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Source file src/math/cmplx/cmath_test.go

Documentation: math/cmplx

     1  // Copyright 2010 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package cmplx
     6  
     7  import (
     8  	"math"
     9  	"testing"
    10  )
    11  
    12  // The higher-precision values in vc26 were used to derive the
    13  // input arguments vc (see also comment below). For reference
    14  // only (do not delete).
    15  var vc26 = []complex128{
    16  	(4.97901192488367350108546816 + 7.73887247457810456552351752i),
    17  	(7.73887247457810456552351752 - 0.27688005719200159404635997i),
    18  	(-0.27688005719200159404635997 - 5.01060361827107492160848778i),
    19  	(-5.01060361827107492160848778 + 9.63629370719841737980004837i),
    20  	(9.63629370719841737980004837 + 2.92637723924396464525443662i),
    21  	(2.92637723924396464525443662 + 5.22908343145930665230025625i),
    22  	(5.22908343145930665230025625 + 2.72793991043601025126008608i),
    23  	(2.72793991043601025126008608 + 1.82530809168085506044576505i),
    24  	(1.82530809168085506044576505 - 8.68592476857560136238589621i),
    25  	(-8.68592476857560136238589621 + 4.97901192488367350108546816i),
    26  }
    27  
    28  var vc = []complex128{
    29  	(4.9790119248836735e+00 + 7.7388724745781045e+00i),
    30  	(7.7388724745781045e+00 - 2.7688005719200159e-01i),
    31  	(-2.7688005719200159e-01 - 5.0106036182710749e+00i),
    32  	(-5.0106036182710749e+00 + 9.6362937071984173e+00i),
    33  	(9.6362937071984173e+00 + 2.9263772392439646e+00i),
    34  	(2.9263772392439646e+00 + 5.2290834314593066e+00i),
    35  	(5.2290834314593066e+00 + 2.7279399104360102e+00i),
    36  	(2.7279399104360102e+00 + 1.8253080916808550e+00i),
    37  	(1.8253080916808550e+00 - 8.6859247685756013e+00i),
    38  	(-8.6859247685756013e+00 + 4.9790119248836735e+00i),
    39  }
    40  
    41  // The expected results below were computed by the high precision calculators
    42  // at http://keisan.casio.com/.  More exact input values (array vc[], above)
    43  // were obtained by printing them with "%.26f".  The answers were calculated
    44  // to 26 digits (by using the "Digit number" drop-down control of each
    45  // calculator).
    46  
    47  var abs = []float64{
    48  	9.2022120669932650313380972e+00,
    49  	7.7438239742296106616261394e+00,
    50  	5.0182478202557746902556648e+00,
    51  	1.0861137372799545160704002e+01,
    52  	1.0070841084922199607011905e+01,
    53  	5.9922447613166942183705192e+00,
    54  	5.8978784056736762299945176e+00,
    55  	3.2822866700678709020367184e+00,
    56  	8.8756430028990417290744307e+00,
    57  	1.0011785496777731986390856e+01,
    58  }
    59  
    60  var acos = []complex128{
    61  	(1.0017679804707456328694569 - 2.9138232718554953784519807i),
    62  	(0.03606427612041407369636057 + 2.7358584434576260925091256i),
    63  	(1.6249365462333796703711823 + 2.3159537454335901187730929i),
    64  	(2.0485650849650740120660391 - 3.0795576791204117911123886i),
    65  	(0.29621132089073067282488147 - 3.0007392508200622519398814i),
    66  	(1.0664555914934156601503632 - 2.4872865024796011364747111i),
    67  	(0.48681307452231387690013905 - 2.463655912283054555225301i),
    68  	(0.6116977071277574248407752 - 1.8734458851737055262693056i),
    69  	(1.3649311280370181331184214 + 2.8793528632328795424123832i),
    70  	(2.6189310485682988308904501 - 2.9956543302898767795858704i),
    71  }
    72  var acosh = []complex128{
    73  	(2.9138232718554953784519807 + 1.0017679804707456328694569i),
    74  	(2.7358584434576260925091256 - 0.03606427612041407369636057i),
    75  	(2.3159537454335901187730929 - 1.6249365462333796703711823i),
    76  	(3.0795576791204117911123886 + 2.0485650849650740120660391i),
    77  	(3.0007392508200622519398814 + 0.29621132089073067282488147i),
    78  	(2.4872865024796011364747111 + 1.0664555914934156601503632i),
    79  	(2.463655912283054555225301 + 0.48681307452231387690013905i),
    80  	(1.8734458851737055262693056 + 0.6116977071277574248407752i),
    81  	(2.8793528632328795424123832 - 1.3649311280370181331184214i),
    82  	(2.9956543302898767795858704 + 2.6189310485682988308904501i),
    83  }
    84  var asin = []complex128{
    85  	(0.56902834632415098636186476 + 2.9138232718554953784519807i),
    86  	(1.5347320506744825455349611 - 2.7358584434576260925091256i),
    87  	(-0.054140219438483051139860579 - 2.3159537454335901187730929i),
