g(21b)n(d,)g(22b,)f(23ac)n(e,)i(24b)p Fh(.)0 2016 |
| y Ft(The)h(previous)h(test)g(migh)o(t)c(ha)o(v)o(e)j(b)q(een)h(passed)g |
| (successfully)g(b)o(y)f(running)g(a)f(relativ)o(ely)h(simple)e(constan) |
| o(t)i(propagator)0 2066 y(rep)q(eatedly)g(if)e(unreac)o(hable)h(co)q |
| (de)g(is)g(remo)o(v)o(ed)e(b)q(et)o(w)o(een)j(passes.)22 |
| b(The)15 b(next)g(case)g(can)g(nev)o(er)h(b)q(e)f(handled)f(b)o(y)h |
| (suc)o(h)g(an)0 2115 y(approac)o(h.)-150 2183 y Fm(22e)98 |
| b Fl("cprop.c")p Fk(\021)104 2229 y Fl(void)18 b(cprop_tes)o(t11)o(\(i) |
| o(nt)e(*data\))104 2275 y({)143 2321 y(int)i(i;)143 2366 |
| y(int)g(stop)h(=)g(data[0];)143 2412 y(int)f(j)i(=)f(1;)143 |
| 2458 y(for)f(\(i=1;)g(i<stop;)f(i++\))182 2503 y(if)i(\(!j\))f(j)h(=)h |
| (i;)143 2549 y(data[1])d(=)i(j;)143 2595 y(data[2])e(=)i(i;)104 |
| 2640 y(})104 2686 y Fi(3)1258 2229 y Fl(void)f(cprop_res)o(ult)o(11)o |
| (\(in)o(t)f(*data\))1258 2275 y({)1297 2321 y(int)h(i;)1297 |
| 2366 y(int)g(stop)h(=)g(data[0];)1297 2412 y(for)f(\(i=1;)g(i<stop;)f |
| (i++\))1336 2458 y(;)1297 2503 y(data[1])g(=)i(1;)1297 |
| 2549 y(data[2])e(=)i(i;)1258 2595 y(})1258 2640 y Fi(3)0 |
| 2743 y Fh(See)11 b Fm(18b,)i(19ac)n(e,)i(20b)n(d,)e(21ac,)h(22ac,)g |
| (23b)n(d,)g(24a)p Fh(.)954 2874 y Ft(22)p eop |
| %%Page: 23 28 |
| 23 27 bop -150 78 a Fm(23a)96 b Fk(h)p Fw(Constan)o(t)13 |
| b(propagation)p Fk(i)h(\021)104 124 y Fl({)143 170 y(int)k(data[3])f(=) |
| j({)f(2)g(};)143 215 y(\(void\))e(test\(ok,)g(cprop_res)o(ult)o(11)o(,) |
| g(cprop_tes)o(t1)o(1,)f(data,)i(11,)g("conditiona)o(l)e(constants")o |
| (\);)104 261 y(})p Fi(3)0 319 y Fh(See)11 b(18a,)f Fm(18c,)k(19b)n(d,)g |
| (20ac)n(e,)g(21b)n(d,)g(22b)n(d,)g(23c)n(e,)g(24b)p Fh(.)0 |
| 433 y Fp(4.4)70 b(Conditional-Based)21 b(Assertions)0 |
| 524 y Ft(W)m(e)14 b(need)h(something)e(exp)q(ensiv)o(e)i(lik)o(e)f(the) |
| h(division;)d(otherwise,)j(the)g(m)o(ultiply)c(can)k(b)q(e)g(hidden)f |
| (b)o(y)g(sc)o(heduling)g(on)g(the)0 574 y(RS/6000.)-150 |
| 653 y Fm(23b)98 b Fl("cprop.c")p Fk(\021)104 699 y Fl(void)18 |
| b(cprop_tes)o(t12)o(\(i)o(nt)e(*data\))104 745 y({)143 |
| 791 y(int)i(j)i(=)f(data[0];)143 836 y(if)g(\(j)g(==)g(5\))182 |
| 882 y(j)g(=)h(j)f(*)g(21)g(+)g(25)g(/)g(j;)143 928 y(data[1])e(=)i(j;) |
| 104 973 y(})104 1019 y Fi(3)1258 699 y Fl(void)f(cprop_res)o(ult)o(12)o |
| (\(in)o(t)f(*data\))1258 745 y({)1297 791 y(int)h(j)i(=)f(data[0];)1297 |
| 836 y(if)g(\(j)g(==)g(5\))1336 882 y(j)g(=)h(110;)1297 |
| 928 y(data[1])d(=)i(j;)1258 973 y(})1258 1019 y Fi(3)0 |
| 1076 y Fh(See)11 b Fm(18b,)i(19ac)n(e,)i(20b)n(d,)e(21ac,)h(22ac)n(e,)h |
| (23d,)e(24a)p Fh(.)-150 1156 y Fm(23c)98 b Fk(h)p Fw(Constan)o(t)13 |
| b(propagation)p Fk(i)h(\021)104 1203 y Fl({)143 1248 |
| y(int)k(data[2])f(=)j({)f(5)g(};)143 1294 y(ok)g(=)g(test\(1,)e |
| (cprop_resu)o(lt)o(12,)f(cprop_tes)o(t12)o(,)g(data,)i(12,)h("conditi)o |
| (ona)o(l-b)o(as)o(ed)d(assertions)o("\);)104 1340 y(})p |
| Fi(3)0 1397 y Fh(See)11 b(18a,)f Fm(18c,)k(19b)n(d,)g(20ac)n(e,)g(21b)n |
| (d,)g(22b)n(d,)g(23ae,)g(24b)p Fh(.)-150 1472 y Fm(23d)96 |
| b Fl("cprop.c")p Fk(\021)104 1519 y Fl(void)18 b(cprop_tes)o(t13)o(\(i) |
| o(nt)e(*data\))104 1564 y({)143 1610 y(int)i(j)i(=)f(data[1];)143 |
| 1656 y(int)f(k)i(=)f(data[0];)143 1701 y(if)g(\(j)g(==)g(5)g(&&)g(k)g |
| (==)g(10\))182 1747 y(j)g(=)h(j)f(*)g(21)g(+)g(100)g(/)g(k;)143 |
| 1793 y(data[2])e(=)i(j;)104 1838 y(})104 1884 y Fi(3)1258 |
| 1519 y Fl(void)f(cprop_res)o(ult)o(13)o(\(in)o(t)f(*data\))1258 |
| 1564 y({)1297 1610 y(int)h(j)i(=)f(data[1];)1297 1656 |
| y(int)f(k)i(=)f(data[0];)1297 1701 y(if)g(\(j)g(==)g(5)g(&&)g(k)g(==)g |
| (10\))1336 1747 y(j)g(=)h(115;)1297 1793 y(data[2])d(=)i(j;)1258 |
| 1838 y(})1258 1884 y Fi(3)0 1941 y Fh(See)11 b Fm(18b,)i(19ac)n(e,)i |
| (20b)n(d,)e(21ac,)h(22ac)n(e,)h(23b,)e(24a)p Fh(.)-150 |
| 2021 y Fm(23e)98 b Fk(h)p Fw(Constan)o(t)13 b(propagation)p |
| Fk(i)h(\021)104 2113 y Fl({)143 2159 y(int)k(data[3])f(=)j({)f(10,)f(5) |
| i(};)143 2205 y(\(void\))d(test\(ok,)g(cprop_res)o(ult)o(13)o(,)g |
| (cprop_tes)o(t1)o(3,)f(data,)i(13,)g("conditiona)o(l-)o(bas)o(ed)e |
| (assertions)o("\))o(;)104 2250 y(})p Fi(3)0 2308 y Fh(See)11 |
| b(18a,)f Fm(18c,)k(19b)n(d,)g(20ac)n(e,)g(21b)n(d,)g(22b)n(d,)g(23ac,)g |
| (24b)p Fh(.)954 2874 y Ft(23)p eop |
| %%Page: 24 29 |
| 24 28 bop 0 91 a Fp(4.5)70 b(Reasso)r(ciation)-150 159 |
| y Fm(24a)96 b Fl("cprop.c")p Fk(\021)104 206 y Fl(void)18 |
| b(cprop_tes)o(t14)o(\(i)o(nt)e(*data\))104 251 y({)143 |
| 297 y(int)i(i)i(=)f(10;)143 343 y(int)f(j)i(=)f(data[0];)143 |
| 388 y(int)f(k)i(=)f(20;)143 434 y(int)f(m)i(=)f(data[1];)143 |
| 480 y(int)f(n)i(=)f(30;)143 525 y(if)g(\(data[2]\))182 |
| 571 y(data[3])e(=)i(i)h(+)f(j)g(+)g(k)h(+)f(m)g(+)g(n;)143 |
| 617 y(else)182 662 y(data[0])e(=)i(i)h(*)f(\(j)g(-)g(k)g(*)g(\(m)g(-)g |
| (n\)\);)104 708 y(})104 754 y Fi(3)1081 206 y Fl(void)f(cprop_resu)o |
| (lt1)o(4\(i)o(nt)e(*data\))1081 251 y({)1121 297 y(int)i(j)h(=)g |
| (data[0];)1121 343 y(int)f(m)h(=)g(data[1];)1121 388 |
| y(if)f(\(data[2]\))1160 434 y(data[3])f(=)i(60)g(+)g(j)g(+)g(m;)1121 |
| 480 y(else)1160 525 y(data[0])e(=)i(10)g(*)g(\(j)g(-)g(20)g(*)g(\(m)g |
| (-)g(30\)\);)1081 571 y(})1081 617 y Fi(3)0 811 y Fh(See)11 |
| b Fm(18b,)i(19ac)n(e,)i(20b)n(d,)e(21ac,)h(22ac)n(e,)h(23b)n(d)p |
| Fh(.)-150 891 y Fm(24b)98 b Fk(h)p Fw(Constan)o(t)13 |
| b(propagation)p Fk(i)h(\021)104 937 y Fl({)143 983 y(int)k(data[4])f(=) |
| j({)f(0,)g(1,)g(2)g(};)143 1029 y(\(void\))e(test\(ok,)g(cprop_res)o |
| (ult)o(14)o(,)g(cprop_tes)o(t1)o(4,)f(data,)i(14,)g("reassociat)o(io)o |
| (n"\))o(;)104 1074 y(})p Fi(3)0 1132 y Fh(See)11 b(18a,)f |
| Fm(18c,)k(19b)n(d,)g(20ac)n(e,)g(21b)n(d,)g(22b)n(d,)g(23ac)n(e)p |
| Fh(.)0 1247 y Fp(4.6)70 b(Algebraic)21 b(Simpli\014cati)o(ons)865 |
| 1379 y Fq(x)9 b Ft(+)g(0)42 b Fn(\))f Fq(x)865 1441 y(x)9 |
| b Fn(\000)g Ft(0)42 b Fn(\))f Fq(x)865 1504 y(x)9 b Fn(\002)g |
| Ft(0)42 b Fn(\))f Ft(0)865 1566 y Fq(x)9 b Fn(\002)g |
| Ft(1)42 b Fn(\))f Fq(x)895 1628 y(x=)p Ft(1)g Fn(\))g |
| Fq(x)811 1690 y(x)9 b Fn(\\)f Ft(false)42 b Fn(\))f Ft(false)816 |
| 1753 y Fq(x)9 b Fn(\\)g Ft(true)43 b Fn(\))e Fq(x)811 |
| 1815 y(x)9 b Fn([)f Ft(false)42 b Fn(\))f Fq(x)816 1877 |
| y(x)9 b Fn([)g Ft(true)43 b Fn(\))e Ft(true)851 1939 |
| y Fq(x)11 b Fn(\034)g Ft(0)42 b Fn(\))f Fq(x)851 2002 |
| y Ft(0)11 b Fn(\034)h Fq(x)41 b Fn(\))g Ft(0)785 2064 |
| y(mo)q(d)o(\()p Fq(x;)7 b Ft(1\))41 b Fn(\))g Ft(0)0 |
| 2263 y Fp(4.7)70 b(Floating-P)n(oin)n(t)21 b(Op)r(erations)0 |
| 2354 y Ft(Sometimes)15 b(propagation)g(of)h(\015oating-p)q(oin)o(t)f |
| (constan)o(ts)j(at)f(compile)e(time)g(can)i(lead)f(to)h(loss)g(of)f |
| (precision.)27 b(In)16 b(other)0 2404 y(cases,)f(it's)e(safe)h(and)g |
| (accurate.)19 b(F)m(urthermore,)14 b(sometimes)e(users)j(don't)e |
| (consider)i(suc)o(h)g(losses)g(imp)q(ortan)o(t.)62 2454 |
| y(W)m(e)h(should)h(at)f(least)h(c)o(hec)o(k)g(to)g(see)h(ho)o(w)e(man)o |
| (y)e(of)i(the)h(safe)g(cases)h(are)f(handled,)g(and)f(p)q(erhaps)i(if)e |
| (they're)h(doing)0 2504 y(some)c(of)g(the)i(shakier)f(cases)h(\(not)f |
| (so)g(m)o(uc)o(h)f(to)h(pass)g(judgemen)o(t)f(as)h(to)g(sho)o(w)f(who)h |
| (do)q(es)h(what\).)62 2554 y(con)o(v)o(ersions,)f(rounding,)f |
| (truncation)954 2874 y(24)p eop |
| %%Page: 25 30 |
| 25 29 bop 0 91 a Fp(4.8)70 b(Protot)n(yp)r(es)-150 176 |
| y Fm(25)114 b Fk(h)p Fw(Protot)o(yp)q(es)p Fk(i)12 b(\021)104 |
| 222 y Fl(extern)17 b(void)h(cprop_test)o(1\(i)o(nt)e(*data\);)104 |
| 268 y(extern)h(void)h(cprop_test)o(2\(i)o(nt)e(*data\);)104 |
| 314 y(extern)h(void)h(cprop_test)o(3\(i)o(nt)e(*data\);)104 |
| 359 y(extern)h(void)h(cprop_test)o(35\()o(in)o(t)f(*data\);)104 |
| 405 y(extern)g(void)h(cprop_test)o(4\(i)o(nt)e(*data\);)104 |
| 451 y(extern)h(void)h(cprop_test)o(5\(i)o(nt)e(*data\);)104 |
| 496 y(extern)h(void)h(cprop_test)o(6\(i)o(nt)e(*data\);)104 |
| 542 y(extern)h(void)h(cprop_test)o(7\(i)o(nt)e(*data\);)104 |
| 588 y(extern)h(void)h(cprop_test)o(8\(i)o(nt)e(*data\);)104 |
| 633 y(extern)h(void)h(cprop_test)o(9\(i)o(nt)e(*data\);)104 |
| 679 y(extern)h(void)h(cprop_test)o(10\()o(in)o(t)f(*data\);)104 |
| 725 y(extern)g(void)h(cprop_test)o(11\()o(in)o(t)f(*data\);)104 |
| 770 y(extern)g(void)h(cprop_test)o(12\()o(in)o(t)f(*data\);)104 |
| 816 y(extern)g(void)h(cprop_test)o(13\()o(in)o(t)f(*data\);)104 |
| 862 y(extern)g(void)h(cprop_test)o(14\()o(in)o(t)f(*data\);)104 |
| 907 y Fi(3)1101 222 y Fl(extern)g(void)h(cprop_resu)o(lt1)o(\(i)o(nt)e |
| (*data\);)1101 268 y(extern)h(void)h(cprop_resu)o(lt2)o(\(i)o(nt)e |
| (*data\);)1101 314 y(extern)h(void)h(cprop_resu)o(lt3)o(\(i)o(nt)e |
| (*data\);)1101 359 y(extern)h(void)h(cprop_resu)o(lt4)o(\(i)o(nt)e |
| (*data\);)1101 405 y(extern)h(void)h(cprop_resu)o(lt5)o(\(i)o(nt)e |
| (*data\);)1101 451 y(extern)h(void)h(cprop_resu)o(lt6)o(\(i)o(nt)e |
| (*data\);)1101 496 y(extern)h(void)h(cprop_resu)o(lt7)o(\(i)o(nt)e |
| (*data\);)1101 542 y(extern)h(void)h(cprop_resu)o(lt8)o(\(i)o(nt)e |
| (*data\);)1101 588 y(extern)h(void)h(cprop_resu)o(lt9)o(\(i)o(nt)e |
| (*data\);)1101 633 y(extern)h(void)h(cprop_resu)o(lt1)o(0\()o(int)e |
| (*data\);)1101 679 y(extern)h(void)h(cprop_resu)o(lt1)o(1\()o(int)e |
| (*data\);)1101 725 y(extern)h(void)h(cprop_resu)o(lt1)o(2\()o(int)e |
| (*data\);)1101 770 y(extern)h(void)h(cprop_resu)o(lt1)o(3\()o(int)e |
| (*data\);)1101 816 y(extern)h(void)h(cprop_resu)o(lt1)o(4\()o(int)e |
| (*data\);)1101 862 y Fi(3)0 965 y Fh(See)11 b(3b,)g Fm(4,)h(7b,)i(8e,)f |
| (17,)g(32b,)h(39,)f(45c)p Fh(.)954 2874 y Ft(25)p eop |
| %%Page: 26 31 |
| 26 30 bop 0 257 a Fu(Chapter)34 b(5)0 423 y(V)-8 b(alue)34 |
| b(Num)m(b)s(ering)0 598 y Ft([11)o(])62 648 y([4])62 |
| 697 y(reasso)q(ciation)62 747 y(basic)14 b(blo)q(c)o(ks,)g(extended)h |
| (basic)f(blo)q(c)o(ks,)g(dominance)e(regions,)i(global,)d(gated)j(SSA) |
| 62 797 y(com)o(bined)f(with)g(constan)o(t)h(prop,)f(unreac)o(hable)i |
| (co)q(de)f(due)g(to)f(cprop,)h(unreac)o(hable)g(co)q(de)h(due)f(to)f(v) |
| n(alue)g(n)o(um)o(b)q(ering)62 847 y(impro)o(v)o(emen)o(ts)f(p)q |
| (ossible)i(via)f(conditionals)g(\(assertions\))-150 931 |
| y Fm(26a)96 b Fk(h)p Fw(Ev)n(aluation)16 b(driv)o(ers)p |
| Fk(i)c(\021)104 977 y Fl({)143 1023 y(int)18 b(ok;)143 |
| 1068 y(puts\("Valu)o(e)e(numbering"\))o(;)143 1114 y |
| Fk(h)p Fw(V)m(alue)e(n)o(um)o(b)q(ering)h Fm(26c,)e Fj(:)6 |
| b(:)g(:)f Fk(i)104 1160 y Fl(})p Fi(3)0 1217 y Fh(See)11 |
| b(3c,)g Fm(11a,)i(18a,)g(33a,)h(40a)p Fh(.)0 1332 y Fp(5.1)70 |
| b(Lo)r(cal)0 1422 y Ft([11)o(])0 1539 y Fo(5.1.1)55 b(Expressions)-150 |
| 1602 y Fm(26b)98 b Fl("valnum.c")o Fk(\021)104 1649 y |
| Fl(void)18 b(vnum_test)o(1\(i)o(nt)e(*data\))104 1694 |
| y({)143 1740 y(data[0])h(=)i(data[1])e(*)i(data[3])e(-)i(data[1])e(*)j |
| (data[3];)104 1786 y(})104 1831 y Fi(3)1297 1649 y Fl(void)e |
| (vnum_resul)o(t1)o(\(in)o(t)f(*data\))1297 1694 y({)1336 |
| 1740 y(data[0])g(=)i(0;)1297 1786 y(})1297 1831 y Fi(3)0 |
| 1889 y Fh(See)11 b Fm(26d,)i(27b)n(d,)h(28ac,)g(29ac,)f(30b)n(d,)h |
