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A pr\303\255mek el oszl\303\241sa, szit\303\241l\303\241s" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 63 "2. Egyszer\305\261 faktoriz\303\241l\303\241si m\303\263 dszerek" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 64 "3. Egyszer\305\261 p r\303\255mtesztel\303\251si m\303\263dszerek" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 18 "4. \+ Lucas-sorozatok" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 23 "5. Alkalmaz \303\241sok " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 36 "6. Sz\303\241mo k \303\251s polinomok" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 205 45 "7. Gyo rs Fourier-transzform\303\241ci\303\263" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 17 "7.1. Polinomszorz" }{TEXT 206 8 "\303\24 1" }{TEXT 206 26 "s gyors Fourier-transzform" }{TEXT 206 8 "\303\241" }{TEXT 206 2 "ci" }{TEXT 206 12 "\303\263val." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 29 "7.2. Gyors Fourier-transzform" }{TEXT 206 8 "\303\24 1" }{TEXT 206 2 "ci" }{TEXT 206 14 "\303\263 (FFT)" }{TEXT 206 1 "." } }{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 16 "7.3. Inverz FFT." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 10 "7.4. Szorz" }{TEXT 206 8 "\303\241" }{TEXT 206 18 "s komplex FFT-vel." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 8 "7.5. Val" }{TEXT 206 8 "\303\263" } {TEXT 206 6 "s FFT." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 10 "7.6. Szorz" }{TEXT 206 8 "\303\241" }{TEXT 206 33 "s komplex FFT-vel \+ a gyakorlatban." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 7gnI,InteractiveG6\"I(animateGF$I*animate3dGF$I-animatecurveGF$I&arrow GF$I-changecoordsGI(_syslibGF$I,complexplotGF$I.complexplot3dGF$I*conf ormalGF$I,conformal3dGF$I,contourplotGF$I.contourplot3dGF$I*coordplotG F$I,coordplot3dGF$I-cylinderplotGF$I,densityplotGF$I(displayGF$I*displ ay3dGF$I*fieldplotGF$I,fieldplot3dGF$I)gradplotGF$I+gradplot3dGF$I,gra phplot3dGF$I-implicitplotGF$I/implicitplot3dGF$I(inequalGF$I,interacti veGF$I2interactiveparamsGF$I-listcontplotGF$I/listcontplot3dGF$I0listd ensityplotGF$I)listplotGF$I+listplot3dGF$I+loglogplotGF$I(logplotGF$I+ matrixplotGF$I)multipleGF$I(odeplotGF$I'paretoGF$I,plotcompareGF$I*poi ntplotGF$I,pointplot3dGF$I*polarplotGF$I,polygonplotGF$I.polygonplot3d GF$I4polyhedra_supportedGF$I.polyhedraplotGF$I'replotGF$I*rootlocusGF$ I,semilogplotGF$I+setoptionsGF$I-setoptions3dGF$I+spacecurveGF$I1spars ematrixplotGF$I+sphereplotGF$I)surfdataGF$I)textplotGF$I+textplot3dGF$ I)tubeplotGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "L:=[[1972, 130],[1982,400],[1985,800],[1985,1700],[1988,2670],[1991,16000],[1995, 100000]];\n" }{MPLTEXT 1 0 38 "LL:=map(x->[x[1],log[10.](x[2])],L);\n" }{MPLTEXT 1 0 30 "L1:=[[1982,0.4],[1996,400]];\n" }{MPLTEXT 1 0 40 "L L1:=map(x->[x[1],log[10.](x[2])],L1);\n" }{MPLTEXT 1 0 63 "fti:=[TIMES ,BOLD,25]; f1:=[TIMES,BOLD,15]; fa:=[TIMES,BOLD,15];" }}{PARA 11 "" 1 "" {XPPMATH 20 "7)7$\"%s>\"$I\"7$\"%#)>\"$+%7$\"%&)>\"$+)7$F*\"%+<7$\" %))>\"%qE7$\"%\"*>\"&+g\"7$\"%&*>\"'++5" }}{PARA 11 "" 1 "" {XPPMATH 20 "7)7$\"%s>$\"+_L%R6#!\"*7$\"%#)>$\"+\"**f?g#F'7$\"%&)>$\"+()**3.HF' 7$F-$\"+@*[/B$F'7$\"%))>$\"+h7^EMF'7$\"%\"*>$\"+$)*>T?%F'7$\"%&*>$\"++ +++]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$7$\"%#)>$\"\"%!\"\"7$\"%'*> \"$+%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$7$\"%#)>$!+(3+%zR!#57$\"%'*>$ \"+\"**f?g#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%I&TIMESG6\"I%BOLDGF $\"#D" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%I&TIMESG6\"I%BOLDGF$\"#:" }} {PARA 11 "" 1 "" {XPPMATH 20 "7%I&TIMESG6\"I%BOLDGF$\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "display([plot(LL,1970..1998,color=b lue,titlefont=fti,title='Supercomputers',\n" }{MPLTEXT 1 0 15 "thickne ss=3),\n" }{MPLTEXT 1 0 59 "plot(LL,1970..1998,color=blue,style=POINT, symbol=CIRCLE),\n" }{MPLTEXT 1 0 57 "plot(LL1,1970..1998,color=red,thi ckness=3,axesfont=fa),\n" }{MPLTEXT 1 0 59 "plot(LL1,1970..1998,color= red,style=POINT,symbol=CIRCLE),\n" }{MPLTEXT 1 0 63 "textplot([1970,5. 3,`log[10] `],align=\{ABOVE,LEFT\},font=fa),\n" }{MPLTEXT 1 0 62 "text plot([1970,4.9,`MFlops `],align=\{ABOVE,LEFT\},font=fa),\n" }{MPLTEXT 1 0 251 "textplot([LL1[1][1],LL1[1][2],`Z80 `],align=\{BELOW,LEFT\},co lor=red,font=f1),textplot([LL1[2][1],LL1[2][2],`UltraSPARC I+ `],ali gn=\{BELOW,LEFT\},color=red,font=f1),textplot([LL[1][1],LL[1][2],`Cray -1 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"[2^13*WS,26.61/(40*(32/33 ))],[2^14*WS,80.18/(40*(32/33))],\n" }{MPLTEXT 1 0 33 "[2^15*WS,240.61 /(40*(32/33))]];\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 60 "fftmul:=[[7 *WS*2,9.96/(4*10^4)],[7*WS*2^2,21.18/(4*10^4)],\n" }{MPLTEXT 1 0 53 "[ 7*WS*2^3,45.44/(4*10^4)],[7*WS*2^4,9.79/(4*10^3)],\n" }{MPLTEXT 1 0 53 "[7*WS*2^5,21.2/(4*10^3)],[7*WS*2^6,46.85/(4*10^3)],\n" }{MPLTEXT 1 0 50 "[15*WS*2^5,51.53/(4*10^3)],[7*WS*2^7,10.42/400],\n" }{MPLTEXT 1 0 67 "[15*WS*2^6,11.16/400],[7*WS*2^8,23.12/400],[15*WS*2^7,24.15/40 0],\n" }{MPLTEXT 1 0 66 "[7*WS*2^9,50.06/400],[15*WS*2^8,51.54/400],[7 *WS*2^10,10.96/40],\n" }{MPLTEXT 1 0 68 "[15*WS*2^9,10.94/40],[15*WS*2 ^10,23.15/40],[15*WS*2^11,49.31/40]];\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 64 "fftsqrold:=[[7*WS*2,73.51/(4*10^5)],[7*WS*2^2,15.62/( 4*10^4)],\n" }{MPLTEXT 1 0 54 "[7*WS*2^3,33.21/(4*10^4)],[7*WS*2^4,70. 96/(4*10^4)],\n" }{MPLTEXT 1 0 54 "[7*WS*2^5,15.45/(4*10^3)],[7*WS*2^6 ,33.06/(4*10^3)],\n" }{MPLTEXT 1 0 55 "[15*WS*2^5,38.68/(4*10^3)],[7*W S*2^7,72.59/(4*10^3)],\n" }{MPLTEXT 1 0 71 "[15*WS*2^6,82.1/(4*10^3)], [7*WS*2^8,16.42/400],[15*WS*2^7,18.05/400],\n" }{MPLTEXT 1 0 67 "[7*WS *2^9,35.79/400],[15*WS*2^8,38.36/400],[7*WS*2^10,79.67/400],\n" } {MPLTEXT 1 0 69 "[15*WS*2^9,81.51/400],[15*WS*2^10,17.42/40],[15*WS*2^ 11,37.43/40]];\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 61 "fftsqr:=[[7*W S*2,70.43/(4*10^5)],[7*WS*2^2,14.92/(4*10^4)],\n" }{MPLTEXT 1 0 54 "[7 *WS*2^3,31.71/(4*10^4)],[7*WS*2^4,67.90/(4*10^4)],\n" }{MPLTEXT 1 0 54 "[7*WS*2^5,14.60/(4*10^3)],[7*WS*2^6,31.32/(4*10^3)],\n" }{MPLTEXT 1 0 55 "[15*WS*2^5,34.34/(4*10^3)],[7*WS*2^7,69.02/(4*10^3)],\n" } {MPLTEXT 1 0 72 "[15*WS*2^6,73.35/(4*10^3)],[7*WS*2^8,15.64/400],[15*W S*2^7,16.24/400],\n" }{MPLTEXT 1 0 67 "[7*WS*2^9,33.90/400],[15*WS*2^8 ,34.71/400],[7*WS*2^10,74.26/400],\n" }{MPLTEXT 1 0 69 "[15*WS*2^9,73. 64/400],[15*WS*2^10,16.03/40],[15*WS*2^11,33.53/40]];\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 62 "rffftmulc:=[[22*2^5,14.80/(4*10^4)],[21*2^6 ,32.03/(4*10^4)],\n" }{MPLTEXT 1 0 50 "[21*2^7,64.06/(4*10^4)],[20*2^8 ,14.34/(4*10^3)],\n" }{MPLTEXT 1 0 71 "[20*2^9,30.21/(4*10^3)],[19*2^1 0,70.39/(4*10^3)],[19*2^11,16.81/400],\n" }{MPLTEXT 1 0 61 "[18*2^12,3 5.45/400],[17*2^13,74.06/400],[17*2^14,15.59/40],\n" }{MPLTEXT 1 0 41 "[16*2^15,32.32/40],[16*2^16,67.46/40]];\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 64 "rffftmul2ss:=[[22*2^5,73.11/(4*10^5)],[21*2^6,14.35/( 4*10^4)],\n" }{MPLTEXT 1 0 50 "[21*2^7,28.78/(4*10^4)],[20*2^8,62.45/( 4*10^4)],\n" }{MPLTEXT 1 0 76 "[20*2^9,14.59/(4*10^3)],[19*2^10,35.65/ (4*10^3)],[19*2^11,92.16/(4*10^3)],\n" }{MPLTEXT 1 0 62 "[18*2^12,18.3 6/400],[17*2^13,42.46/400],[17*2^14,85.89/400],\n" }{MPLTEXT 1 0 41 "[ 16*2^15,18.37/40],[16*2^16,37.84/40]];\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 62 "rffftsqrc:=[[22*2^5,12.83/(4*10^4)],[21*2^6,26.39/(4* 10^4)],\n" }{MPLTEXT 1 0 50 "[21*2^7,54.81/(4*10^4)],[20*2^8,11.35/(4* 10^3)],\n" }{MPLTEXT 1 0 71 "[20*2^9,24.22/(4*10^3)],[19*2^10,54.75/(4 *10^3)],[19*2^11,13.53/400],\n" }{MPLTEXT 1 0 61 "[18*2^12,28.36/400], [17*2^13,60.39/400],[17*2^14,12.04/40],\n" }{MPLTEXT 1 0 41 "[16*2^15, 25.62/40],[16*2^16,52.58/40]];\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 64 "rffftsqr2ss:=[[22*2^5,51.75/(4*10^5)],[21*2^6,10.44/(4*10^4)],\n" }{MPLTEXT 1 0 50 "[21*2^7,19.83/(4*10^4)],[20*2^8,43.66/(4*10^4)],\n" }{MPLTEXT 1 0 76 "[20*2^9,95.11/(4*10^4)],[19*2^10,25.53/(4*10^3)],[19 *2^11,63.42/(4*10^3)],\n" }{MPLTEXT 1 0 62 "[18*2^12,13.22/400],[17*2^ 13,28.36/400],[17*2^14,59.23/400],\n" }{MPLTEXT 1 0 41 "[16*2^15,12.56 /40],[16*2^16,25.85/40]];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%7$\"$g\"$\"\"$!