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Parameterized and Exact Computation 9th International Symposium IPEC 2014 Wroclaw Poland September 10 12 2014 Revised Selected Papers 1st Edition Marek Cygan
Foundations and Practice of Security 7th International Symposium FPS 2014 Montreal QC Canada November 3 5 2014 Revised Selected Papers 1st Edition Frédéric Cuppens
Cellular Automata and Discrete Complex Systems 20th International Workshop AUTOMATA 2014 Himeji Japan July 7 9 2014 Revised Selected Papers 1st Edition Teijiro Isokawa
Importantly,aprogramtransformationapproachallowstheseparationofconcerns:existinganalysesbasedonanyscalarabstractdomainscanbeuseddirectly toinferarraycontentproperties,eveninterprocedurally.Whileotherapproaches liftascalarabstractdomaintoarraysbyliftingeachtransferfunction,ourapproachusesexistingtransferfunctionsunchanged,onlyrequiringtheadditionof twosimpletransferfunctionseasilydefinedintermsofoperationsthatalready existformostdomains.Theapproachisalsoparametricinthegranularityof arrayindexsets,rangingfromarraysmashing[2]tomoreprecise(andexpensive) instances.Whenwegobeyondarraysmashing,thetransformationalapproach inheritstheexponentialsearchcostpresentintheHalbwachs/P´eronapproach, asforsomeprograms P ,thetransformedprograms P areexponentiallylarger than P .However,forsimplearray-basedsort/searchprograms[9, 11],atransformationalapproachisperfectlyaffordable,inparticularaswecancapitalizeon codeoptimizationsupportofferedbytheLLVMinfrastructure.
Target. Theabstractmachineweconsideroperatesonvariablesovertwokinds ofdomains:standardscalartypes,andsetsofvectorsoflength k ,where k is thenumberofarraysinthesource.Thescalarvariablesrepresentscalarsofthe sourceprogram,includingindexvariables,aswellassingletonarraysegments; setsofvectorsrepresentnon-singletonsegmentsofallextantarrays.Let V bethe
Instructions I → v1 = constant | v1 = ◦ v2 | v1 = v2 v3 | S
Example1. Consideraprogramwithonescalarvariable x,andonesetvariable S ,withinitialstate {x → 0}, {S →{1, 2}} .Ifweintroduceascalarvariable y thatselectsavaluefrom S viaawehavetwopossiblestates:
Ifwerepresent S byscalarvariable S ,wehaveinitialstates {x → 0,S → 1} and {x → 0,S → 2} .Whenwewishtoselectavaluefor y ,itischosen nondeterministicallyfromthepossiblevaluesof S ,resultinginthestates:
Ifwegroupstateswithequalvaluesof x and y ,wecanseethatthesecorrespond tothefinalstatesoftheoriginalset-machinefragment.
Notethatthisisan(over-)approximation.Wecanonlyinferthesetofvaluesthat may beelementsof S —thisrepresentationcannotdistinguishsetsofelements whichmayoccurtogether,northecardinalityof S .Forexample,assumewe havepossibleset-machinestates ∅, {S →{1}} and ∅, {S →{2}} .Thescalar approximationis {S → 1}, {S → 2} whichcoversthefeasibleset-machine states,butalsoincludes ∅, {S →{1, 2}} ,whichisnotfeasible.Moregenerally, iftheset ϕ ofconcretestatesallowssets S → X1 ,...,S → Xk ,wehave: ∀X (X ⊆ X1 ∪ ... ∪ Xk ⇒ (S → X ) ∈ γ ◦ α(ϕ))
Considera(notnecessarilynumeric)abstractdomain A,withmeet( ),join( ) andrenameoperations,aswellasatransferfunction F : I →A→A forthe scalarfragmentofthelanguage.Therenameoperationconstructsanewstate whereeachvariable xi isreplacedwith yi (thenremovestheexistingbindings of xi ).Formally,theconcretesemanticsof rename isgivenby rename(σ, [x1 ,...,xk ], [y1 ,...,yk ])= σ y1 → σ (x1 ),...,yk → σ (xk ), x1 → ,...,xk →
Foreachsetvariable S ,weintroduce k scalarvariables[s1 ,...,sk ]denotingthe possiblevaluesofeachvectorin S .Wethenextend F tosetoperationsasshown inFig. 5
Ourgoalistopartitionthearrayindexspace(−∞, ∞)intocontiguous regionsboundedbyindexvariables.Forindexvariables i and j ,weneedto beabletodistinguishbetweenthecaseswhere i<j , i = j and i>j .However, thisisnotenough;ifweassign A[i]= x,butonlyknowthat i<j ,wecannot distinguishbetweenthecases i = j 1(everyelementbetween i and j is x)and i<j 1(thereareadditionalelementswithsomeotherproperty).So,forindex variables i and j ,wechoosetodistinguishthesefivecases:
Forconvenienceinexpressingtheseorderings,wewillintroduceforeachindex variable i anewterm i+ denotingthevalue i +1,andforasetofindexvariables I wewilldenoteby I+ theaugmentedset I ∪{v + | v ∈ I}.Wecanthendefinea totalorderingofasetofindexvariables I tobeasequenceofsets[B1 ,...,Bk ], Bs ⊆ I+ ,suchthatthe Bs ’scover I+ ,arepairwisedisjoint,andsatisfy i ∈ Bs ⇔ i+ ∈ Bs+1
Anordering π (plusvirtualbounds {−∞, ∞})partitionsthespaceofpossible arrayindicesintocontiguousregions,givenby[σ (e),σ (e ))for e ∈ Bi ,e ∈ Bi+1 Foranyindexvariable i,asegmentcontaining i+ intherightboundisnecessarily asingletonsegment;allothersegmentsareconsideredaggregate.