    88  	(-0.47776875817017739283471738 + 3.0795576791204117911123886i),
    89  	(1.2745850059041659464064402 + 3.0007392508200622519398814i),
    90  	(0.50434073530148095908095852 + 2.4872865024796011364747111i),
    91  	(1.0839832522725827423311826 + 2.463655912283054555225301i),
    92  	(0.9590986196671391943905465 + 1.8734458851737055262693056i),
    93  	(0.20586519875787848611290031 - 2.8793528632328795424123832i),
    94  	(-1.0481347217734022116591284 + 2.9956543302898767795858704i),
    95  }
    96  var asinh = []complex128{
    97  	(2.9113760469415295679342185 + 0.99639459545704326759805893i),
    98  	(2.7441755423994259061579029 - 0.035468308789000500601119392i),
    99  	(-2.2962136462520690506126678 - 1.5144663565690151885726707i),
   100  	(-3.0771233459295725965402455 + 1.0895577967194013849422294i),
   101  	(3.0048366100923647417557027 + 0.29346979169819220036454168i),
   102  	(2.4800059370795363157364643 + 1.0545868606049165710424232i),
   103  	(2.4718773838309585611141821 + 0.47502344364250803363708842i),
   104  	(1.8910743588080159144378396 + 0.56882925572563602341139174i),
   105  	(2.8735426423367341878069406 - 1.362376149648891420997548i),
   106  	(-2.9981750586172477217567878 + 0.5183571985225367505624207i),
   107  }
   108  var atan = []complex128{
   109  	(1.5115747079332741358607654 + 0.091324403603954494382276776i),
   110  	(1.4424504323482602560806727 - 0.0045416132642803911503770933i),
   111  	(-1.5593488703630532674484026 - 0.20163295409248362456446431i),
   112  	(-1.5280619472445889867794105 + 0.081721556230672003746956324i),
   113  	(1.4759909163240799678221039 + 0.028602969320691644358773586i),
   114  	(1.4877353772046548932715555 + 0.14566877153207281663773599i),
   115  	(1.4206983927779191889826 + 0.076830486127880702249439993i),
   116  	(1.3162236060498933364869556 + 0.16031313000467530644933363i),
   117  	(1.5473450684303703578810093 - 0.11064907507939082484935782i),
   118  	(-1.4841462340185253987375812 + 0.049341850305024399493142411i),
   119  }
   120  var atanh = []complex128{
   121  	(0.058375027938968509064640438 + 1.4793488495105334458167782i),
   122  	(0.12977343497790381229915667 - 1.5661009410463561327262499i),
   123  	(-0.010576456067347252072200088 - 1.3743698658402284549750563i),
   124  	(-0.042218595678688358882784918 + 1.4891433968166405606692604i),
   125  	(0.095218997991316722061828397 + 1.5416884098777110330499698i),
   126  	(0.079965459366890323857556487 + 1.4252510353873192700350435i),
   127  	(0.15051245471980726221708301 + 1.4907432533016303804884461i),
   128  	(0.25082072933993987714470373 + 1.392057665392187516442986i),
   129  	(0.022896108815797135846276662 - 1.4609224989282864208963021i),
   130  	(-0.08665624101841876130537396 + 1.5207902036935093480142159i),
   131  }
   132  var conj = []complex128{
   133  	(4.9790119248836735e+00 - 7.7388724745781045e+00i),
   134  	(7.7388724745781045e+00 + 2.7688005719200159e-01i),
   135  	(-2.7688005719200159e-01 + 5.0106036182710749e+00i),
   136  	(-5.0106036182710749e+00 - 9.6362937071984173e+00i),
   137  	(9.6362937071984173e+00 - 2.9263772392439646e+00i),
   138  	(2.9263772392439646e+00 - 5.2290834314593066e+00i),
   139  	(5.2290834314593066e+00 - 2.7279399104360102e+00i),
   140  	(2.7279399104360102e+00 - 1.8253080916808550e+00i),
   141  	(1.8253080916808550e+00 + 8.6859247685756013e+00i),
   142  	(-8.6859247685756013e+00 - 4.9790119248836735e+00i),
   143  }
   144  var cos = []complex128{
   145  	(3.024540920601483938336569e+02 + 1.1073797572517071650045357e+03i),
   146  	(1.192858682649064973252758e-01 + 2.7857554122333065540970207e-01i),
   147  	(7.2144394304528306603857962e+01 - 2.0500129667076044169954205e+01i),
   148  	(2.24921952538403984190541e+03 - 7.317363745602773587049329e+03i),
   149  	(-9.148222970032421760015498e+00 + 1.953124661113563541862227e+00i),
   150  	(-9.116081175857732248227078e+01 - 1.992669213569952232487371e+01i),
   151  	(3.795639179042704640002918e+00 + 6.623513350981458399309662e+00i),
   152  	(-2.9144840732498869560679084e+00 - 1.214620271628002917638748e+00i),
   153  	(-7.45123482501299743872481e+02 + 2.8641692314488080814066734e+03i),
   154  	(-5.371977967039319076416747e+01 + 4.893348341339375830564624e+01i),
   155  }
   156  var cosh = []complex128{
   157  	(8.34638383523018249366948e+00 + 7.2181057886425846415112064e+01i),
   158  	(1.10421967379919366952251e+03 - 3.1379638689277575379469861e+02i),