\"&7$\"%+K$\"\"(!\"$7$\"'CAL$F&\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$7$\"#K$\"+++++D!#;7$\"%C5$\"++++gD!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(7$\"#K$\"+++++D!#;7$\"#k$\"++++vyF' 7$\"$G\"$\"++++DE!#:7$\"$c#$\"++++D*)F07$\"$7&$\"++++qN!#97$\"%C5$\"++ ++'Q\"!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "707$\"$G\"$\"++++NS!#:7$\"$ c#$\"+++]P7!#97$\"$7&$\"++++&=%F,7$\"%C5$\"+++Dc8!#87$\"%[?$\"+++]#H%F 57$\"%'4%$\"+++vH8!#77$\"%#>)$\"++++vSF>7$\"&%Q;$\"++++_7!#67$\"&oF$$ \"++++DQFG7$\"&Ob'$\"+++]p6!#57$\"'s58$\"+++]iNFP7$\"'W@E$\"+++Dx5!\"* 7$\"')GC&$\"++++ZKFY7$\"(w&[5$\"+++vp(*FY" }}{PARA 11 "" 1 "" {XPPMATH 20 "707$\"$G\"$\"++++bE!#:7$\"$c#$\"++++5()F'7$\"$7&$\"++++5J !#97$\"%C5$\"+++]v5!#87$\"%[?$\"++++!e$F57$\"%'4%$\"++++c6!#77$\"%#>)$ \"+++]iOF>7$\"&%Q;$\"+++]Z6!#67$\"&oF$$\"+++]#f$FG7$\"&Ob'$\"++++16!#5 7$\"'s58$\"+++](R$FP7$\"'W@E$\"++++O5!\"*7$\"')GC&$\"+++v[JFY7$\"(w&[5 $\"+++]S&*FY" }}{PARA 11 "" 1 "" {XPPMATH 20 "707$\"$G\"$\"+++]AF!#:7$ \"$c#$\"+++]7')F'7$\"$7&$\"++++XH!#97$\"%C5$\"+++]U%*F07$\"%[?$\"++++& )H!#87$\"%'4%$\"+++]A\"*F97$\"%#>)$\"+++]_E!#77$\"&%Q;$\"+++](4)FB7$\" &oF$$\"+++DKC!#67$\"&Ob'$\"+++]!#57$\"'gdC$\"+++vP?Fh n7$\"'?:\\$\"++++bVFhn7$\"'SI)*$\"+++]d$*Fhn" }}{PARA 11 "" 1 "" {XPPMATH 20 "737$\"$[%$\"+++vg$\"+++vf(F'7$\"%?^$\"+++Dh:!#77$\"&S-\"$\"+++]ZOF 47$\"&c%>$\"+++]7*)F47$\"&7*Q$\"++++/B!#67$\"&GP($\"++++!f%FA7$\"'k#R \"$\"+++]h5!#57$\"'G&y#$\"+++DZ@FJ7$\"')GC&$\"+++]#f%FJ7$\"(w&[5$\"+++ +g%*FJ" }}{PARA 11 "" 1 "" {XPPMATH 20 "7.7$\"$/($\"+++]2K!#87$\"%W8$ \"+++](f'F'7$\"%)o#$\"+++Dq8!#77$\"%?^$\"+++]PGF07$\"&S-\"$\"++++bgF07 $\"&c%>$\"+++vo8!#67$\"&7*Q$\"+++]#Q$F=7$\"&GP($\"++++!4(F=7$\"'k#R\"$ \"+++v4:!#57$\"'G&y#$\"++++5IFJ7$\"')GC&$\"++++0kFJ7$\"(w&[5$\"+++]98! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "7.7$\"$/($\"+++v$H\"!#87$\"%W8$\" ++++5EF'7$\"%)o#$\"+++]d\\F'7$\"%?^$\"+++]\"4\"!#77$\"&S-\"$\"+++vxBF4 7$\"&c%>$\"+++]#Q'F47$\"&7*Q$\"+++]&e\"!#67$\"&GP($\"++++0LFA7$\"'k#R \"$\"++++!4(FA7$\"'G&y#$\"+++v![\"!#57$\"')GC&$\"++++SJFN7$\"(w&[5$\"+ ++]ikFN" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "lTpb:=proc(T) lo cal x;\n" }{MPLTEXT 1 0 52 "map(x->[log[b](x[1]),log[b](4*10^7*x[2]/x[ 1])],T);\n" }{MPLTEXT 1 0 6 "end;\n" }{MPLTEXT 1 0 14 "ppl:=proc(L)\n" }{MPLTEXT 1 0 48 "pointplot([log[b](L[1]),log[b](24*3600/L[2])],\n" } {MPLTEXT 1 0 59 "title=`Primality testing, log[2](test/day)-log[2](bit )`),\n" }{MPLTEXT 1 0 73 "textplot([log[b](L[1]),log[b](24*3600/L[2]), L[3]],align=\{BELOW,LEFT\})\n" }{MPLTEXT 1 0 6 "end;\n" }{MPLTEXT 1 0 15 "pplb:=proc(L)\n" }{MPLTEXT 1 0 48 "pointplot([log[b](L[1]),log[b]( 24*3600/L[2])],\n" }{MPLTEXT 1 0 59 "title=`Primality testing, log[2]( test/day)-log[2](bit)`),\n" }{MPLTEXT 1 0 68 "textplot([log[b](L[1]),l og[b](24*3600/L[2]),L[3]],align=\{BELOW\})\n" }{MPLTEXT 1 0 6 "end;\n" }{MPLTEXT 1 0 23 "pll:=proc(L) local x;\n" }{MPLTEXT 1 0 53 "plot(map (x->[log[b](x[1]),log[b](24*3600/x[2])],L))\n" }{MPLTEXT 1 0 6 "end;\n " }{MPLTEXT 1 0 24 "ltpb:=proc(L) local x;\n" }{MPLTEXT 1 0 63 "plot(m ap(x->[log[b](x[1]),log[b](24*3600/(f*x[2]*x[1]))],L));\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"TG6\"6#I\"xGF%F%F% -I$mapG%*protectedG6$f*F&F%6$I)operatorGF%I&arrowGF%F%7$-&I$logG6$F*I( _syslibGF%6#I\"bGF%6#&F'6#\"\"\"-F26#,$*(\")+++SF;&F'6#\"\"#F;F9!\"\"F ;F%F%F%F$F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"LG6\"F%F%F%6$- I*pointplotGF%6$7$-&I$logG6$%*protectedGI(_syslibGF%6#I\"bGF%6#&F$6#\" \"\"-F,6#,$*&\"&+k)F6&F$6#\"\"#!\"\"F6/I&titleGF%IPPrimality~testing,~ log[2](test/day)-log[2](bit)GF%-I)textplotGF%6$7%F+F7&F$6#\"\"$/I&alig nGF%<$I&BELOWGF%I%LEFTGF%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I \"LG6\"F%F%F%6$-I*pointplotGF%6$7$-&I$logG6$%*protectedGI(_syslibGF%6# I\"bGF%6#&F$6#\"\"\"-F,6#,$*&\"&+k)F6&F$6#\"\"#!\"\"F6/I&titleGF%IPPri mality~testing,~log[2](test/day)-log[2](bit)GF%-I)textplotGF%6$7%F+F7& F$6#\"\"$/I&alignGF%<#I&BELOWGF%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"LG6\"6#I\"xGF%F%F%-I%plotG6$%*protectedGI(_syslibGF%6#-I$mapG F+6$f*F&F%6$I)operatorGF%I&arrowGF%F%7$-&I$logGF*6#I\"bGF%6#&F'6#\"\" \"-F76#,$*&\"&+k)F>&F'6#\"\"#!\"\"F>F%F%F%F$F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"LG6\"6#I\"xGF%F%F%-I%plotG6$%*protectedGI(_syslib GF%6#-I$mapGF+6$f*F&F%6$I)operatorGF%I&arrowGF%F%7$-&I$logGF*6#I\"bGF% 6#&F'6#\"\"\"-F76#,$**\"&+k)F>I\"fGF%!\"\"&F'6#\"\"#FEFF%F%F%F$F% F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "display([plot(lTpb (schmul),style=POINT,title=`usqr, SuperSPARC, log[2](cycle/bit)-log[2] (bit)`,color=magenta),\n" }{MPLTEXT 1 0 50 "textplot([lTpb(schmul)[2][ 1],lTpb(schmul)[2][2],\n" }{MPLTEXT 1 0 45 "`Schoenhage et al.`],align =\{ABOVE,LEFT\}),\n" }{MPLTEXT 1 0 34 "plot(lTpb(karamul),color=green) ,\n" }{MPLTEXT 1 0 34 "plot(lTpb(karasqr),color=green),\n" }{MPLTEXT 1 0 54 "textplot([lTpb(karamul)[10][1],lTpb(karamul)[10][2],\n" } {MPLTEXT 1 0 37 "`Karatsuba`],align=\{ABOVE,LEFT\}),\n" }{MPLTEXT 1 0 36 "plot(lTpb(classicmul),color=blue),\n" }{MPLTEXT 1 0 36 "plot(lTpb( classicsqr),color=blue),\n" }{MPLTEXT 1 0 58 "textplot([lTpb(classicmu l)[2][1],lTpb(classicmul)[2][2],\n" }{MPLTEXT 1 0 35 "`Classic`],align =\{ABOVE,LEFT\}),\n" }{MPLTEXT 1 0 31 "plot(lTpb(fftmul),color=red),\n " }{MPLTEXT 1 0 31 "plot(lTpb(fftsqr),color=red),\n" }{MPLTEXT 1 0 60 "textplot([lTpb(fftmul)[1][1],lTpb(fftmul)[1][2],`Fermat`],\n" } {MPLTEXT 1 0 24 "align=\{ABOVE,LEFT\}),\n" }{MPLTEXT 1 0 39 "plot(lTpb (rffftmul2ss),color=yellow),\n" }{MPLTEXT 1 0 39 "plot(lTpb(rffftsqr2s s),color=yellow),\n" }{MPLTEXT 1 0 62 "textplot([lTpb(rffftmul2ss)[12] [1],lTpb(rffftmul2ss)[12][2],\n" }{MPLTEXT 1 0 33 "`Float`],align=\{AB OVE,LEFT\})]);" }}{PARA 13 "" 1 "" {TEXT 207 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "63-%+AXESLABELSG6'Q!6\"F&-%%FONTG6$%*HELVETICAG\"#5%+ HORIZONTALGF--%'CURVESG6%7%7$$\"3k*****\\4G>K(!#<$\"3A+++'f!*o!HF57$$ \"3$*******=cQk6!#;$\"3I*****>667X'F57$$\"3%)*****pnzT$=F;$\"33,++#Rim \\)F5-%&STYLEG6#%&POINTG-%&COLORG6&%$RGBG$F,!\"\"$\"\"!FLFK-%%TEXTG6&7 $$\"2/++!>cQk6!#:$\"+76@^k!\"*Q2Schoenhage~et~al.F'%*ALIGNLEFTG%+ALIGN ABOVEG-F/6$707$$\"\"(FN$\"3y*****Ron\\M$!#=7$$\"\")FN$\"3.+++]r%G^*F^o 7$$\"\"*FN$\"3!******H\"Q34FN$\"3i* *****[Sg_zF57$$\"#?FN$\"3%*******3$==a)F5-FH6&FJFMFKFM-F/6$707$Fjn$!3& ******>c)RJBF^o7$F`o$\"3')*****ps,OG%F^o7$Feo$\"31+++CQ7-7F57$Fjo$\"3- +++o]-$)=F57$F^p$\"3')*****f@:Na#F57$Fcp$\"3!)*****4`8_:$F57$Fhp$\"3y* ****48l]p$F57$F]q$\"35+++V*)=0VF57$Fbq$\"3_+++**>$>*[F57$Fgq$\"3`***** p\\t0]&F57$F\\r$\"3E+++$)eT.hF57$Far$\"3<*****HHf)4nF57$Ffr$\"3&)***** 4?L6I(F57$F[s$\"32+++#[:l)yF5F_s-FP6&7$Fgq$\"23++5Vgu:'F;Q*KaratsubaF' FZFen-F/6$7$7$$\"\"&FN$!3\"******\\!>2y;F57$Fjo$\"33+++&4G>K$F5-FH6&FJ FMFMFK-F/6$7(Fgv7$$\"\"'FN$!3#******f2?F-\"F57$Fjn$!3,+++B[adGF^o7$F`o $\"37+++SE!yz%F^o7$Feo$\"3'******RE!yz9F57$Fjo$\"3%)*****>a6nV#F5F_w-F P6&7$Fjo$\"+&4G>K$FXQ(ClassicF'FZFen-F/6$737$$\"3.+++A\\N2))F5$\"3c*** **\\5vXZ%F57$$\"3.+++A\\N2)*F5$\"3X+++Z+1jXF57$$\"3*******>\\N23\"F;$ \"3?+++#H?Vm%F57$$\"3*******>\\N2=\"F;$\"3I+++=jmrZF57$$\"3*******>\\N 2G\"F;$\"3:+++<)\\j)[F57$$\"3*******>\\N2Q\"F;$\"3x*******fM..&F57$$\" 3/+++g!*o!R\"F;$\"3&******4Zi\"o]F57$$\"3*******>\\N2[\"F;$\"3K+++D*oN =&F57$$\"3/+++g!*o!\\\"F;$\"3B+++,],$=&F57$$\"3*******>\\N2e\"F;$\"3C+ ++X]NL`F57$$\"3/+++g!*o!f\"F;$\"3%)*****H;,nH&F57$$\"3;+++#\\N2o\"F;$ \"3b+++R>(yW&F57$$\"3/+++g!