Whenanewindexvariable k entersscope,severalpossibleorderingsmay result.Figure 6(c)givesaprocedureforenumeratingthem.Whenanindexvariable k leavesscope,computingtheresultingorderingconsistssimplyofeliminating k and k + from π ,anddiscardinganynow-emptysets.Assignmentofan indexvariableishandledasaremovalfollowedbyanintroduction.1
Thetransformationresolvesthisbyreplicatingbasicblockstoensurethat,at anyprogrampoint,auniquepartitioningofthearrayintosegmentsisidentifiable.Anytimeasegment-definingvariableismodified,introducedoreliminated, weemitstatementstodistinguishthepossibleresultingpartitions,andduplicate theremainderofthebasicblockforeachcase.Foreachpartition,wealsoemit setoperationstorestorethecorrespondencebetweensetvariablesandarray segments,using nondet-elt and nondet-subset whenasegmentissubdivided, and ∪,whenaboundaryisremoved,causingsegmentstobemerged.Thisway everyarrayread/writeintheresultingprogramcanbeuniquelyidentifiedwith asingletonsegment.Assingletonsetsarerepresentedbytuplesofscalars,we canfinallyeliminatearrayoperations,replacingthemwithscalarassignments.
Inthefollowing,weassumetheexistenceoffunctions next block,whichallocatesafreshblockidentifier,and push block,whichtakesanidentifier,asequence ofstatementsandabranch,andaddstheresultingblocktotheprogram.We alsoassumethatthereisamutableglobaltable T mappingblockidentifierand indexvariableorderingpairs id,π to ids,usedtostorepreviouslycomputed partialtransformations,andanimmutableset I ofsegmentboundvariablesand constants.Thefunction get block takesablockidentifier,andreturnsthebodyof thecorrespondingblock.Thefunction vars returnsthesetofvariablesappearing lexicallyinthegivenexpression.Thefunction find avar givesthevariablename towhichagivenarrayandindexwillbetranslated,givenanordering.
Thecoreofthetransformationisdonebyacallto transform body (B,π,id,ss). Here B istheportionofthecurrentblocktobetransformedand π thecurrent ordering. id and ss holdtheidentifierandbodyofthepartially-transformed
%Checkiftheblockhasalreadybeentransformed
%under π .Ifnot,transformit.
transform(id, π ) if ((id,π ) ∈ T ) return T [(id,π )]
idt := nextblock()
T := T [(id,π ) idt ] (stmts ,br ):= getblock (id)
transformbody((stmts ,br ),π,id, []) return idt
%Evaluateabranch.
transformbody(([], Jmp b),π,id, ss ) idb := transform(b, π ) pushblock(id, ss , Jmp idb )
transformbody(([], If l then t else f ),π,id, ss ) if vars(l) ⊆ I
dest := if eval(l,π ) then t else f iddest := transform(dest,π ) pushblock(id, ss , Jmp iddest ) else
idt := transform(t, π ) idf := transform(f , π ) pushblock(id, ss , If l then idt else idf )
%(Potentially)updateanindex.
transformbody(([x=expr |stmts ],br ),π,id, ss ) if x ∈ I
splittransform(x, (stmts ,br ),π,id, ss ::[x=expr ]) else
transformbody((stmts ,br ),π,id, ss ::[x = expr])
%Transformanarrayread...
transformbody(([x = A[i]|stmts ],br ),π,id, ss )
Ai := findavar(π,A,i) transformbody((stmts ,br ),π,id, ss ::[x = Ai ])
%oranarraywrite.
transformbody(([A[i]= x|stmts ],br ),π,id, ss )
Ai := findavar(π,A,i) transformbody((stmts ,br ),π,id, ss ::[Ai = x])
(a)Thetop-leveltransformationprocess
splittransform(x, (stmts ,br ),π,id, ss ) Π := feasibleorders(π,x) splitrec(x,Π , (stmts ,br ),π,id, ss )
splitrec(x, [π ], (stmts ,br ),π,id, ss ) asts := remapavars(π,π ) transformbody((stmts ,br ),π ,id, ss :: asts)
π previouslyheld. ord cond checksthepositionofboth x and x+ .If x ispart ofalargerequivalenceclassin π , ord cond generatesthecorrespondingequality; otherwise,itchecksthat x isgreaterthanitsleftneighbour;similarly,itchecks that x+ isinitsclassorlessthanitsrightneighbour.Figure 6(b)showsthe processofsplittingablockuponintroducinganindexvariable x.
5.1ReadingandWriting
Transformationofarrayreadsandwritesissimple,ifthearrayindexisinthe set I ofindexvariables.Figure 7(a–c)showsthestep-by-steptransformation ofablock,underthespecifiedordering.AfterStep1,reference A[i]hasbeen transformedtoscalar a2 ,since {i} isasingleton.Similarly,Step2transforms B [i]to b2 .
Figure 8 illustratesthisprocess,implementedbytheprocedure remap avars,asit splitsablockintothree:onetotestanindexexpressiontodeterminewhatorderingapplies,andoneforeachordering.Intheoriginalcode,ordering π applies,but followingtheassignment,eitherordering π0 or π1 mayapply.Thetestinserted byStep2distinguishesthesecases,leavingonlyoneorderingapplicabletoeach ofthe sπ0 and split1 blocks.
2 Detailedpseudo-codeforthisisinAppendix A
. transformbody : π
i := i +1
Jmp guard
(a)Original . . i := i +1
splitrec : π [π0 ,π1 ]
Jmp guard
(b)AfterStep1 . i := i +1
If i +1 <n then sπ0 else split1 [sπ0 ]
remapavars : π i π0
transformbody : π0 Jmp guard
[split1 ] splitrec : π i [π1 ] Jmp guard
(c)AfterStep2 . i := i +1
If i +1 <n then sπ0 else split1 [sπ0 ]
remap avars : π i π0
transformbody : π0 Jmp guard
[split1 ]
remapavars : π i π1
transformbody : π1
Jmp guard
(d)AfterStep3
Fig.8. Exampleofupdatinganindexassignment.Weassumeanexistingscalaranalysiswhichhasdeterminedthat,after i = i +1,wehave1 <i<n.