| (31ac)p Fh(.)-150 1969 y Fm(26c)98 b Fk(h)p Fw(V)m(alue)14 |
| b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 2015 y Fl({)143 |
| 2061 y(int)18 b(data[4])f(=)j({0,)e(1,)h(2,)g(3)g(};)143 |
| 2106 y(ok)g(=)g(test\(1,)37 b(vnum_resu)o(lt)o(1,)16 |
| b(vnum_test1)o(,)h(data,)g(1,)i("expressio)o(ns)o("\);)104 |
| 2152 y(})p Fi(3)0 2210 y Fh(See)11 b(26a,)f Fm(27ac)n(e,)15 |
| b(28b)n(d,)e(29b,)h(30ac)n(e,)g(31b,)g(32a)p Fh(.)-150 |
| 2285 y Fm(26d)96 b Fl("valnum.c")o Fk(\021)104 2331 y |
| Fl(void)18 b(vnum_test)o(2\(i)o(nt)e(*data\))104 2377 |
| y({)143 2422 y(data[0])h(=)i(data[1])e(*)i(data[3])e(-)i(data[3])e(*)j |
| (data[1];)104 2468 y(})104 2514 y Fi(3)1297 2331 y Fl(void)e |
| (vnum_resul)o(t2)o(\(in)o(t)f(*data\))1297 2377 y({)1336 |
| 2422 y(data[0])g(=)i(0;)1297 2468 y(})1297 2514 y Fi(3)0 |
| 2571 y Fh(See)11 b Fm(26b,)i(27b)n(d,)h(28ac,)g(29ac,)g(30b)n(d,)g |
| (31ac)p Fh(.)954 2874 y Ft(26)p eop |
| %%Page: 27 32 |
| 27 31 bop -150 78 a Fm(27a)96 b Fk(h)p Fw(V)m(alue)14 |
| b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 124 y Fl({)143 |
| 170 y(int)18 b(data[4])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 |
| 215 y(\(void\))37 b(test\(ok,)16 b(vnum_result)o(2,)g(vnum_test2)o(,)g |
| (data,)i(2,)h("expressi)o(ons)o("\);)104 261 y(})p Fi(3)0 |
| 319 y Fh(See)11 b(26a,)f Fm(26c,)k(27c)n(e,)g(28b)n(d,)g(29b,)f(30ac)n |
| (e,)i(31b,)e(32a)p Fh(.)0 422 y Fo(5.1.2)55 b(Basic)19 |
| b(Blo)r(c)n(ks)-150 476 y Fm(27b)98 b Fl("valnum.c")o |
| Fk(\021)104 522 y Fl(void)18 b(vnum_test)o(3\(i)o(nt)e(*data\))104 |
| 568 y({)143 613 y(int)i(n;)143 659 y(int)g(j)i(=)f(data[1])e(*)i |
| (data[3];)143 705 y(int)f(i)i(=)f(data[3];)143 750 y(int)f(m)i(=)f |
| (data[1];)143 796 y(int)f(k)i(=)f(data[2];)143 842 y(data[k])e(=)i(2;) |
| 143 887 y(n)g(=)g(m)h(*)f(i;)143 933 y(data[0])e(=)i(n)g(-)h(j;)104 |
| 979 y(})104 1024 y Fi(3)1297 522 y Fl(void)e(vnum_resul)o(t3)o(\(in)o |
| (t)f(*data\))1297 568 y({)1336 613 y(int)i(k)g(=)g(data[2];)1336 |
| 659 y(data[k])e(=)i(2;)1336 705 y(data[0])e(=)i(0;)1297 |
| 750 y(})1297 796 y Fi(3)0 1082 y Fh(See)11 b Fm(26b)n(d,)j(27d,)f |
| (28ac,)h(29ac,)f(30b)n(d,)h(31ac)p Fh(.)-150 1162 y Fm(27c)98 |
| b Fk(h)p Fw(V)m(alue)14 b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 |
| 1208 y Fl({)143 1254 y(int)18 b(data[4])f(=)j({)f(0,)g(1,)g(2,)f(3)i |
| (};)143 1299 y(ok)f(=)g(test\(ok,)e(vnum_resu)o(lt)o(3,)f(vnum_test3)o |
| (,)h(data,)g(3,)i("basic)e(block"\);)104 1345 y(})p Fi(3)0 |
| 1403 y Fh(See)11 b(26a,)f Fm(26c,)k(27ae,)f(28b)n(d,)h(29b,)g(30ac)n |
| (e,)g(31b,)g(32a)p Fh(.)0 1484 y Ft(Chec)o(k)h(comm)o(utati)o(vit)o(y)c |
| (since)j(some)f(compilers)g(seem)h(to)g(miss)e(it.)-150 |
| 1560 y Fm(27d)96 b Fl("valnum.c")o Fk(\021)104 1607 y |
| Fl(void)18 b(vnum_test)o(4\(i)o(nt)e(*data\))104 1652 |
| y({)143 1698 y(int)i(n;)143 1744 y(int)g(j)i(=)f(data[1])e(*)i |
| (data[3];)143 1789 y(int)f(i)i(=)f(data[3];)143 1835 |
| y(int)f(m)i(=)f(data[1];)143 1881 y(int)f(k)i(=)f(data[2];)143 |
| 1926 y(data[k])e(=)i(2;)143 1972 y(n)g(=)g(i)h(*)f(m;)143 |
| 2018 y(data[0])e(=)i(n)g(-)h(j;)104 2063 y(})104 2109 |
| y Fi(3)1297 1607 y Fl(void)e(vnum_resul)o(t4)o(\(in)o(t)f(*data\))1297 |
| 1652 y({)1336 1698 y(int)i(k)g(=)g(data[2];)1336 1744 |
| y(data[k])e(=)i(2;)1336 1789 y(data[0])e(=)i(0;)1297 |
| 1835 y(})1297 1881 y Fi(3)0 2166 y Fh(See)11 b Fm(26b)n(d,)j(27b,)f |
| (28ac,)h(29ac,)g(30b)n(d,)g(31ac)p Fh(.)-150 2246 y Fm(27e)98 |
| b Fk(h)p Fw(V)m(alue)14 b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 |
| 2293 y Fl({)143 2338 y(int)18 b(data[4])f(=)j({)f(0,)g(1,)g(2,)f(3)i |
| (};)143 2384 y(\(void\))d(test\(ok,)g(vnum_resu)o(lt4)o(,)f |
| (vnum_test4,)g(data,)h(4,)i("basic)f(block"\);)104 2430 |
| y(})p Fi(3)0 2487 y Fh(See)11 b(26a,)f Fm(26c,)k(27ac,)f(28b)n(d,)h |
| (29b,)g(30ac)n(e,)g(31b,)g(32a)p Fh(.)954 2874 y Ft(27)p |
| eop |
| %%Page: 28 33 |
| 28 32 bop 0 91 a Fo(5.1.3)55 b(Extended)18 b(Basic)g(Blo)r(c)n(ks)-150 |
| 145 y Fm(28a)96 b Fl("valnum.c")o Fk(\021)104 191 y Fl(void)18 |
| b(vnum_test)o(5\(i)o(nt)e(*data\))104 237 y({)143 283 |
| y(int)i(j)i(=)f(data[1])e(*)i(data[3];)143 328 y(if)g(\(data[3])d(==)j |
| (3\))g({)182 374 y(int)g(n;)182 420 y(int)g(i)g(=)g(data[3];)182 |
| 465 y(int)g(m)g(=)g(data[1];)182 511 y(int)g(k)g(=)g(data[2];)182 |
| 557 y(data[k])e(=)i(2;)182 602 y(n)g(=)h(m)f(*)g(i;)182 |
| 648 y(data[0])e(=)i(n)h(-)f(j;)143 694 y(})143 739 y(else)f(if)h |
| (\(data[0])d(&)k(1\))f({)182 785 y(j)g(=)h(3)f(+)g(data[2])e(-)i(j;)182 |
| 831 y(data[j])e(=)i(2;)143 876 y(})104 922 y(})104 968 |
| y Fi(3)1297 191 y Fl(void)f(vnum_resul)o(t5)o(\(in)o(t)f(*data\))1297 |
| 237 y({)1336 283 y(int)i(j)g(=)g(data[1])e(*)i(data[3];)1336 |
| 328 y(if)g(\(data[3])e(==)h(3\))h({)1375 374 y(int)g(k)g(=)g(data[2];) |
| 1375 420 y(data[k])e(=)j(2;)1375 465 y(data[0])d(=)j(0;)1336 |
| 511 y(})1336 557 y(else)e(if)h(\(data[0])e(&)i(1\))g({)1375 |
| 602 y(j)h(=)f(3)g(+)g(data[2])e(-)j(j;)1375 648 y(data[j])d(=)j(2;)1336 |
| 694 y(})1297 739 y(})1297 785 y Fi(3)0 1025 y Fh(See)11 |
| b Fm(26b)n(d,)j(27b)n(d,)g(28c,)f(29ac,)h(30b)n(d,)g(31ac)p |
| Fh(.)-150 1105 y Fm(28b)98 b Fk(h)p Fw(V)m(alue)14 b(n)o(um)o(b)q |
| (ering)p Fk(i)e(\021)104 1151 y Fl({)143 1197 y(int)18 |
| b(data[4])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 1243 y(ok)f(=)g |
| (test\(ok,)e(vnum_resu)o(lt)o(5,)f(vnum_test5)o(,)h(data,)g(5,)i |
| ("extended)d(basic)i(block"\);)104 1288 y(})p Fi(3)0 |
| 1346 y Fh(See)11 b(26a,)f Fm(26c,)k(27ac)n(e,)g(28d,)f(29b,)h(30ac)n |
| (e,)g(31b,)g(32a)p Fh(.)0 1461 y Fp(5.2)70 b(Dominators)0 |
| 1551 y Ft(Can)14 b(b)q(e)g(handled)g(prett)o(y)h(easily)e(using)h |
| Fw(SSA)p Ft(.)k(Not)c(published)g({)g(due)g(to)g(Jonathan)f(Brezin.) |
| -150 1628 y Fm(28c)98 b Fl("valnum.c")o Fk(\021)104 1674 |
| y Fl(void)18 b(vnum_test)o(6\(i)o(nt)e(*data\))104 1720 |
| y({)143 1766 y(int)i(n;)143 1811 y(int)g(j)i(=)f(data[1])e(*)i |
| (data[3];)143 1857 y(int)f(m)i(=)f(data[1];)143 1903 |
| y(int)f(k)i(=)f(j;)143 1948 y(if)g(\(data[0]\))182 1994 |
| y(j)g(=)h(j)f(+)g(3;)143 2040 y(else)182 2085 y(j)g(=)h(j)f(-)g(3;)143 |
| 2131 y(n)g(=)g(data[3];)143 2177 y(j)g(=)g(data[2])e(+)j(j;)143 |
| 2222 y(data[j])d(=)i(2;)143 2268 y(data[4])e(=)i(k)g(-)h(m)f(*)g(n;)104 |
| 2314 y(})104 2359 y Fi(3)1297 1674 y Fl(void)f(vnum_resul)o(t6)o(\(in)o |
| (t)f(*data\))1297 1720 y({)1336 1766 y(int)i(j)g(=)g(data[1])e(*)i |
| (data[3];)1336 1811 y(if)g(\(data[0]\))1375 1857 y(j)h(=)f(j)g(+)g(3;) |
| 1336 1903 y(else)1375 1948 y(j)h(=)f(j)g(-)g(3;)1336 |
| 1994 y(j)g(=)h(data[2])d(+)i(j;)1336 2040 y(data[j])e(=)i(2;)1336 |
| 2085 y(data[4])e(=)i(0;)1297 2131 y(})1297 2177 y Fi(3)0 |
| 2417 y Fh(See)11 b Fm(26b)n(d,)j(27b)n(d,)g(28a,)f(29ac,)h(30b)n(d,)g |
| (31ac)p Fh(.)-150 2497 y Fm(28d)96 b Fk(h)p Fw(V)m(alue)14 |
| b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 2543 y Fl({)143 |
| 2589 y(int)18 b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3,)h(4)g(};)143 |
| 2634 y(ok)g(=)g(test\(ok,)e(vnum_resu)o(lt)o(6,)f(vnum_test6)o(,)h |
| (data,)g(6,)i("dominator)o(s")o(\);)104 2680 y(})p Fi(3)0 |
| 2738 y Fh(See)11 b(26a,)f Fm(26c,)k(27ac)n(e,)g(28b,)g(29b,)f(30ac)n |
| (e,)h(31b,)g(32a)p Fh(.)954 2874 y Ft(28)p eop |
| %%Page: 29 34 |
| 29 33 bop 0 91 a Fp(5.3)70 b(Global)0 182 y Ft([4)o(])0 |
| 298 y Fo(5.3.1)55 b(D)n(A)n(Gs)-150 352 y Fm(29a)96 b |
| Fl("valnum.c")o Fk(\021)104 398 y Fl(void)18 b(vnum_test)o(7\(i)o(nt)e |
| (*data\))104 444 y({)143 490 y(int)i(i,)h(j,)g(k;)143 |
| 535 y(int)f(m)i(=)f(data[1];)143 581 y(int)f(n)i(=)f(data[3];)143 |
| 627 y(if)g(\(data[0]\))d({)182 672 y(j)j(=)h(m)f(*)g(n;)182 |
| 718 y(i)g(=)h(data[2];)182 764 y(data[i])d(=)i(2;)182 |
| 809 y(k)g(=)h(m)f(*)g(n;)143 855 y(})143 901 y(else)f({)182 |
| 946 y(j)h(=)h(5;)182 992 y(k)f(=)h(5;)143 1038 y(})143 |
| 1083 y(data[0])d(=)i(k)g(-)h(j;)104 1129 y(})104 1175 |
| y Fi(3)1297 398 y Fl(void)e(vnum_resul)o(t7)o(\(in)o(t)f(*data\))1297 |
| 444 y({)1336 490 y(int)i(i;)1336 535 y(if)g(\(data[0]\))d({)1375 |
| 581 y(i)k(=)f(data[2];)1375 627 y(data[i])e(=)j(2;)1336 |
| 672 y(})1336 718 y(data[0])d(=)i(0;)1297 764 y(})1297 |
| 809 y Fi(3)0 1232 y Fh(See)11 b Fm(26b)n(d,)j(27b)n(d,)g(28ac,)f(29c,)h |
| (30b)n(d,)g(31ac)p Fh(.)-150 1312 y Fm(29b)98 b Fk(h)p |
| Fw(V)m(alue)14 b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 |
| 1359 y Fl({)143 1404 y(int)18 b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3,)h |
| (4)g(};)143 1450 y(ok)g(=)g(test\(1,)37 b(vnum_resu)o(lt)o(7,)16 |
| b(vnum_test7)o(,)h(data,)g(7,)i("global)e(DAGs"\);)104 |
| 1495 y(})p Fi(3)0 1553 y Fh(See)11 b(26a,)f Fm(26c,)k(27ac)n(e,)g(28b)n |
| (d,)g(30ac)n(e,)g(31b,)g(32a)p Fh(.)0 1656 y Fo(5.3.2)55 |
| b(Lo)r(ops)-150 1719 y Fm(29c)98 b Fl("valnum.c")o Fk(\021)104 |
| 1766 y Fl(void)18 b(vnum_test)o(8\(i)o(nt)e(*data\))104 |
| 1811 y({)143 1857 y(int)i(i;)143 1903 y(int)g(stop)h(=)g(data[3];)143 |
| 1948 y(int)f(m)i(=)f(data[4];)143 1994 y(int)f(n)i(=)f(m;)143 |
| 2040 y(for)f(\(i=0;)g(i<stop;)f(i++\))h({)182 2085 y(int)h(k)g(=)g |
| (data[2];)182 2131 y(data[k])e(=)i(2;)182 2177 y(data[0])e(=)i(m)h(-)f |
| (n;)182 2222 y(k)g(=)h(data[1];)182 2268 y(m)f(=)h(m)f(+)g(k;)182 |
| 2313 y(n)g(=)h(n)f(+)g(k;)143 2359 y(})104 2405 y(})104 |
| 2450 y Fi(3)1297 1766 y Fl(void)f(vnum_resul)o(t8)o(\(in)o(t)f(*data\)) |
| 1297 1811 y({)1336 1857 y(int)i(i;)1336 1903 y(int)g(stop)f(=)h |
| (data[3];)1336 1948 y(for)g(\(i=0;)e(i<stop;)g(i++\))h({)1375 |
| 1994 y(int)h(k)g(=)g(data[2];)1375 2040 y(data[k])e(=)j(2;)1375 |
| 2085 y(data[0])d(=)j(0;)1336 2131 y(})1297 2177 y(})1297 |
| 2222 y Fi(3)0 2508 y Fh(See)11 b Fm(26b)n(d,)j(27b)n(d,)g(28ac,)f(29a,) |
| h(30b)n(d,)g(31ac)p Fh(.)954 2874 y Ft(29)p eop |
| %%Page: 30 35 |
| 30 34 bop -150 78 a Fm(30a)96 b Fk(h)p Fw(V)m(alue)14 |
| b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 124 y Fl({)143 |
| 170 y(int)18 b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3,)h(4)g(};)143 |
| 215 y(ok)g(=)g(test\(ok,)e(vnum_resu)o(lt)o(8,)f(vnum_test8)o(,)h |
| (data,)g(8,)i("global)e(loops"\);)104 261 y(})p Fi(3)0 |
| 319 y Fh(See)11 b(26a,)f Fm(26c,)k(27ac)n(e,)g(28b)n(d,)g(29b,)f(30c)n |
| (e,)i(31b,)e(32a)p Fh(.)0 433 y Fp(5.4)70 b(Conditional-Based)21 |
| b(Assertions)0 532 y Fo(5.4.1)55 b(Simple)-150 596 y |
| Fm(30b)98 b Fl("valnum.c")o Fk(\021)104 642 y Fl(void)18 |
| b(vnum_test)o(9\(i)o(nt)e(*data\))104 688 y({)143 734 |
| y(int)i(i)i(=)f(data[0];)143 779 y(int)f(j)i(=)f(data[1];)143 |
| 825 y(if)g(\(i)g(==)g(j\))182 871 y(data[2])e(=)i(\(i)g(-)g(j\))g(*)h |
| (21;)143 916 y(else)182 962 y(data[2])d(=)i(i)h(+)f(j;)104 |
| 1008 y(})104 1053 y Fi(3)1297 642 y Fl(void)f(vnum_resul)o(t9)o(\(in)o |
| (t)f(*data\))1297 688 y({)1336 734 y(int)i(i)g(=)g(data[0];)1336 |
| 779 y(int)g(j)g(=)g(data[1];)1336 825 y(if)g(\(i)g(==)g(j\))1375 |
| 871 y(data[2])e(=)j(0;)1336 916 y(else)1375 962 y(data[2])d(=)j(i)f(+)g |
| (j;)1297 1008 y(})1297 1053 y Fi(3)0 1111 y Fh(See)11 |
| b Fm(26b)n(d,)j(27b)n(d,)g(28ac,)f(29ac,)h(30d,)f(31ac)p |