*o!p\"F;$\"3K+++50P!R&F57$$\"3;+++#\\N2y\"F ;$\"3&******4a*QybF57$$\"3/+++g!*o!z\"F;$\"3U+++2)=iZ&F57$$\"3/+++g!*o !*=F;$\"34+++i#=wb&F57$$\"3/+++g!*o!*>F;$\"37+++Aj[[cF5-FH6&FJFKFMFM-F /6$737$F_y$\"34+++X%>Y(RF57$Fdy$\"33+++%*\\gdSF57$Fiy$\"39+++N`HXTF57$ F^z$\"3L+++K!pPC%F57$Fcz$\"3T+++@RD[VF57$Fhz$\"39+++l(p$\\WF57$F][l$\" 3G+++=*RE[%F57$Fb[l$\"34+++E+I*e%F57$Fg[l$\"3X+++WoaxXF57$F\\\\l$\"3W+ ++gTXpZF57$Fa\\l$\"3v*****fgHUs%F57$Ff\\l$\"3%******4#*)\\&)[F57$F[]l$ \"3T+++R$H+#[F57$F`]l$\"3G+++j*)z;]F57$Fe]l$\"3T++++w;0\\F57$Fj]l$\"3) ******R\\!QF]F57$F_^l$\"37+++_&e?4&F5Fc^l-FP6&7$$\"+A\\N2))FX$\"+0^duW FXQ'FermatF'FZFen-F/6$7.7$$\"32+++>;Vf%*F5$\"31+++=9UwLF57$$\"3&****** >uJ#R5F;$\"3++++$pXkT$F57$$\"3&******>uJ#R6F;$\"35+++\\:Y?MF57$$\"3,++ +4G>K7F;$\"3;+++ce[3OF57$$\"3,+++4G>K8F;$\"3@+++jApKQF57$$\"3-+++^FzC9 F;$\"3o*****z.:c>%F57$$\"3-+++^FzC:F;$\"3')*****zn`ec%F57$$\"3#******* *\\#*ph\"F;$\"3<+++F'4#QYF57$$\"31+++%GY(3 " 0 "" {MPLTEXT 1 0 16 "f:=1.05*40/60;\n" }{MPLTEXT 1 0 56 "T1:=[log[2](66377 7)+7650,6,`Twin, Amdahl 1200, 1989`];\n" }{MPLTEXT 1 0 59 "T2:=[log[2] (1706595)+11235,10,`Twin, Amdahl 1200, 1989`];\n" }{MPLTEXT 1 0 68 "T3 :=[log[2](697053813)+16352,212,`Twin, SuperSPARC 60 MHz, 1994`];\n" } {MPLTEXT 1 0 69 "T4:=[log[2](697053813)+16352,2*24*3600,`Maple, SuperS PARC 60 MHz`];\n" }{MPLTEXT 1 0 61 "T5:=[log[2](697053813)+16352,42.5* 60,`LiDIA, MIPS RS4000`];\n" }{MPLTEXT 1 0 59 "T6:=[log[2](697053813)+ 16352,3.5*3600,`LiDIA, SUN4 ELC`];\n" }{MPLTEXT 1 0 68 "T7:=[log[2](24 2206083)+38880,7*60,`Twin, SuperSPARC 60MHz, 1995`];\n" }{MPLTEXT 1 0 63 "T8:=[log[2](242206083)+38880,5*3600,`LiDIA, SPARCstation20`];\n" } {MPLTEXT 1 0 72 "T:=[[WS*2^7,36.49/40000],[WS*2^8,10.61/4000],[19*2^10 ,25.53/(4*10^3)],\n" }{MPLTEXT 1 0 67 "[19*2^11,63.42/(4*10^3)],[18*2^ 12,13.22/400],[17*2^13,28.36/400],\n" }{MPLTEXT 1 0 61 "[17*2^14,59.23 /400],[16*2^15,12.56/40],[16*2^16,25.85/40]];\n" }{MPLTEXT 1 0 52 "M29 :=[110503,0.03*110503,`Prime, NEC SX-2, 1988`];\n" }{MPLTEXT 1 0 42 "M 28:=[86243,5782,`Prime, CRAY-1, 1983`];\n" }{MPLTEXT 1 0 53 "M31:=[216 091,3*3600,`Prime, 1 CPU CRAY XMP, 1985`];\n" }{MPLTEXT 1 0 53 "M33:=[ 859433,25924,`Prime, 1 CPU CRAY C916, 1994`];\n" }{MPLTEXT 1 0 50 "P1: =[216100,33*60,`Prime, Amdahl 1200 E, 1990`];\n" }{MPLTEXT 1 0 65 "# P :=[[128000,128000*0.2],[256000,256000*0.5],[512000,512000]];\n" } {MPLTEXT 1 0 75 "display([ppl(T1),ppl(T2),ppl(T3),ppl(T4),ppl(T5),ppl( T6),ppl(T7),ppl(T8),\n" }{MPLTEXT 1 0 55 "ltpb(T),ppl(M28),ppl(M29),pp l(M31),pplb(M33),ppl(P1)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++q !#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%,&*&-I#lnG6$%*protectedGI(_sysl ibG6\"6#\"'xPm\"\"\"-F&6#\"\"#!\"\"F-\"%]wF-\"\"'I8Twin,~Amdahl~1200,~ 1989GF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%,&*&-I#lnG6$%*protectedGI(_ syslibG6\"6#\"(&f1<\"\"\"-F&6#\"\"#!\"\"F-\"&N7\"F-\"#5I8Twin,~Amdahl~ 1200,~1989GF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%,&*&-I#lnG6$%*protect edGI(_syslibG6\"6#\"*8Q0(p\"\"\"-F&6#\"\"#!\"\"F-\"&_j\"F-\"$7#I>Twin, ~SuperSPARC~60~MHz,~1994GF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%,&*&-I# lnG6$%*protectedGI(_syslibG6\"6#\"*8Q0(p\"\"\"-F&6#\"\"#!\"\"F-\"&_j\" F-\"'+G)$ \"+++]_E!#77$\"&c%>$\"+++]#Q'F,7$\"&7*Q$\"+++]&e\"!#67$\"&GP($\"++++0L F57$\"'k#R\"$\"++++!4(F57$\"'G&y#$\"+++v![\"!#57$\"')GC&$\"++++SJFB7$ \"(w&[5$\"+++]ikFB" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"'.06$\"'4:L!\" #I6Prime,~NEC~SX-2,~1988G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"&Vi) \"%#y&I4Prime,~CRAY-1,~1983G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"' \"4;#\"&+3\"II;Prime,~Amdahl~1200~E,~19 90G6\"" }}{PARA 13 "" 1 "" {TEXT 207 0 "" }{GLPLOT2D 565 407 407 {PLOTDATA 2 "6@-%+AXESLABELSG6$Q!6\"F&-%'POINTSG6#7$$\"+y')[!H\"!\")$ \"+>\"y8Q\"F.-%%TEXTG6&F+Q8Twin,~Amdahl~1200,~1989F'%*ALIGNLEFTG%+ALIG NBELOWG-F)6#7$$\"+^o$eM\"F.$\"+g:o28F.-F26&7$F:$\"*c\"o28!\"(F4F5F6-F) 6#7$$\"+**o(**R\"F.$\"+PK#3n)!\"*-F26&FFQ>Twin,~SuperSPARC~60~MHz,~199 4F'F5F6-F)6#7$FG$!+++++5FK-F26&7$FG$!#5!\"\"Q9Maple,~SuperSPARC~60~MHz F'F5F6-F)6#7$FG$\"+g@Y#3&FK-F26&7$FG$\"*;iC3&F.Q3LiDIA,~MIPS~RS4000F'F 5F6-F)6#7$FG$\"+zvgxFFK-F26&FboQ0LiDIA,~SUN4~ELCF'F5F6-F)6#7$$\"+qtxC: F.$\"+u\")\\%o(FK-F26&7$$\"*PxZ_\"FC$\"1-++u\")\\%o(!#:Q=Twin,~SuperSP ARC~60MHz,~1995F'F5F6-F)6#7$F[p$\"+1W.jAFK-F26&7$FbpF[qQ6LiDIA,~SPARCs tation20F'F5F6-%'CURVESG6$7+7$$\"#7\"\"!$\"3'**********f6]\"!#;7$$\"#8 Fhq$\"3#*******R[y(fic Ffr7$$\"31+++%GY(3Fhq$!3<+++!*f>bT!#=7$$\"#?Fhq$!3#******\\TZoX#Ffr-% &COLORG6&%$RGBG$\"#5FY$FhqFYF\\u-F)6#7$$\"+u>hR;F.$\"+)z!R,RFK-F26&7$$ \"2-++S(>hR;Ffp$\"23++!)z!R,RF[rQ4Prime,~CRAY-1,~1983F'F5F6-F)6#7$$\"+ ,EPv;F.$\"+q8\"Rq%FK-F26&7$$\"2-++5gs`n\"Ffp$\"*P6Rq%F.Q6Prime,~NEC~SX -2,~1988F'F5F6-F)6#7$$\"+Yz7sF.$\"+tHuO " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 10 "7.8. FF T v" }{TEXT 206 8 "\303\251" }{TEXT 206 18 "ges testek felett." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 14 "7.9. Fermat-sz" } {TEXT 206 8 "\303\241" }{TEXT 206 12 "m transzform" }{TEXT 206 8 "\303 \241" }{TEXT 206 2 "ci" }{TEXT 206 8 "\303\263" }{TEXT 206 1 "." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "7.10. Sch" }{TEXT 206 8 "\303\266" }{TEXT 206 16 "nhage-Strassen-f" }{TEXT 206 8 "\303\251" }{TEXT 206 13 "le gyorsszorz" }{TEXT 206 8 "\303\263" }{TEXT 206 12 " \+ algoritmus." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 7 "7.11. P" }{TEXT 206 8 "\303\251" }{TEXT 206 4 "lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 33 "7.12. Ritka polinomok es ritka sz" } {TEXT 206 8 "\303\241" }{TEXT 206 4 "mok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 14 "7.13. Feladat." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 10 "7.14. Oszt" }{TEXT 206 8 "\303\241" } {TEXT 206 14 "s, polinomoszt" }{TEXT 206 8 "\303\241" }{TEXT 206 2 "s. " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "#\n" }{MPLTEXT 1 0 60 "# This procedure calculate the approxim ate reciprocal b of\n" }{MPLTEXT 1 0 62 "# a given number a. The binar y length of a must be 2^logn+1,\n" }{MPLTEXT 1 0 60 "# where logn>2 is an integer. The result is [b,alpha,beta]\n" }{MPLTEXT 1 0 63 "# where the parameters 0F,)\"\"#F*@$1F* \"\"&C%>F--I&floorGF&6#*&)F4,$*&F4\"\"\"F,FAFAFAF%!\"\"@$/*&F%FAF-FAF> >F-,&F-FAFAFB-I'RETURNGF(6#7%F-,$*&F4FAF,FBFA!\"#>F.-I%iquoGF(6$F%)F4, $*&#FAF4FAF,FAFA>F0-I'apprecGF&6$F.,&F*FAFAFB>F/&F06#FA-FQ6$,&*&)F4,&* &#\"\"$F4FAF,FAFAFAFAFAF/FAFA*(F/FAF/FAF%FAFB)F4F,7%I\"%GF&&F06#F4&F06 #FaoF&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "apprec(256,3) ; apprec(257,3); apprec(300,3);\n" }{MPLTEXT 1 0 48 "apprec(511,3); ap prec(65536,4); apprec(65537,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"$ b##\"\"\"\"\"%!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"$b##\"\"\"\"\" %!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"$=##\"\"\"\"\"%!\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "7%\"$G\"#\"\"\"\"\"%!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"&Nb'#\"\"\"\"\")!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"&Nb'#\"\"\"\"\")!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "#\n" }{MPLTEXT 1 0 54 "# This is a Maple demo program \+ to show the procedure\n" }{MPLTEXT 1 0 54 "# for division using the ap proximation of reciprocal\n" }{MPLTEXT 1 0 53 "# based on Newton's met hod. Here, with the notation\n" }{MPLTEXT 1 0 54 "# n=2^logn, c has at most 2n digit and a has at most\n" }{MPLTEXT 1 0 52 "# n digit. logn \+ must be an integer greater then 1.