Ifwenormalizeindexassignmentssuchthatfor k := E , k/ ∈ E ,wecanseparatetheupdatingofsegmentvariablesintotwostages;first,computingintermediatesegmentvariables Ai aftereliminating k from π ,andthencomputingthe newsegmentvariablesafterintroducingtheupdatedvalueof k .Pseudo-codefor thesestepsaregiveninFigs. 9(a)and 10(a).Inpractice,wecanofteneliminate manyoftheseintermediateassignments,assegmentsnotadjacenttotheinitial orupdatedvaluesof k remainunchanged.
Whenwe eliminate anindexvariable k from π ,wemergesegmentsthatwere boundedonlyby k or k + .If k or k + appearsaloneattheverybeginningor endof π ,thesegmentsarediscardedentirely.Ifeitherappearsalonebetween othervariablesin π ,thesegmentsoneithersidearemergedtoformasingle segment.However,if k and k + arebothequaltosomeothervariables,the originalsegmentsaresimplycopiedtothecorrespondingtemporaryvariables. ThisisillustratedinFig. 9(b).
Incases(1)and(2),thetransformationprocessoperatesasnormal;werecursivelytransformthejumptargets,andconstructthecorrespondingjumpwith thetransformedidentifiers.However,whenwehaveaconditionaljump If i j then t else f where i and j arebothindexterms,therelationshipbetween i and j isstaticallydeterminedbythecurrentordering π .Asaresult,wecansimplyevaluatethecondition i j undertheordering π ,anduseanunconditional branchtothecorrespondingblock.ThisisillustratedinFig. 11.
Fig.10. (a)Generatinginstructionsfor(re-)introducingavariable k intoagivenordering,and(b)theresultingassignmentswhen k isintroducedintovariousorderings.Note thedifferencebetweenintroducingsingletonandaggregatesegments.
transformbody : π If i<n then body else tail let bodyπ = transform(body,π ) in
Untilnowwehaveassumedapre-selectedsetof interesting segmentbounds. Theselectionofsegmentboundariesinvolvesatrade-off:wecanimprovethe precisionoftheanalysisbyintroducingadditionalsegmentbounds,butthe transformedprogramgrowsexponentiallyasthenumberofsegmentbounds increases.Asdo[11],wecanrunadata-flowanalysistofindthesetofvariables thatmay(possiblyindirectly)beusedas,ortocompute,arrayindices.Formally, wecollecttheset I ofvariablesandconstants i occurringinthesecontexts:
A[i]where A isanarray (2) i = op(i)where i ∈ I (3) i = op(i )where i ∈ I and i isnotaconstant (4)
Anyvariablewhichdoesnotsatisfytheseconditionscansafelybediscardedas apossiblesegmentbound.FortheexperimentsinSect. 7 weusedallelementsof I assegmentbounds(so I = I),whichyieldsananalysiscorrespondingroughly totheapproachesof[9, 11].Wecould,however,discardsomesubsetof I toyield asmaller,butlessprecise,approximationoftheoriginalprogram.Thecases(3) and(4)areneededbecauseofpossiblealiasing;thisisparticularlycriticalin anSSA-basedlanguage,asSSAessentiallyreplacesmutationwithaliasing.Itis worthnotingthatthesedependenciesextendtoaliasesintroducedpriortothe relevantarrayoperation,asinthesnippet“i := x;... A[i]:= k ;... y := x +1;”
arraycopy(int* A, int* B , int n) { int i; for(i =0; i<n; i++)
A[i]= B [i]; } arrayinit(int* A, int n) { int i; for(i =0; i<n; i++) A[i]=5; } arraymax(int* A, int n) { int i, max = A[0]; for(i =1; i<n; i++) { if(max<A[i]) max = A[i] } } search(int* A, int key ) { int i =0; while(A[i] = key ) i++; } firstnotnull(int* A, int n) { int i, s = n; for(i =0; i<n; i++) if(s == n && A[i] =0) s = i; } sentinel(int* A, int n, int sent) { int i; A[n 1]= sent; for(i =0; A[i] = sent; i++); }
Fig.12. Simpletestprograms
Table1. Sizesoftransformedtestprogramsandanalysistimefor polka and uva
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CHAP. XXIV.
PROVINCE OF SOLIMOES.
Jurisdiction Origin of its Name Boundaries and Extent Partially known Division into Six Districts Rivers Various Indians Customs Povoaçoes
The province of Solimoes, and the western part of Guianna, with the western portion of Mundrucania, form a government, subordinate to Grand Para. The eastern part of Guianna is immediately under the jurisdiction of Para. The first Portuguese who proceeded up the Amazons, from the mouth of Rio Negro, gave it the name of Solimoes, by which it is yet designated; not in allusion to the venoms with which the Indians of these latitudes, as well as those of the low Amazons, infected their arrows, nor to the tribes inhabiting the banks of Rio Negro, who used the same weapon, but to the nation denominated Soriman, and, by corruption, Solimao and Solimoes.
The province of Solimoes is bounded on the north by the river of the same name, or rather the Amazons; on the west by the Hyabary, which separates it from the Spanish dominions; on the south by the same dominions, the divisionary line between the two territories having been adjusted by the Portuguese and Spanish commissioners in the year 1751, and ratified in 1757; and on the east by the Madeira.
It is two hundred and fifty miles on the eastern side, from north to south, nearly six hundred miles from east to west, and lies between 3° 23′ and 7° 30′ south latitude. It is a country but little known excepting along the Madeira, and in the vicinity of the Amazons: it is occupied by numerous Indian nations, speaking divers idioms, and watered by many large and navigable rivers. It produces all the quadrupeds, reptiles, and birds of the provinces, eastward of the river Madeira; a vast variety of plants and trees known to be of great utility, amongst which are the clove, cupahyba, or capivi, cocoa, elastic gum, puchery, and cotton. It is well known also that the soil is highly adapted to the culture of Indian corn, rice, legumes, the cane,
tobacco, mandioco, coffee, bahunilha, or vanilla, inhumes, (growing like potatoes,) potatoes, and a variety of fruits: however, these articles will not prosper equally in all parts. Domestic cattle are universally in small numbers, and their augmentation depends upon the Christian portion of population, which, at present, is very inconsiderable. Nothing satisfactory is known of the mineralogy of the province; but it appears natural that the minerals peculiar to the adjoining provinces should also be found here.
