{ **********************************************************************
  *                           Program TESTW.PAS                        *
  *                              Version 1.0                           *
  *                      (c) J. Debord, August 2003                    *
  **********************************************************************
  This programs tests Lambert's W function by computing this function
  for a series of predefined arguments and comparing the results to the
  reference values. The program also displays the number of exact digits
  found.
  **********************************************************************
  This program has been translated from a FORTRAN program written by
  Barry et al. (http://www.netlib.org/toms/743)
  ********************************************************************** }

uses
  fmath;

{ Upper branch, X given as offset from -1/e }
const DX1 : array[1..68] of Extended =
  (1.E-40, 2.E-40, 3.E-40, 4.E-40, 5.E-40, 6.E-40, 7.E-40, 8.E-40,
   9.E-40, 1.E-39, 1.E-30, 2.E-30, 3.E-30, 4.E-30, 5.E-30, 6.E-30,
   7.E-30, 8.E-30, 9.E-30, 1.E-29, 1.E-20, 2.E-20, 3.E-20, 4.E-20,
   5.E-20, 6.E-20, 7.E-20, 8.E-20, 9.E-20, 1.E-19, 1.E-10, 2.E-10,
   3.E-10, 4.E-10, 5.E-10, 6.E-10, 7.E-10, 8.E-10, 9.E-10, 1.E-9, 1.E-5,
   2.E-5, 3.E-5, 4.E-5, 5.E-5, 6.E-5, 7.E-5, 8.E-5, 9.E-5, 1.E-4, 2.E-4,
   3.E-4, 4.E-4, 5.E-4, 6.E-4, 7.E-4, 8.E-4, 9.E-4, 1.E-3, 2.E-3, 3.E-3,
   4.E-3, 5.E-3, 6.E-3, 7.E-3, 8.E-3, 9.E-3, 1.E-2);

const WP1 : array[1..68] of Extended =
  (- 0.9999999999999999999766835601840287579665,
   - 0.9999999999999999999670255745859974370634,
   - 0.9999999999999999999596147415871158855702,
   - 0.9999999999999999999533671203680575159335,
   - 0.9999999999999999999478628555782056161596,
   - 0.9999999999999999999428866198325571498809,
   - 0.9999999999999999999383104987875354650364,
   - 0.9999999999999999999340511491719948741275,
   - 0.9999999999999999999300506805520862739007,
   - 0.9999999999999999999262669432552936235556,
   - 0.9999999999999976683560184028776088243496,
   - 0.9999999999999967025574585997473306784697,
   - 0.9999999999999959614741587115939935280812,
   - 0.9999999999999953367120368057588420244704,
   - 0.9999999999999947862855578205706768098859,
   - 0.9999999999999942886619832557258611080314,
   - 0.9999999999999938310498787535591888253966,
   - 0.999999999999993405114917199501910108482,
   - 0.9999999999999930050680552086436996003626,
   - 0.9999999999999926266943255293804772564852,
   - 0.9999999997668356018584094585181033975713,
   - 0.9999999996702557458962181283375794922681,
   - 0.9999999995961474159255244922555603070484,
   - 0.9999999995336712037530626747373742782638,
   - 0.9999999994786285558726655558473617503914,
   - 0.9999999994288661984343027719079710168757,
   - 0.9999999993831049880022078023099082447845,
   - 0.9999999993405114918649237720678678043098,
   - 0.9999999993005068056839596486461928553989,
   - 0.9999999992626694327341550240404575805522,
   - 0.9999766837414008807143234266407434345965,
   - 0.9999670259370180970391011806287847685011,
   - 0.9999596152852334187587360603177913882165,
   - 0.9999533678452277190993205651165793258207,
   - 0.9999478637616504968301143759542621752943,
   - 0.9999428877071168268324462680980110604599,
   - 0.999938311767283189655618359697592754013,
   - 0.999934052598878483932035240348113191731,
   - 0.9999300523114688962155368933174163936848,
   - 0.9999262687553819399632780281900349826094,
   - 0.9926447551971221136721993073029112268763,
   - 0.9896086425917686478635208903220735023288,
   - 0.9872831094708759013315476674998231771112,
   - 0.9853253899681719161468126266199947992874,
   - 0.9836027178149637071691226667555243369797,
   - 0.9820470029764667038452666345865058694192,
   - 0.9806177971936827573257045283891513709368,
   - 0.97928874641099293421931043027104578327,
   - 0.9780415451927629881943028498821429186059,
   - 0.9768628655744219140604871252425961901255,
   - 0.967382626983074241885253344632666448927,
   - 0.9601485420712594199373375259293860324633,
   - 0.9540768694875733222057908617314370634111,
   - 0.9487478690765183543410579996573536771348,
   - 0.9439462911219380338176477772712853402016,
   - 0.9395442782590063946376623684916441100361,
   - 0.9354585313336439336066341889767099608018,
   - 0.9316311953818583253420613278986500351794,
   - 0.9280201500545670487600430252549212247489,
   - 0.8991857663963733198571950343133631348347,
   - 0.8774287170665477623395641312875506084256,
   - 0.8593275036837387237312746018678000939451,
   - 0.8435580020488052057849697812109882706542,
   - 0.8294416857114015557682843481727604063558,
   - 0.8165758053803078481644781849709953302847,
   - 0.8046981564792468915744561969751509934994,
   - 0.7936267540949175059651534957734689407879,
   - 0.7832291989812967764330746819464532478021);