\n" }{MPLTEXT 1 0 3 "#\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 50 "division:=proc(c::posint,a::posint,logn:: posint)\n" }{MPLTEXT 1 0 35 "local n,k,l,as,bs,cs,qs,rs,alpha;\n" } {MPLTEXT 1 0 19 "n:=2^logn; as:=a;\n" }{MPLTEXT 1 0 43 "for k from 0 w hile as<2^n do as:=2*as od;\n" }{MPLTEXT 1 0 47 "if c=0 then RETURN([0 ,0]) fi; cs:=floor(c/2);\n" }{MPLTEXT 1 0 50 "for l from -1 while cs<2 ^(2*n-1) do cs:=2*cs od;\n" }{MPLTEXT 1 0 21 "print(l); print(k);\n" } {MPLTEXT 1 0 53 "if k<=0 or l<0 or k>l+1 then RETURN(`overflow`) fi;\n " }{MPLTEXT 1 0 36 "cs:=iquo(cs,2^n); apprec(as,logn);\n" }{MPLTEXT 1 0 72 "bs:=%[1]; alpha:=%%[2]; qs:=iquo(cs*bs,2^(n-k+l)); rs:=c -qs*a;\n" }{MPLTEXT 1 0 72 "if k-l+alpha*n>1 then division(rs,a,logn); qs:=qs+%[1]; rs:=%%[2]; fi;\n" }{MPLTEXT 1 0 40 "while rs>=a do qs:=q s+1; rs:=rs-a; od;\n" }{MPLTEXT 1 0 40 "if qs>=2^n then RETURN(`overfl ow`) fi;\n" }{MPLTEXT 1 0 10 "[qs,rs];\n" }{MPLTEXT 1 0 4 "end;" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6%'I\"cG6\"I'posintG%*protectedG'I\"aG F&F''I%lognGF&F'6+I\"nGF&I\"kGF&I\"lGF&I#asGF&I#bsGF&I#csGF&I#qsGF&I#r sGF&I&alphaGF&F&F&C5>F.)\"\"#F,>F1F*?(F/\"\"!\"\"\"F&2F1)F:F.>F1,$*&F: F>F1F>F>@$/F%F=-I'RETURNGF(6#7$F=F=>F3-I&floorG6$F(I(_syslibGF&6#,$*&# F>F:F>F%F>F>?(F0!\"\"F>F&2F3)F:,&*&F:F>F.F>F>F>FT>F3,$*&F:F>F3F>F>-I&p rintGF(6#F0-Fgn6#F/@$551F/F=2F0F=2,&F0F>F>F>F/-FG6#I)overflowGF(>F3-I% iquoGF(6$F3F@-I'apprecGF&6$F1F,>F2&I\"%GF&6#F>>F6&I#%%GF&6#F:>F4-Fgo6$ *&F3F>F2F>)F:,(F.F>F/FTF0F>>F5,&F%F>*&F4F>F*F>FT@$2F>,(F/F>F0FT*&F6F>F .F>F>C%-I)divisionGF&6%F5F*F,>F4,&F4F>F]pF>>F5Fap?(F&F>F>F&1F*F5C$>F4, &F4F>F>F>>F5,&F5F>F*FT@$1F@F4Fbo7$F4F5F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "division(2^32,2^16,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I)overflowG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "debug(division);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I)divisionG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "division (2^32-10*2^16,2^16-1,4);" }}{PARA 9 "" 1 "" {TEXT 208 49 "\{--> enter \+ division, args = 4294311936, 65535, 4" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Nb'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'q58" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"+of:Z@" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"+O>J%H%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Eb'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"&oF$#\"\"\"\" \")!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&oF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "#\"\"\"\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Eb'" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"&Eb'" }}{PARA 9 "" 1 "" {TEXT 208 44 " \{--> enter division, args = 65526, 65535, 4" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Nb'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'q58" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&jF$" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"&Eb'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'_58" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'/@E" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'3U_" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"(;%[5" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"(Ko4#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"(kO >%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"(GtQ)" }}{PARA 11 "" 1 "" {XPPMATH 20 "\")cYx;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\")7$\\N$" }} {PARA 11 "" 1 "" {XPPMATH 20 "\")C')4n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*[s>M\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*'\\%Ro#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*#**)yO&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"+%)zd t5" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"+of:Z@" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"+O>J%H%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Eb' " }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"&oF$#\"\"\"\"\")!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&oF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "#\"\"\" \"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Eb'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!\"&Eb'" }} {PARA 9 "" 1 "" {TEXT 208 50 "<-- exit division (now in division) = [0 , 65526]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!\"&Eb'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Eb'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Eb'" } }{PARA 11 "" 1 "" {XPPMATH 20 "7$\"&Eb'F#" }}{PARA 9 "" 1 "" {TEXT 208 55 "<-- exit division (now at top level) = [65526, 65526]\}" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$\"&Eb'F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "%[1]*(2^16-1)+%[2]-(2^32-10*2^16);" }}{PARA 11 "" 1 " " {XPPMATH 20 "\"\"!" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 16 "7.15. \+ Polinom ki" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "rt" }{TEXT 206 8 "\3 03\251" }{TEXT 206 3 "kel" }{TEXT 206 8 "\303\251" }{TEXT 206 8 "se te tsz" }{TEXT 206 8 "\305\221" }{TEXT 206 15 "leges helyeken." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 14 "7.16. Interpol" }{TEXT 206 8 "\303\241" }{TEXT 206 2 "ci" }{TEXT 206 8 "\303\263" }{TEXT 206 1 "." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 14 "7.17. Feladat." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 14 "7.18. Feladat." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 14 "7.19. Feladat." }}} {SECT 0 {PARA 4 "" 0 "" {TEXT 206 23 "7.20. Feladat: kontroll" }{TEXT 206 8 "\303\241" }{TEXT 206 9 "lt euklid" }{TEXT 206 8 "\303\251" } {TEXT 206 8 "szi lesz" }{TEXT 206 8 "\303\241" }{TEXT 206 2 "ll" } {TEXT 206 8 "\303\241" }{TEXT 206 2 "s." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "# This function makes an upper or lower division step. The\n" }{MPLTEXT 1 0 61 "# function \+ updapes the incoming list [a,b,x,y,u,v], but the\n" }{MPLTEXT 1 0 28 " # remainder is given back.\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 32 "q step:=proc(L,s) local q,r,LL;\n" }{MPLTEXT 1 0 21 " if L[1]>L[2] then \n" }{MPLTEXT 1 0 45 " q:=iquo(L[1],L[2]); r:=irem(L[1],L[2]);\n" } {MPLTEXT 1 0 18 " if r>=s then\n" }{MPLTEXT 1 0 55 " LL:=[r,L[ 2],L[3],L[4]+q*L[3],L[5],L[6]+q*L[5]];\n" }{MPLTEXT 1 0 11 " else \+ \n" }{MPLTEXT 1 0 63 " LL:=[r,L[2],L[3],L[4]+(q-1)*L[3],L[5],L[6] +(q-1)*L[5]];\n" }{MPLTEXT 1 0 9 " fi;\n" }{MPLTEXT 1 0 8 " else\n " }{MPLTEXT 1 0 45 " q:=iquo(L[2],L[1]); r:=irem(L[2],L[1]);\n" } {MPLTEXT 1 0 18 " if r>=s then\n" }{MPLTEXT 1 0 55 " LL:=[L[1] ,r,L[3]+q*L[4],L[4],L[5]+q*L[6],L[6]];\n" }{MPLTEXT 1 0 10 " else\n " }{MPLTEXT 1 0 63 " LL:=[L[1],r,L[3]+(q-1)*L[4],L[4],L[5]+(q-1)* L[6],L[6]];\n" }{MPLTEXT 1 0 9 " fi;\n" }{MPLTEXT 1 0 7 " fi;\n" } {MPLTEXT 1 0 7 " LL;\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"LG6\"I\"sGF%6%I\"qGF%I\"rGF%I#LLGF%F%F%C$@%2&F$6# \"\"#&F$6#\"\"\"C%>F(-I%iquoG%*protectedG6$F1F.>F)-I%iremGF8F9@%1F&F)> F*7(F)F.&F$6#\"\"$,&&F$6#\"\"%F3*&F(F3FAF3F3&F$6#\"\"&,&&F$6#\"\"'F3*& F(F3FIF3F3>F*7(F)F.FA,&FEF3*&,&F(F3F3!\"\"F3FAF3F3FI,&FMF3*&FUF3FIF3F3 C%>F(-F76$F.F1>F)-F>F*7(F1F),&FAF3*&F(F3FEF3F3FE,&FIF3*&F(F3FM F3F3FM>F*7(F1F),&FAF3*&FUF3FEF3F3FE,&FIF3*&FUF3FMF3F3FMF*F%F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "# This is a slow version of \+ ced. It works for arbitrary input.\n" }{MPLTEXT 1 0 47 "# The matrix \+ and the remainder is given back.\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 28 "sced:=proc(a,b,s) local L;\n" }{MPLTEXT 1 0 21 " L:=[a,b,1,0,0, 1];\n" }{MPLTEXT 1 0 32 " while L[1]>=s and L[2]>=s do\n" }{MPLTEXT 1 0 20 " L:=qstep(L,s);\n" }{MPLTEXT 1 0 7 " od;\n" }{MPLTEXT 1 0 6 " L;\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6% I\"aG6\"I\"bGF%I\"sGF%6#I\"LGF%F%F%C%>F)7(F$F&\"\"\"\"\"!F.F-?(F%F-F-F %31F'&F)6#F-1F'&F)6#\"\"#>F)-I&qstepGF%6$F)F'F)F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "debug(sced);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%scedG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " a:=floor(evalf(Pi*10.