| Fh(.)-150 1191 y Fm(30c)98 b Fk(h)p Fw(V)m(alue)14 b(n)o(um)o(b)q |
| (ering)p Fk(i)e(\021)104 1237 y Fl({)143 1283 y(int)18 |
| b(data[3])f(=)j({)f(0,)g(0)g(};)143 1328 y(ok)g(=)g(test\(1,)e |
| (vnum_resul)o(t9)o(,)g(vnum_tes)o(t9,)f(data,)i(9,)g("conditiona)o(l-)o |
| (bas)o(ed)e(assertions)o("\))o(;)104 1374 y(})p Fi(3)0 |
| 1432 y Fh(See)11 b(26a,)f Fm(26c,)k(27ac)n(e,)g(28b)n(d,)g(29b,)f |
| (30ae,)h(31b,)g(32a)p Fh(.)0 1535 y Fo(5.4.2)55 b(Deriv)n(ed)0 |
| 1612 y Ft(This)14 b(one)g(is)g(quite)g(hard.)-150 1688 |
| y Fm(30d)96 b Fl("valnum.c")o Fk(\021)104 1734 y Fl(void)18 |
| b(vnum_test)o(10\()o(in)o(t)f(*data\))104 1780 y({)143 |
| 1826 y(int)h(i)i(=)f(data[0];)143 1871 y(int)f(m)i(=)f(i)g(+)g(1;)143 |
| 1917 y(int)f(j)i(=)f(data[1];)143 1963 y(int)f(n)i(=)f(j)g(+)g(1;)143 |
| 2008 y(data[2])e(=)i(m)g(+)h(n;)143 2054 y(if)f(\(i)g(==)g(j\))182 |
| 2100 y(data[3])e(=)i(\(m)g(-)g(n\))g(*)h(21;)104 2145 |
| y(})104 2191 y Fi(3)1277 1734 y Fl(void)e(vnum_result)o(10)o(\(in)o(t)f |
| (*data\))1277 1780 y({)1317 1826 y(int)h(i)h(=)h(data[0];)1317 |
| 1871 y(int)e(m)h(=)h(i)f(+)g(1;)1317 1917 y(int)f(j)h(=)h(data[1];)1317 |
| 1963 y(int)e(n)h(=)h(j)f(+)g(1;)1317 2008 y(data[2])e(=)i(m)g(+)g(n;) |
| 1317 2054 y(if)f(\(i)h(==)g(j\))1356 2100 y(data[3])e(=)i(0;)1277 |
| 2145 y(})1277 2191 y Fi(3)0 2249 y Fh(See)11 b Fm(26b)n(d,)j(27b)n(d,)g |
| (28ac,)f(29ac,)h(30b,)g(31ac)p Fh(.)-150 2329 y Fm(30e)98 |
| b Fk(h)p Fw(V)m(alue)14 b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 |
| 2375 y Fl({)143 2421 y(int)18 b(data[4])f(=)j({)f(0,)g(0)g(};)143 |
| 2466 y(ok)g(=)g(test\(ok,)e(vnum_resu)o(lt)o(10,)f(vnum_test)o(10,)g |
| (data,)h(10,)i("conditio)o(nal)o(-ba)o(se)o(d)e(assertio)o(ns")o(\);) |
| 104 2512 y(})p Fi(3)0 2569 y Fh(See)11 b(26a,)f Fm(26c,)k(27ac)n(e,)g |
| (28b)n(d,)g(29b,)f(30ac,)h(31b,)g(32a)p Fh(.)954 2874 |
| y Ft(30)p eop |
| %%Page: 31 36 |
| 31 35 bop 0 91 a Fp(5.5)70 b(Conditional)21 b(V)-6 b(alue)22 |
| b(Num)n(b)r(ers)0 182 y Ft(Analogous)9 b(to)i(the)g(conditional)d |
| (constan)o(ts)k(found)e(b)o(y)g(W)m(egman)e(and)i(Zadec)o(ks's)h |
| (constan)o(t)g(propagation)e(algorithm)f([22)o(],)0 232 |
| y(com)o(bines)13 b(v)n(alue)h(n)o(um)o(b)q(ering)e(and)i(remo)o(v)n(al) |
| e(of)i(unreac)o(hable)h(co)q(de)g(to)f(\014nd)g(more)f(equalities)h |
| (than)g(could)g(b)q(e)g(found)g(b)o(y)0 282 y(running)j(the)h(passes)h |
| (separately)m(.)28 b(This)17 b(example)f(is)i(due)f(to)h(Cli\013)e |
| (Clic)o(k,)h(who)g(has)g(an)h(algorithm)c(to)j(handle)h(these)0 |
| 332 y(cases.)-150 400 y Fm(31a)96 b Fl("valnum.c")o Fk(\021)104 |
| 446 y Fl(void)18 b(vnum_test)o(11\()o(in)o(t)f(*data\))104 |
| 492 y({)143 538 y(int)h(n;)143 583 y(int)g(stop)h(=)g(data[3];)143 |
| 629 y(int)f(j)i(=)f(data[1];)143 675 y(int)f(k)i(=)f(j;)143 |
| 720 y(int)f(i)i(=)f(1;)143 766 y(for)f(\(n=0;)g(n<stop;)f(n++\))h({)182 |
| 812 y(if)h(\(j)g(!=)g(k\))g(i)g(=)g(2;)182 857 y(if)g(\(i)g(!=)g(1\))g |
| (k)g(=)g(2;)182 903 y(data[data[)o(2]])d(=)j(2;)143 949 |
| y(})143 994 y(data[1])e(=)i(i;)104 1040 y(})104 1086 |
| y Fi(3)1277 446 y Fl(void)f(vnum_result)o(11)o(\(in)o(t)f(*data\))1277 |
| 492 y({)1317 538 y(int)h(n;)1317 583 y(int)g(stop)g(=)h(data[3];)1317 |
| 629 y(for)f(\(n=0;)g(n<stop;)f(n++\))1356 675 y(data[data)o([2])o(])f |
| (=)k(2;)1317 720 y(data[1])d(=)i(1;)1277 766 y(})1277 |
| 812 y Fi(3)0 1143 y Fh(See)11 b Fm(26b)n(d,)j(27b)n(d,)g(28ac,)f(29ac,) |
| h(30b)n(d,)g(31c)p Fh(.)-150 1223 y Fm(31b)98 b Fk(h)p |
| Fw(V)m(alue)14 b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 |
| 1269 y Fl({)143 1315 y(int)18 b(data[4])f(=)j({)f(0,)g(1,)g(2,)f(3)i |
| (};)143 1361 y(ok)f(=)g(test\(1,)e(vnum_resul)o(t1)o(1,)f(vnum_test1)o |
| (1,)g(data,)i(11,)g("condition)o(al)e(value)i(numbers"\))o(;)104 |
| 1406 y(})p Fi(3)0 1464 y Fh(See)11 b(26a,)f Fm(26c,)k(27ac)n(e,)g(28b)n |
| (d,)g(29b,)f(30ac)n(e,)i(32a)p Fh(.)0 1579 y Fp(5.6)70 |
| b(Com)n(bining)21 b(V)-6 b(alue)22 b(Num)n(b)r(ering)g(and)i(Constan)n |
| (t)f(Propagation)0 1670 y Ft(This)12 b(one)f(is)h(quite)g(hard.)17 |
| b(Com)o(bines)10 b(global)g(v)n(alue)h(n)o(um)o(b)q(ering,)f(constan)o |
| (t)j(propagation,)d(and)i(elimination)c(of)j(unreac)o(h-)0 |
| 1719 y(able)j(co)q(de.)k(Again,)13 b(Clic)o(k's)g(approac)o(h)h(should) |
| g(handle)f(this)h(sort)h(of)e(case.)-150 1796 y Fm(31c)98 |
| b Fl("valnum.c")o Fk(\021)104 1842 y Fl(void)18 b(vnum_test)o(12\()o |
| (in)o(t)f(*data\))104 1888 y({)143 1933 y(int)h(n;)143 |
| 1979 y(int)g(stop)h(=)g(data[3];)143 2025 y(int)f(j)i(=)f(data[1];)143 |
| 2070 y(int)f(k)i(=)f(j;)143 2116 y(int)f(i)i(=)f(1;)143 |
| 2162 y(for)f(\(n=0;)g(n<stop;)f(n++\))h({)182 2207 y(if)h(\(j)g(!=)g |
| (k\))g(i)g(=)g(2;)182 2253 y(i)g(=)h(2)f(-)g(i;)182 2299 |
| y(if)g(\(i)g(!=)g(1\))g(k)g(=)g(2;)182 2344 y(data[data[)o(2]])d(=)j |
| (2;)143 2390 y(})143 2436 y(data[1])e(=)i(i;)104 2481 |
| y(})104 2527 y Fi(3)1277 1842 y Fl(void)f(vnum_result)o(12)o(\(in)o(t)f |
| (*data\))1277 1888 y({)1317 1933 y(int)h(n;)1317 1979 |
| y(int)g(stop)g(=)h(data[3];)1317 2025 y(for)f(\(n=0;)g(n<stop;)f(n++\)) |
| 1356 2070 y(data[data)o([2])o(])f(=)k(2;)1317 2116 y(data[1])d(=)i(1;) |
| 1277 2162 y(})1277 2207 y Fi(3)0 2585 y Fh(See)11 b Fm(26b)n(d,)j(27b)n |
| (d,)g(28ac,)f(29ac,)h(30b)n(d,)g(31a)p Fh(.)954 2874 |
| y Ft(31)p eop |
| %%Page: 32 37 |
| 32 36 bop -150 78 a Fm(32a)96 b Fk(h)p Fw(V)m(alue)14 |
| b(n)o(um)o(b)q(ering)p Fk(i)e(\021)104 124 y Fl({)143 |
| 170 y(int)18 b(data[4])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 |
| 215 y(ok)f(=)g(test\(ok,)e(vnum_resu)o(lt)o(12,)f(vnum_test)o(12,)g |
| (data,)h(12,)i("cprop)e(+)i(vnum"\);)104 261 y(})p Fi(3)0 |
| 319 y Fh(See)11 b(26a,)f Fm(26c,)k(27ac)n(e,)g(28b)n(d,)g(29b,)f(30ac)n |
| (e,)i(31b)p Fh(.)0 433 y Fp(5.7)70 b(Reasso)r(ciation)0 |
| 532 y Fo(5.7.1)55 b(Expressions)0 617 y(5.7.2)g(Lo)r(cal)0 |
| 702 y(5.7.3)g(Global)0 804 y Fp(5.8)70 b(Algebraic)21 |
| b(Simpli\014cati)o(ons)821 936 y Fq(x)12 b Ft(=)g Fq(x)41 |
| b Fn(\))g Ft(true)821 998 y Fq(x)12 b Fn(6)p Ft(=)g Fq(x)41 |
| b Fn(\))g Ft(false)821 1061 y Fq(x)12 b(>)g(x)41 b Fn(\))g |
| Ft(false)821 1123 y Fq(x)12 b Fn(\025)g Fq(x)41 b Fn(\))g |
| Ft(true)821 1185 y Fq(x)12 b(<)g(x)41 b Fn(\))g Ft(false)821 |
| 1248 y Fq(x)12 b Fn(\024)g Fq(x)41 b Fn(\))g Ft(true)831 |
| 1310 y Fq(x)9 b Fn(\\)g Fq(x)41 b Fn(\))g Fq(x)831 1372 |
| y(x)9 b Fn([)g Fq(x)41 b Fn(\))g Fq(x)826 1434 y(x)9 |
| b Fn(\000)h Fq(x)41 b Fn(\))g Ft(0)0 1634 y Fp(5.9)70 |
| b(Protot)n(yp)r(es)-150 1719 y Fm(32b)98 b Fk(h)p Fw(Protot)o(yp)q(es)p |
| Fk(i)12 b(\021)104 1765 y Fl(extern)17 b(void)h(vnum_test1)o(\(in)o(t)e |
| (*\);)104 1811 y(extern)h(void)h(vnum_test2)o(\(in)o(t)e(*\);)104 |
| 1856 y(extern)h(void)h(vnum_test3)o(\(in)o(t)e(*\);)104 |
| 1902 y(extern)h(void)h(vnum_test4)o(\(in)o(t)e(*\);)104 |
| 1948 y(extern)h(void)h(vnum_test5)o(\(in)o(t)e(*\);)104 |
| 1993 y(extern)h(void)h(vnum_test6)o(\(in)o(t)e(*\);)104 |
| 2039 y(extern)h(void)h(vnum_test7)o(\(in)o(t)e(*\);)104 |
| 2085 y(extern)h(void)h(vnum_test8)o(\(in)o(t)e(*\);)104 |
| 2130 y(extern)h(void)h(vnum_test9)o(\(in)o(t)e(*\);)104 |
| 2176 y(extern)h(void)h(vnum_test1)o(0\(i)o(nt)e(*\);)104 |
| 2222 y(extern)h(void)h(vnum_test1)o(1\(i)o(nt)e(*\);)104 |
| 2267 y(extern)h(void)h(vnum_test1)o(2\(i)o(nt)e(*\);)104 |
| 2313 y Fi(3)1199 1765 y Fl(extern)h(void)h(vnum_resul)o(t1\()o(int)e |
| (*\);)1199 1811 y(extern)h(void)h(vnum_resul)o(t2\()o(int)e(*\);)1199 |
| 1856 y(extern)h(void)h(vnum_resul)o(t3\()o(int)e(*\);)1199 |
| 1902 y(extern)h(void)h(vnum_resul)o(t4\()o(int)e(*\);)1199 |
| 1948 y(extern)h(void)h(vnum_resul)o(t5\()o(int)e(*\);)1199 |
| 1993 y(extern)h(void)h(vnum_resul)o(t6\()o(int)e(*\);)1199 |
| 2039 y(extern)h(void)h(vnum_resul)o(t7\()o(int)e(*\);)1199 |
| 2085 y(extern)h(void)h(vnum_resul)o(t8\()o(int)e(*\);)1199 |
| 2130 y(extern)h(void)h(vnum_resul)o(t9\()o(int)e(*\);)1199 |
| 2176 y(extern)h(void)h(vnum_resul)o(t10)o(\(in)o(t)e(*\);)1199 |
| 2222 y(extern)h(void)h(vnum_resul)o(t11)o(\(in)o(t)e(*\);)1199 |
| 2267 y(extern)h(void)h(vnum_resul)o(t12)o(\(in)o(t)e(*\);)1199 |
| 2313 y Fi(3)0 2370 y Fh(See)11 b(3b,)g Fm(4,)h(7b,)i(8e,)f(17,)g(25,)g |
| (39,)g(45c)p Fh(.)954 2874 y Ft(32)p eop |
| %%Page: 33 38 |
| 33 37 bop 0 257 a Fu(Chapter)34 b(6)0 423 y(Co)s(de)g(Motion)0 |
| 598 y Ft(Redundancies)15 b(that)g(can't)f(simply)e(b)q(e)j(remo)o(v)o |
| (ed.)k(The)14 b(examples)g(I'll)f(test)i(for)f(are)h(partial)e |
| (redundancy)j(eliminatio)o(n,)0 648 y(lo)q(op)d(unswitc)o(hing,)g(and)h |
| (the)h(p)q(ossibilit)o(y)d(of)h(hoisting)g(en)o(tire)i(in)o(v)n(arian)o |
| (t)d(con)o(trol)i(structures)i(out)e(of)f(lo)q(ops.)-150 |
| 711 y Fm(33a)96 b Fk(h)p Fw(Ev)n(aluation)16 b(driv)o(ers)p |
| Fk(i)c(\021)104 758 y Fl({)143 803 y(int)18 b(ok;)143 |
| 849 y(puts\("Code)e(motion"\);)143 895 y Fk(h)p Fw(Co)q(de)d(motion)h |
| Fm(33c,)g Fj(:)5 b(:)h(:)g Fk(i)104 940 y Fl(})p Fi(3)0 |
| 997 y Fh(See)11 b(3c,)g Fm(11a,)i(18a,)g(26a,)h(40a)p |
| Fh(.)0 1109 y Fp(6.1)70 b(In)n(v)l(arian)n(t)24 b(Expressions)0 |
| 1200 y Ft([18)o(])0 1313 y Fo(6.1.1)55 b(D)n(A)n(Gs)0 |
| 1390 y Ft(b)q(oth)12 b(of)g(these)i(examples)d(could)h(b)q(e)h(done)f |
| (via)g(cloning)f(follo)o(w)o(ed)g(b)o(y)g(v)n(alue)h(n)o(um)o(b)q |
| (ering)f(\(or)h(some)g(other)g(form)f(of)g(simple)0 1440 |
| y(redundancy)k(elimination\))0 1544 y Fs(The)h(Protot)o(ypi)o(cal)d |
| (Case)-150 1606 y Fm(33b)98 b Fl("motion.c")o Fk(\021)104 |
| 1653 y Fl(void)18 b(motion_te)o(st1)o(\(i)o(nt)e(*data\))104 |
| 1698 y({)143 1744 y(int)i(i;)143 1790 y(if)h(\(data[1]\))182 |
| 1835 y(i)g(=)h(data[0])d(+)i(data[3];)143 1881 y(else)f({)182 |
| 1927 y(data[data[)o(2]])e(=)j(2;)182 1972 y(i)g(=)h(5;)143 |
| 2018 y(})143 2064 y(data[3])d(=)i(data[0])e(+)i(data[3];)143 |
| 2109 y(data[4])e(=)i(i;)104 2155 y(})104 2201 y Fi(3)1258 |
| 1653 y Fl(void)f(motion_re)o(sul)o(t1)o(\(in)o(t)f(*data\))1258 |
| 1698 y({)1297 1744 y(int)h(i;)1297 1790 y(int)g(j;)1297 |
| 1835 y(if)h(\(data[1]\))d({)1336 1881 y(j)j(=)h(data[0])d(+)i(data[3];) |
| 1336 1927 y(i)g(=)h(j;)1297 1972 y(})1297 2018 y(else)e({)1336 |
| 2064 y(data[data[)o(2]])e(=)j(2;)1336 2109 y(i)g(=)h(5;)1336 |
| 2155 y(j)f(=)h(data[0])d(+)i(data[3];)1297 2201 y(})1297 |
| 2246 y(data[4])e(=)i(j;)1297 2292 y(data[5])e(=)i(i;)1258 |
| 2338 y(})1258 2383 y Fi(3)0 2440 y Fh(See)11 b Fm(34ac,)i(35ac,)h |
| (36ac,)g(37ac,)g(38ac)p Fh(.)-150 2503 y Fm(33c)98 b |
| Fk(h)p Fw(Co)q(de)13 b(motion)p Fk(i)f(\021)104 2549 |
| y Fl({)143 2595 y(int)18 b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 |
| 2640 y(ok)f(=)g(test\(1,)e(motion_res)o(ul)o(t1,)f(motion_te)o(st1)o(,) |
| g(data,)i(1,)h("DAGs"\);)104 2686 y(})p Fi(3)0 2743 y |
| Fh(See)11 b(33a,)f Fm(34b)n(d,)k(35b)n(d,)g(36b)n(d,)g(37b)n(d,)g(38b)n |
| (d)p Fh(.)954 2874 y Ft(33)p eop |
| %%Page: 34 39 |
| 34 38 bop 0 91 a Fs(Edge)16 b(Placemen)o(t)-150 153 y |
| Fm(34a)96 b Fl("motion.c")o Fk(\021)104 199 y Fl(void)18 |
| b(motion_te)o(st2)o(\(i)o(nt)e(*data\))104 245 y({)143 |
| 291 y(int)i(j;)143 336 y(int)g(i)i(=)f(1;)143 382 y(if)g(\(data[1]\))d |