The five following large rivers, Hyutahy, Hyurba, Teffe, Coary, and Puru, which traverse the province from south to north, with the Madeira and Hyabary, divide it into six districts of unequal size, and almost of the same length from north to south: each one takes the name of the river that serves for its western limit. We will describe the above districts according to the following order:—
Puru
Coary
Teffe
Hyurba
Hyutahy
Hyabary
The principal povoaçoes, or towns, of these districts, four having only one each, another two, and the last three, were founded by the Slippered Carmalites. Condamine, the French writer, says, “Toute la partie découverte des bords de Rio Negro est peuple de missions Portugaises, des mêmes religieux du Mont Carmel que nous avions rencontres en descendant l’Amazone, depuis que nous avions laisse les missions Espagnoles.”
District of P
Puru, which lies between the Madeira, and the river from which it derives its name, has been more explored than any of the contiguous districts, and enjoys the best situation for commerce. From its centre various other considerable rivers flow into the three which form its confines. The Capanna and the Uhautas are the largest amongst those which run to the Madeira.
The Capanna empties itself one hundred and forty miles above the town of Borba, after having traversed a considerable lake, which receives divers small streams, and from whence there is also an outlet to the river Puru. Its environs are inhabited by the Catauixi and Itatapriya Indians, who are great hunters and fishers.
The Uhautas, which has a course of fifty miles, discharges itself fifteen miles from Borba, and originates in a lake of the same name, which is vast and studded with islands that are overspread with the clove-tree.
From this lake, which is the receptacle of various small streams, two other rivers issue and flow to the Amazons; one of them enters it eight miles above the mouth of the Madeira, and the other, called Paratary, one hundred miles further to the west. Eighteen miles below the principal mouth of the Rio Negro is the lake d’El Rey, near the southern margin of the Amazons. The Purupuru Indians, who inhabit the central part of the country, give their chief the name of Maranuxauha.
The margins of the Amazons and the Rio Negro, upwards, are infested with a small musquito, called pium, whose painful sting leaves a red mark, accompanied with insufferable itching and a disposition to ulcerate. One hundred and sixty miles is about the width of this district on the northern side.
Cratto, yet a small town, but well situated upon the margin of the Madeira, a considerable distance above Borba, has a church dedicated to St. Joam Baptista, and its inhabitants are generally Indians and Mesticoes, who collect some cocoa, cloves, and sarsaparilla, with provisions of the first necessity. They catch great numbers of the tortoise at the beach of Tamandoa, which they keep in an enclosure in the water. It is one of the ports for canoes coming from Matto-Grosso, and many circumstances concur in warranting the prediction that it will become one of the principal towns of Solimoes.
District of C .
This district extends between the river from which it takes its name and the principal arm of the Puru, with one hundred and twenty miles of width on the northern part. The Muras possess the environs of the Amazons; the Purupurus, and the Catauixis, the centre of the country, with other uncivilized nations. Three channels from the Puru irrigate a portion of the eastern part of this comarca in the proximity of the Amazons;—the Cochiuara which discharges itself twenty-five miles from the mouth of its superior; the Coyuanna, twenty miles above the preceding; and the Arupanna, more to the westward. The first gives also its name to this portion of the district; the margins of the whole afford cocoa, sarsaparilla, and the oil of capivi.
Alvellos, a small town, is situated upon a large bay, fifteen miles above the mouth of the Coary, of which it formerly had the name. Its inhabitants, for the main part descendants of the Uamanys, Sorimoes, Catauyseys, Jumas, Irijus, Cuchiuaras, and Uayupes, collect cloves, cocoa, capivi, and sarsaparilla, and make butter from the eggs of the Tortoise, which are very numerous; and they are also employed in making earthenware, mats, and in weaving cotton cloth. The ants are here particularly destructive.
This town was commenced upon the eastern margin and twentyfive miles above the month of the river Paratary, from whence the Padre, Frey Joze da Magdalena, removed it to the same side of the Guanama, which enters the northern side of the Amazons, below the eastern arm of the Hyapura: from hence the Padre, Frey Antonio de Miranda, removed it to the site of Guarayatyba, more to the eastward upon the margin of the Amazons, eight miles below the Puru, from whence it was finally removed by Frey Mauricio Moreyra to its present situation.
The islands with which the Amazons in this part is studded, were for some time inhabited by Cambeva, otherwise Omagoa Indians— names which signify flat heads, from the custom which the mothers had of compressing their children’s heads between two boards, thus distinguishing them from other nations. This custom ceasing, their descendants are at the present day unknown.
District of T .
This comarca, situated between the river from which it is named, and the Coary, that separates it from the preceding one, is nearly ninety miles in width along the Amazons. The two first rivers are very considerable; but their origins are not yet ascertained, nor the number and names of their principal confluents, which issue from the centre of the district. All accounts are equally silent as to any mountains existing in the interior, while the lands in the vicinity of the Amazons, although flat, are never inundated by the floods, which overflow a considerable portion of its northern margin, in consequence of being lower.
The Coary discharges itself into a bay of the Amazons, almost seven miles in width, and near it the Urucuparana, and the Urauba, or Cuanu, both of short navigation.
Forty miles above, the river Catua enters the Amazons, and twenty more, westward, the Cayama, its margins abounding with sarsaparilla; and, further on, the small river Giticaparana, a name implying the river of potatoes. Its mouth is fifteen miles below the Teffe. From the number of Christians being so small, and the only persons who clear away any of the woods for the purposes of agriculture, the country exhibits the same aspect to the navigators of the Amazons at this day that was presented to its first discoverers. The majestic size of various kinds of trees demonstrates the fecundity and substantial nature of the soil.