   159  	(3.051485206773701584738512e-01 - 2.6805384730105297848044485e-01i),
   160  	(-7.33294728684187933370938e+01 + 1.574445942284918251038144e+01i),
   161  	(-7.478643293945957535757355e+03 + 1.6348382209913353929473321e+03i),
   162  	(4.622316522966235701630926e+00 - 8.088695185566375256093098e+00i),
   163  	(-8.544333183278877406197712e+01 + 3.7505836120128166455231717e+01i),
   164  	(-1.934457815021493925115198e+00 + 7.3725859611767228178358673e+00i),
   165  	(-2.352958770061749348353548e+00 - 2.034982010440878358915409e+00i),
   166  	(7.79756457532134748165069e+02 + 2.8549350716819176560377717e+03i),
   167  }
   168  var exp = []complex128{
   169  	(1.669197736864670815125146e+01 + 1.4436895109507663689174096e+02i),
   170  	(2.2084389286252583447276212e+03 - 6.2759289284909211238261917e+02i),
   171  	(2.227538273122775173434327e-01 + 7.2468284028334191250470034e-01i),
   172  	(-6.5182985958153548997881627e-03 - 1.39965837915193860879044e-03i),
   173  	(-1.4957286524084015746110777e+04 + 3.269676455931135688988042e+03i),
   174  	(9.218158701983105935659273e+00 - 1.6223985291084956009304582e+01i),
   175  	(-1.7088175716853040841444505e+02 + 7.501382609870410713795546e+01i),
   176  	(-3.852461315830959613132505e+00 + 1.4808420423156073221970892e+01i),
   177  	(-4.586775503301407379786695e+00 - 4.178501081246873415144744e+00i),
   178  	(4.451337963005453491095747e-05 - 1.62977574205442915935263e-04i),
   179  }
   180  var log = []complex128{
   181  	(2.2194438972179194425697051e+00 + 9.9909115046919291062461269e-01i),
   182  	(2.0468956191154167256337289e+00 - 3.5762575021856971295156489e-02i),
   183  	(1.6130808329853860438751244e+00 - 1.6259990074019058442232221e+00i),
   184  	(2.3851910394823008710032651e+00 + 2.0502936359659111755031062e+00i),
   185  	(2.3096442270679923004800651e+00 + 2.9483213155446756211881774e-01i),
   186  	(1.7904660933974656106951860e+00 + 1.0605860367252556281902109e+00i),
   187  	(1.7745926939841751666177512e+00 + 4.8084556083358307819310911e-01i),
   188  	(1.1885403350045342425648780e+00 + 5.8969634164776659423195222e-01i),
   189  	(2.1833107837679082586772505e+00 - 1.3636647724582455028314573e+00i),
   190  	(2.3037629487273259170991671e+00 + 2.6210913895386013290915234e+00i),
   191  }
   192  var log10 = []complex128{
   193  	(9.6389223745559042474184943e-01 + 4.338997735671419492599631e-01i),
   194  	(8.8895547241376579493490892e-01 - 1.5531488990643548254864806e-02i),
   195  	(7.0055210462945412305244578e-01 - 7.0616239649481243222248404e-01i),
   196  	(1.0358753067322445311676952e+00 + 8.9043121238134980156490909e-01i),
   197  	(1.003065742975330237172029e+00 + 1.2804396782187887479857811e-01i),
   198  	(7.7758954439739162532085157e-01 + 4.6060666333341810869055108e-01i),
   199  	(7.7069581462315327037689152e-01 + 2.0882857371769952195512475e-01i),
   200  	(5.1617650901191156135137239e-01 + 2.5610186717615977620363299e-01i),
   201  	(9.4819982567026639742663212e-01 - 5.9223208584446952284914289e-01i),
   202  	(1.0005115362454417135973429e+00 + 1.1383255270407412817250921e+00i),
   203  }
   204  
   205  type ff struct {
   206  	r, theta float64
   207  }
   208  
   209  var polar = []ff{
   210  	{9.2022120669932650313380972e+00, 9.9909115046919291062461269e-01},
   211  	{7.7438239742296106616261394e+00, -3.5762575021856971295156489e-02},
   212  	{5.0182478202557746902556648e+00, -1.6259990074019058442232221e+00},
   213  	{1.0861137372799545160704002e+01, 2.0502936359659111755031062e+00},
   214  	{1.0070841084922199607011905e+01, 2.9483213155446756211881774e-01},
   215  	{5.9922447613166942183705192e+00, 1.0605860367252556281902109e+00},
   216  	{5.8978784056736762299945176e+00, 4.8084556083358307819310911e-01},
   217  	{3.2822866700678709020367184e+00, 5.8969634164776659423195222e-01},
   218  	{8.8756430028990417290744307e+00, -1.3636647724582455028314573e+00},
   219  	{1.0011785496777731986390856e+01, 2.6210913895386013290915234e+00},
   220  }
   221  var pow = []complex128{
   222  	(-2.499956739197529585028819e+00 + 1.759751724335650228957144e+00i),
   223  	(7.357094338218116311191939e+04 - 5.089973412479151648145882e+04i),
   224  	(1.320777296067768517259592e+01 - 3.165621914333901498921986e+01i),
   225  	(-3.123287828297300934072149e-07 - 1.9849567521490553032502223E-7i),
   226  	(8.0622651468477229614813e+04 - 7.80028727944573092944363e+04i),
   227  	(-1.0268824572103165858577141e+00 - 4.716844738244989776610672e-01i),