| ({)182 428 y(data[data[)o(2]])g(=)j(2;)182 473 y(j)g(=)h(data[0])d(+)i |
| (data[3];)182 519 y(i)g(=)h(i)f(+)g(j;)143 565 y(})143 |
| 610 y(data[4])e(=)i(data[0])e(+)i(data[3];)143 656 y(data[5])e(=)i(i;) |
| 104 702 y(})104 747 y Fi(3)1258 199 y Fl(void)f(motion_re)o(sul)o(t2)o |
| (\(in)o(t)f(*data\))1258 245 y({)1297 291 y(int)h(j;)1297 |
| 336 y(int)g(i)i(=)f(1;)1297 382 y(if)g(\(data[1]\))d({)1336 |
| 428 y(data[data[)o(2]])g(=)j(2;)1336 473 y(j)g(=)h(data[0])d(+)i |
| (data[3];)1336 519 y(i)g(=)h(i)f(+)g(j;)1297 565 y(})1297 |
| 610 y(else)1336 656 y(j)g(=)h(data[0])d(+)i(data[3];)1297 |
| 702 y(data[4])e(=)i(j;)1297 747 y(data[5])e(=)i(i;)1258 |
| 793 y(})1258 839 y Fi(3)0 896 y Fh(See)11 b Fm(33b,)i(34c,)h(35ac,)g |
| (36ac,)f(37ac,)h(38ac)p Fh(.)-150 976 y Fm(34b)98 b Fk(h)p |
| Fw(Co)q(de)13 b(motion)p Fk(i)f(\021)104 1022 y Fl({)143 |
| 1068 y(int)18 b(data[6])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 |
| 1114 y(ok)f(=)g(test\(ok,)e(motion_re)o(su)o(lt2)o(,)f(motion_test)o |
| (2,)g(data,)i(2,)h("DAGs)e(\(edge)h(placement)o(\)"\))o(;)104 |
| 1159 y(})p Fi(3)0 1217 y Fh(See)11 b(33a,)f Fm(33c,)k(34d,)f(35b)n(d,)h |
| (36b)n(d,)g(37b)n(d,)g(38b)n(d)p Fh(.)0 1320 y Fo(6.1.2)55 |
| b(Lo)r(ops)-150 1383 y Fm(34c)98 b Fl("motion.c")o Fk(\021)104 |
| 1430 y Fl(void)18 b(motion_te)o(st3)o(\(i)o(nt)e(*data\))104 |
| 1475 y({)143 1521 y(int)i(i)i(=)f(0;)143 1566 y(int)f(k)i(=)f(data[2];) |
| 143 1612 y(int)f(j)i(=)f(data[0];)143 1658 y(do)182 1703 |
| y(i)g(=)h(21)f(*)g(j)g(+)g(i)g(+)h(1;)143 1749 y(while)e(\(i)h(<)g |
| (k\);)143 1795 y(data[4])e(=)i(i;)104 1840 y(})104 1886 |
| y Fi(3)1258 1430 y Fl(void)f(motion_re)o(sul)o(t3)o(\(in)o(t)f(*data\)) |
| 1258 1475 y({)1297 1521 y(int)h(i)i(=)f(0;)1297 1566 |
| y(int)f(k)i(=)f(data[2];)1297 1612 y(int)f(j)i(=)f(21)g(*)g(data[0];) |
| 1297 1658 y(do)1336 1703 y(i)g(=)h(j)f(+)g(i)g(+)h(1;)1297 |
| 1749 y(while)e(\(i)h(<)g(k\);)1297 1795 y(data[4])e(=)i(i;)1258 |
| 1840 y(})1258 1886 y Fi(3)0 1944 y Fh(See)11 b Fm(33b,)i(34a,)h(35ac,)f |
| (36ac,)h(37ac,)g(38ac)p Fh(.)-150 2024 y Fm(34d)96 b |
| Fk(h)p Fw(Co)q(de)13 b(motion)p Fk(i)f(\021)104 2070 |
| y Fl({)143 2116 y(int)18 b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 |
| 2161 y(ok)f(=)g(test\(1,)e(motion_res)o(ul)o(t3,)f(motion_te)o(st3)o(,) |
| g(data,)i(3,)h("loops"\);)104 2207 y(})p Fi(3)0 2264 |
| y Fh(See)11 b(33a,)f Fm(33c,)k(34b,)f(35b)n(d,)h(36b)n(d,)g(37b)n(d,)g |
| (38b)n(d)p Fh(.)0 2348 y Ft(See)h(if)e(they're)h(smart)f(enough)h(to)g |
| (hoist)g(a)f(divide)h(\(in)f(this)h(case,)h(a)e(safe)h(mo)o(v)o(e\).) |
| 954 2874 y(34)p eop |
| %%Page: 35 40 |
| 35 39 bop -150 73 a Fm(35a)96 b Fl("motion.c")o Fk(\021)104 |
| 119 y Fl(void)18 b(motion_te)o(st4)o(\(i)o(nt)e(*data\))104 |
| 164 y({)143 210 y(int)i(i)i(=)f(0;)143 256 y(int)f(j)i(=)f(data[2];)143 |
| 301 y(do)g({)182 347 y(data[i])e(=)i(2)h(/)f(j)g(+)g(i)h(-)f(1;)182 |
| 393 y(i++;)143 438 y(})g(while)f(\(i)h(<)g(data[2]\);)104 |
| 484 y(})104 530 y Fi(3)1258 119 y Fl(void)f(motion_re)o(sul)o(t4)o |
| (\(in)o(t)f(*data\))1258 164 y({)1297 210 y(int)h(i)i(=)f(0;)1297 |
| 256 y(int)f(j)i(=)f(2)g(/)g(data[2];)1297 301 y(do)g({)1336 |
| 347 y(data[i])e(=)i(j)h(+)f(i)g(-)g(1;)1336 393 y(i++;)1297 |
| 438 y(})g(while)f(\(i)h(<)g(data[2]\);)1258 484 y(})1258 |
| 530 y Fi(3)0 587 y Fh(See)11 b Fm(33b,)i(34ac,)h(35c,)g(36ac,)f(37ac,)h |
| (38ac)p Fh(.)-150 667 y Fm(35b)98 b Fk(h)p Fw(Co)q(de)13 |
| b(motion)p Fk(i)f(\021)104 714 y Fl({)143 759 y(int)18 |
| b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 805 y(\(void\))d |
| (test\(ok,)g(motion_re)o(sul)o(t4)o(,)g(motion_te)o(st)o(4,)f(data,)i |
| (4,)h("loops)e(\(hoisting)f(divide\)"\);)104 851 y(})p |
| Fi(3)0 908 y Fh(See)11 b(33a,)f Fm(33c,)k(34b)n(d,)g(35d,)f(36b)n(d,)h |
| (37b)n(d,)g(38b)n(d)p Fh(.)0 1006 y Fs(Irreducible)e(Lo)q(ops)-150 |
| 1068 y Fm(35c)98 b Fl("motion.c")o Fk(\021)104 1114 y |
| Fl(void)18 b(motion_te)o(st5)o(\(i)o(nt)e(*data\))104 |
| 1159 y({)143 1205 y(int)i(i)i(=)f(0;)143 1251 y(int)f(j)i(=)f(data[0];) |
| 143 1296 y(if)g(\(data[1]\))182 1342 y(goto)f(here;)143 |
| 1388 y(j)h(=)g(data[3])e(+)j(j;)143 1433 y(do)f({)182 |
| 1479 y(i++;)104 1525 y(here:)182 1570 y(data[i])e(=)i(21)g(*)g(j)h(+)f |
| (i;)143 1616 y(})g(while)f(\(i)h(<)g(data[2]\);)104 1662 |
| y(})104 1707 y Fi(3)1258 1114 y Fl(void)f(motion_re)o(sul)o(t5)o(\(in)o |
| (t)f(*data\))1258 1159 y({)1297 1205 y(int)h(i)i(=)f(0;)1297 |
| 1251 y(int)f(j)i(=)f(data[0];)1297 1296 y(if)g(\(data[1]\))d({)1336 |
| 1342 y(j)j(=)h(j)f(*)g(21;)1336 1388 y(goto)f(here;)1297 |
| 1433 y(})1297 1479 y(j)h(=)g(data[3])e(+)j(j;)1297 1525 |
| y(j)f(=)g(j)h(*)f(21;)1297 1570 y(do)g({)1336 1616 y(i++;)1258 |
| 1662 y(here:)1336 1707 y(data[i])e(=)i(j)h(+)f(i;)1297 |
| 1753 y(})g(while)f(\(i)h(<)g(data[2]\);)1258 1799 y(})1258 |
| 1844 y Fi(3)0 1902 y Fh(See)11 b Fm(33b,)i(34ac,)h(35a,)f(36ac,)h |
| (37ac,)g(38ac)p Fh(.)-150 1982 y Fm(35d)96 b Fk(h)p Fw(Co)q(de)13 |
| b(motion)p Fk(i)f(\021)104 2028 y Fl({)143 2074 y(int)18 |
| b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 2119 y(\(void\))d |
| (test\(ok,)g(motion_re)o(sul)o(t5)o(,)g(motion_te)o(st)o(5,)f(data,)i |
| (5,)h("irreduci)o(ble)d(loops"\);)104 2165 y(})p Fi(3)0 |
| 2223 y Fh(See)11 b(33a,)f Fm(33c,)k(34b)n(d,)g(35b,)f(36b)n(d,)h(37b)n |
| (d,)g(38b)n(d)p Fh(.)954 2874 y Ft(35)p eop |
| %%Page: 36 41 |
| 36 40 bop 0 91 a Fo(6.1.3)55 b(Reasso)r(ciation)-150 |
| 145 y Fm(36a)96 b Fl("motion.c")o Fk(\021)104 191 y Fl(void)18 |
| b(motion_te)o(st6)o(\(i)o(nt)e(*data\))104 237 y({)143 |
| 283 y(int)i(j)i(=)f(data[1];)143 328 y(int)f(k)i(=)f(data[2];)143 |
| 374 y(int)f(i)i(=)f(data[0];)143 420 y(int)f(n)i(=)f(data[3];)143 |
| 465 y(do)182 511 y(i)g(=)h(j)f(+)g(i)g(+)h(k;)143 557 |
| y(while)e(\(i)h(<)g(n\);)143 602 y(data[4])e(=)i(i;)104 |
| 648 y(})104 694 y Fi(3)1258 191 y Fl(void)f(motion_re)o(sul)o(t6)o |
| (\(in)o(t)f(*data\))1258 237 y({)1297 283 y(int)h(j)i(=)f(data[1];)1297 |
| 328 y(int)f(k)i(=)f(data[2];)1297 374 y(int)f(i)i(=)f(data[0];)1297 |
| 420 y(int)f(n)i(=)f(data[3];)1297 465 y(int)f(m)i(=)f(j)g(+)g(k;)1297 |
| 511 y(do)1336 557 y(i)g(=)h(m)f(+)g(i;)1297 602 y(while)f(\(i)h(<)g |
| (n\);)1297 648 y(data[4])e(=)i(i;)1258 694 y(})1258 739 |
| y Fi(3)0 797 y Fh(See)11 b Fm(33b,)i(34ac,)h(35ac,)g(36c,)f(37ac,)h |
| (38ac)p Fh(.)-150 877 y Fm(36b)98 b Fk(h)p Fw(Co)q(de)13 |
| b(motion)p Fk(i)f(\021)104 923 y Fl({)143 969 y(int)18 |
| b(data[5])f(=)j({)f(0,)g(1,)g(0,)f(3)i(};)143 1014 y(\(void\))d |
| (test\(ok,)g(motion_re)o(sul)o(t6)o(,)g(motion_te)o(st)o(6,)f(data,)i |
| (6,)h("reassoci)o(ati)o(on)o("\);)104 1060 y(})p Fi(3)0 |
| 1118 y Fh(See)11 b(33a,)f Fm(33c,)k(34b)n(d,)g(35b)n(d,)g(36d,)f(37b)n |
| (d,)h(38b)n(d)p Fh(.)0 1215 y Fs(Aggressiv)o(e)g(Co)q(de)i(Motion)0 |
| 1292 y Ft(mo)o(ving)11 b(an)j(expression)h(on)o(to)e(a)h(path)g(where)h |
| (it)e(ma)o(y)f(not)i(ha)o(v)o(e)g(b)q(een)h(executed,)g(p)q(ossibly)f |
| (slo)o(wing)e(the)j(co)q(de.)-150 1368 y Fm(36c)98 b |
| Fl("motion.c")o Fk(\021)104 1414 y Fl(void)18 b(motion_te)o(st7)o(\(i)o |
| (nt)e(*data\))104 1460 y({)143 1506 y(int)i(i)i(=)f(data[1];)143 |
| 1551 y(int)f(j)i(=)f(data[0];)143 1597 y(do)g({)182 1643 |
| y(if)g(\(i)g(&)g(1\))g(data[data[)o(2])o(])e(=)i(21)g(*)g(j)g(+)g(i;) |
| 182 1688 y(i++;)143 1734 y(})g(while)f(\(i)h(<)g(data[3]\);)104 |
| 1780 y(})104 1825 y Fi(3)1121 1414 y Fl(void)f(motion_r)o(esu)o(lt7)o |
| (\(i)o(nt)e(*data\))1121 1460 y({)1160 1506 y(int)i(i)h(=)h(data[1];) |
| 1160 1551 y(int)e(j)h(=)h(data[0])d(*)i(21;)1160 1597 |
| y(do)g({)1199 1643 y(if)g(\(i)g(&)g(1\))g(data[data)o([2)o(]])d(=)k(j)f |
| (+)g(i;)1199 1688 y(i++;)1160 1734 y(})g(while)f(\(i)g(<)i(data[3]\);) |
| 1121 1780 y(})1121 1825 y Fi(3)0 1883 y Fh(See)11 b Fm(33b,)i(34ac,)h |
| (35ac,)g(36a,)f(37ac,)h(38ac)p Fh(.)-150 1963 y Fm(36d)96 |
| b Fk(h)p Fw(Co)q(de)13 b(motion)p Fk(i)f(\021)104 2009 |
| y Fl({)143 2055 y(int)18 b(data[5])f(=)j({)f(0,)g(1,)g(4,)f(10)h(};)143 |
| 2101 y(ok)g(=)g(!test\(1,)e(motion_re)o(su)o(lt7)o(,)f(motion_test)o |
| (7,)g(data,)i(7,)h("aggress)o(ive)o("\);)104 2146 y(})p |
| Fi(3)0 2204 y Fh(See)11 b(33a,)f Fm(33c,)k(34b)n(d,)g(35b)n(d,)g(36b,)f |
| (37b)n(d,)h(38b)n(d)p Fh(.)954 2874 y Ft(36)p eop |
| %%Page: 37 42 |
| 37 41 bop 0 91 a Fs(Lo)q(op)15 b(Rotation)-150 153 y |
| Fm(37a)96 b Fl("motion.c")o Fk(\021)104 199 y Fl(void)18 |
| b(motion_te)o(st8)o(\(i)o(nt)e(*data\))104 245 y({)143 |
| 291 y(int)i(i)i(=)f(0;)143 336 y(int)f(j)i(=)f(data[0];)143 |
| 382 y(while)f(\(i)h(<)g(data[2]\))d({)182 428 y(data[i])h(=)i(21)g(*)g |
| (j)h(+)f(i;)182 473 y(i++;)143 519 y(})104 565 y(})104 |
| 610 y Fi(3)1258 199 y Fl(void)f(motion_re)o(sul)o(t8)o(\(in)o(t)f |
| (*data\))1258 245 y({)1297 291 y(int)h(i)i(=)f(0;)1297 |
| 336 y(int)f(j)i(=)f(data[0];)1297 382 y(if)g(\(i)g(<)g(data[2]\))d({) |
| 1336 428 y(j)j(=)h(j)f(*)g(21;)1336 473 y(do)g({)1375 |
| 519 y(data[i])e(=)j(j)f(+)g(i;)1375 565 y(i++;)1336 610 |
| y(})g(while)f(\(i)h(<)g(data[2]\);)1297 656 y(})1258 |
| 702 y(})1258 747 y Fi(3)0 805 y Fh(See)11 b Fm(33b,)i(34ac,)h(35ac,)g |
| (36ac,)f(37c,)h(38ac)p Fh(.)0 886 y Ft(If)h(they're)h(doing)e |
| (aggressiv)o(e)h(co)q(de)h(motion,)d(then)j(w)o(e)f(w)o(on't)g(b)q(e)h |
| (able)e(to)h(distinguish)g(the)h(conserv)n(ativ)o(e)f(approac)o(h)h(of) |
| 0 936 y(using)e(lo)q(op)f(rotation.)-150 1017 y Fm(37b)98 |
| b Fk(h)p Fw(Co)q(de)13 b(motion)p Fk(i)f(\021)104 1064 |
| y Fl({)143 1109 y(int)18 b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 |
| 1155 y(\(void\))d(test\(ok,)g(motion_re)o(sul)o(t8)o(,)g(motion_te)o |
| (st)o(8,)f(data,)i(8,)h("loop)e(rotation"\);)104 1201 |
| y(})p Fi(3)0 1258 y Fh(See)11 b(33a,)f Fm(33c,)k(34b)n(d,)g(35b)n(d,)g |
| (36b)n(d,)f(37d,)h(38b)n(d)p Fh(.)0 1339 y Ft(The)k(test)h(ab)q(o)o(v)o |
| (e)f(migh)o(t)e(ha)o(v)o(e)i(b)q(een)h(handled)f(b)o(y)g(the)g(fron)o |
| (t)g(end)g(simply)e(translating)i(the)g Fg(while)f Ft(lo)q(op)g(in)o |
| (to)h(an)f Fg(if)0 1389 y Ft(con)o(taining)d(a)h Fg(do-while)f |
| Ft(\(whic)o(h)h(I)h(think)f(of)g(as)g(the)h(correct)h(approac)o(h\).)23 |
| b(Here)16 b(w)o(e)g(try)g(the)g(same)e(test,)j(but)e(using)g(a)0 |
| 1439 y(lo)q(op)e(built)g(with)h Fg(goto)f Ft(statemen)o(ts.)-150 |
| 1516 y Fm(37c)98 b Fl("motion.c")o Fk(\021)104 1562 y |
| Fl(void)18 b(motion_te)o(st9)o(\(i)o(nt)e(*data\))104 |
| 1608 y({)143 1654 y(int)i(i)i(=)f(0;)143 1699 y(int)f(j)i(=)f(data[0];) |
| 104 1745 y(loop:)143 1791 y(if)g(\(i)g(>=)g(data[2]\))d(return;)182 |
| 1836 y(data[i])h(=)i(21)g(*)g(j)h(+)f(i;)182 1882 y(i++;)182 |
| 1928 y(goto)f(loop;)104 1973 y(})104 2019 y Fi(3)1258 |
| 1562 y Fl(void)g(motion_re)o(sul)o(t9)o(\(in)o(t)f(*data\))1258 |
| 1608 y({)1297 1654 y(int)h(i)i(=)f(0;)1297 1699 y(int)f(j)i(=)f |
| (data[0];)1297 1745 y(if)g(\(i)g(>=)g(data[2]\))d(return;)1297 |
| 1791 y(j)j(=)g(j)h(*)f(21;)1258 1836 y(loop:)1336 1882 |
| y(data[i])e(=)i(j)h(+)f(i;)1336 1928 y(i++;)1297 1973 |
| y(if)g(\(i)g(<)g(data[2]\))d(goto)j(loop;)1258 2019 y(})1258 |