^8)); b:=floor(evalf(exp(1.)*10^8));\n" }{MPLTEXT 1 0 12 "sced(a,b,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*l#fTJ" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"*#=G=F" }}{PARA 9 "" 1 "" {TEXT 208 48 "\{--> enter sced, args = 314159265, 271828182, 1" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"*l#fTJ\"*#=G=F\"\"\"\"\"!F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\")$3JB%\"*#=G=F\"\"\"F%\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\")$3JB%\")%oTy\"\"\"(\"\"\"\"\"'F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"(:xk'\")%oTy\"\"\"(\"#:\"\"'\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"(:xk'\"(aia%\"#P\"#:\"#K\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"(h95#\"(aia%\"#P\"#_\"#K\"#X" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"(h95#\"'KLM\"$T\"\"#_\"$A\"\"#X" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"&p9%\"'KLM\"$T\"\"$)*)\"$A\"\"$x(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"&p9%\"&!e6\"%Dt\"$)*)\"%Qj\"$x(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"%Hn\"&!e6\"%Dt\"&tG#\"%Qj\"&\"z>" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"%Hn\"%^[\"&)>I\"&tG#\"&Hh#\"&\"z>" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"%y=\"%^[\"&)>I\"&rI&\"&Hh#\"&?f%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"%y=\"%&4\"\"'Sj8\"&rI&\"'pz6\"&?f%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$$y\"%&4\"\"'Sj8\"'6%*=\"'pz6\"'*)Q;" }}{PARA 11 " " 1 "" {XPPMATH 20 "7(\"$$y\"$7$\"'^dK\"'6%*=\"'e=G\"'*)Q;" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$f\"\"$7$\"'^dK\"'84%)\"'e=G\"'0ws" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$f\"\"$`\"\"(km;\"\"'84%)\"(j%45\"'0ws" }} {PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"'\"$`\"\"(km;\"\"(xv+#\"(j%45\"(oq t\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"'\"\"$\")*3c8&\"(xv+#\")jhV W\"(oqt\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"!\"\"$\")*3c8&\")mOO` \")jhVW\")JK " 0 "" {MPLTEXT 1 0 48 "3*(%[3]+%[4]),3*(%[5]+ %[6]),%[3]*%[6]-%[4]*%[5];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"*l#fTJ \"*#=G=F\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "lB:=4; B: =2^lB; # wordsize and base of number system" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "cedmulQM:=proc(Q,M) local i,x,y,u,v ,q;\n" }{MPLTEXT 1 0 37 "x:=M[1]; y:=M[2]; u:=M[3]; v:=M[4];\n" } {MPLTEXT 1 0 39 "for i from nops(Q) by -1 while i>0 do\n" }{MPLTEXT 1 0 12 " q:=Q[i];\n" }{MPLTEXT 1 0 18 " if q[1]=0 then\n" }{MPLTEXT 1 0 34 " q:=q[2]; u:=u+q*x; v:=v+q*y;\n" }{MPLTEXT 1 0 8 " else\n" } {MPLTEXT 1 0 34 " q:=q[1]; x:=x+q*u; y:=y+q*v;\n" }{MPLTEXT 1 0 7 " fi;\n" }{MPLTEXT 1 0 5 "od;\n" }{MPLTEXT 1 0 12 "[x,y,u,v];\n" } {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"QG6\"I\"M GF%6(I\"iGF%I\"xGF%I\"yGF%I\"uGF%I\"vGF%I\"qGF%F%F%C(>F)&F&6#\"\"\">F* &F&6#\"\"#>F+&F&6#\"\"$>F,&F&6#\"\"%?(F(-I%nopsG%*protectedG6#F$!\"\"F %2\"\"!F(C$>F-&F$6#F(@%/&F-F1FFC%>F-&F-F5>F+,&F+F2*&F-F2F)F2F2>F,,&F,F 2*&F-F2F*F2F2C%>F-FM>F),&F)F2*&F-F2F+F2F2>F*,&F*F2*&F-F2F,F2F27&F)F*F+ F,F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "cedmulMQ:=proc( M,Q) local i,x,y,u,v,q;\n" }{MPLTEXT 1 0 37 "x:=M[1]; y:=M[2]; u:=M[3] ; v:=M[4];\n" }{MPLTEXT 1 0 27 "for i while i<=nops(Q) do\n" }{MPLTEXT 1 0 12 " q:=Q[i];\n" }{MPLTEXT 1 0 18 " if q[1]=0 then\n" }{MPLTEXT 1 0 34 " q:=q[2]; x:=x+q*y; u:=u+q*v;\n" }{MPLTEXT 1 0 8 " else\n " }{MPLTEXT 1 0 34 " q:=q[1]; y:=y+q*x; v:=v+q*u;\n" }{MPLTEXT 1 0 7 " fi;\n" }{MPLTEXT 1 0 5 "od;\n" }{MPLTEXT 1 0 12 "[x,y,u,v];\n" } {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"MG6\"I\"Q GF%6(I\"iGF%I\"xGF%I\"yGF%I\"uGF%I\"vGF%I\"qGF%F%F%C(>F)&F$6#\"\"\">F* &F$6#\"\"#>F+&F$6#\"\"$>F,&F$6#\"\"%?(F(F2F2F%1F(-I%nopsG%*protectedG6 #F&C$>F-&F&6#F(@%/&F-F1\"\"!C%>F-&F-F5>F),&F)F2*&F-F2F*F2F2>F+,&F+F2*& F-F2F,F2F2C%>F-FK>F*,&F*F2*&F-F2F)F2F2>F,,&F,F2*&F-F2F+F2F27&F)F*F+F,F %F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "cedmulMM:=proc(M,M M) local x,y,u,v;\n" }{MPLTEXT 1 0 27 "x:=M[1]*MM[1]+M[2]*MM[3];\n" } {MPLTEXT 1 0 27 "y:=M[1]*MM[2]+M[2]*MM[4];\n" }{MPLTEXT 1 0 27 "u:=M[3 ]*MM[1]+M[4]*MM[3];\n" }{MPLTEXT 1 0 27 "v:=M[3]*MM[2]+M[4]*MM[4];\n" }{MPLTEXT 1 0 12 "[x,y,u,v];\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"MG6\"I#MMGF%6&I\"xGF%I\"yGF%I\"uGF%I\"vGF%F%F% C'>F(,&*&&F$6#\"\"\"F2&F&F1F2F2*&&F$6#\"\"#F2&F&6#\"\"$F2F2>F),&*&F0F2 &F&F6F2F2*&F5F2&F&6#\"\"%F2F2>F*,&*&&F$F9F2F3F2F2*&&F$FAF2F8F2F2>F+,&* &FFF2F>F2F2*&FHF2F@F2F27&F(F)F*F+F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "cedret:=proc(M,L) local x,y,u,v,q,MM,LL;\n" }{MPLTEXT 1 0 37 "x:=M[1]; y:=M[2]; u:=M[3]; v:=M[4];\n" }{MPLTEXT 1 0 16 "if L [4]=0 then\n" }{MPLTEXT 1 0 32 " q:=L[5]; x:=x+q*y; u:=u+q*v;\n" } {MPLTEXT 1 0 6 "else\n" }{MPLTEXT 1 0 12 " q:=L[4];\n" }{MPLTEXT 1 0 23 " y:=y+q*x; v:=v+q*u;\n" }{MPLTEXT 1 0 5 "fi;\n" }{MPLTEXT 1 0 22 "[L[1],L[2],x,y,u,v];\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"MG6\"I\"LGF%6)I\"xGF%I\"yGF%I\"uGF%I\"vGF%I\"qGF%I #MMGF%I#LLGF%F%F%C(>F(&F$6#\"\"\">F)&F$6#\"\"#>F*&F$6#\"\"$>F+&F$6#\" \"%@%/&F&F>\"\"!C%>F,&F&6#\"\"&>F(,&F(F3*&F,F3F)F3F3>F*,&F*F3*&F,F3F+F 3F3C%>F,FB>F),&F)F3*&F,F3F(F3F3>F+,&F+F3*&F,F3F*F3F37(&F&F2&F&F6F(F)F* F+F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "# Set the minim al positive integer l such that u,v=B^l1 or v>=B^l1 do l0: =l1; l1:=2*l1; od;\n" }{MPLTEXT 1 0 23 " l:=ceil((l0+l1)/2);\n" } {MPLTEXT 1 0 17 " while lF)\"\"\">F*F-?(F%F-F-F%51)I\"BGF%F*F$1F2F&C$>F)F*>F*,$*&\"\"# F-F*F-F->F(-I%ceilG6$%*protectedGI(_syslibGF%6#,&*&#F-F:F-F)F-F-*&FDF- F*F-F-?(F%F-F-F%2F(F*C$@%32F$)F3F(2F&FL>F*F(>F)F(F;F(F%F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "min_l(a,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "c ed:=proc(a,b,n,w,e) local nn,np,ep,wp,aa,bb,ap,bp,app,bpp,f,s,L,M,MM,Q ,t;\n" }{MPLTEXT 1 0 11 "s:=w*B^e;\n" }{MPLTEXT 1 0 38 "if n<=2 then r eturn(sced(a,b,s)) fi;\n" }{MPLTEXT 1 0 22 "nn:=n; aa:=a; bb:=b;\n" } {MPLTEXT 1 0 27 "ep:=ceil(nn/4); np:=2*ep;\n" }{MPLTEXT 1 0 40 "if nn- ep=ep and e>=nn-3*ep then\n" }{MPLTEXT 1 0 70 " if ap*f+w*B^(e+ep)>B^nn or bp*f+w*B^(e+ep)>B^nn then wp:=2; fi; \+ \n" }{MPLTEXT 1 0 7 " fi;\n" }{MPLTEXT 1 0 5 "fi;\n" }{MPLTEXT 1 0 37 "if ap>=wp*B^ep and bp>=wp*B^ep then\n" }{MPLTEXT 1 0 27 " L:=ced( ap,bp,np,wp,ep);\n" }{MPLTEXT 1 0 29 " M:=[L[3],L[4],L[5],L[6]];\n" } {MPLTEXT 1 0 66 " aa:=L[1]; bb:=L[2]; if aa=f*B^ep or bb>=f* B^ep do\n" }{MPLTEXT 1 0 32 " L:=qstep([aa,bb,1,0,0,1],s);\n" } {MPLTEXT 1 0 23 " aa:=L[1]; bb:=L[2];\n" }{MPLTEXT 1 0 24 " if aa=ep and e>= nn-3*ep then\n" }{MPLTEXT 1 0 70 " if ap*f+w*B^(e+ep)>B^nn or bp*f+ w*B^(e+ep)>B^nn then wp:=2; fi; \n" }{MPLTEXT 1 0 7 " fi;\n" } {MPLTEXT 1 0 5 "fi;\n" }{MPLTEXT 1 0 37 "if ap>=wp*B^ep and bp>=wp*B^e p then\n" }{MPLTEXT 1 0 27 " L:=ced(ap,bp,np,wp,ep);\n" }{MPLTEXT 1 0 30 " MM:=[L[3],L[4],L[5],L[6]];\n" }{MPLTEXT 1 0 66 " aa:=L[1]; bb :=L[2]; if aa=f*B^ep or bb>=f*B^ep do\n" }{MPLTEXT 1 0 32 " L:=qstep([aa,bb,1,0,0,1],s);\n" }{MPLTEXT 1 0 23 " aa:=L[1]; bb :=L[2];\n" }{MPLTEXT 1 0 24 " if aaF6*&F(\"\"\")I\"BGF%F)F?@$1F'\"\"#O-I%scedGF%6%F$F &F6>F+F'>F/F$>F0F&>F--I%ceilG6$%*protectedGI(_syslibGF%6#,$*&#F?\"\"%F ?F+F?F?>F,,$*&FDF?F-F?F?@$2,&F+F?F-!\"\"F)C$>F-,&F+F?F)FgnFW>F5)FA,&F+ F?F,Fgn>F1-I&floorGFO6#*&F/F?F5Fgn>F2-F`o6#*&F0F?F5Fgn>F3,&F/F?*&F1F?F 5F?Fgn>F4,&F0F?*&F2F?F5F?Fgn@%/,&F)F?F-F?F+>F.,&F(F?F?F?C$>F.F?@$31F-F )1,&F+F?*&\"\"$F?F-F?FgnF)@$52)FAF+,&FioF?*&F(F?)FAF_pF?F?2F^q,&F\\pF? F`qF?>F.FD@%31*&F.F?)FAF-F?F11FhqF2C)>F7-I$cedGF%6'F1F2F,F.F->F87&&F76 #Fjp&F76#FV&F76#\"\"&&F76#\"\"'>F/&F76#F?>F0&F76#FD@%2F/F0>F/,&F/F?F0F ?>F0Fes>F/,(*&F/F?F5F?F?*&&F8FerF?F3F?F?*&&F8FasF?F4F?Fgn>F0,(*&F0F?F5 F?F?*&&F8FcrF?F3F?Fgn*&&F8F^sF?F4F?F?>F87&F?\"\"!FgtF?>F;,&*&FdtF?F/F? F?*&F]tF?F0F?F?