   228  	(-4.35953819012244175753187e+01 + 2.2036445974645306917648585e+02i),
   229  	(8.3556092283250594950239e-01 - 1.2261571947167240272593282e+01i),
   230  	(1.582292972120769306069625e+03 + 1.273564263524278244782512e+04i),
   231  	(6.592208301642122149025369e-08 + 2.584887236651661903526389e-08i),
   232  }
   233  var sin = []complex128{
   234  	(-1.1073801774240233539648544e+03 + 3.024539773002502192425231e+02i),
   235  	(1.0317037521400759359744682e+00 - 3.2208979799929570242818e-02i),
   236  	(-2.0501952097271429804261058e+01 - 7.2137981348240798841800967e+01i),
   237  	(7.3173638080346338642193078e+03 + 2.249219506193664342566248e+03i),
   238  	(-1.964375633631808177565226e+00 - 9.0958264713870404464159683e+00i),
   239  	(1.992783647158514838337674e+01 - 9.11555769410191350416942e+01i),
   240  	(-6.680335650741921444300349e+00 + 3.763353833142432513086117e+00i),
   241  	(1.2794028166657459148245993e+00 - 2.7669092099795781155109602e+00i),
   242  	(2.8641693949535259594188879e+03 + 7.451234399649871202841615e+02i),
   243  	(-4.893811726244659135553033e+01 - 5.371469305562194635957655e+01i),
   244  }
   245  var sinh = []complex128{
   246  	(8.34559353341652565758198e+00 + 7.2187893208650790476628899e+01i),
   247  	(1.1042192548260646752051112e+03 - 3.1379650595631635858792056e+02i),
   248  	(-8.239469336509264113041849e-02 + 9.9273668758439489098514519e-01i),
   249  	(7.332295456982297798219401e+01 - 1.574585908122833444899023e+01i),
   250  	(-7.4786432301380582103534216e+03 + 1.63483823493980029604071e+03i),
   251  	(4.595842179016870234028347e+00 - 8.135290105518580753211484e+00i),
   252  	(-8.543842533574163435246793e+01 + 3.750798997857594068272375e+01i),
   253  	(-1.918003500809465688017307e+00 + 7.4358344619793504041350251e+00i),
   254  	(-2.233816733239658031433147e+00 - 2.143519070805995056229335e+00i),
   255  	(-7.797564130187551181105341e+02 - 2.8549352346594918614806877e+03i),
   256  }
   257  var sqrt = []complex128{
   258  	(2.6628203086086130543813948e+00 + 1.4531345674282185229796902e+00i),
   259  	(2.7823278427251986247149295e+00 - 4.9756907317005224529115567e-02i),
   260  	(1.5397025302089642757361015e+00 - 1.6271336573016637535695727e+00i),
   261  	(1.7103411581506875260277898e+00 + 2.8170677122737589676157029e+00i),
   262  	(3.1390392472953103383607947e+00 + 4.6612625849858653248980849e-01i),
   263  	(2.1117080764822417640789287e+00 + 1.2381170223514273234967850e+00i),
   264  	(2.3587032281672256703926939e+00 + 5.7827111903257349935720172e-01i),
   265  	(1.7335262588873410476661577e+00 + 5.2647258220721269141550382e-01i),
   266  	(2.3131094974708716531499282e+00 - 1.8775429304303785570775490e+00i),
   267  	(8.1420535745048086240947359e-01 + 3.0575897587277248522656113e+00i),
   268  }
   269  var tan = []complex128{
   270  	(-1.928757919086441129134525e-07 + 1.0000003267499169073251826e+00i),
   271  	(1.242412685364183792138948e+00 - 3.17149693883133370106696e+00i),
   272  	(-4.6745126251587795225571826e-05 - 9.9992439225263959286114298e-01i),
   273  	(4.792363401193648192887116e-09 + 1.0000000070589333451557723e+00i),
   274  	(2.345740824080089140287315e-03 + 9.947733046570988661022763e-01i),
   275  	(-2.396030789494815566088809e-05 + 9.9994781345418591429826779e-01i),
   276  	(-7.370204836644931340905303e-03 + 1.0043553413417138987717748e+00i),
   277  	(-3.691803847992048527007457e-02 + 9.6475071993469548066328894e-01i),
   278  	(-2.781955256713729368401878e-08 - 1.000000049848910609006646e+00i),
   279  	(9.4281590064030478879791249e-05 + 9.9999119340863718183758545e-01i),
   280  }
   281  var tanh = []complex128{
   282  	(1.0000921981225144748819918e+00 + 2.160986245871518020231507e-05i),
   283  	(9.9999967727531993209562591e-01 - 1.9953763222959658873657676e-07i),
   284  	(-1.765485739548037260789686e+00 + 1.7024216325552852445168471e+00i),
   285  	(-9.999189442732736452807108e-01 + 3.64906070494473701938098e-05i),
   286  	(9.9999999224622333738729767e-01 - 3.560088949517914774813046e-09i),
   287  	(1.0029324933367326862499343e+00 - 4.948790309797102353137528e-03i),
   288  	(9.9996113064788012488693567e-01 - 4.226995742097032481451259e-05i),
   289  	(1.0074784189316340029873945e+00 - 4.194050814891697808029407e-03i),
   290  	(9.9385534229718327109131502e-01 + 5.144217985914355502713437e-02i),
   291  	(-1.0000000491604982429364892e+00 - 2.901873195374433112227349e-08i),
   292  }
   293  
   294  // special cases
   295  var vcAbsSC = []complex128{