| 2065 y Fi(3)0 2122 y Fh(See)11 b Fm(33b,)i(34ac,)h(35ac,)g(36ac,)f |
| (37a,)h(38ac)p Fh(.)-150 2202 y Fm(37d)96 b Fk(h)p Fw(Co)q(de)13 |
| b(motion)p Fk(i)f(\021)104 2249 y Fl({)143 2294 y(int)18 |
| b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(3)i(};)143 2340 y(\(void\))d |
| (test\(ok,)g(motion_re)o(sul)o(t9)o(,)g(motion_te)o(st)o(9,)f(data,)i |
| (9,)h("loop)e(rotation"\);)104 2386 y(})p Fi(3)0 2443 |
| y Fh(See)11 b(33a,)f Fm(33c,)k(34b)n(d,)g(35b)n(d,)g(36b)n(d,)f(37b,)h |
| (38b)n(d)p Fh(.)0 2558 y Fp(6.2)70 b(In)n(v)l(arian)n(t)24 |
| b(Con)n(trol)e(Flo)n(w)0 2657 y Fo(6.2.1)55 b(Hoisting)18 |
| b(In)n(v)m(arian)n(t)h(Con)n(trol)g(Flo)n(w)0 2734 y |
| Ft([14)o(].)f(Hmmm)n(.)d(This)f(one)g(could)g(also)f(b)q(e)i(done)f |
| (via)f(lo)q(op)g(unswitc)o(hing.)954 2874 y(37)p eop |
| %%Page: 38 43 |
| 38 42 bop -150 73 a Fm(38a)96 b Fl("motion.c")o Fk(\021)104 |
| 119 y Fl(void)18 b(motion_te)o(st1)o(0\()o(int)e(*data\))104 |
| 164 y({)143 210 y(int)i(j;)143 256 y(int)g(p)i(=)f(data[1];)143 |
| 301 y(int)f(i)i(=)f(data[0];)143 347 y(do)g({)182 393 |
| y(if)g(\(p\))221 438 y(j)h(=)f(1;)182 484 y(else)221 |
| 530 y(j)h(=)f(2;)182 575 y(i)g(=)h(i)f(+)g(j;)182 621 |
| y(data[data[)o(2]])d(=)j(2;)143 667 y(})g(while)f(\(i)h(<)g(data[3]\);) |
| 104 712 y(})104 758 y Fi(3)1238 119 y Fl(void)f(motion_res)o(ult)o(10)o |
| (\(in)o(t)f(*data\))1238 164 y({)1277 210 y(int)i(j;)1277 |
| 256 y(int)g(p)g(=)g(data[1];)1277 301 y(int)g(i)g(=)g(data[0];)1277 |
| 347 y(if)g(\(p\))1317 393 y(j)g(=)g(1;)1277 438 y(else)1317 |
| 484 y(j)g(=)g(2;)1277 530 y(do)g({)1317 575 y(i)g(=)g(i)g(+)h(j;)1317 |
| 621 y(data[data)o([2)o(]])c(=)j(2;)1277 667 y(})h(while)d(\(i)i(<)g |
| (data[3]\);)1238 712 y(})1238 758 y Fi(3)0 816 y Fh(See)11 |
| b Fm(33b,)i(34ac,)h(35ac,)g(36ac,)f(37ac,)h(38c)p Fh(.)-150 |
| 896 y Fm(38b)98 b Fk(h)p Fw(Co)q(de)13 b(motion)p Fk(i)f(\021)104 |
| 988 y Fl({)143 1033 y(int)18 b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(10)h |
| (};)143 1079 y(\(void\))e(test\(ok,)g(motion_re)o(sul)o(t1)o(0,)f |
| (motion_tes)o(t10)o(,)g(data,)i(10,)h("invarian)o(t)d(control)h |
| (structures)o("\);)104 1125 y(})p Fi(3)0 1182 y Fh(See)11 |
| b(33a,)f Fm(33c,)k(34b)n(d,)g(35b)n(d,)g(36b)n(d,)f(37b)n(d,)h(38d)p |
| Fh(.)0 1285 y Fo(6.2.2)55 b(Lo)r(op)18 b(Unswitc)n(hing)0 |
| 1362 y Ft([2)o(])62 1412 y(opp)q(ortunit)o(y)12 b(arises)i(when)f |
| (using)f(nested)i(DO)e(lo)q(ops)g(in)g(F)m(ortran)h(77)e(and)i |
| (sometimes)d(with)j(nested)h Fg(for)d Ft(lo)q(ops)h(in)g(C.)-150 |
| 1488 y Fm(38c)98 b Fl("motion.c")o Fk(\021)104 1535 y |
| Fl(void)18 b(motion_te)o(st1)o(1\()o(int)e(*data\))104 |
| 1580 y({)143 1626 y(int)i(p)i(=)f(data[1];)143 1672 y(int)f(i)i(=)f |
| (data[0];)143 1717 y(do)g({)182 1763 y(if)g(\(p\))221 |
| 1809 y(i)h(=)f(i)g(+)g(1;)182 1854 y(else)221 1900 y(i)h(=)f(i)g(+)g |
| (2;)182 1946 y(data[data[)o(2]])d(=)j(2;)143 1991 y(})g(while)f(\(i)h |
| (<)g(data[3]\);)104 2037 y(})104 2083 y Fi(3)1238 1535 |
| y Fl(void)f(motion_res)o(ult)o(11)o(\(in)o(t)f(*data\))1238 |
| 1580 y({)1277 1626 y(int)i(p)g(=)g(data[1];)1277 1672 |
| y(int)g(i)g(=)g(data[0];)1277 1717 y(if)g(\(p\))1317 |
| 1763 y(do)f({)1356 1809 y(i)h(=)g(i)h(+)f(1;)1356 1854 |
| y(data[data)o([2])o(])d(=)k(2;)1317 1900 y(})f(while)f(\(i)g(<)i |
| (data[3]\);)1277 1946 y(else)1317 1991 y(do)e({)1356 |
| 2037 y(i)h(=)g(i)h(+)f(2;)1356 2083 y(data[data)o([2])o(])d(=)k(2;)1317 |
| 2128 y(})f(while)f(\(i)g(<)i(data[3]\);)1238 2174 y(})1238 |
| 2219 y Fi(3)0 2277 y Fh(See)11 b Fm(33b,)i(34ac,)h(35ac,)g(36ac,)f |
| (37ac,)h(38a)p Fh(.)-150 2357 y Fm(38d)96 b Fk(h)p Fw(Co)q(de)13 |
| b(motion)p Fk(i)f(\021)104 2403 y Fl({)143 2449 y(int)18 |
| b(data[5])f(=)j({)f(0,)g(1,)g(2,)f(10)h(};)143 2495 y(\(void\))e |
| (test\(ok,)g(motion_re)o(sul)o(t1)o(1,)f(motion_tes)o(t11)o(,)g(data,)i |
| (11,)h("loop)e(unswitchin)o(g"\))o(;)104 2540 y(})p Fi(3)0 |
| 2598 y Fh(See)11 b(33a,)f Fm(33c,)k(34b)n(d,)g(35b)n(d,)g(36b)n(d,)f |
| (37b)n(d,)h(38b)p Fh(.)954 2874 y Ft(38)p eop |
| %%Page: 39 44 |
| 39 43 bop 0 91 a Fp(6.3)70 b(Protot)n(yp)r(es)-150 176 |
| y Fm(39)114 b Fk(h)p Fw(Protot)o(yp)q(es)p Fk(i)12 b(\021)104 |
| 222 y Fl(extern)17 b(void)h(motion_tes)o(t1\()o(in)o(t)f(*\);)104 |
| 268 y(extern)g(void)h(motion_tes)o(t2\()o(in)o(t)f(*\);)104 |
| 314 y(extern)g(void)h(motion_tes)o(t3\()o(in)o(t)f(*\);)104 |
| 359 y(extern)g(void)h(motion_tes)o(t4\()o(in)o(t)f(*\);)104 |
| 405 y(extern)g(void)h(motion_tes)o(t5\()o(in)o(t)f(*\);)104 |
| 451 y(extern)g(void)h(motion_tes)o(t6\()o(in)o(t)f(*\);)104 |
| 496 y(extern)g(void)h(motion_tes)o(t7\()o(in)o(t)f(*\);)104 |
| 542 y(extern)g(void)h(motion_tes)o(t8\()o(in)o(t)f(*\);)104 |
| 588 y(extern)g(void)h(motion_tes)o(t9\()o(in)o(t)f(*\);)104 |
| 633 y(extern)g(void)h(motion_tes)o(t10)o(\(i)o(nt)e(*\);)104 |
| 679 y(extern)h(void)h(motion_tes)o(t11)o(\(i)o(nt)e(*\);)104 |
| 725 y Fi(3)1160 222 y Fl(extern)h(void)h(motion_res)o(ul)o(t1\()o(int)e |
| (*\);)1160 268 y(extern)h(void)h(motion_res)o(ul)o(t2\()o(int)e(*\);) |
| 1160 314 y(extern)h(void)h(motion_res)o(ul)o(t3\()o(int)e(*\);)1160 |
| 359 y(extern)h(void)h(motion_res)o(ul)o(t4\()o(int)e(*\);)1160 |
| 405 y(extern)h(void)h(motion_res)o(ul)o(t5\()o(int)e(*\);)1160 |
| 451 y(extern)h(void)h(motion_res)o(ul)o(t6\()o(int)e(*\);)1160 |
| 496 y(extern)h(void)h(motion_res)o(ul)o(t7\()o(int)e(*\);)1160 |
| 542 y(extern)h(void)h(motion_res)o(ul)o(t8\()o(int)e(*\);)1160 |
| 588 y(extern)h(void)h(motion_res)o(ul)o(t9\()o(int)e(*\);)1160 |
| 633 y(extern)h(void)h(motion_res)o(ul)o(t10)o(\(in)o(t)e(*\);)1160 |
| 679 y(extern)h(void)h(motion_res)o(ul)o(t11)o(\(in)o(t)e(*\);)1160 |
| 725 y Fi(3)0 782 y Fh(See)11 b(3b,)g Fm(4,)h(7b,)i(8e,)f(17,)g(25,)g |
| (32b,)h(45c)p Fh(.)954 2874 y Ft(39)p eop |
| %%Page: 40 45 |
| 40 44 bop 0 257 a Fu(Chapter)34 b(7)0 423 y(Strength)h(Reduction)0 |
| 598 y Ft([10)o(,)10 b(3])62 648 y([9])j(and)h(other)g(v)o(ersions)h |
| (based)f(on)g(partial)f(redundancy)i(eliminatio)o(n)c(are)k(w)o(eak)o |
| (er)62 697 y(linear)g(function)f(test)i(replacemen)o(t,)e(o)q(dd)h |
| (induction)f(v)n(ariables,)g(con)o(trol)g(\015o)o(w)h(in)f(lo)q(op,)g |
| (goto)g(lo)q(ops,)g(nested)i(lo)q(ops,)0 747 y(irreducible)e(lo)q(ops,) |
| f(reduction)i(of)e(mo)q(d,)f(div,)h(etc.)62 797 y(straigh)o(t-line)g |
| (co)q(de,)i(lo)q(op)e(in)o(v)n(arian)o(ts)f(\(vs.)19 |
| b(constan)o(ts\))-150 881 y Fm(40a)96 b Fk(h)p Fw(Ev)n(aluation)16 |
| b(driv)o(ers)p Fk(i)c(\021)104 927 y Fl({)143 973 y(int)18 |
| b(ok;)143 1019 y(puts\("Stre)o(ng)o(th)e(reduction")o(\);)143 |
| 1064 y Fk(h)p Fw(Strength)e(reduction)h Fm(40c,)e Fj(:)6 |
| b(:)g(:)f Fk(i)104 1110 y Fl(})p Fi(3)0 1167 y Fh(See)11 |
| b(3c,)g Fm(11a,)i(18a,)g(26a,)h(33a)p Fh(.)0 1282 y Fp(7.1)70 |
| b(Induction)22 b(V)-6 b(ariable)22 b(and)i(Constan)n(t)0 |
| 1373 y Ft(T)m(esting)15 b(a)f Fg(while)g Ft(lo)q(op)g(migh)o(t)e(also)i |
| (b)q(e)i(in)o(teresting;)f(ho)o(w)o(ev)o(er,)g(the)g(prop)q(er)h(metho) |
| q(d)e(of)g(handling)g(them)g(w)o(ould)g(b)q(e)h(to)0 |
| 1422 y(p)q(erform)e(lo)q(op)g(rotation)g(\014rst,)i(whic)o(h)e(is)h |
| (already)g(co)o(v)o(ered)h(elsewhere.)-150 1499 y Fm(40b)98 |
| b Fl("strength.)o(c")o Fk(\021)104 1545 y Fl(void)18 |
| b(strength_)o(tes)o(t1)o(\(in)o(t)f(*data\))104 1591 |
| y({)143 1637 y(int)h(i)i(=)f(0;)143 1682 y(do)g({)182 |
| 1728 y(data[data[)o(2]])d(=)j(2;)182 1774 y(i)g(=)h(i)f(+)g(1;)143 |
| 1819 y(})g(while)f(\(i)h(*)g(21)g(<)g(data[1]\);)104 |
| 1865 y(})104 1911 y Fi(3)1219 1545 y Fl(void)f(strength_)o(re)o(sul)o |
| (t1)o(\(in)o(t)f(*data\))1219 1591 y({)1258 1637 y(int)h(i)h(=)h(0;) |
| 1258 1682 y(do)f({)1297 1728 y(data[data[)o(2])o(])e(=)i(2;)1297 |
| 1774 y(i)g(=)g(i)h(+)f(21;)1258 1819 y(})g(while)f(\(i)h(<)g |
| (data[1]\);)1219 1865 y(})1219 1911 y Fi(3)0 1968 y Fh(See)11 |
| b Fm(41ac,)i(42ac,)h(43ac,)g(44ac,)g(45a)p Fh(.)-150 |
| 2048 y Fm(40c)98 b Fk(h)p Fw(Strength)14 b(reduction)p |
| Fk(i)e(\021)104 2094 y Fl({)143 2140 y(int)18 b(data[3])f(=)j({)f(0,)g |
| (22,)f(2)h(};)143 2186 y(ok)g(=)g(test\(1,)e(strength_r)o(es)o(ult)o |
| (1,)f(strength_t)o(es)o(t1,)g(data,)i(1,)g("iv)h(*)g(constant"\))o(;) |
| 104 2231 y(})p Fi(3)0 2289 y Fh(See)11 b(40a,)f Fm(41b)n(d,)k(42b)n(d,) |
| g(43b)n(d,)g(44b)n(d,)g(45b)p Fh(.)954 2874 y Ft(40)p |
| eop |
| %%Page: 41 46 |
| 41 45 bop 0 91 a Fp(7.2)70 b(Induction)22 b(V)-6 b(ariable)22 |
| b(and)i(Region)e(Constan)n(t)-150 171 y Fm(41a)96 b Fl("strength.)o(c") |
| o Fk(\021)104 217 y Fl(void)18 b(strength_)o(tes)o(t2)o(\(in)o(t)f |
| (*data\))104 263 y({)143 309 y(int)h(k)i(=)f(data[0];)143 |
| 354 y(int)f(i)i(=)f(0;)143 400 y(do)g({)182 446 y(data[data[)o(2]])d(=) |
| j(2;)182 491 y(i)g(=)h(i)f(+)g(1;)143 537 y(})g(while)f(\(i)h(*)g(k)g |
| (<)g(data[1]\);)104 583 y(})104 628 y Fi(3)1219 217 y |
| Fl(void)f(strength_)o(re)o(sul)o(t2)o(\(in)o(t)f(*data\))1219 |
| 263 y({)1258 309 y(int)h(k)h(=)h(data[0];)1258 354 y(int)e(i)h(=)h(0;) |
| 1258 400 y(do)f({)1297 446 y(data[data[)o(2])o(])e(=)i(2;)1297 |
| 491 y(i)g(=)g(i)h(+)f(k;)1258 537 y(})g(while)f(\(i)h(<)g(data[1]\);) |
| 1219 583 y(})1219 628 y Fi(3)0 686 y Fh(See)11 b Fm(40b,)i(41c,)h |
| (42ac,)g(43ac,)f(44ac,)h(45a)p Fh(.)-150 766 y Fm(41b)98 |
| b Fk(h)p Fw(Strength)14 b(reduction)p Fk(i)e(\021)104 |
| 812 y Fl({)143 858 y(int)18 b(data[3])f(=)j({)f(1,)g(3,)g(2)g(};)143 |
| 903 y(\(void\))e(test\(ok,)g(strength_)o(res)o(ul)o(t2,)f(strength_)o |
| (tes)o(t2)o(,)h(data,)g(2,)i("iv)g(*)g(rc"\);)104 949 |
| y(})p Fi(3)0 1007 y Fh(See)11 b(40a,)f Fm(40c,)k(41d,)f(42b)n(d,)h(43b) |
| n(d,)g(44b)n(d,)g(45b)p Fh(.)0 1121 y Fp(7.3)70 b(Multiplying)20 |
| b(Tw)n(o)j(Induction)f(V)-6 b(ariables)-150 1201 y Fm(41c)98 |
| b Fl("strength.)o(c")o Fk(\021)104 1247 y Fl(void)18 |
| b(strength_)o(tes)o(t3)o(\(in)o(t)f(*data\))104 1293 |
| y({)143 1338 y(int)h(i)i(=)f(data[0];)143 1384 y(int)f(j)i(=)f |
| (data[1];)143 1430 y(do)g({)182 1475 y(data[data[)o(2]])d(=)j(2;)182 |
| 1521 y(i)g(=)h(i)f(+)g(1;)182 1567 y(j)g(=)h(j)f(+)g(1;)143 |
| 1612 y(})g(while)f(\(i)h(*)g(j)g(<)g(data[3]\);)104 1658 |
| y(})104 1704 y Fi(3)1219 1247 y Fl(void)f(strength_)o(re)o(sul)o(t3)o |
| (\(in)o(t)f(*data\))1219 1293 y({)1258 1338 y(int)h(i)h(=)h(data[0];) |
| 1258 1384 y(int)e(j)h(=)h(data[1];)1258 1430 y(int)e(k)h(=)h(i)f(*)g |
| (j;)1258 1475 y(do)g({)1297 1521 y(data[data[)o(2])o(])e(=)i(2;)1297 |
| 1567 y(i)g(=)g(i)h(+)f(1;)1297 1612 y(k)g(=)g(k)h(+)f(j;)1297 |
| 1658 y(j)g(=)g(j)h(+)f(1;)1297 1704 y(k)g(=)g(k)h(+)f(i;)1258 |
| 1749 y(})g(while)f(\(k)h(<)g(data[3]\);)1219 1795 y(})1219 |
| 1841 y Fi(3)0 1898 y Fh(See)11 b Fm(40b,)i(41a,)h(42ac,)f(43ac,)h |
| (44ac,)g(45a)p Fh(.)-150 1978 y Fm(41d)96 b Fk(h)p Fw(Strength)14 |
| b(reduction)p Fk(i)e(\021)104 2025 y Fl({)143 2070 y(int)18 |
| b(data[4])f(=)j({)f(0,)g(1,)g(2,)f(100)h(};)143 2116 |
| y(\(void\))e(test\(ok,)g(strength_)o(res)o(ul)o(t3,)f(strength_)o(tes)o |
| (t3)o(,)h(data,)g(3,)i("iv)g(*)g(iv"\);)104 2162 y(})p |
| Fi(3)0 2219 y Fh(See)11 b(40a,)f Fm(40c,)k(41b,)f(42b)n(d,)h(43b)n(d,)g |