>F;,&*&FbtF?F/F?F?*&F[tF?F0F?F?>F;,&*&FdtF?F[tF?F?*&F]t F?FbtF?Fgn>F:7\"?(F%F?F?F%51*&F5F?FiqF?F/1FiuF0C'>F7-I&qstepGF%6$7(F/F 0F?FgtFgtF?F6F\\sF_s@$52F/F62F0F6C*>F7-I'cedretGF%6$-I)cedmulMQGF%6$F8 F:F7F\\sF_sFbs>F;,&*&FbrF?F/F?F?*&FdrF?F0F?F?>F;,&*&FfrF?F/F?F?*&FirF? F0F?F?>F;,&*&FbrF?FirF?F?*&FdrF?FfrF?FgnOF7>F:7$-I#opGFP6#F:7$FdrFfr>F 9Fjv>F;,&*&&F9F^sF?F/F?F?*&&F9FasF?F0F?F?>F;,&*&&F9FcrF?F/F?F?*&&F9Fer F?F0F?F?>F;,&*&FdxF?F\\yF?F?*&FfxF?FjxF?Fgn>F+FfnFZF[oF^oFcoFgoFjoF]p@ %FfqC)F\\r>F9FarF\\sF_sFbs>F/,(FisF?*&F\\yF?F3F?F?*&FfxF?F4F?Fgn>F0,(F `tF?*&FjxF?F3F?Fgn*&FdxF?F4F?F?>F9Fft>F9-I)cedmulQMGF%6$F:F9>F8-I)cedm ulMMGF%6$F8F9FhtF\\uF`uFduFfuF`xFaxFgxF]y>F7-F^r6'F/F0FfnF(F)FdyF^zFbz F\\sF_sFbsFhtF\\uF`u7(F]sF`sFdtF]tFbtF[tF%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "debug(ced);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$ cedG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "ced(a,b,min_l(a, b),1,0);" }}{PARA 9 "" 1 "" {TEXT 208 53 "\{--> enter ced, args = 3141 59265, 271828182, 8, 1, 0" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"*l#fTJ" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*#=G=F" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Ob'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%$z%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%ZT" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&<_%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&!R]" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 43 "\{--> enter ced, \+ args = 4793, 4147, 4, 1, 2" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$c#" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"%$z%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%ZT" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$c#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" $&=" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#^" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 39 "\{--> enter ced, \+ args = 18, 16, 2, 1, 1" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 9 "" 1 "" {TEXT 208 35 "\{--> enter sced, args = 18, 16, 16" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#=\"#;\"\"\"\"\"!F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"#\"#;\"\"\"\"\"!F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"#\"#;\"\"\"\"\"!F&F%" }}{PARA 9 "" 1 "" {TEXT 208 52 "<-- ex it sced (now in ced) = [2, 16, 1, 0, 0, 1]\}\n" }{TEXT 208 49 "<-- exi t ced (now in ced) = [2, 16, 1, 0, 0, 1]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"#\"#;\"\"\"\"\"!F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"\"\"\"!F$F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#=" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"%$z%" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"%ZT" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%$z%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%ZT" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$Y'\"%Z T\"\"\"F%\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$Y'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%ZT" }}{PARA 11 "" 1 "" {XPPMATH 20 "7#7$\"\"\"\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$Y'\"$r#\"\"\"\"\"!\"\"'F%" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"$Y'" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"$r#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$7$\"\"\"\"\"!7$F%\"\"'" }} {PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"(\"\"\"\"\"'F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%$z%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%ZT" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#S" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"\"\" \"!F$F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"(\"\"\"\"\"'F$" }} {PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"(\"\"\"\"\"'F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%$z%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%ZT" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$/\"\"$r#\"\"\"F%\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$/\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$r#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$/\"\"$r#\"\"(\"\")\"\"'F%" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"$/\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"$r#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$v$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%$z%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%ZT" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 52 "<-- exit ced (now in ced) = [104, 271, 7, 8, 6, 7]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$/\"\"$r#\"\"(\"\")\"\"'F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"(\"\")\"\"'F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$/ \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$r#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$v$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\")*R*[C" }}{PARA 11 "" 1 "" {XPPMATH 20 "\")%oTy\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"* l#fTJ" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*#=G=F" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "7(\"(:xk'\")%oTy\"\"\"\"F%\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"(:xk'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\")%oTy\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "7#7$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"(:xk'\"(aia%\"\"\"\"\"!\"\"#F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"(:xk'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"(aia%" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$7$\"\"\"\"\"!7$F%\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"#P\"#:\"#K\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"*l#fTJ" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*#=G=F" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$c#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&nf#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&ex\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$j\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$1#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 45 "\{--> enter ced, \+ args = 25967, 17758, 4, 1, 2" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$c#" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"&nf#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&ex\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$c#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$,\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"#p" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"$6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#%*" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 40 "\{--> enter ced, \+ args = 101, 69, 2, 1, 1" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }} {PARA 9 "" 1 "" {TEXT 208 36 "\{--> enter sced, args = 101, 69, 16" }} {PARA 11 "" 1 "" {XPPMATH 20 "7(\"$,\"\"#p\"\"\"\"\"!F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#K\"#p\"\"\"F%\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#K\"\"&\"\"#\"\"\"F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#K\"\"&\"\"#\"\"\"F&F&" }}{PARA 9 "" 1 "" {TEXT 208 50 "<-- ex it sced (now in ced) = [32, 5, 2, 1, 1, 1]\}" }}{PARA 9 "" 1 "" {TEXT 208 49 "<-- exit ced (now in ced) = [32, 5, 2, 1, 1, 1]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#K\"\"&\"\"#\"\"\"F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"#\"\"\"F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#P" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%4#)" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%\\&*" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&nf#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&ex\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"%4#)\"%S8\"\"\"\"\"!F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%4 #)" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%S8" }}{PARA 11 "" 1 "" {XPPMATH 20 "7#7$\"\"!