   296  	NaN(),
   297  }
   298  var absSC = []float64{
   299  	math.NaN(),
   300  }
   301  var vcAcosSC = []complex128{
   302  	NaN(),
   303  }
   304  var acosSC = []complex128{
   305  	NaN(),
   306  }
   307  var vcAcoshSC = []complex128{
   308  	NaN(),
   309  }
   310  var acoshSC = []complex128{
   311  	NaN(),
   312  }
   313  var vcAsinSC = []complex128{
   314  	NaN(),
   315  }
   316  var asinSC = []complex128{
   317  	NaN(),
   318  }
   319  var vcAsinhSC = []complex128{
   320  	NaN(),
   321  }
   322  var asinhSC = []complex128{
   323  	NaN(),
   324  }
   325  var vcAtanSC = []complex128{
   326  	NaN(),
   327  }
   328  var atanSC = []complex128{
   329  	NaN(),
   330  }
   331  var vcAtanhSC = []complex128{
   332  	NaN(),
   333  }
   334  var atanhSC = []complex128{
   335  	NaN(),
   336  }
   337  var vcConjSC = []complex128{
   338  	NaN(),
   339  }
   340  var conjSC = []complex128{
   341  	NaN(),
   342  }
   343  var vcCosSC = []complex128{
   344  	NaN(),
   345  }
   346  var cosSC = []complex128{
   347  	NaN(),
   348  }
   349  var vcCoshSC = []complex128{
   350  	NaN(),
   351  }
   352  var coshSC = []complex128{
   353  	NaN(),
   354  }
   355  var vcExpSC = []complex128{
   356  	NaN(),
   357  }
   358  var expSC = []complex128{
   359  	NaN(),
   360  }
   361  var vcIsNaNSC = []complex128{
   362  	complex(math.Inf(-1), math.Inf(-1)),
   363  	complex(math.Inf(-1), math.NaN()),
   364  	complex(math.NaN(), math.Inf(-1)),
   365  	complex(0, math.NaN()),
   366  	complex(math.NaN(), 0),
   367  	complex(math.Inf(1), math.Inf(1)),
   368  	complex(math.Inf(1), math.NaN()),
   369  	complex(math.NaN(), math.Inf(1)),
   370  	complex(math.NaN(), math.NaN()),
   371  }
   372  var isNaNSC = []bool{
   373  	false,
   374  	false,
   375  	false,
   376  	true,
   377  	true,
   378  	false,
   379  	false,
   380  	false,
   381  	true,
   382  }
   383  var vcLogSC = []complex128{
   384  	NaN(),
   385  }
   386  var logSC = []complex128{
   387  	NaN(),
   388  }
   389  var vcLog10SC = []complex128{
   390  	NaN(),
   391  }
   392  var log10SC = []complex128{
   393  	NaN(),
   394  }
   395  var vcPolarSC = []complex128{
   396  	NaN(),
   397  }
   398  var polarSC = []ff{
   399  	{math.NaN(), math.NaN()},
   400  }
   401  var vcPowSC = [][2]complex128{
   402  	{NaN(), NaN()},
   403  }
   404  var powSC = []complex128{
   405  	NaN(),
   406  }
   407  var vcSinSC = []complex128{
   408  	NaN(),
   409  }
   410  var sinSC = []complex128{
   411  	NaN(),
   412  }
   413  var vcSinhSC = []complex128{
   414  	NaN(),
   415  }
   416  var sinhSC = []complex128{
   417  	NaN(),
   418  }
   419  var vcSqrtSC = []complex128{
   420  	NaN(),
   421  }
   422  var sqrtSC = []complex128{
   423  	NaN(),
   424  }
   425  var vcTanSC = []complex128{
   426  	NaN(),
   427  }
   428  var tanSC = []complex128{
   429  	NaN(),
   430  }
   431  var vcTanhSC = []complex128{
   432  	NaN(),
   433  }
   434  var tanhSC = []complex128{
   435  	NaN(),
   436  }
   437  
   438  // branch cut continuity checks
   439  // points on each axis at |z| > 1 are checked for one-sided continuity from both the positive and negative side
   440  // all possible branch cuts for the elementary functions are at one of these points
   441  
   442  var zero = 0.0
   443  var eps = 1.0 / (1 << 53)
   444  
   445  var branchPoints = [][2]complex128{
   446  	{complex(2.0, zero), complex(2.0, eps)},
   447  	{complex(2.0, -zero), complex(2.0, -eps)},
   448  	{complex(-2.0, zero), complex(-2.0, eps)},
   449  	{complex(-2.0, -zero), complex(-2.0, -eps)},
   450  	{complex(zero, 2.0), complex(eps, 2.0)},
   451  	{complex(-zero, 2.0), complex(-eps, 2.0)},
   452  	{complex(zero, -2.0), complex(eps, -2.0)},
   453  	{complex(-zero, -2.0), complex(-eps, -2.0)},
   454  }
   455  
   456  // functions borrowed from pkg/math/all_test.go
   457  func tolerance(a, b, e float64) bool {
   458  	d := a - b
   459  	if d < 0 {
   460  		d = -d
   461  	}
   462  
   463  	// note: b is correct (expected) value, a is actual value.
   464  	// make error tolerance a fraction of b, not a.
   465  	if b != 0 {
   466  		e = e * b
   467  		if e < 0 {
   468  			e = -e
   469  		}
   470  	}
   471  	return d < e
   472  }
   473  func veryclose(a, b float64) bool { return tolerance(a, b, 4e-16) }
   474  func alike(a, b float64) bool {
   475  	switch {
   476  	case a != a && b != b: // math.IsNaN(a) && math.IsNaN(b):