| (44b)n(d,)g(45b)p Fh(.)954 2874 y Ft(41)p eop |
| %%Page: 42 47 |
| 42 46 bop 0 91 a Fp(7.4)70 b(Irreducible)21 b(Lo)r(ops)-150 |
| 171 y Fm(42a)96 b Fl("strength.)o(c")o Fk(\021)104 217 |
| y Fl(void)18 b(strength_)o(tes)o(t4)o(\(in)o(t)f(*data\))104 |
| 263 y({)143 309 y(int)h(i;)143 354 y(if)h(\(data[1]\))d({)182 |
| 400 y(i)j(=)h(2;)182 446 y(goto)e(here;)143 491 y(})143 |
| 537 y(i)h(=)g(0;)143 583 y(do)g({)182 628 y(i)g(=)h(i)f(+)g(1;)104 |
| 674 y(here:)182 720 y(data[data[)o(2]])d(=)j(2;)143 765 |
| y(})g(while)f(\(i)h(*)g(21)g(<)g(data[3]\);)104 811 y(})104 |
| 856 y Fi(3)1219 217 y Fl(void)f(strength_)o(re)o(sul)o(t4)o(\(in)o(t)f |
| (*data\))1219 263 y({)1258 309 y(int)h(i;)1258 354 y(if)h(\(data[1]\))d |
| ({)1297 400 y(i)j(=)g(42;)1297 446 y(goto)f(here;)1258 |
| 491 y(})1258 537 y(i)h(=)g(0;)1258 583 y(do)g({)1297 |
| 628 y(i)g(=)g(i)h(+)f(21;)1219 674 y(here:)1297 720 y(data[data[)o(2])o |
| (])e(=)i(2;)1258 765 y(})g(while)f(\(i)h(<)g(data[3]\);)1219 |
| 811 y(})1219 856 y Fi(3)0 914 y Fh(See)11 b Fm(40b,)i(41ac,)h(42c,)g |
| (43ac,)f(44ac,)h(45a)p Fh(.)-150 994 y Fm(42b)98 b Fk(h)p |
| Fw(Strength)14 b(reduction)p Fk(i)e(\021)104 1040 y Fl({)143 |
| 1086 y(int)18 b(data[4])f(=)j({)f(0,)g(1,)g(2,)f(100)h(};)143 |
| 1132 y(\(void\))e(test\(ok,)g(strength_)o(res)o(ul)o(t4,)f(strength_)o |
| (tes)o(t4)o(,)h(data,)g(4,)i("irreducib)o(le)d(loop"\);)104 |
| 1177 y(})p Fi(3)0 1235 y Fh(See)11 b(40a,)f Fm(40c,)k(41b)n(d,)g(42d,)f |
| (43b)n(d,)h(44b)n(d,)g(45b)p Fh(.)0 1349 y Fp(7.5)70 |
| b(Con)n(trol)22 b(Flo)n(w)h(in)f(the)g(Lo)r(op)-150 1429 |
| y Fm(42c)98 b Fl("strength.)o(c")o Fk(\021)104 1475 y |
| Fl(void)18 b(strength_)o(tes)o(t5)o(\(in)o(t)f(*data\))104 |
| 1521 y({)143 1567 y(int)h(i)i(=)f(0;)143 1612 y(while)f(\(1\))g({)182 |
| 1658 y(i)h(=)h(i)f(+)g(1;)182 1704 y(if)g(\(data[1])e(&&)h(i)i(*)f(21)g |
| (>)g(data[3]\))221 1749 y(break;)182 1795 y(data[data[)o(2]])d(=)j(2;) |
| 143 1841 y(})104 1886 y(})104 1932 y Fi(3)1219 1475 y |
| Fl(void)f(strength_)o(re)o(sul)o(t5)o(\(in)o(t)f(*data\))1219 |
| 1521 y({)1258 1567 y(int)h(i)h(=)h(0;)1258 1612 y(while)d(\(1\))i({) |
| 1297 1658 y(i)g(=)g(i)h(+)f(21;)1297 1704 y(if)g(\(data[1])d(&&)j(i)g |
| (>)h(data[3]\))1336 1749 y(break;)1297 1795 y(data[data[)o(2])o(])d(=)i |
| (2;)1258 1841 y(})1219 1886 y(})1219 1932 y Fi(3)0 1990 |
| y Fh(See)11 b Fm(40b,)i(41ac,)h(42a,)f(43ac,)h(44ac,)g(45a)p |
| Fh(.)-150 2070 y Fm(42d)96 b Fk(h)p Fw(Strength)14 b(reduction)p |
| Fk(i)e(\021)104 2116 y Fl({)143 2162 y(int)18 b(data[4])f(=)j({)f(0,)g |
| (1,)g(2,)f(100)h(};)143 2207 y(\(void\))e(test\(ok,)g(strength_)o(res)o |
| (ul)o(t5,)f(strength_)o(tes)o(t5)o(,)h(data,)g(5,)i("control)e(flow)h |
| (in)h(loop"\);)104 2253 y(})p Fi(3)0 2310 y Fh(See)11 |
| b(40a,)f Fm(40c,)k(41b)n(d,)g(42b,)f(43b)n(d,)h(44b)n(d,)g(45b)p |
| Fh(.)0 2425 y Fp(7.6)70 b(More)23 b(Complex)e(Induction)i(V)-6 |
| b(ariables)0 2516 y Ft(There)15 b(are)f(man)o(y)e(p)q(ossibilities)i |
| ([24)o(].)j(I'm)12 b(only)h(co)o(v)o(ering)h(a)f(few)h(cases.)954 |
| 2874 y(42)p eop |
| %%Page: 43 48 |
| 43 47 bop 0 91 a Fo(7.6.1)55 b(Incremen)n(t)17 b(b)n(y)i(a)g(Region)e |
| (Constan)n(t)-150 155 y Fm(43a)96 b Fl("strength.)o(c")o |
| Fk(\021)104 201 y Fl(void)18 b(strength_)o(tes)o(t6)o(\(in)o(t)f |
| (*data\))104 247 y({)143 292 y(int)h(j)i(=)f(data[0];)143 |
| 338 y(int)f(i)i(=)f(data[1];)143 384 y(do)g({)182 429 |
| y(data[data[)o(2]])d(=)j(2;)182 475 y(i)g(=)h(i)f(+)g(j;)143 |
| 521 y(})g(while)f(\(i)h(*)g(21)g(<)g(data[3]\);)104 566 |
| y(})104 612 y Fi(3)1219 201 y Fl(void)f(strength_)o(re)o(sul)o(t6)o |
| (\(in)o(t)f(*data\))1219 247 y({)1258 292 y(int)h(j)h(=)h(data[0])d(*)i |
| (21;)1258 338 y(int)f(i)h(=)h(data[1])d(*)i(21;)1258 |
| 384 y(do)g({)1297 429 y(data[data[)o(2])o(])e(=)i(2;)1297 |
| 475 y(i)g(=)g(i)h(+)f(j;)1258 521 y(})g(while)f(\(i)h(<)g(data[3]\);) |
| 1219 566 y(})1219 612 y Fi(3)0 669 y Fh(See)11 b Fm(40b,)i(41ac,)h |
| (42ac,)g(43c,)f(44ac,)h(45a)p Fh(.)-150 750 y Fm(43b)98 |
| b Fk(h)p Fw(Strength)14 b(reduction)p Fk(i)e(\021)104 |
| 796 y Fl({)143 841 y(int)18 b(data[4])f(=)j({)f(1,)g(1,)g(2,)f(100)h |
| (};)143 887 y(\(void\))e(test\(ok,)g(strength_)o(res)o(ul)o(t6,)f |
| (strength_)o(tes)o(t6)o(,)h(data,)g(6,)i("inc)f(by)h(rc"\);)104 |
| 933 y(})p Fi(3)0 990 y Fh(See)11 b(40a,)f Fm(40c,)k(41b)n(d,)g(42b)n |
| (d,)g(43d,)f(44b)n(d,)h(45b)p Fh(.)0 1094 y Fo(7.6.2)55 |
| b(Monotonic)19 b(Induction)f(V)-5 b(ariables)-150 1147 |
| y Fm(43c)98 b Fl("strength.)o(c")o Fk(\021)104 1194 y |
| Fl(void)18 b(strength_)o(tes)o(t7)o(\(in)o(t)f(*data\))104 |
| 1239 y({)143 1285 y(int)h(i)i(=)f(0;)143 1331 y(do)g({)182 |
| 1376 y(if)g(\(data[1]\))221 1422 y(i)h(=)f(i)g(+)g(1;)182 |
| 1468 y(else)221 1513 y(i)h(=)f(i)g(+)g(2;)182 1559 y(data[data[)o(2]])d |
| (=)j(2;)143 1604 y(})g(while)f(\(i)h(*)g(21)g(<)g(data[3]\);)104 |
| 1650 y(})104 1696 y Fi(3)1219 1194 y Fl(void)f(strength_)o(re)o(sul)o |
| (t7)o(\(in)o(t)f(*data\))1219 1239 y({)1258 1285 y(int)h(i)h(=)h(0;) |
| 1258 1331 y(do)f({)1297 1376 y(if)g(\(data[1]\))1336 |
| 1422 y(i)g(=)h(i)f(+)g(21;)1297 1468 y(else)1336 1513 |
| y(i)g(=)h(i)f(+)g(42;)1297 1559 y(data[data[)o(2])o(])e(=)i(2;)1258 |
| 1604 y(})g(while)f(\(i)h(<)g(data[3]\);)1219 1650 y(})1219 |
| 1696 y Fi(3)0 1753 y Fh(See)11 b Fm(40b,)i(41ac,)h(42ac,)g(43a,)f |
| (44ac,)h(45a)p Fh(.)-150 1833 y Fm(43d)96 b Fk(h)p Fw(Strength)14 |
| b(reduction)p Fk(i)e(\021)104 1880 y Fl({)143 1925 y(int)18 |
| b(data[4])f(=)j({)f(0,)g(1,)g(2,)f(100)h(};)143 1971 |
| y(\(void\))e(test\(ok,)g(strength_)o(res)o(ul)o(t7,)f(strength_)o(tes)o |
| (t7)o(,)h(data,)g(7,)i("monotonic)d(iv"\);)104 2017 y(})p |
| Fi(3)0 2074 y Fh(See)11 b(40a,)f Fm(40c,)k(41b)n(d,)g(42b)n(d,)g(43b,)f |
| (44b)n(d,)h(45b)p Fh(.)954 2874 y Ft(43)p eop |
| %%Page: 44 49 |
| 44 48 bop 0 91 a Fo(7.6.3)55 b(Mutual)19 b(Induction)f(V)-5 |
| b(ariables)-150 145 y Fm(44a)96 b Fl("strength.)o(c")o |
| Fk(\021)104 191 y Fl(void)18 b(strength_)o(tes)o(t8)o(\(in)o(t)f |
| (*data\))104 237 y({)143 283 y(int)h(i)i(=)f(0;)143 328 |
| y(do)g({)182 374 y(int)g(j)g(=)g(i)g(+)h(1;)182 420 y(data[data[)o(2]]) |
| c(=)j(j;)182 465 y(i)g(=)h(j)f(+)g(1;)143 511 y(})g(while)f(\(i)h(*)g |
| (21)g(<)g(data[3]\);)104 557 y(})104 602 y Fi(3)1219 |
| 191 y Fl(void)f(strength_)o(re)o(sul)o(t8)o(\(in)o(t)f(*data\))1219 |
| 237 y({)1258 283 y(int)h(i)h(=)h(0;)1258 328 y(int)e(n)h(=)h(0;)1258 |
| 374 y(do)f({)1297 420 y(int)f(j)i(=)f(i)g(+)g(1;)1297 |
| 465 y(n)g(=)g(n)h(+)f(21;)1297 511 y(data[data[)o(2])o(])e(=)i(j;)1297 |
| 557 y(i)g(=)g(j)h(+)f(1;)1297 602 y(n)g(=)g(n)h(+)f(21;)1258 |
| 648 y(})g(while)f(\(n)h(<)g(data[3]\);)1219 694 y(})1219 |
| 739 y Fi(3)0 797 y Fh(See)11 b Fm(40b,)i(41ac,)h(42ac,)g(43ac,)f(44c,)h |
| (45a)p Fh(.)-150 877 y Fm(44b)98 b Fk(h)p Fw(Strength)14 |
| b(reduction)p Fk(i)e(\021)104 923 y Fl({)143 969 y(int)18 |
| b(data[4])f(=)j({)f(0,)g(1,)g(1,)f(100)h(};)143 1014 |
| y(\(void\))e(test\(ok,)g(strength_)o(res)o(ul)o(t8,)f(strength_)o(tes)o |
| (t8)o(,)h(data,)g(8,)i("mutual)e(iv's"\);)104 1060 y(})p |
| Fi(3)0 1118 y Fh(See)11 b(40a,)f Fm(40c,)k(41b)n(d,)g(42b)n(d,)g(43b)n |
| (d,)f(44d,)h(45b)p Fh(.)0 1232 y Fp(7.7)70 b(Multiple)20 |
| b(Strides)-150 1312 y Fm(44c)98 b Fl("strength.)o(c")o |
| Fk(\021)104 1358 y Fl(void)18 b(strength_)o(tes)o(t9)o(\(in)o(t)f |
| (*data\))104 1404 y({)143 1449 y(int)h(i)i(=)f(0;)143 |
| 1495 y(do)g({)182 1541 y(data[data[)o(2]])d(=)j(i;)182 |
| 1586 y(i)g(=)h(i)f(+)g(1;)143 1632 y(})g(while)f(\(i)h(*)g(21)g(<)g |
| (data[3]\);)104 1678 y(})104 1723 y Fi(3)1219 1358 y |
| Fl(void)f(strength_)o(re)o(sul)o(t9)o(\(in)o(t)f(*data\))1219 |
| 1404 y({)1258 1449 y(int)h(i)h(=)h(0;)1258 1495 y(int)e(j)h(=)h(0;)1258 |
| 1541 y(do)f({)1297 1586 y(data[data[)o(2])o(])e(=)i(i;)1297 |
| 1632 y(i)g(=)g(i)h(+)f(1;)1297 1678 y(j)g(=)g(j)h(+)f(21;)1258 |
| 1723 y(})g(while)f(\(j)h(<)g(data[3]\);)1219 1769 y(})1219 |
| 1815 y Fi(3)0 1872 y Fh(See)11 b Fm(40b,)i(41ac,)h(42ac,)g(43ac,)f |
| (44a,)h(45a)p Fh(.)-150 1952 y Fm(44d)96 b Fk(h)p Fw(Strength)14 |
| b(reduction)p Fk(i)e(\021)104 1999 y Fl({)143 2044 y(int)18 |
| b(data[4])f(=)j({)f(0,)g(1,)g(1,)f(100)h(};)143 2090 |
| y(\(void\))e(test\(ok,)g(strength_)o(res)o(ul)o(t9,)f(strength_)o(tes)o |
| (t9)o(,)h(data,)g(9,)i("multiple)d(strides"\);)104 2136 |
| y(})p Fi(3)0 2193 y Fh(See)11 b(40a,)f Fm(40c,)k(41b)n(d,)g(42b)n(d,)g |
| (43b)n(d,)f(44b,)h(45b)p Fh(.)954 2874 y Ft(44)p eop |
| %%Page: 45 50 |
| 45 49 bop 0 91 a Fp(7.8)70 b(Linear)22 b(F)-6 b(unction)23 |
| b(T)-6 b(est)22 b(Replacemen)n(t)-150 171 y Fm(45a)96 |
| b Fl("strength.)o(c")o Fk(\021)104 217 y Fl(void)18 b(strength_)o(tes)o |
| (t1)o(0\(i)o(nt)e(*data\))104 263 y({)143 309 y(int)i(stop)h(=)g |
| (data[3];)143 354 y(int)f(i)i(=)f(0;)143 400 y(do)g({)182 |
| 446 y(data[data[)o(2]])d(=)j(21)g(*)g(i;)182 491 y(i)g(=)h(i)f(+)g(1;) |
| 143 537 y(})g(while)f(\(i)h(<)g(stop\);)104 583 y(})104 |
| 628 y Fi(3)1199 217 y Fl(void)f(strength_r)o(es)o(ult)o(10)o(\(in)o(t)f |
| (*data\))1199 263 y({)1238 309 y(int)i(stop)f(=)h(data[3])e(*)i(21;) |
| 1238 354 y(int)g(i)g(=)g(0;)1238 400 y(do)g({)1277 446 |
| y(data[data[2)o(]])d(=)j(i;)1277 491 y(i)h(=)f(i)g(+)g(21;)1238 |
| 537 y(})g(while)f(\(i)h(<)g(stop\);)1199 583 y(})1199 |
| 628 y Fi(3)0 686 y Fh(See)11 b Fm(40b,)i(41ac,)h(42ac,)g(43ac,)f(44ac)p |
| Fh(.)-150 766 y Fm(45b)98 b Fk(h)p Fw(Strength)14 b(reduction)p |
| Fk(i)e(\021)104 812 y Fl({)143 858 y(int)18 b(data[4])f(=)j({)f(0,)g |
| (1,)g(1,)f(20)h(};)143 903 y(\(void\))e(test\(ok,)g(strength_)o(res)o |
| (ul)o(t10)o(,)f(strength_te)o(st)o(10,)g(data,)i(10,)g("test)g |
| (replaceme)o(nt)o("\);)104 949 y(})p Fi(3)0 1007 y Fh(See)11 |
| b(40a,)f Fm(40c,)k(41b)n(d,)g(42b)n(d,)g(43b)n(d,)f(44b)n(d)p |
| Fh(.)0 1121 y Fp(7.9)70 b(Protot)n(yp)r(es)-150 1206 |
| y Fm(45c)98 b Fk(h)p Fw(Protot)o(yp)q(es)p Fk(i)12 b(\021)104 |
| 1252 y Fl(extern)17 b(void)h(strength_t)o(est)o(1\()o(int)e(*\);)104 |
| 1297 y(extern)h(void)h(strength_t)o(est)o(2\()o(int)e(*\);)104 |
| 1343 y(extern)h(void)h(strength_t)o(est)o(3\()o(int)e(*\);)104 |
| 1389 y(extern)h(void)h(strength_t)o(est)o(4\()o(int)e(*\);)104 |
| 1434 y(extern)h(void)h(strength_t)o(est)o(5\()o(int)e(*\);)104 |
| 1480 y(extern)h(void)h(strength_t)o(est)o(6\()o(int)e(*\);)104 |
| 1526 y(extern)h(void)h(strength_t)o(est)o(7\()o(int)e(*\);)104 |
| 1571 y(extern)h(void)h(strength_t)o(est)o(8\()o(int)e(*\);)104 |
| 1617 y(extern)h(void)h(strength_t)o(est)o(9\()o(int)e(*\);)104 |
| 1663 y(extern)h(void)h(strength_t)o(est)o(10)o(\(in)o(t)e(*\);)104 |
| 1708 y Fi(3)1121 1252 y Fl(extern)h(void)h(strength_)o(res)o(ul)o(t1\() |
| o(int)e(*\);)1121 1297 y(extern)h(void)h(strength_)o(res)o(ul)o(t2\()o |
| (int)e(*\);)1121 1343 y(extern)h(void)h(strength_)o(res)o(ul)o(t3\()o |
| (int)e(*\);)1121 1389 y(extern)h(void)h(strength_)o(res)o(ul)o(t4\()o |
| (int)e(*\);)1121 1434 y(extern)h(void)h(strength_)o(res)o(ul)o(t5\()o |
| (int)e(*\);)1121 1480 y(extern)h(void)h(strength_)o(res)o(ul)o(t6\()o |