Ega, a middling town, well situated upon the right bank of the Teffe, is eight miles from the Amazons, with a church dedicated to St. Thereza de Jezus. Almost all its inhabitants are pure Indians, descended from the Uayupys, Sorimoes, Coretus, Cocurunas, Jumas, Hyupiuhas, Tamuanas, and Achouaris, and cultivate mandioca, feijao, rice, Indian corn, hortulans, and fruits, in sufficient quantities for their subsistence; they gather honey, and collect some cocoa, cloves, and pechurim, from the proceeds of which they supply themselves with iron tools, baize, and other manufactures for dresses. They all pursue hunting and fishing. The women spin cotton, of which they manufacture nets and coarse cloths. This town
was begun in the island of Veados, which is below the mouth of the river Hyurba, from whence Frey Andre da Costa removed it to the situation where it now exists.
District of H .
This district is confined on the north by the Amazons; on the west by the river from which it derives its name; on the south by the Spanish dominions; and on the east by the river Teffe, which separates it from the comarca of that name. It has eighty miles of width on the northern part, and abounds in timber. The rivers are stored with the same fish as the Amazons, and the woods with a great variety of birds and game, as well as formidable wild beasts, that wage war with the central Indians, of whom little more is known than the names.
Nogueyra, a middling town, pleasantly situated upon the left of the river Teffe, almost in front of Ega, is ten miles from the Amazons and ornamented with a church of Nossa Senhora do Rozario. The houses are intermixed with orange trees, and the streets, being full of them, have the appearance of groves. Its inhabitants are principally Indians of divers nations, and Mesticos, respiring a fresh and salubrious atmosphere. They are fond of fishing, collect abundance of the necessaries of life peculiar to the country, some articles of exportation, and possess cattle. The first site of this town was more to the west, on the southern bank of the Amazons, for the habitation of a numerous assemblage of Indians, namely, Jumas, Ambuas, Cirus, Catauixis, Uayupes, Hyauhauhays, and Mariaranas, brought together by the Carmalite priests. From that situation it was removed to Point Parauary, five miles higher upon the same side of the river, where Condamine found it with the name of that point in 1743, and from whence the priest, Frey Joze de Santa Thereza Ribeyro removed it, in the year 1753, to the place where we have stated it to be situated.
Alvarens, originally and at times yet called Cahissara, is a small town, situated upon a lake, near the margin of the Amazons, eighteen miles above the river Teffe. Its church is dedicated to St. Joaquim. The population is an accumulation of various tribes of
Indians, with many Mesticos, who, besides absolute necessaries, cultivate some cocoa and sarsaparilla, but are much incommoded by the pium musquito, and alike annoyed by the voracity of the ants. Its first situation was upon the channel connecting the Hyapura with the lake Amana, two days’ voyage from the Amazons. The Ambuas and Uaruecocas were then its inhabitants; it was removed from thence to its present site, by one Giraldo Gonsalves, in 1758. In Nogueyra there is a creek or outlet, opened by nature, by which canoes, &c. proceed to Alvarens when the rivers are overflowed.
District of H .
This district is confined by the Amazons on the north; by the river of its name on the west; by the Spanish possessions on the south; and by the district of Hyurba on the east: its width along the Amazons is about sixty miles. The middle and southern parts are not better known than the same portions of the surrounding districts, in consequence of being in the power of various untamed Indian tribes, such as the Marauhas, Catuquinas, Urubus, Cauaxis, Uacarauhas, Gemias, Toquedas, Maturuas, Chibaras, Buges, and Apenaris, with some others, who pass the rivers into the adjoining districts, and use the esgaravatana, bow and arrow, and envenomed lance, when they go to war
It remains in a state of uncertainty whether the rivers Hyurba, upwards of six hundred yards in width at its mouth, the Hyutahy, still more spacious, and the before-mentioned Teffe and Puru, the largest of all, have their origins in the serras of Peru or issue from the lake of Rogagualo; their sources have been attributed to both, without any exploration of their courses or any satisfactory evidence being adduced in support of those statements. The extensive volume of water which each brings to the Amazons indicates a very considerable course from remote origins. It will be interesting to the future traveller to explore their unknown sources and extending margins. The Portuguese do not carry their researches amongst the central Indians; and, when they advance up the rivers any distance, they never proceed beyond the limits of the pacific Indians, with whom they have some commerce.
Fonteboa, a middling povoaçao, is situated on the eastern margin of the small river Cayarahy, two miles above its mouth, twenty miles from the embouchure of the Hyurba, and thirty-five below that of the Hyutahy. It has a church dedicated to Nossa Senhora de Guadalupe. The first site of this town was upon the small river Capury, which empties itself into another called Moroentyba, and which latter discharges itself below the Manhana, the third branch of the Hyapura. From the Capury it was removed to the mouth of the Moroentyba, and from thence to the situation of Taracoatyba, a short distance from the Manhana, from whence it was removed seven miles below the mouth of the Hyutahy, where Condamine says he saw it, and which situation was changed for its present one. It is not known what nation were its first inhabitants. When it was in the fourth station—the Padre, Frey Joam St. Jeronymo, collected in it many Pacuna Indians, who were previously living in aldeias upon the eastern margin of the river Icapo: these were afterwards joined by the Araycas, Marauhas, and Momanas, and, ultimately, by the Tacunas, Tumbiras, and Passes. The whole are now agriculturists, fishermen, and hunters.
Between Fonteboa and the Hyurba the Annamapiu is discharged; and, in the interval, between that town and the Hyutahy, five rivers more—the Campina, Gurumaty, Puruini, Mannarua, and Icapo, which afford so many sheltering places for the canoes at the periods of tempests in the Amazons.
District of H .