\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$p\" \"%S8\"\"\"\"\"&\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$p\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"%S8" }}{PARA 11 "" 1 "" {XPPMATH 20 "7 (\"$p\"\"%S8\"\"$\"#;\"\"#\"#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$p\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%S8" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%4:" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&nf#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&ex\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 55 "<-- exit ced (now in ced) = [169, 1340, 3, 16, 2, 11]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$p\"\"%S8\"\"$\"#;\"\"# \"#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"$\"#;\"\"#\"#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$p\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%S8" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"%4:" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"',[Q" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'KLM" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"#6\"#f\"\")\"#V" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\" $T\"\"$d(\"$A\"\"$b'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*l#fTJ" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"*#=G=F" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"&p9%\"'KLM\"\"\"F%\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&p9%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"'KLM" }}{PARA 11 "" 1 "" {XPPMATH 20 "7#7$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"&p9%\"&!e6\"\"\"\"\"!\"\")F%" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"&p9%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&!e6" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$7$\"\"\"\"\"!7$F%\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"%Dt\"$)*)\"%Qj\"$x(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"*l#fTJ" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"*#=G=F" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 45 "\{--> enter ced, args = 4146 9, 11580, 4, 1, 0" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&p9%" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"&!e6" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$c#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$h\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#X" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$`#" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#g" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" \"\"" }}{PARA 9 "" 1 "" {TEXT 208 40 "\{--> enter ced, args = 161, 45, 2, 1, 1" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 9 "" 1 "" {TEXT 208 36 "\{--> enter sced, args = 161, 45, 16" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$h\"\"#X\"\"\"\"\"!F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#E\"#X\"\"\"\"\"$\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#E\"#>\"\"%\"\"$\"\"\"F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"(\"#>\"\"%\"\"$\"\"\"F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"(\"#>\"\"%\"\"$\"\"\"F'" }}{PARA 9 "" 1 "" {TEXT 208 52 "<-- exit sced (now in ced) = [7, 19, 4, 3, 1, 1]\}\n" }{TEXT 208 49 "<-- exit ced (now in ced) = [7, 19, 4, 3, 1, 1]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"(\"#>\"\"%\"\"$\"\"\"F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"%\"\"$\"\"\"F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" \"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#>" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#E" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%Hn" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"%^[" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&p9%" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"&!e6" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"%y=\"%^[\"\"\"F%\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%y=" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%^[" }}{PARA 11 "" 1 "" {XPPMATH 20 "7#7$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"%y= \"%&4\"\"\"\"\"\"!\"\"#F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%y=" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"%&4\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$7$\"\"\"\"\"!7$F%\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"#=\"\"( \"\"&\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&p9%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&!e6" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"$<\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#o" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 40 "\{--> enter ced, args = 117, 68, 2, 1, 1" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 9 "" 1 "" {TEXT 208 36 "\{ --> enter sced, args = 117, 68, 16" }}{PARA 11 "" 1 "" {XPPMATH 20 "7( \"$<\"\"#o\"\"\"\"\"!F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#\\\"#o \"\"\"F%\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#\\\"#>\"\"#\"\" \"F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#6\"#>\"\"#\"\"$\"\"\"F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#6\"#>\"\"#\"\"$\"\"\"F%" }}{PARA 9 "" 1 "" {TEXT 208 51 "<-- exit sced (now in ced) = [11, 19, 2, 3, 1, 2]\}" }}{PARA 9 "" 1 "" {TEXT 208 50 "<-- exit ced (now in ced) = [11 , 19, 2, 3, 1, 2]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"#6\"#>\"\"#\" \"$\"\"\"F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"#\"\"$\"\"\"F#" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" #>" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$r%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$7$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"(\"#6\"\"&\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "7& \"#V\"#o\"#7\"#>" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&p9%" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"&!e6" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7( \"$f\"\"$7$\"\"\"F%\"\"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$f\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"$7$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7 #7$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$f\"\"$`\"\"\"\"\" \"!F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$f\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$`\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$7$\"\"\"\"\"!7$ F%F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"$a\"\"$6\"\"#V\"#J" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&p9%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&!e6 " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 41 "\{--> enter ced, args = 159, 153, 2, 1, 0" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 9 "" 1 "" {TEXT 208 36 "\{--> enter sced, args = 159, 153, 1" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"$f\"\"$`\"\" \"\"\"\"!F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"'\"$`\"\"\"\"F%\" \"!F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"'\"\"$\"#E\"\"\"\"#DF&" } }{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"!\"\"$\"#E\"#F\"#DF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"!\"\"$\"#E\"#F\"#DF%" }}{PARA 9 "" 1 "" {TEXT 208 53 "<-- exit sced (now in ced) = [0, 3, 26, 27, 25, 26]\}" } }{PARA 9 "" 1 "" {TEXT 208 52 "<-- exit ced (now in ced) = [0, 3, 26, \+ 27, 25, 26]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"!\"\"$\"#E\"#F\"# DF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"#E\"#F\"#DF#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"#x\"#!)