| (int)e(*\);)1121 1526 y(extern)h(void)h(strength_)o(res)o(ul)o(t7\()o |
| (int)e(*\);)1121 1571 y(extern)h(void)h(strength_)o(res)o(ul)o(t8\()o |
| (int)e(*\);)1121 1617 y(extern)h(void)h(strength_)o(res)o(ul)o(t9\()o |
| (int)e(*\);)1121 1663 y(extern)h(void)h(strength_)o(res)o(ul)o(t10)o |
| (\(in)o(t)e(*\);)1121 1708 y Fi(3)0 1766 y Fh(See)11 |
| b(3b,)g Fm(4,)h(7b,)i(8e,)f(17,)g(25,)g(32b,)h(39)p Fh(.)954 |
| 2874 y Ft(45)p eop |
| %%Page: 46 51 |
| 46 50 bop 0 257 a Fu(App)s(endix)34 b(A)0 423 y(Indices)0 |
| 623 y Fp(A.1)69 b(Files)0 709 y Fl("cprop.c")9 b Fb(18b,)k(19ac)n(e,)e |
| (20b)n(d,)h(21ac,)g(22ac)n(e,)g(23b)n(d,)g(24a)p Fw(.)0 |
| 755 y Fl("dead.c")e Fb(11b,)i(12ac,)g(13ac,)g(14ac,)g(15ac,)g(16ac)p |
| Fw(.)0 801 y Fl("global.h")d Fb(3a)p Fw(.)0 846 y Fl("main.c")h |
| Fb(3b)n(c,)i(6b,)h(8c)n(d,)f(9e,)h(10)p Fw(.)0 892 y |
| Fl("motion.c")c Fb(33b,)j(34ac,)g(35ac,)g(36ac,)g(37ac,)g(38ac)p |
| Fw(.)0 938 y Fl("strength.)o(c")d Fb(40b,)j(41ac,)g(42ac,)g(43ac,)g |
| (44ac,)g(45a)p Fw(.)0 983 y Fl("valnum.c")d Fb(26b)n(d,)j(27b)n(d,)g |
| (28ac,)g(29ac,)g(30b)n(d,)g(31ac)p Fw(.)0 1121 y Fp(A.2)69 |
| b(Macros)0 1207 y Fk(h)p Fw(Analyze)14 b(timing)h(results)p |
| Fk(i)f Fw(6b,)f Fb(7c)p Fw(.)0 1253 y Fk(h)p Fw(Chec)o(k)g(for)g |
| (exceptionally)j(noisy)f(data)p Fk(i)e Fw(7c,)g Fb(8a)p |
| Fw(.)0 1299 y Fk(h)p Fw(Co)q(de)g(motion)p Fk(i)h Fw(33a,)f |
| Fb(33c,)g(34b)n(d,)f(35b)n(d,)g(36b)n(d,)g(37b)n(d,)f(38b)n(d)p |
| Fw(.)0 1344 y Fk(h)p Fw(Constan)o(t)i(propagation)p Fk(i)j |
| Fw(18a,)d Fb(18c,)f(19b)n(d,)g(20ac)n(e,)g(21b)n(d,)g(22b)n(d,)g(23ac)n |
| (e,)f(24b)p Fw(.)0 1390 y Fk(h)p Fw(Constan)o(ts)p Fk(i)j |
| Fw(3b,)f Fb(7ad)p Fw(.)0 1436 y Fk(h)p Fw(Dead)h(co)q(de)f(eliminatio)q |
| (n)p Fk(i)j Fw(11a,)d Fb(11c,)f(12b)n(d,)g(13b)n(d,)g(14b)n(d,)g(15b)n |
| (d,)g(16b)n(d)p Fw(.)0 1481 y Fk(h)p Fw(Ev)n(aluation)k(driv)o(ers)p |
| Fk(i)e Fw(3c,)e Fb(11a,)h(18a,)f(26a,)g(33a,)h(40a)p |
| Fw(.)0 1527 y Fk(h)p Fw(Include)h(\014les)p Fk(i)g Fw(3a,)f |
| Fb(3d,)g(6a,)g(9a)p Fw(.)0 1573 y Fk(h)p Fw(Initialize)p |
| Fk(i)j Fw(3c,)d Fb(9c)p Fw(.)0 1618 y Fk(h)p Fw(Mak)o(e)g(sure)h |
| Fl(clock\(\))c Fw(w)o(orks)j(on)g(this)h(system)p Fk(i)f |
| Fw(9c,)g Fb(9d)p Fw(.)0 1664 y Fk(h)p Fw(Prin)o(t)h(times)f(and)h |
| (statistical)h(measures)p Fk(i)f Fw(8a,)f Fb(8b)p Fw(.)0 |
| 1710 y Fk(h)p Fw(Protot)o(yp)q(es)p Fk(i)h Fw(3b,)f Fb(4,)g(7b,)g(8e,)f |
| (17,)h(25,)g(32b,)f(39,)h(45c)p Fw(.)0 1755 y Fk(h)p |
| Fw(Strength)h(reduction)p Fk(i)h Fw(40a,)e Fb(40c,)f(41b)n(d,)g(42b)n |
| (d,)g(43b)n(d,)g(44b)n(d,)g(45b)p Fw(.)0 1801 y Fk(h)p |
| Fw(T)o(yp)q(es)p Fk(i)h Fw(3a,)g Fb(3e)p Fw(.)0 1847 |
| y Fk(h)p Fw(V)m(alue)h(n)o(um)o(b)q(ering)p Fk(i)h Fw(26a,)e |
| Fb(26c,)f(27ac)n(e,)g(28b)n(d,)g(29b,)g(30ac)n(e,)f(31b,)i(32a)p |
| Fw(.)0 1892 y Fk(h)p Fw(V)m(ariables)p Fk(i)i Fw(3b,)e |
| Fb(9b)p Fw(.)0 2030 y Fp(A.3)69 b(Iden)n(ti\014ers)0 |
| 2116 y Fl(clock)p Fw(:)15 b Fb(9a,)d Fw(9cde,)h(10.)0 |
| 2162 y Fl(CLOCKS_PER)o(_S)o(EC)p Fw(:)c(7a,)k Fb(9a,)f |
| Fw(9ce,)g(10.)0 2208 y Fl(clock_t)p Fw(:)i Fb(9a,)e Fw(9b)q(ce,)h(10.)0 |
| 2253 y Fl(collect_ti)o(mi)o(ngs)o Fw(:)h(6b,)f Fb(7b,)g(10)p |
| Fw(.)0 2299 y Fl(cprop_resu)o(lt)o(1)p Fw(:)h Fb(18b,)d |
| Fw(18c,)i(25.)0 2345 y Fl(cprop_resu)o(lt)o(10)p Fw(:)g |
| Fb(22c,)f Fw(22d,)h(25.)0 2390 y Fl(cprop_resu)o(lt)o(11)p |
| Fw(:)g Fb(22e,)f Fw(23a,)h(25.)0 2436 y Fl(cprop_resu)o(lt)o(12)p |
| Fw(:)g Fb(23b,)f Fw(23c,)h(25.)0 2482 y Fl(cprop_resu)o(lt)o(13)p |
| Fw(:)g Fb(23d,)f Fw(23e,)h(25.)0 2527 y Fl(cprop_resu)o(lt)o(14)p |
| Fw(:)g Fb(24a,)f Fw(24b,)h(25.)0 2573 y Fl(cprop_resu)o(lt)o(2)p |
| Fw(:)h Fb(19a,)d Fw(19b,)i(25.)0 2619 y Fl(cprop_resu)o(lt)o(3)p |
| Fw(:)h Fb(19c,)d Fw(19d,)i(25.)0 2664 y Fl(cprop_resu)o(lt)o(4)p |
| Fw(:)h Fb(19e,)d Fw(20a,)i(25.)0 2710 y Fl(cprop_resu)o(lt)o(5)p |
| Fw(:)h Fb(20b,)d Fw(20c,)i(25.)954 2874 y Ft(46)p eop |
| %%Page: 47 52 |
| 47 51 bop 0 91 a Fl(cprop_resu)o(lt)o(6)p Fw(:)14 b Fb(20d,)d |
| Fw(20e,)i(25.)0 137 y Fl(cprop_resu)o(lt)o(7)p Fw(:)h |
| Fb(21a,)d Fw(21b,)i(25.)0 183 y Fl(cprop_resu)o(lt)o(8)p |
| Fw(:)h Fb(21c,)d Fw(21d,)i(25.)0 228 y Fl(cprop_resu)o(lt)o(9)p |
| Fw(:)h Fb(22a,)d Fw(22b,)i(25.)0 274 y Fl(cprop_test)o(1)p |
| Fw(:)g Fb(18b,)f Fw(18c,)h(25.)0 320 y Fl(cprop_test)o(10)o |
| Fw(:)h Fb(22c,)e Fw(22d,)h(25.)0 365 y Fl(cprop_test)o(11)o |
| Fw(:)h Fb(22e,)e Fw(23a,)h(25.)0 411 y Fl(cprop_test)o(13)o |
| Fw(:)h Fb(23d,)d Fw(23e,)i(25.)0 457 y Fl(cprop_test)o(14)o |
| Fw(:)h Fb(24a,)d Fw(24b,)j(25.)0 502 y Fl(cprop_test)o(2)p |
| Fw(:)f Fb(19a,)f Fw(19b,)h(25.)0 548 y Fl(cprop_test)o(3)p |
| Fw(:)g Fb(19c,)f Fw(19d,)h(25.)0 594 y Fl(cprop_test)o(4)p |
| Fw(:)g Fb(19e,)f Fw(20a,)h(25.)0 639 y Fl(cprop_test)o(5)p |
| Fw(:)g Fb(20b,)f Fw(20c,)h(25.)0 685 y Fl(cprop_test)o(6)p |
| Fw(:)g Fb(20d,)f Fw(20e,)h(25.)0 731 y Fl(cprop_test)o(7)p |
| Fw(:)g Fb(21a,)f Fw(21b,)h(25.)0 776 y Fl(cprop_test)o(8)p |
| Fw(:)g Fb(21c,)f Fw(21d,)h(25.)0 822 y Fl(cprop_test)o(9)p |
| Fw(:)g Fb(22a,)f Fw(22b,)h(25.)0 868 y Fl(CUTOFF)p Fw(:)d(7c,)j |
| Fb(7d)p Fw(.)0 913 y Fl(dead_resul)o(t1)o Fw(:)h Fb(11b,)e |
| Fw(11c,)g(17.)0 959 y Fl(dead_resul)o(t1)o(0)p Fw(:)i |
| Fb(16a,)d Fw(16b,)i(17.)0 1005 y Fl(dead_resul)o(t1)o(1)p |
| Fw(:)h Fb(16c,)d Fw(16d,)i(17.)0 1050 y Fl(dead_resul)o(t2)o |
| Fw(:)h Fb(12a,)d Fw(12b,)j(17.)0 1096 y Fl(dead_resul)o(t3)o |
| Fw(:)g Fb(12c,)e Fw(12d,)h(17.)0 1142 y Fl(dead_resul)o(t4)o |
| Fw(:)h Fb(13a,)d Fw(13b,)j(17.)0 1187 y Fl(dead_resul)o(t5)o |
| Fw(:)g Fb(13c,)e Fw(13d,)h(17.)0 1233 y Fl(dead_resul)o(t6)o |
| Fw(:)h Fb(14a,)d Fw(14b,)j(17.)0 1279 y Fl(dead_resul)o(t7)o |
| Fw(:)g Fb(14c,)e Fw(14d,)h(17.)0 1324 y Fl(dead_resul)o(t8)o |
| Fw(:)h Fb(15a,)d Fw(15b,)j(17.)0 1370 y Fl(dead_resul)o(t9)o |
| Fw(:)g Fb(15c,)e Fw(15d,)h(17.)0 1416 y Fl(dead_test1)o |
| Fw(:)h Fb(11b,)d Fw(11c,)i(17.)0 1461 y Fl(dead_test1)o(0)p |
| Fw(:)g Fb(16a,)f Fw(16b,)h(17.)0 1507 y Fl(dead_test1)o(1)p |
| Fw(:)g Fb(16c,)f Fw(16d,)h(17.)0 1553 y Fl(dead_test2)o |
| Fw(:)h Fb(12a,)d Fw(12b,)i(17.)0 1598 y Fl(dead_test3)o |
| Fw(:)h Fb(12c,)d Fw(12d,)i(17.)0 1644 y Fl(dead_test4)o |
| Fw(:)h Fb(13a,)d Fw(13b,)i(17.)0 1689 y Fl(dead_test5)o |
| Fw(:)h Fb(13c,)d Fw(13d,)i(17.)0 1735 y Fl(dead_test6)o |
| Fw(:)h Fb(14a,)d Fw(14b,)i(17.)0 1781 y Fl(dead_test7)o |
| Fw(:)h Fb(14c,)d Fw(14d,)i(17.)0 1826 y Fl(dead_test8)o |
| Fw(:)h Fb(15a,)d Fw(15b,)i(17.)0 1872 y Fl(dead_test9)o |
| Fw(:)h Fb(15c,)d Fw(15d,)i(17.)0 1918 y Fl(determine_)o(it)o(era)o(ti)o |
| (ons)o Fw(:)h(6b,)f Fb(7b,)g(9e)p Fw(.)0 1963 y Fl(exit)p |
| Fw(:)i(3c,)e Fb(3d,)f Fw(9d.)0 2009 y Fl(fabs)p Fw(:)j |
| Fb(6a,)d Fw(7c.)0 2055 y Fl(fputs)p Fw(:)j Fb(3d,)d Fw(9d.)0 |
| 2100 y Fl(FunPar)p Fw(:)i Fb(3e,)e Fw(4,)h(6b,)g(7b,)g(9e,)g(10.)0 |
| 2146 y Fl(main)p Fw(:)i Fb(3c)p Fw(.)0 2192 y Fl(mean)p |
| Fw(:)g(7c,)e Fb(8de)p Fw(.)0 2237 y Fl(motion_res)o(ul)o(t1)p |
| Fw(:)g Fb(33b,)f Fw(33c,)h(39.)0 2283 y Fl(motion_res)o(ul)o(t10)o |
| Fw(:)h Fb(38a,)d Fw(38b,)j(39.)0 2329 y Fl(motion_res)o(ul)o(t11)o |
| Fw(:)g Fb(38c,)d Fw(38d,)j(39.)0 2374 y Fl(motion_res)o(ul)o(t2)p |
| Fw(:)f Fb(34a,)f Fw(34b,)h(39.)0 2420 y Fl(motion_res)o(ul)o(t3)p |
| Fw(:)g Fb(34c,)f Fw(34d,)h(39.)0 2466 y Fl(motion_res)o(ul)o(t4)p |
| Fw(:)g Fb(35a,)f Fw(35b,)h(39.)0 2511 y Fl(motion_res)o(ul)o(t5)p |
| Fw(:)g Fb(35c,)f Fw(35d,)h(39.)0 2557 y Fl(motion_res)o(ul)o(t6)p |
| Fw(:)g Fb(36a,)f Fw(36b,)h(39.)0 2603 y Fl(motion_res)o(ul)o(t7)p |
| Fw(:)g Fb(36c,)f Fw(36d,)h(39.)0 2648 y Fl(motion_res)o(ul)o(t8)p |
| Fw(:)g Fb(37a,)f Fw(37b,)h(39.)0 2694 y Fl(motion_res)o(ul)o(t9)p |
| Fw(:)g Fb(37c,)f Fw(37d,)h(39.)0 2740 y Fl(motion_tes)o(t1)o |
| Fw(:)h Fb(33b,)e Fw(33c,)g(39.)954 2874 y Ft(47)p eop |
| %%Page: 48 53 |
| 48 52 bop 0 91 a Fl(motion_tes)o(t1)o(0)p Fw(:)14 b Fb(38a,)d |
| Fw(38b,)i(39.)0 137 y Fl(motion_tes)o(t1)o(1)p Fw(:)h |
| Fb(38c,)d Fw(38d,)i(39.)0 183 y Fl(motion_tes)o(t2)o |
| Fw(:)h Fb(34a,)d Fw(34b,)j(39.)0 228 y Fl(motion_tes)o(t3)o |
| Fw(:)g Fb(34c,)e Fw(34d,)h(39.)0 274 y Fl(motion_tes)o(t4)o |
| Fw(:)h Fb(35a,)d Fw(35b,)j(39.)0 320 y Fl(motion_tes)o(t5)o |
| Fw(:)g Fb(35c,)e Fw(35d,)h(39.)0 365 y Fl(motion_tes)o(t6)o |
| Fw(:)h Fb(36a,)d Fw(36b,)j(39.)0 411 y Fl(motion_tes)o(t7)o |
| Fw(:)g Fb(36c,)e Fw(36d,)h(39.)0 457 y Fl(motion_tes)o(t8)o |
| Fw(:)h Fb(37a,)d Fw(37b,)j(39.)0 502 y Fl(motion_tes)o(t9)o |
| Fw(:)g Fb(37c,)e Fw(37d,)h(39.)0 548 y Fl(noisy)p Fw(:)i(7c,)e(8a,)f |
| Fb(8c)p Fw(.)0 594 y Fl(printf)p Fw(:)i Fb(3d,)e Fw(6b,)h(8b,)g(9c.)0 |
| 639 y Fl(puts)p Fw(:)i(3c,)e Fb(3d,)f Fw(6b,)h(7c,)f(8ab,)i(11a,)f |
| (18a,)g(26a,)g(33a,)g(40a.)0 685 y Fl(SAMPLES)p Fw(:)d(6b,)j |
| Fb(7a,)f Fw(7c,)g(8b)q(d,)i(10.)0 731 y Fl(sqrt)p Fw(:)h |
| Fb(6a,)d Fw(7c,)h(8b)q(c.)0 776 y Fl(stderr)p Fw(:)h |
| Fb(3d,)e Fw(9d.)0 822 y Fl(strength_r)o(es)o(ult)o(1)p |
| Fw(:)i Fb(40b,)d Fw(40c,)i(45c.)0 868 y Fl(strength_r)o(es)o(ult)o(10)o |
| Fw(:)h Fb(45a,)e Fw(45b)q(c.)0 913 y Fl(strength_r)o(es)o(ult)o(2)p |
| Fw(:)i Fb(41a,)d Fw(41b,)i(45c.)0 959 y Fl(strength_r)o(es)o(ult)o(3)p |
| Fw(:)h Fb(41c,)d Fw(41d,)i(45c.)0 1005 y Fl(strength_r)o(es)o(ult)o(4)p |
| Fw(:)h Fb(42a,)d Fw(42b,)i(45c.)0 1050 y Fl(strength_r)o(es)o(ult)o(5)p |
| Fw(:)h Fb(42c,)d Fw(42d,)i(45c.)0 1096 y Fl(strength_r)o(es)o(ult)o(6)p |
| Fw(:)h Fb(43a,)d Fw(43b,)i(45c.)0 1142 y Fl(strength_r)o(es)o(ult)o(7)p |
| Fw(:)h Fb(43c,)d Fw(43d,)i(45c.)0 1187 y Fl(strength_r)o(es)o(ult)o(8)p |
| Fw(:)h Fb(44a,)d Fw(44b,)i(45c.)0 1233 y Fl(strength_r)o(es)o(ult)o(9)p |
| Fw(:)h Fb(44c,)d Fw(44d,)i(45c.)0 1279 y Fl(strength_t)o(es)o(t1)p |
| Fw(:)g Fb(40b,)f Fw(40c,)h(45c.)0 1324 y Fl(strength_t)o(es)o(t10)o |
| Fw(:)h Fb(45a,)d Fw(45b)q(c.)0 1370 y Fl(strength_t)o(es)o(t2)p |
| Fw(:)i Fb(41a,)f Fw(41b,)h(45c.)0 1416 y Fl(strength_t)o(es)o(t3)p |
| Fw(:)g Fb(41c,)f Fw(41d,)h(45c.)0 1461 y Fl(strength_t)o(es)o(t4)p |
| Fw(:)g Fb(42a,)f Fw(42b,)h(45c.)0 1507 y Fl(strength_t)o(es)o(t5)p |
| Fw(:)g Fb(42c,)f Fw(42d,)h(45c.)0 1553 y Fl(strength_t)o(es)o(t6)p |
| Fw(:)g Fb(43a,)f Fw(43b,)h(45c.)0 1598 y Fl(strength_t)o(es)o(t7)p |
| Fw(:)g Fb(43c,)f Fw(43d,)h(45c.)0 1644 y Fl(strength_t)o(es)o(t8)p |
| Fw(:)g Fb(44a,)f Fw(44b,)h(45c.)0 1689 y Fl(strength_t)o(es)o(t9)p |
| Fw(:)g Fb(44c,)f Fw(44d,)h(45c.)0 1735 y Fl(test)p Fw(:)i |
| Fb(4,)e(6b,)e Fw(7c,)h(11c,)h(12b)q(d,)g(13b)q(d,)g(14b)q(d,)g(15b)q |
| (d,)g(16b)q(d,)g(18c,)g(19b)q(d,)g(20ace,)g(21b)q(d,)g(22b)q(d,)g |
| (23ace,)g(24b,)f(26c,)h(27ace,)f(28b)q(d,)i(29b,)104 |
| 1781 y(30ace,)f(31b,)g(32a,)g(33c,)g(34b)q(d,)h(35b)q(d,)f(36b)q(d,)h |
| (37b)q(d,)g(38b)q(d,)f(40c,)g(41b)q(d,)h(42b)q(d,)f(43b)q(d,)h(44b)q |
| (d,)f(45b.)0 1826 y Fl(ticks_per_)o(se)o(c)p Fw(:)h(8c,)e |
| Fb(9b,)g Fw(9ce.)0 1872 y Fl(variance)p Fw(:)i(7c,)e(8c,)h |
| Fb(8de)p Fw(.)0 1918 y Fl(vnum_resul)o(t1)o Fw(:)h Fb(26b,)e |
| Fw(26c,)g(32b.)0 1963 y Fl(vnum_resul)o(t1)o(0)p Fw(:)i |
| Fb(30d,)d Fw(30e,)i(32b.)0 2009 y Fl(vnum_resul)o(t1)o(1)p |
| Fw(:)h Fb(31a,)d Fw(31b,)i(32b.)0 2055 y Fl(vnum_resul)o(t1)o(2)p |
| Fw(:)h Fb(31c,)d Fw(32ab.)0 2100 y Fl(vnum_resul)o(t2)o |