{ Upper branch, X close to 0 }
const X2 : array[1..20] of Extended =
  (1.E-9, 2.E-9, 3.E-9, 4.E-9, 5.E-9, 6.E-9, 7.E-9, 8.E-9, 9.E-9, 1.E-8,
   1.E-2, 2.E-2, 3.E-2, 4.E-2, 5.E-2, 6.E-2, 7.E-2, 8.E-2, 9.E-2, 1.E-1);

const WP2 : array[1..40] of Extended =
  (9.999999990000000014999999973333333385417E-10,
   1.9999999960000000119999999573333335E-9,
   2.999999991000000040499999784000001265625E-9,
   3.999999984000000095999999317333338666667E-9,
   4.999999975000000187499998333333349609375E-9,
   5.999999964000000323999996544000040499999E-9,
   6.99999995100000051449999359733342086979E-9,
   7.999999936000000767999989077333503999997E-9,
   8.999999919000001093499982504000307546869E-9,
   9.999999900000001499999973333333854166656E-9,
   9.901473843595011885336326816570107953628E-3,
   1.961158933740562729168248268298370977812E-2,
   2.913845916787001265458568152535395243296E-2,
   3.848966594197856933287598180923987047561E-2,
   4.767230860012937472638890051416087074706E-2,
   5.669304377414432493107872588796066666126E-2,
   6.555812274442272075701853672870305774479E-2,
   7.427342455278083997072135190143718509109E-2,
   8.284448574644162210327285639805993759142E-2,
   9.127652716086226429989572142317956865312E-2,
   - 1.000000001000000001500000002666666671875E-9,
   - 2.000000004000000012000000042666666833333E-9,
   - 3.000000009000000040500000216000001265625E-9,
   - 4.000000016000000096000000682666672E-9,
   - 5.000000025000000187500001666666682942709E-9,
   - 6.000000036000000324000003456000040500001E-9,
   - 7.000000049000000514500006402666754203126E-9,
   - 8.000000064000000768000010922666837333336E-9,
   - 9.000000081000001093500017496000307546881E-9,
   - 1.000000010000000150000002666666718750001E-8,
   - 1.010152719853875327292018767138623973671E-2,
   - 2.041244405580766725973605390749548004159E-2,
   - 3.094279498284817939791038065611524917276E-2,
   - 4.170340843648447389872733812553976786256E-2,
   - 5.270598355154634795995650617915721289428E-2,
   - 6.396318935617251019529498180168867456393E-2,
   - 7.548877886579220591933915955796681153525E-2,
   - 8.729772086157992404091975866027313992649E-2,
   - 9.940635280454481474353567186786621057821E-2,
   - 1.118325591589629648335694568202658422726E-1);

{ Other results }
const X3 : array[1..10] of Extended =
  (1.E1, 1.E2, 1.E3, 1.E4, 1.E5, 1.E6, 1.E7, 1.E8, 1.E9, 1.E10);

const WP3 : array[1..10] of Extended =
  (1.745528002740699383074301264875389911535,
   3.385630140290050184888244364529726867492,
   5.249602852401596227126056319697306282521,
   7.231846038093372706475618500141253883968,
   9.284571428622108983205132234759581939317,
   11.38335808614005262200015678158500428903,
   13.5143440103060912090067238511621580283,
   15.66899671545096218719628189389457073619,
   17.84172596742146918254060066535711011039,
   20.02868541330495078123430607181488729749);

{ Lower branch, X close to -1/e }
const WM1 : array[1..68] of Extended =
  (- 1.000000000000000000023316439815971242034,
   - 1.000000000000000000032974425414002562937,
   - 1.000000000000000000040385258412884114431,
   - 1.000000000000000000046632879631942484068,
   - 1.000000000000000000052137144421794383842,
   - 1.000000000000000000057113380167442850121,
   - 1.000000000000000000061689501212464534966,
   - 1.000000000000000000065948850828005125875,
   - 1.000000000000000000069949319447913726103,
   - 1.000000000000000000073733056744706376448,
   - 1.000000000000002331643981597126015551422,
   - 1.000000000000003297442541400259918073073,
   - 1.000000000000004038525841288416879599233,
   - 1.000000000000004663287963194255655478615,
   - 1.00000000000000521371444217944744506897,
   - 1.000000000000005711338016744295885146596,
   - 1.000000000000006168950121246466181805002,
   - 1.000000000000006594885082800527084897688,
   - 1.000000000000006994931944791388919781579,
   - 1.000000000000007373305674470655766501228,
   - 1.000000000233164398177834299194683872234,
   - 1.000000000329744254176269387087995047343,
   - 1.00000000040385258418320678088280150237,
   - 1.000000000466328796391912356113774800963,
   - 1.000000000521371444308553232716574598644,
   - 1.00000000057113380178315977436875260197,
   - 1.000000000616895012251498501679602643872,
   - 1.000000000659488508425026289634430354159,
   - 1.000000000699493194642234170768892572882,
   - 1.000000000737330567628282553087415117543,
   - 1.000023316621036696460620295453277856456,
   - 1.000032974787857057404928311684626421503,
   - 1.000040385802079313048521250390482335902,
   - 1.00004663360452259016530661221213359488,
   - 1.0000521380505373899860247162705706318,
   - 1.000057114467508637629346787348726350223,
   - 1.000061690769779852545970707346938004879,