This district, which is the most westerly, is confined on the north by the Amazons, as the others are on the west by the river from which it takes its name, separating it from the Spanish dominions; on the south by the line of demarcation between the two countries, common to the other districts; and on the east by the Hyutahy, from whose mouth to that of the Hyabary may be computed one hundred and seventy miles. Both these boundary rivers produce the same fish as the Amazons, and both afford extensive navigation for the exportation of such productions as may be collected upon their
respective margins. In the vicinity of both there is sarsaparilla, and also cocoa. Their confluents are totally unknown.
Their extensive woods, which produce in vain, for the benefit of man, the most precious timber, are occupied by the wild boar, anta, deer, and other quadrupeds and bipeds, which are pursued as game by the hitherto savage nations of Marauhas, Uaraycus, and the Tapaxanas, who inhabit the lower part of the country in the vicinity of the Amazons. At a greater distance are the Panos and the Mayurunas, who make a crown upon the top of the head, and allow the hair to grow to the utmost length. They have perforations in the nose and lips, into which they introduce long thorns; in the corners of the mouth they carry feathers of the macaw; from the lower lip and the extremity of the nose and ears strings of shells are pendant. They are cannibals, and, when any are seriously ill, their relations kill and eat them, before the disease can cut the thread of life. The Chimanos and the Culinos are well known, amongst other tribes, from having the face very round and the eyes extremely large.
Castro d’ Avelaens is inhabited by Indians of different nations, with a church dedicated to St. Christovam, on the margin of the Amazons, twenty miles above the mouth of the Ica. It was first established lower down, between the small rivers Aruty and Matura, in the territory of the Cambevas, and experienced four other changes, similar to the preceding povoaçoes, before it was finally fixed in its present situation. In the interval from this town to the river Hyutahy, the small rivers Capatana, Aruty, Matura, Maturacupa, and the Patia enter the Amazons.
Ollivença, ci-devant St. Paulo, by which name it is yet occasionally called, is a small place, well situated upon the margin of the Amazons, forty miles above Castro d’Avaleans. It has had several removals, and was incorporated with the aldeia of St. Pedro, about one mile above the place where it now stands. Its first inhabitants were Cambeva, Tecuna, Juri, and Passe Indians. In the interval between Castro d’Avaleans and Ollivença the small rivers Acuruhy and Jandiatiba discharge themselves.
The town of St. Joze, situated upon the Amazons, thirty-five miles from Ollivença and ten below the Hyabary, is occupied by Tacuna Indians, who cultivate the necessaries of life and pursue hunting and fishing. Between this town and Ollivença are the rivers Acuty, Camatia, Pacuty, Macapuana, and Hyuruparitapera, and between the same town and the Hyabary is the lake Maracanatyba.
Near the embouchure of the Hyabary is the prezidio of Tabatinga, dedicated to St. Francisco Xavier. Upwards of sixteen hundred miles are computed by the canoe-men from Para to this place, and they consume eighty-seven days in the voyage.
CHAP. XXV.
PROVINCE OF GUIANNA.
Boundaries—Islands—Rivers—Towns—Indians.
Guianna forms the eastern and southern portion of the region denominated Terra Firma, confined on the north by the ocean and the river Oronoco; on the south by the Amazons; on the east by the ocean; and on the west by the rivers Hyapura and Oronoco.
The Portuguese Guianna, which includes that belonging to the French since 1809, comprises the southern part of that vast province and celebrated island, and is bounded on the north by the Spanish possessions and Surinam: the other boundaries are those already mentioned. It is nine hundred miles in length from east to west, and three hundred at its greatest width, and extends from 6° north to 4° south latitude. The days and nights, with very little variation, are equal all the year, and the climate is exceedingly warm. The territory is not generally fertile, and has more of a flat than mountainous aspect. In many parts of the interior it is very stony, with indications of ancient volcanos. It is irrigated by many navigable rivers, some of which originate in an extensive range of mountains, of no great altitude, prolonged with the Amazons from east to west, but at a considerable distance from it.
Trees are only of magnitude in the vicinity of the rivers and in the substantial and humid soils. The most useful are those of the clove, pechurim, capivi, Indian rubber, and cocoa.
Minerals of iron have been found; there are symptoms of silver, and some stones of estimation.
North Cape (Cabo do Norte) is the principal cape, situated in 2° north.
I .—Terra dos Coelhos is between the mouths of the Aruary and the Carapapury, with a channel on the west and the
ocean on the east, on which side is the point called North Cape above mentioned.
Maraca is an island eighteen miles in length, with proportionable width, a little to the north-west of the Coelhos. It has in the centre a large lake, stored with fish, and its eastern coast is assailed by the Pororoca.
Between Macappa and North Cape a narrow channel is formed by the islands which range along the coast; and here is remarked a singular phenomenon, denominated pororoca, (the same term we have already described as given to the contention of the waters at the mouth of the Mearim, in the province of Maranham,) which continues three days, at the periods of the change and full moon, when the tides are at the highest. An immense volume of water, twelve to fifteen feet in height, rolls from one beach to the other, followed by a second, and third, and sometimes a fourth, of equal magnitude, with little interval, and with such prodigious rapidity that it destroys every thing opposed to its overwhelming course. The tide, in place of gradually rising in six hours, reaches its greatest height in one or two minutes, with such a terrific noise that it is heard seven or eight miles off.
The island of Penitencia, called Baylique by the Portuguese, in consequence of the tossing which the canoes here sustain from the sea, is six miles long, and sixty south of North Cape.
The islands of Croa are five in a file, separated by narrow channels, and lie to the south-west of Baylique. The whole are flat, and covered with mangroves, where there is an infinity of musquitos and insects.
The river Nhamunda, by corruption Jamunda, divides this vast province into eastern and western, serving also for a limit between the jurisdictions of the ouvidores of Para and of Rio Negro.
R .—In the western part are, first, the Hyapuru and the Rio Negro; afterwards the Rio Branco (White River); the Matary, with two mouths; the Urubu, communicating with the river Aniba by the great
lake Saraca, which is near the Amazons, and is there discharged by six mouths.
In the eastern part are the Trombetas, originally Oriximina, large, and entering the Amazons below Rio Negro; the Gurupatuba; the Anauirapucu, by corruption Arannapucu, the Vaccarapy, and the Aruary, which enters the ocean.