\"#^\"#`" }}{PARA 11 "" 1 "" {XPPMATH 20 " 7&\"%zn\"%Wq\"%$*=\"%n>" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&p9%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&!e6" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"!\"\"$\"%zn\"%Wq\"%$*=\"%n>" }}{PARA 9 " " 1 "" {TEXT 208 60 "<-- exit ced (now in ced) = [0, 3, 6779, 7044, 18 93, 1967]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "7(\"\"!\"\"$\"%zn\"%Wq\"% $*=\"%n>" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"%zn\"%Wq\"%$*=\"%n>" }} {PARA 11 "" 1 "" {XPPMATH 20 "7&\"&/H'\"&j`'\"&Dh&\"&>$e" }}{PARA 11 " " 1 "" {XPPMATH 20 "7&\")*3c8&\")mOO`\")jhVW\")JK " 0 "" {MPLTEXT 1 0 48 "3*(%[3]+%[4]),3*(% [5]+%[6]),%[3]*%[6]-%[4]*%[5];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"*l #fTJ\"*#=G=F\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 69 "# m is the number of clock cycles used to multiple \+ an n-word number\n" }{MPLTEXT 1 0 24 "# by a one-word number\n" } {MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 48 "m:='m'; m1:='m1'; m:=proc(n) m1* n end; # m1:=10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"mG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#m1G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I \"nG6\"F%F%F%*&I#m1GF%\"\"\"F$F(F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "m(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"\"#\"\"\" I#m1G6\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "# M is the \+ number of clock cycles used to multiple two n-word numbers\n" } {MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 20 "M:='M'; M1:='M1'; \n" }{MPLTEXT 1 0 13 "M:=proc(n) \n" }{MPLTEXT 1 0 24 " if n<=4 then n*n*M1 \n" } {MPLTEXT 1 0 37 " elif n<=512 then 2*3^log[2](n)*M1\n" }{MPLTEXT 1 0 29 " else 15*n*log[2](n)*M1 fi\n" }{MPLTEXT 1 0 7 "end; \n" }{MPLTEXT 1 0 9 "# M1:=10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"MG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#M1G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6# I\"nG6\"F%F%F%@'1F$\"\"%*(F$\"\"\"F$F*I#M1GF%F*1F$\"$7&,$*(\"\"#F*)\" \"$-&I$logG6$%*protectedGI(_syslibGF%6#F0F#F*F+F*F*,$**\"#:F*F$F*F3F*F +F*F*F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "n:=2^13; eva lf(log[2](32*n)); evalf(M(n)); evalf(log[2](M(n)/(32*n)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%#>)" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"#=\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"(Suf\"\"\"!\"\"\"I#M1G6\"F 'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+T]pU9!\"*\"\"\"-I#lnG6$%* protectedGI(_syslibG6\"6#,$*&$\"+++v$4'F&F'I#M1GF-F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "# a is the number of clock cycles u sed to calculate sum or difference\n" }{MPLTEXT 1 0 25 "# of two n-wor d numbers\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 20 "a:='a'; a1:='a1'; \+ \n" }{MPLTEXT 1 0 22 "a:=proc(n) n*a1 end;\n" }{MPLTEXT 1 0 8 "# a1:=6 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"aG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#a1G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"nG6\"F%F %F%*&F$\"\"\"I#a1GF%F'F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "a(1024);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"%C5\"\"\"I#a1G6\" F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "# r is the number o f clock cycles used to calculate remainder\n" }{MPLTEXT 1 0 47 "# by o ne-word quotient for two n-word numbers\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 20 "r:='r'; r1:='r1'; \n" }{MPLTEXT 1 0 22 "r:=proc(n) n* r1 end;\n" }{MPLTEXT 1 0 12 "# r1:=a1+m1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"rG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#r1G6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"nG6\"F%F%F%*&F$\"\"\"I#r1GF%F'F%F %F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r(1024);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"%C5\"\"\"I#r1G6\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "# q is the number of clock cycles used to cal culate a one-word quotient\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 9 "q: ='q';\n" }{MPLTEXT 1 0 8 "# q:=60;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I \"qG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "# This the numbe r of clock cycles used by ced to reduce a 2^n word\n" }{MPLTEXT 1 0 29 "# number to the half length\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 63 "C:=proc(n) 2*C(n-1)+8*q+4*m(2^n)+4*m(3*2^(n-2))+24*M(2^(n-2))\n" } {MPLTEXT 1 0 29 " +16*a(2^(n-1))+58*c1 end;\n" }{MPLTEXT 1 0 12 "C(0) :=300;\n" }{MPLTEXT 1 0 13 "C(1):=1000;\n" }{MPLTEXT 1 0 22 "# c1:=20 \+ # for call\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"nG6\"F%F%F%,0*& \"\"#\"\"\"-I\"CGF%6#,&F$F)F)!\"\"F)F)*&\"\")F)I\"qGF%F)F)*&\"\"%F)-I \"mGF%6#)F(F$F)F)*&F3F)-F56#,$*&\"\"$F))F(,&F$F)F(F.F)F)F)F)*&\"#CF)-I \"MGF%6#F>F)F)*&\"#;F)-I\"aGF%6#)F(F-F)F)*&\"#eF)I#c1GF%F)F)F%F%F%" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"$+$" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"%+5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C(2);" }}{PARA 11 " " 1 "" {XPPMATH 20 ",.\"%+?\"\"\"*&\"\")F$I\"qG6\"F$F$*&\"#GF$I#m1GF(F $F$*&\"#CF$I#M1GF(F$F$*&\"#KF$I#a1GF(F$F$*&\"#eF$I#c1GF(F$F$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"%+S\"\"\"*&\"#CF$I\"qG6\"F$F$*&\"$7\"F$I#m1GF(F$F$*& \"$W\"F$I#M1GF(F$F$*&\"$G\"F$I#a1GF(F$F$*&\"$u\"F$I#c1GF(F$F$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C(4);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"%+!)\"\"\"*&\"#cF$I\"qG6\"F$F$*&\"$O$F$I#m1GF(F$F$*& \"$s'F$I#M1GF(F$F$*&\"$%QF$I#a1GF(F$F$*&\"$1%F$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"&+g\"\"\"\"*&\"$?\"F$I\"qG6\"F$F$*&\"$'*)F$I#m1GF(F$F$*&\"%SEF $I#M1GF(F$F$*&\"%C5F$I#a1GF(F$F$*&\"$q)F$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",. \"&+?$\"\"\"*&\"$[#F$I\"qG6\"F$F$*&\"%SAF$I#m1GF(F$F$*&\"%o\"*F$I#M1GF (F$F$*&\"%gDF$I#a1GF(F$F$*&\"%)z\"F$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 5 "C(7);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"&+S' \"\"\"*&\"$/&F$I\"qG6\"F$F$*&\"%w`F$I#m1GF(F$F$*&\"&++$F$I#M1GF(F$F$*& \"%WhF$I#a1GF(F$F$*&\"%aOF$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C(8);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"'+!G\"\"\" \"*&\"%;5F$I\"qG6\"F$F$*&\"&WD\"F$I#m1GF(F$F$*&\"&#*\\*F$I#M1GF(F$F$*& \"&OV\"F$I#a1GF(F$F$*&\"%mtF$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "C(9);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"'+gD\"\"\"* &\"%S?F$I\"qG6\"F$F$*&\"&s'GF$I#m1GF(F$F$*&\"'g\\HF$I#M1GF(F$F$*&\"&oF $F$I#a1GF(F$F$*&\"&!z9F$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "C(10);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"'+?^\"\"\" *&\"%)3%F$I\"qG6\"F$F$*&\"&7X'F$I#m1GF(F$F$*&\"'[[!*F$I#M1GF(F$F$*&\"& GP(F$I#a1GF(F$F$*&\"&Q'HF$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "C(11);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"(+S-\"\"\" \"*&\"%%=)F$I\"qG6\"F$F$*&\"'gL9F$I#m1GF(F$F$*&\"(![aFF$I#M1GF(F$F$*& \"'SQ;F$I#a1GF(F$F$*&\"&M$fF$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "C(12);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"(+![?\"\" \"*&\"&wj\"F$I\"qG6\"F$F$*&\"'#R:$F$I#m1GF(F$F$*&\"(g`>*F$I#M1GF(F$F$* &\"'[/OF$I#a1GF(F$F$*&\"'E(=\"F$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "C(13);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"(+g4%\" \"\"*&\"&gF$F$I\"qG6\"F$F$*&\"'G\")oF$I#m1GF(F$F$*&\")+3]EF$I#M1GF(F$F $*&\"'KkyF$I#a1GF(F$F$*&\"'5vBF$I#c1GF(F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "C(14);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"(+?>)\" \"\"*&\"&Gb'F$I\"qG6\"F$F$*&\"(W4\\\"F$I#m1GF(F$F$*&\")?jpqF$I#M1GF(F$ 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