   477  		return true
   478  	case a == b:
   479  		return math.Signbit(a) == math.Signbit(b)
   480  	}
   481  	return false
   482  }
   483  
   484  func cTolerance(a, b complex128, e float64) bool {
   485  	d := Abs(a - b)
   486  	if b != 0 {
   487  		e = e * Abs(b)
   488  		if e < 0 {
   489  			e = -e
   490  		}
   491  	}
   492  	return d < e
   493  }
   494  func cSoclose(a, b complex128, e float64) bool { return cTolerance(a, b, e) }
   495  func cVeryclose(a, b complex128) bool          { return cTolerance(a, b, 4e-16) }
   496  func cAlike(a, b complex128) bool {
   497  	switch {
   498  	case IsNaN(a) && IsNaN(b):
   499  		return true
   500  	case a == b:
   501  		return math.Signbit(real(a)) == math.Signbit(real(b)) && math.Signbit(imag(a)) == math.Signbit(imag(b))
   502  	}
   503  	return false
   504  }
   505  
   506  func TestAbs(t *testing.T) {
   507  	for i := 0; i < len(vc); i++ {
   508  		if f := Abs(vc[i]); !veryclose(abs[i], f) {
   509  			t.Errorf("Abs(%g) = %g, want %g", vc[i], f, abs[i])
   510  		}
   511  	}
   512  	for i := 0; i < len(vcAbsSC); i++ {
   513  		if f := Abs(vcAbsSC[i]); !alike(absSC[i], f) {
   514  			t.Errorf("Abs(%g) = %g, want %g", vcAbsSC[i], f, absSC[i])
   515  		}
   516  	}
   517  }
   518  func TestAcos(t *testing.T) {
   519  	for i := 0; i < len(vc); i++ {
   520  		if f := Acos(vc[i]); !cSoclose(acos[i], f, 1e-14) {
   521  			t.Errorf("Acos(%g) = %g, want %g", vc[i], f, acos[i])
   522  		}
   523  	}
   524  	for i := 0; i < len(vcAcosSC); i++ {
   525  		if f := Acos(vcAcosSC[i]); !cAlike(acosSC[i], f) {
   526  			t.Errorf("Acos(%g) = %g, want %g", vcAcosSC[i], f, acosSC[i])
   527  		}
   528  	}
   529  	for _, pt := range branchPoints {
   530  		if f0, f1 := Acos(pt[0]), Acos(pt[1]); !cVeryclose(f0, f1) {
   531  			t.Errorf("Acos(%g) not continuous, got %g want %g", pt[0], f0, f1)
   532  		}
   533  	}
   534  }
   535  func TestAcosh(t *testing.T) {
   536  	for i := 0; i < len(vc); i++ {
   537  		if f := Acosh(vc[i]); !cSoclose(acosh[i], f, 1e-14) {
   538  			t.Errorf("Acosh(%g) = %g, want %g", vc[i], f, acosh[i])
   539  		}
   540  	}
   541  	for i := 0; i < len(vcAcoshSC); i++ {
   542  		if f := Acosh(vcAcoshSC[i]); !cAlike(acoshSC[i], f) {
   543  			t.Errorf("Acosh(%g) = %g, want %g", vcAcoshSC[i], f, acoshSC[i])
   544  		}
   545  	}
   546  	for _, pt := range branchPoints {
   547  		if f0, f1 := Acosh(pt[0]), Acosh(pt[1]); !cVeryclose(f0, f1) {
   548  			t.Errorf("Acosh(%g) not continuous, got %g want %g", pt[0], f0, f1)
   549  		}
   550  	}
   551  }
   552  func TestAsin(t *testing.T) {
   553  	for i := 0; i < len(vc); i++ {
   554  		if f := Asin(vc[i]); !cSoclose(asin[i], f, 1e-14) {
   555  			t.Errorf("Asin(%g) = %g, want %g", vc[i], f, asin[i])
   556  		}
   557  	}
   558  	for i := 0; i < len(vcAsinSC); i++ {
   559  		if f := Asin(vcAsinSC[i]); !cAlike(asinSC[i], f) {
   560  			t.Errorf("Asin(%g) = %g, want %g", vcAsinSC[i], f, asinSC[i])
   561  		}
   562  	}
   563  	for _, pt := range branchPoints {
   564  		if f0, f1 := Asin(pt[0]), Asin(pt[1]); !cVeryclose(f0, f1) {
   565  			t.Errorf("Asin(%g) not continuous, got %g want %g", pt[0], f0, f1)
   566  		}
   567  	}
   568  }
   569  func TestAsinh(t *testing.T) {
   570  	for i := 0; i < len(vc); i++ {
   571  		if f := Asinh(vc[i]); !cSoclose(asinh[i], f, 4e-15) {
   572  			t.Errorf("Asinh(%g) = %g, want %g", vc[i], f, asinh[i])
   573  		}
   574  	}
   575  	for i := 0; i < len(vcAsinhSC); i++ {
   576  		if f := Asinh(vcAsinhSC[i]); !cAlike(asinhSC[i], f) {
   577  			t.Errorf("Asinh(%g) = %g, want %g", vcAsinhSC[i], f, asinhSC[i])
   578  		}
   579  	}
   580  	for _, pt := range branchPoints {
   581  		if f0, f1 := Asinh(pt[0]), Asinh(pt[1]); !cVeryclose(f0, f1) {
   582  			t.Errorf("Asinh(%g) not continuous, got %g want %g", pt[0], f0, f1)
   583  		}
   584  	}
   585  }
   586  func TestAtan(t *testing.T) {
   587  	for i := 0; i < len(vc); i++ {
   588  		if f := Atan(vc[i]); !cVeryclose(atan[i], f) {
   589  			t.Errorf("Atan(%g) = %g, want %g", vc[i], f, atan[i])
   590  		}
   591  	}
   592  	for i := 0; i < len(vcAtanSC); i++ {
   593  		if f := Atan(vcAtanSC[i]); !cAlike(atanSC[i], f) {
   594  			t.Errorf("Atan(%g) = %g, want %g", vcAtanSC[i], f, atanSC[i])
   595  		}
   596  	}
   597  	for _, pt := range branchPoints {
   598  		if f0, f1 := Atan(pt[0]), Atan(pt[1]); !cVeryclose(f0, f1) {