The river Hyapura originates in the province of Popayan, and, after having watered eleven hundred miles of country, running towards the south-east, forming numerous islands of all dimensions, incorporates itself with the Amazons by its several mouths. Its adjacent lands are flat, inundated, and bad: Caqueta is its first name in the country where it rises.
The Rio Negro rises also in the province of Popayan, to the north-east of the Hyapura, with which it runs parallel an equal distance. Forty miles before it enters the Amazons it is divided into two unequal branches. Condamine says that he measured the eastern branch, ten miles from the Amazons, and that he found it in the narrowest part seven thousand two hundred and eighteen feet in width. This river augments considerably as it approaches the Amazons, is in parts from twelve to eighteen miles in width, and is divided into various branches by numerous islands, which render the navigation not unfavourable. Its water exhibits such a dark aspect that it has been said to appear like black ink; it is, notwithstanding, transparent, diuretic, and salubrious, retaining its clearness for many leagues after it enters the bed of the Amazons. It has the same fish as the latter, and affords navigation to the centre of various districts. The greatest floods are in August. We will describe its numerous confluents, together with the povoaçoes upon its margins.
The towns of the eastern portion of the province are
Macappa
Mazagao
Villanova
Arrayollos
Espozende
Almeyrim
Outeyro
Montalegre
Prado
Alemquer
Obydos
Faro
Cayenna.
The towns of the western portion are
Sylves
Serpa
Marippy
Rio Negro
Barcellos
Moura
Thomar
Macappa is the most considerable town of the province, situated upon the margin of the Amazons, four miles north of the equator, on elevated land, with a very good fort, a church dedicated to St. Joze, an hospital, tolerable streets, and houses covered with tiles. It had its commencement twelve miles further to the west, at the embouchure of the Matapy. Its inhabitants cultivate Indian corn, mandioca, rice, some cocoa, cotton, and various fruits. Amongst other trees of estimation in its environs there is one called quatiara, the wood of which is yellow, having black stripes; also the macaco wood.
Sixty-five miles east of Macappa is Robordello, reduced to little note by the desertion of the Indians who inhabited it. It is situated upon the southern margin of the island of Cavianna, which is thirtyfive miles in length and twenty in width; the land is flat and fertile, with a fine farm or fazenda of cattle, belonging to the Hospital da
Santa Caza, (Holy House,) of Mizericordia, at Para. It produces the macaco wood, and the whole of its circuit abounds with fish.
Villanova is situated on the eastern bank, and twenty-five miles above the embouchure of the considerable river Anauirapucu, which originates in the territory of the Armabutos. It was founded for the establishment of white people, but is going into a state of decay in consequence of its desertion by them; those who remain are cultivators of mandioca, Indian corn, and rice; and fish in the channels of the island of Croa. It possesses fine campinhas for breeding cattle; and in its environs the macaco wood grows, which is heavy,—those growing in dry lands are entirely red, and others in a different soil are shaded with black.
Mazagao originated on an island at the mouth of the Matapy, experienced several changes of situation, and was ultimately fixed five miles above the bar of the Matuaca, where it runs into the Amazons, and nearly fifteen miles west of the Anauirapucu. St. Anna was its primitive name, which it lost on the establishment in it of the people of the Praca de Mazagao, from the kingdom of Marrocos, who were afterwards augmented by various families from the Azore islands. Cotton and rice are the riches of its dwellers, who are diminishing in consequence of the prevalence of fevers. In its districts there are various excellent earths for potteries, but their productions are very indifferent.
Forty miles to the south-west of Mazagao, and near twenty-five from the Amazons, is the parish of Fragozo, on the right margin of the Jary, with a church of St. Antonio. Its inhabitants collect cloves, cocoa, cotton, sarsaparilla, &c. and advance up the Amazons in search of the tortoise. Between Fragozo and Mazagao is the parish of St. Anna, on the margin of the fine river Cajary: rice, cotton, and some cocoa, are its productions.
Arrayollos is a small town, agreeably situated upon a small hill near the eastern margin, and fifteen miles above the mouth of the Aramucu. It has two large open spaces, with some semblance to squares, a church dedicated to Nossa Senhora do Rozario, and inhabitants who are agriculturists and fishermen.
Espozende a Villota, or Small Town, in an elevated situation upon the Tubare, commanding fine views of the surrounding Campinhas, has a church of Our Lady do Rozario, and is ten miles north-west of Arrayollos. Fishing, hunting, the cultivation of cotton, Indian corn, rice, and mandioca, is the occupation of its inhabitants.
Almeyrim is a middling town, occupying an advantageous site at the mouth of the Paru, of which it first took the name, and originating in a Dutch fort, which is yet preserved. There is a diversity of excellent timber in its environs, and the inhabitants are fishermen, and cultivate mandioca, Indian corn, rice, legumes, and cotton. Twenty miles above Almeyrim is the parish of Our Lady of Desterro, at the mouth of the considerable Vaccarapy. Fishing, hunting, and the culture of cotton and common necessaries, occupy its inhabitants.
Outeyro, a middling town, well supplied with fish, is situated upon a small hill on the eastern side of the lake Urubuquara, formed by the river of the same name; it is fifteen miles from the Amazons, and sixty-five west of Almeyrim. The church is dedicated to Nossa Senhora of Graca, and its productions are similar to those of the preceding place.
Montalegre, a considerable town, also abounding with fish, is situated on the highest portion of a small island, near the eastern margin of the Gurupatuba, which forms it. It is thirty-five miles above Outeyro, and seven from the Amazons, and was one of the principal missions of the Jesuits, whose Hospicio is now the residence of the vicar. Mandioca, feijao, cotton, cocoa, and coffee, are its productions. In its district the clove-tree prospers, and it has a sawpit, on account of the treasury, for sawing the trunks of the cedars that the floods of the Amazons deposit upon a neighbouring island.