| Fw(:)j Fb(26d,)d Fw(27a,)j(32b.)0 2146 y Fl(vnum_resul)o(t3)o |
| Fw(:)g Fb(27b,)e Fw(27c,)g(32b.)0 2192 y Fl(vnum_resul)o(t4)o |
| Fw(:)i Fb(27d,)d Fw(27e.)0 2237 y Fl(vnum_resul)o(t5)o |
| Fw(:)j Fb(28a,)d Fw(28b,)j(32b.)0 2283 y Fl(vnum_resul)o(t6)o |
| Fw(:)g Fb(28c,)e Fw(28d,)h(32b.)0 2329 y Fl(vnum_resul)o(t7)o |
| Fw(:)h Fb(29a,)d Fw(29b,)j(32b.)0 2374 y Fl(vnum_resul)o(t8)o |
| Fw(:)g Fb(29c,)e Fw(30a,)h(32b.)0 2420 y Fl(vnum_resul)o(t9)o |
| Fw(:)h Fb(30b,)e Fw(30c,)g(32b.)0 2466 y Fl(vnum_test1)o |
| Fw(:)i Fb(26b,)d Fw(26c,)i(32b.)0 2511 y Fl(vnum_test1)o(0)p |
| Fw(:)g Fb(30d,)f Fw(30e,)h(32b.)0 2557 y Fl(vnum_test1)o(1)p |
| Fw(:)g Fb(31a,)f Fw(31b,)h(32b.)0 2603 y Fl(vnum_test1)o(2)p |
| Fw(:)g Fb(31c,)f Fw(32ab.)0 2648 y Fl(vnum_test2)o Fw(:)i |
| Fb(26d,)d Fw(27a,)i(32b.)0 2694 y Fl(vnum_test3)o Fw(:)h |
| Fb(27b,)d Fw(27c,)i(32b.)0 2740 y Fl(vnum_test4)o Fw(:)h |
| Fb(27d,)d Fw(27e,)i(32b.)954 2874 y Ft(48)p eop |
| %%Page: 49 54 |
| 49 53 bop 0 91 a Fl(vnum_test5)o Fw(:)14 b Fb(28a,)d |
| Fw(28b,)i(32b.)0 137 y Fl(vnum_test6)o Fw(:)h Fb(28c,)d |
| Fw(28d,)i(32b.)0 183 y Fl(vnum_test7)o Fw(:)h Fb(29a,)d |
| Fw(29b,)i(32b.)0 228 y Fl(vnum_test8)o Fw(:)h Fb(29c,)d |
| Fw(30a,)i(32b.)0 274 y Fl(vnum_test9)o Fw(:)h Fb(30b,)d |
| Fw(30c,)i(32b.)954 2874 y Ft(49)p eop |
| %%Page: 50 55 |
| 50 54 bop 0 257 a Fu(App)s(endix)34 b(B)0 423 y(Results)0 |
| 598 y Ft(T)m(ry)15 b(to)f(rep)q(ort)i(dispassionately)m(.)21 |
| b(Just)16 b(giv)o(e)e(the)i(facts,)f(with)f(some)h(in)o(terpretation)g |
| (when)g(helpful;)g(but)g(don't)f(accuse)0 648 y(of)f(laziness)i(or)e |
| (stupidit)o(y)m(.)18 b(Similarl)o(y)m(,)10 b(don't)k(brag)f(on)h(an)o |
| (y)o(one.)62 697 y(Need)h(v)o(ersion)f(n)o(um)o(b)q(er)f(of)h(compiler) |
| 62 747 y(can)g(w)o(e)g(get)h(Cra)o(y)e(Researc)o(h,)i(KSR,)e(P)o |
| (aragon)g(\(P)o(ortland)h(Group\),)f(other)i(sup)q(ers?)62 |
| 797 y(design)f(a)g(form)e(for)i(rep)q(orting)g(results)h |
| (electronically)0 934 y Fp(B.1)69 b(Apple)0 1025 y Ft(MPW)0 |
| 1162 y Fp(B.2)g(Borland)0 1278 y(B.3)g(Con)n(v)n(ex)0 |
| 1394 y(B.4)g(Cra)n(y)24 b(Computer)0 1510 y(B.5)69 b(Cra)n(y)24 |
| b(Researc)n(h)0 1626 y(B.6)69 b(DEC)0 1725 y Fo(B.6.1)55 |
| b(Alpha)0 1802 y Ft(Rob)0 1918 y Fo(B.6.2)g(DECstation)0 |
| 1994 y Ft(MIPS,)14 b(Rob)0 2132 y Fp(B.7)69 b(Gn)n(u)24 |
| b(CC)0 2223 y Ft(need)15 b(rep)q(ort)g(b)o(y)e(mac)o(hine)g(\(since)i |
| (SP)m(AR)o(C)e(v)o(ersion)h(seems)g(fairly)f(inferior\))0 |
| 2360 y Fp(B.8)69 b(Hewlett-P)n(ac)n(k)l(ard)0 2451 y |
| Ft(Stev)o(e)954 2874 y(50)p eop |
| %%Page: 51 56 |
| 51 55 bop 0 91 a Fp(B.9)69 b(IBM)0 191 y Fo(B.9.1)55 |
| b(RS/6000)0 292 y Fp(B.10)69 b(Microsoft)0 408 y(B.11)g(Silicon)21 |
| b(Graphics)0 499 y Ft(Rob)0 636 y Fp(B.12)69 b(Sun)0 |
| 735 y Fo(B.12.1)55 b(Solaris)0 837 y Fp(B.13)69 b(T)-6 |
| b(era)0 928 y Ft(Brian)0 1065 y Fp(B.14)69 b(T)-6 b(exas)24 |
| b(Instrumen)n(ts)0 1156 y Ft(Reid)954 2874 y(51)p eop |
| %%Page: 52 57 |
| 52 56 bop 0 257 a Fu(Bibliograph)m(y)21 432 y Ft([1])19 |
| b(Alfred)h(V.)f(Aho,)i(Ra)o(vi)d(Sethi,)j(and)e(Je\013rey)j(D.)d |
| (Ullman.)32 b Fa(Compilers:)d(Principles,)21 b(T)m(e)n(chniques,)g(and) |
| g(T)m(o)n(ols)p Ft(.)85 482 y(Addison-W)m(esley)m(,)13 |
| b(1986.)21 565 y([2])19 b(F)m(rances)14 b(E.)e(Allen)g(and)h(John)f(Co) |
| q(c)o(k)o(e.)k(A)d(catalogue)f(of)g(optimizing)e(transformations.)k(In) |
| f(Rustin,)f(editor,)g Fa(Design)85 614 y(and)k(Optimization)e(of)h |
| (Compilers)p Ft(,)d(pages)j(1{30.)d(Pren)o(tice-Hall,)i(1972.)21 |
| 697 y([3])19 b(F)m(rances)12 b(E.)e(Allen,)g(John)h(Co)q(c)o(k)o(e,)g |
| (and)f(Ken)h(Kennedy)m(.)i(Reduction)e(of)f(op)q(erator)g(strength.)k |
| (In)c(Stev)o(en)i(S.)e(Muc)o(hnic)o(k)85 747 y(and)k(Neil)g(D.)f |
| (Jones,)h(editors,)g Fa(Pr)n(o)n(gr)n(am)g(Flow)g(A)o(nalysis:)19 |
| b(The)n(ory)c(and)g(Applic)n(ations)p Ft(.)e(Pren)o(tice-Hall,)h(1981.) |
| 21 830 y([4])19 b(Bo)o(w)o(en)h(Alp)q(ern,)g(Mark)f(N.)g(W)m(egman,)f |
| (and)g(F.)h(Kenneth)i(Zadec)o(k.)34 b(Detecting)20 b(equalit)o(y)e(of)g |
| (v)n(ariables)g(in)h(pro-)85 880 y(grams.)g(In)c Fa(Confer)n(enc)n(e)g |
| (R)n(e)n(c)n(or)n(d)g(of)h(the)g(Fifte)n(enth)f(A)o(nnual)h(A)o(CM)f |
| (Symp)n(osium)h(on)g(Principles)f(of)h(Pr)n(o)n(gr)n(amming)85 |
| 930 y(L)n(anguages)p Ft(,)f(pages)f(1{11,)f(San)g(Diego,)g(California,) |
| e(Jan)o(uary)j(1988.)21 1013 y([5])19 b(Marc)f(A.)g(Auslander)g(and)g |
| (Martin)f(E.)g(Hopkins.)29 b(An)18 b(o)o(v)o(erview)g(of)f(the)h |
| Fw(PL)p Ft(.8)f(compiler.)28 b Fa(SIGPLAN)19 b(Notic)n(es)p |
| Ft(,)85 1063 y(17\(6\):22{31,)11 b(June)i(1982.)j Fa(Pr)n(o)n(c)n(e)n |
| (e)n(dings)e(of)f(the)h(A)o(CM)g(SIGPLAN)g('82)g(Symp)n(osium)h(on)g |
| (Compiler)d(Construction)p Ft(.)21 1146 y([6])19 b(Rob)q(ert)14 |
| b(L.)e(Bernstein.)19 b(Pro)q(ducing)13 b(go)q(o)q(d)g(co)q(de)h(for)e |
| (the)i(case)g(statemen)o(t.)j Fa(Softwar)n(e)c({)i(Pr)n(actic)n(e)e |
| (and)i(Exp)n(erienc)n(e)p Ft(,)85 1196 y(15\(10\):1024{1024,)10 |
| b(Octob)q(er)16 b(1985.)21 1279 y([7])j(Rob)q(ert)11 |
| b(L.)e(Bernstein.)k(Multiplication)8 b(b)o(y)h(in)o(teger)i(constan)o |
| (ts.)h Fa(Softwar)n(e)f({)g(Pr)n(actic)n(e)g(and)g(Exp)n(erienc)n(e)p |
| Ft(,)g(16\(7\):641{)85 1328 y(652,)i(July)h(1986.)21 |
| 1411 y([8])19 b(Gregory)h(J.)f(Chaitin,)h(Marc)g(A.)f(Auslander,)i |
| (Ashok)f(K.)f(Chandra,)i(John)e(Co)q(c)o(k)o(e,)i(Martin)f(E.)f |
| (Hopkins,)h(and)85 1461 y(P)o(eter)c(W.)d(Markstein.)18 |
| b(Register)c(allo)q(cation)f(via)g(coloring.)k Fa(Computer)d(L)n |
| (anguages)p Ft(,)h(6:47{57,)c(Jan)o(uary)j(1981.)21 1544 |
| y([9])19 b(F)m(red)d(C.)f(Cho)o(w.)22 b Fa(A)16 b(Portable)g |
| (Machine-Indep)n(endent)i(Glob)n(al)e(Optimizer)f({)i(Design)f(and)h |
| (Me)n(asur)n(ements)p Ft(.)23 b(PhD)85 1594 y(thesis,)15 |
| b(Stanford)e(Univ)o(ersit)o(y)m(,)g(Decem)o(b)q(er)h(1983.)0 |
| 1677 y([10])19 b(John)d(Co)q(c)o(k)o(e)g(and)g(Ken)h(Kennedy)m(.)24 |
| b(An)16 b(algorithm)d(for)j(reduction)g(of)g(op)q(erator)g(strength.)25 |
| b Fa(Communic)n(ations)17 b(of)85 1727 y(the)e(A)o(CM)p |
| Ft(,)e(20\(11\),)g(No)o(v)o(em)o(b)q(er)g(1977.)0 1810 |
| y([11])19 b(John)d(Co)q(c)o(k)o(e)g(and)g(Jacob)g(T.)f(Sc)o(h)o(w)o |
| (artz.)24 b(Programming)12 b(languages)k(and)f(their)h(compilers:)21 |
| b(Preliminary)14 b(notes.)85 1860 y(T)m(ec)o(hnical)g(rep)q(ort,)g |
| (Couran)o(t)g(Institute)h(of)e(Mathematical)f(Sciences,)j(New)g(Y)m |
| (ork)e(Univ)o(ersit)o(y)m(,)g(1970.)0 1943 y([12])19 |
| b(Keith)14 b(D.)e(Co)q(op)q(er,)i(Mary)f(W.)f(Hall,)g(and)h(Linda)g(T)m |
| (orczon.)k(An)c(exp)q(erimen)o(t)g(with)g(inline)g(substitution.)k |
| Fa(Softwar)n(e)85 1993 y({)e(Pr)n(actic)n(e)g(and)g(Exp)n(erienc)n(e)p |
| Ft(,)f(21\(6\):581{601,)d(June)k(1991.)0 2076 y([13])k(Ron)14 |
| b(Cytron,)g(Jeanne)h(F)m(erran)o(te,)g(Barry)f(K.)g(Rosen,)g(Mark)h(N.) |
| e(W)m(egman,)f(and)i(F.)g(Kenneth)h(Zadec)o(k.)20 b(E\016cien)o(tly)85 |
| 2125 y(computing)d(static)j(single)e(assignmen)o(t)g(form)f(and)h(the)i |
| (con)o(trol)e(dep)q(endence)k(graph.)32 b Fa(A)o(CM)19 |
| b(T)m(r)n(ansactions)g(on)85 2175 y(Pr)n(o)n(gr)n(amming)c(L)n |
| (anguages)h(and)f(Systems)p Ft(,)f(13\(4\):451{490,)d(Octob)q(er)k |
| (1991.)0 2258 y([14])k(Ron)12 b(Cytron,)h(Andy)g(Lo)o(wry)m(,)e(and)i |
| (F.)f(Kenneth)j(Zadec)o(k.)h(Co)q(de)e(motion)c(of)i(con)o(trol)h |
| (structures)i(in)d(high-lev)o(el)g(lan-)85 2308 y(guages.)j(In)c |
| Fa(Confer)n(enc)n(e)i(R)n(e)n(c)n(or)n(d)f(of)h(the)g(Thirte)n(enth)f |
| (A)o(nnual)h(A)o(CM)f(Symp)n(osium)i(on)f(Principles)f(of)h(Pr)n(o)n |
| (gr)n(amming)85 2358 y(L)n(anguages)p Ft(,)i(pages)f(70{85,)e(St.)i(P)o |
| (etersburg)i(Beac)o(h,)e(Florida,)e(Jan)o(uary)i(1986.)0 |
| 2441 y([15])19 b(Ken)j(Kennedy)m(.)38 b(Global)19 b(dead)i(computation) |
| d(elimination.)35 b(SETL)21 b(Newsletter)h(111,)f(Couran)o(t)f |
| (Institute)i(of)85 2491 y(Mathematical)12 b(Sciences,)k(New)e(Y)m(ork)f |
| (Univ)o(ersit)o(y)m(,)g(August)i(1973.)0 2574 y([16])k(Ken)c(Kennedy)m |
| (.)k(Use-de\014nition)14 b(c)o(hains)g(with)f(applications.)k |
| Fa(Computer)e(L)n(anguages)p Ft(,)g(3:163{179,)c(1978.)0 |
| 2657 y([17])19 b(Ken)f(Kennedy)m(.)26 b(A)17 b(surv)o(ey)g(of)f(data)g |
| (\015o)o(w)g(analysis)g(tec)o(hniques.)27 b(In)16 b(Stev)o(en)i(S.)e |
| (Muc)o(hnic)o(k)g(and)h(Neil)f(D.)f(Jones,)85 2707 y(editors,)f |
| Fa(Pr)n(o)n(gr)n(am)g(Flow)h(A)o(nalysis:)j(The)n(ory)d(and)h(Applic)n |
| (ations)p Ft(.)d(Pren)o(tice-Hall,)g(1981.)954 2874 y(52)p |
| eop |
| %%Page: 53 58 |
| 53 57 bop 0 91 a Ft([18])19 b(Etienne)14 b(Morel)e(and)g(Claude)g(Ren)o |
| (v)o(oise.)k(Global)10 b(optimization)g(b)o(y)i(suppression)i(of)e |
| (partial)f(redundancies.)17 b Fa(Com-)85 141 y(munic)n(ations)f(of)f |
| (the)f(A)o(CM)p Ft(,)g(22\(2\):96{103,)d(F)m(ebruary)j(1979.)0 |
| 224 y([19])19 b(Mic)o(hael)d(L.)g(P)o(o)o(w)o(ell.)25 |
| b(A)17 b(p)q(ortable)f(optimizing)e(compiler)h(for)h(Mo)q(dula-2.)25 |
| b Fa(SIGPLAN)18 b(Notic)n(es)p Ft(,)e(19\(6\):310{318,)85 |
| 274 y(June)f(1984.)i Fa(Pr)n(o)n(c)n(e)n(e)n(dings)e(of)g(the)g(A)o(CM) |
| f(SIGPLAN)h('84)g(Symp)n(osium)h(on)f(Compiler)f(Construction)p |
| Ft(.)0 357 y([20])19 b(Rafael)11 b(H.)g(Saa)o(v)o(edra)g(and)g(Alan)g |
| (J.)h(Smith.)g(P)o(erformance)f(c)o(haracterization)h(of)f(optimizing)e |
| (compilers.)k(T)m(ec)o(hnical)85 407 y(Rep)q(ort)i(525,)d(Departmen)o |
| (t)h(of)h(Computer)f(Science,)i(Univ)o(ersit)o(y)f(of)f(Southern)i |
| (California,)c(August)j(1992.)0 490 y([21])19 b(Mark)12 |
| b(N.)g(W)m(egman)d(and)j(F.)f(Kenneth)j(Zadec)o(k.)h(Constan)o(t)d |
| (propagation)f(with)g(conditional)g(branc)o(hes.)16 b(In)c |
| Fa(Confer-)85 540 y(enc)n(e)17 b(R)n(e)n(c)n(or)n(d)g(of)f(the)h |
| (Twelfth)e(A)o(nnual)i(A)o(CM)f(Symp)n(osium)h(on)h(Principles)d(of)i |
| (Pr)n(o)n(gr)n(amming)f(L)n(anguages)p Ft(,)h(pages)85 |
| 589 y(291{299,)12 b(New)i(Orleans,)g(Louisiana,)f(Jan)o(uary)g(1985.)0 |
| 672 y([22])19 b(Mark)f(N.)g(W)m(egman)d(and)j(F.)g(Kenneth)h(Zadec)o |
| (k.)31 b(Constan)o(t)18 b(propagation)f(with)g(conditional)g(branc)o |
| (hes.)31 b Fa(A)o(CM)85 722 y(T)m(r)n(ansactions)15 b(on)g(Pr)n(o)n(gr) |
| n(amming)g(L)n(anguages)h(and)f(Systems)p Ft(,)f(13\(2\):181{210,)d |
| (April)i(1991.)0 805 y([23])19 b(F)m(rank)14 b(L.)f(W)m(olf.)j |
| Fa(Elements)f(of)g(Pr)n(ob)n(ability)f(and)h(Statistics)p |
| Ft(.)j(McGra)o(w-Hill,)12 b(second)j(edition,)d(1974.)0 |
| 888 y([24])19 b(Mic)o(hael)14 b(W)m(olfe.)k(Bey)o(ond)d(induction)f(v)n |
| (ariables.)19 b Fa(SIGPLAN)d(Notic)n(es)p Ft(,)d(27\(7\):162{174,)f |
| (July)i(1992.)k Fa(Pr)n(o)n(c)n(e)n(e)n(dings)85 938 |
| y(of)d(the)g(A)o(CM)g(SIGPLAN)g('92)g(Confer)n(enc)n(e)g(on)g(Pr)n(o)n |
| (gr)n(amming)f(L)n(anguage)i(Design)g(and)f(Implementation)p |
| Ft(.)0 1021 y([25])k(Mic)o(hael)12 b(W)m(olfe)f(and)h(T)m(om)e(Mac)o(k) |
| o(e.)15 b(Where)e(are)g(the)f(optimizing)e(compilers?)20 |
| b Fa(SIGPLAN)13 b(Notic)n(es)p Ft(,)f(20\(11\):64{68,)85 |
| 1071 y(No)o(v)o(em)o(b)q(er)h(1985.)954 2874 y(53)p eop |
| %%Trailer |
| end |
| userdict /end-hook known{end-hook}if |
| %%EOF |