   599  			t.Errorf("Atan(%g) not continuous, got %g want %g", pt[0], f0, f1)
   600  		}
   601  	}
   602  }
   603  func TestAtanh(t *testing.T) {
   604  	for i := 0; i < len(vc); i++ {
   605  		if f := Atanh(vc[i]); !cVeryclose(atanh[i], f) {
   606  			t.Errorf("Atanh(%g) = %g, want %g", vc[i], f, atanh[i])
   607  		}
   608  	}
   609  	for i := 0; i < len(vcAtanhSC); i++ {
   610  		if f := Atanh(vcAtanhSC[i]); !cAlike(atanhSC[i], f) {
   611  			t.Errorf("Atanh(%g) = %g, want %g", vcAtanhSC[i], f, atanhSC[i])
   612  		}
   613  	}
   614  	for _, pt := range branchPoints {
   615  		if f0, f1 := Atanh(pt[0]), Atanh(pt[1]); !cVeryclose(f0, f1) {
   616  			t.Errorf("Atanh(%g) not continuous, got %g want %g", pt[0], f0, f1)
   617  		}
   618  	}
   619  }
   620  func TestConj(t *testing.T) {
   621  	for i := 0; i < len(vc); i++ {
   622  		if f := Conj(vc[i]); !cVeryclose(conj[i], f) {
   623  			t.Errorf("Conj(%g) = %g, want %g", vc[i], f, conj[i])
   624  		}
   625  	}
   626  	for i := 0; i < len(vcConjSC); i++ {
   627  		if f := Conj(vcConjSC[i]); !cAlike(conjSC[i], f) {
   628  			t.Errorf("Conj(%g) = %g, want %g", vcConjSC[i], f, conjSC[i])
   629  		}
   630  	}
   631  }
   632  func TestCos(t *testing.T) {
   633  	for i := 0; i < len(vc); i++ {
   634  		if f := Cos(vc[i]); !cSoclose(cos[i], f, 3e-15) {
   635  			t.Errorf("Cos(%g) = %g, want %g", vc[i], f, cos[i])
   636  		}
   637  	}
   638  	for i := 0; i < len(vcCosSC); i++ {
   639  		if f := Cos(vcCosSC[i]); !cAlike(cosSC[i], f) {
   640  			t.Errorf("Cos(%g) = %g, want %g", vcCosSC[i], f, cosSC[i])
   641  		}
   642  	}
   643  }
   644  func TestCosh(t *testing.T) {
   645  	for i := 0; i < len(vc); i++ {
   646  		if f := Cosh(vc[i]); !cSoclose(cosh[i], f, 2e-15) {
   647  			t.Errorf("Cosh(%g) = %g, want %g", vc[i], f, cosh[i])
   648  		}
   649  	}
   650  	for i := 0; i < len(vcCoshSC); i++ {
   651  		if f := Cosh(vcCoshSC[i]); !cAlike(coshSC[i], f) {
   652  			t.Errorf("Cosh(%g) = %g, want %g", vcCoshSC[i], f, coshSC[i])
   653  		}
   654  	}
   655  }
   656  func TestExp(t *testing.T) {
   657  	for i := 0; i < len(vc); i++ {
   658  		if f := Exp(vc[i]); !cSoclose(exp[i], f, 1e-15) {
   659  			t.Errorf("Exp(%g) = %g, want %g", vc[i], f, exp[i])
   660  		}
   661  	}
   662  	for i := 0; i < len(vcExpSC); i++ {
   663  		if f := Exp(vcExpSC[i]); !cAlike(expSC[i], f) {
   664  			t.Errorf("Exp(%g) = %g, want %g", vcExpSC[i], f, expSC[i])
   665  		}
   666  	}
   667  }
   668  func TestIsNaN(t *testing.T) {
   669  	for i := 0; i < len(vcIsNaNSC); i++ {
   670  		if f := IsNaN(vcIsNaNSC[i]); isNaNSC[i] != f {
   671  			t.Errorf("IsNaN(%v) = %v, want %v", vcIsNaNSC[i], f, isNaNSC[i])
   672  		}
   673  	}
   674  }
   675  func TestLog(t *testing.T) {
   676  	for i := 0; i < len(vc); i++ {
   677  		if f := Log(vc[i]); !cVeryclose(log[i], f) {
   678  			t.Errorf("Log(%g) = %g, want %g", vc[i], f, log[i])
   679  		}
   680  	}
   681  	for i := 0; i < len(vcLogSC); i++ {
   682  		if f := Log(vcLogSC[i]); !cAlike(logSC[i], f) {
   683  			t.Errorf("Log(%g) = %g, want %g", vcLogSC[i], f, logSC[i])
   684  		}
   685  	}
   686  	for _, pt := range branchPoints {
   687  		if f0, f1 := Log(pt[0]), Log(pt[1]); !cVeryclose(f0, f1) {
   688  			t.Errorf("Log(%g) not continuous, got %g want %g", pt[0], f0, f1)
   689  		}
   690  	}
   691  }
   692  func TestLog10(t *testing.T) {
   693  	for i := 0; i < len(vc); i++ {
   694  		if f := Log10(vc[i]); !cVeryclose(log10[i], f) {
   695  			t.Errorf("Log10(%g) = %g, want %g", vc[i], f, log10[i])
   696  		}
   697  	}
   698  	for i := 0; i < len(vcLog10SC); i++ {
   699  		if f := Log10(vcLog10SC[i]); !cAlike(log10SC[i], f) {
   700  			t.Errorf("Log10(%g) = %g, want %g", vcLog10SC[i], f, log10SC[i])
   701  		}
   702  	}
   703  }
   704  func TestPolar(t *testing.T) {
   705  	for i := 0; i < len(vc); i++ {
   706  		if r, theta := Polar(vc[i]); !veryclose(polar[i].r, r) && !veryclose(polar[i].theta, theta) {
   707  			t.Errorf("Polar(%g) = %g, %g want %g, %g", vc[i], r, theta, polar[i].r, polar[i].theta)
   708  		}
   709  	}
   710  	for i := 0; i < len(vcPolarSC); i++ {
   711  		if r, theta := Polar(vcPolarSC[i]); !alike(polarSC[i].r, r) && !alike(polarSC[i].theta, theta) {
   712  			t.Errorf("Polar(%g) = %g, %g, want %g, %g", vcPolarSC[i], r, theta, polarSC[i].r, polarSC[i].theta)
   713  		}
   714  	}
   715  }
   716  func TestPow(t *testing.T) {
   717  	// Special cases for Pow(0, c).