Prado is yet a small place, upon the eastern branch of the river Surubui, twenty miles from the Amazons, and fifty west of Montalegre. Its inhabitants are Indians, and live by some agriculture, hunting, and fishing.
Alemquer is a considerable town, supplied with excellent meat, and well situated upon the central embouchure of the lake Surubui,
fifteen miles from the Amazons, and fifty north of Santarem. It is a country infested with the musquito, called carapana. The church is dedicated to St. Antonio. Mandioca, Indian corn, rice, tobacco, and cocoa, are its productions.
Curuamanema is the name of the third and western outlet of the lake Surubui.
Obydos, formerly Pauxis, the name of the Indians for whose establishment it began, is a considerable town, upon a small hill, with some regularity, and a large square in the centre, near the eastern mouth of the Trombetas, with an extensive view of the Amazons, the whole of whose waters here rapidly descend by a channel about a mile in width, but of such profundity, that the attempts to find the bottom by sounding, have been unsuccessful. It has a magnificent church, dedicated to St. Anna, and is fifty miles west of Alemquer. The inhabitants cultivate divers necessaries of life, cotton, and a large quantity of cocoa, which is in the highest repute at the capital.
Faro is a middling town, near a large lake, traversed by the river Jamunda, forty miles west-north-west of Obydos, and above twenty from the Amazons. Its church is dedicated to St. Joam Baptista, and the soil is well adapted to the produce of cocoa, the principal wealth of its inhabitants.
Sylves is a small place, situated upon the summit of an island near the margin of the lake Saraca, eighty miles west-north-west of Faro, and twenty distant from the Amazons. It abounds in fish and the necessaries of life peculiar to the country. It has a church of St. Anna, and the inhabitants are of various classes and colours, as are those of the other towns, and cultivate excellent tobacco, cotton, cocoa, cloves, and sarsaparilla.
Serpa is a middling town upon a small island of the Amazons, near its northern bank, fifty miles from Sylves, and thirty-five below the mouth of the Madeira. It has a church of Nossa Senhora of Rozario, and inhabitants who derive a partial benefit from the rich productions that nature has bestowed upon this country.
Forty miles to the north-west of Serpa is the parish of Our Lady of Conceiçao, advantageously situated on the margin of the great lake Canuma. Its productions are among the commerce and necessaries of life. Twenty miles north-west of the preceding, and forty from the Amazons, the parish of St. Raymundo, on the margin of the Urubu, is occupied by Indians, who collect some articles of exportation. Fifty miles west of Conceiçao and forty from the Amazons, is the parish of Nossa Senhora do Socorro, near the lake of Matary, with productions similar to the preceding one.
Fifteen miles above the parish of St. Raymundo is that of St. Pedro Nolasco, also on the margin of the Urubu. Its inhabitants are Indians, and their mode of life and productions do not differ from the others.
Marippy is a middling town, on the left bank of the Hyapura, thirty miles from the Amazons, the church is of St. Antonio, and its inhabitants are an accumulation of divers Indian nations, amongst whom are the Miranhas, who possessed part of the territory between the Hyapura and the Ica. They are fishermen and hunters, and collect a portion of the productions of nature in its environs. Fevers do not permit Europeans to reside here in any number.
Rio Negro, a considerable and flourishing town, capital of the province, and head of the Ouvidoria of the same name, has a church of Nossa Senhora da Conceiçao, and is situated near a small hill, on the left margin of the eastern branch of the Rio Negro, ten miles from the Amazons. Its origin was a fort, now existing, near which various families were established, of the Bamba, Barre, and Passe nations. It is the depository of divers mercantile productions, which descend by the river, and are destined for exportation. It has a manufactory of cord from piacaba, one for weaving cotton cloth, and a pottery, all worked on account of the treasury The main part of the cattle killed here are embarked from the royal fazendas of Rio Branco. Above the extremity of the town the Cachoeira discharges itself, which, four miles distant, forms a handsome cataract, whose murmuring descent is heard at this place.
One hundred miles above the capital is the parish of Ayrao, with a church of St. Elias, on the southern margin of the Rio Negro. It first began upon a large bay near the capital, for the habitation of the Taruma and Aroaqui Indians. In the interval between these places the Rio Negro receives, on the southern margin, the Hyborena, and on the northern, the Ayurim, the Anauene, and the small rivers Cunamau, Mapauhau, and Uacriuan, which empties itself almost in front of Ayrao.
Moura is a small town, forty miles above Ayrao, of an agreeable aspect, and with some regularity, upon the right bank of the Rio Negro. The church is of St. Ritta, and its inhabitants are principally descendants of whites and Indian females. It originated in the assemblage of four Indian nations—the Carahyahys, Cocuannas, Mannaus, and Jumas, after which it had one or two removals previously to being fixed in its present situation. A little above Ayrao, the Jaumuhi enters the Rio Negro, and fifteen miles below Moura the Anany, both connecting the river that receives them with the Cadaya, the eastern arm of the Hyapura, through the medium of the large lake Atinineni, in whose vicinity the cupahyba, or capivi, trees abound. The Hyanapary, by corruption Jaguapiri, enters the northern margin of the Rio Negro, almost in front of Moura. This river, whose waters are white, has an extensive course. The Aroaqui Indians extend themselves from its banks to those of the before-mentioned Anauene.
Twenty-eight miles above Moura, on the southern margin of the Rio Negro, is the parish of Carvoeyro, having experienced several changes of situation, with a church of St. Alberto, and inhabitants mainly of the Manau, Parauanno, and Maranacuacena nations. Between Moura and Carvoeyro not one river enters the Rio Negro by the southern bank; on the northern the large river Branco, (White,) so called from the colour of its waters, discharges itself by four mouths, three very near, being formed by two small islands, the other, called Amayauhau, is fifteen miles above. This river is the largest confluent of the Rio Negro, and rises in the southern skirts of the serra Barocayna, receiving, on the eastern side, in the following order, the small river Macoary, the outlet of the lake Uadauhau, the