   718  	var zero = complex(0, 0)
   719  	zeroPowers := [][2]complex128{
   720  		{0, 1 + 0i},
   721  		{1.5, 0 + 0i},
   722  		{-1.5, complex(math.Inf(0), 0)},
   723  		{-1.5 + 1.5i, Inf()},
   724  	}
   725  	for _, zp := range zeroPowers {
   726  		if f := Pow(zero, zp[0]); f != zp[1] {
   727  			t.Errorf("Pow(%g, %g) = %g, want %g", zero, zp[0], f, zp[1])
   728  		}
   729  	}
   730  	var a = complex(3.0, 3.0)
   731  	for i := 0; i < len(vc); i++ {
   732  		if f := Pow(a, vc[i]); !cSoclose(pow[i], f, 4e-15) {
   733  			t.Errorf("Pow(%g, %g) = %g, want %g", a, vc[i], f, pow[i])
   734  		}
   735  	}
   736  	for i := 0; i < len(vcPowSC); i++ {
   737  		if f := Pow(vcPowSC[i][0], vcPowSC[i][0]); !cAlike(powSC[i], f) {
   738  			t.Errorf("Pow(%g, %g) = %g, want %g", vcPowSC[i][0], vcPowSC[i][0], f, powSC[i])
   739  		}
   740  	}
   741  	for _, pt := range branchPoints {
   742  		if f0, f1 := Pow(pt[0], 0.1), Pow(pt[1], 0.1); !cVeryclose(f0, f1) {
   743  			t.Errorf("Pow(%g, 0.1) not continuous, got %g want %g", pt[0], f0, f1)
   744  		}
   745  	}
   746  }
   747  func TestRect(t *testing.T) {
   748  	for i := 0; i < len(vc); i++ {
   749  		if f := Rect(polar[i].r, polar[i].theta); !cVeryclose(vc[i], f) {
   750  			t.Errorf("Rect(%g, %g) = %g want %g", polar[i].r, polar[i].theta, f, vc[i])
   751  		}
   752  	}
   753  	for i := 0; i < len(vcPolarSC); i++ {
   754  		if f := Rect(polarSC[i].r, polarSC[i].theta); !cAlike(vcPolarSC[i], f) {
   755  			t.Errorf("Rect(%g, %g) = %g, want %g", polarSC[i].r, polarSC[i].theta, f, vcPolarSC[i])
   756  		}
   757  	}
   758  }
   759  func TestSin(t *testing.T) {
   760  	for i := 0; i < len(vc); i++ {
   761  		if f := Sin(vc[i]); !cSoclose(sin[i], f, 2e-15) {
   762  			t.Errorf("Sin(%g) = %g, want %g", vc[i], f, sin[i])
   763  		}
   764  	}
   765  	for i := 0; i < len(vcSinSC); i++ {
   766  		if f := Sin(vcSinSC[i]); !cAlike(sinSC[i], f) {
   767  			t.Errorf("Sin(%g) = %g, want %g", vcSinSC[i], f, sinSC[i])
   768  		}
   769  	}
   770  }
   771  func TestSinh(t *testing.T) {
   772  	for i := 0; i < len(vc); i++ {
   773  		if f := Sinh(vc[i]); !cSoclose(sinh[i], f, 2e-15) {
   774  			t.Errorf("Sinh(%g) = %g, want %g", vc[i], f, sinh[i])
   775  		}
   776  	}
   777  	for i := 0; i < len(vcSinhSC); i++ {
   778  		if f := Sinh(vcSinhSC[i]); !cAlike(sinhSC[i], f) {
   779  			t.Errorf("Sinh(%g) = %g, want %g", vcSinhSC[i], f, sinhSC[i])
   780  		}
   781  	}
   782  }
   783  func TestSqrt(t *testing.T) {
   784  	for i := 0; i < len(vc); i++ {
   785  		if f := Sqrt(vc[i]); !cVeryclose(sqrt[i], f) {
   786  			t.Errorf("Sqrt(%g) = %g, want %g", vc[i], f, sqrt[i])
   787  		}
   788  	}
   789  	for i := 0; i < len(vcSqrtSC); i++ {
   790  		if f := Sqrt(vcSqrtSC[i]); !cAlike(sqrtSC[i], f) {
   791  			t.Errorf("Sqrt(%g) = %g, want %g", vcSqrtSC[i], f, sqrtSC[i])
   792  		}
   793  	}
   794  	for _, pt := range branchPoints {
   795  		if f0, f1 := Sqrt(pt[0]), Sqrt(pt[1]); !cVeryclose(f0, f1) {
   796  			t.Errorf("Sqrt(%g) not continuous, got %g want %g", pt[0], f0, f1)
   797  		}
   798  	}
   799  }
   800  func TestTan(t *testing.T) {
   801  	for i := 0; i < len(vc); i++ {
   802  		if f := Tan(vc[i]); !cSoclose(tan[i], f, 3e-15) {
   803  			t.Errorf("Tan(%g) = %g, want %g", vc[i], f, tan[i])
   804  		}
   805  	}
   806  	for i := 0; i < len(vcTanSC); i++ {
   807  		if f := Tan(vcTanSC[i]); !cAlike(tanSC[i], f) {
   808  			t.Errorf("Tan(%g) = %g, want %g", vcTanSC[i], f, tanSC[i])
   809  		}
   810  	}
   811  }
   812  func TestTanh(t *testing.T) {
   813  	for i := 0; i < len(vc); i++ {
   814  		if f := Tanh(vc[i]); !cSoclose(tanh[i], f, 2e-15) {
   815  			t.Errorf("Tanh(%g) = %g, want %g", vc[i], f, tanh[i])
   816  		}
   817  	}
   818  	for i := 0; i < len(vcTanhSC); i++ {
   819  		if f := Tanh(vcTanhSC[i]); !cAlike(tanhSC[i], f) {
   820  			t.Errorf("Tanh(%g) = %g, want %g", vcTanhSC[i], f, tanhSC[i])
   821  		}
   822  	}
   823  }
   824  
   825  // See issue 17577
   826  func TestInfiniteLoopIntanSeries(t *testing.T) {
   827  	want := Inf()
   828  	if got := Cot(0); got != want {
   829  		t.Errorf("Cot(0): got %g, want %g", got, want)
   830  	}
   831  }
   832  
   833  func BenchmarkAbs(b *testing.B) {
   834  	for i := 0; i < b.N; i++ {
   835  		Abs(complex(2.5, 3.5))
   836  	}
   837  }
   838  func BenchmarkAcos(b *testing.B) {
   839  	for i := 0; i < b.N; i++ {
   840  		Acos(complex(2.5, 3.5))
   841  	}
   842  }
   843  func BenchmarkAcosh(b *testing.B) {
   844  	for i := 0; i < b.N; i++ {
   845  		Acosh(complex(2.5, 3.5))
   846  	}
   847  }
   848  func BenchmarkAsin(b *testing.B) {
   849  	for i := 0; i < b.N; i++ {
   850  		Asin(complex(2.5, 3.5))
   851  	}
   852  }
   853  func BenchmarkAsinh(b *testing.B) {
   854  	for i := 0; i < b.N; i++ {
   855  		Asinh(complex(2.5, 3.5))
   856  	}
   857  }
   858  func BenchmarkAtan(b *testing.B) {
   859  	for i := 0; i < b.N; i++ {
   860  		Atan(complex(2.5, 3.5))
   861  	}
   862  }
   863  func BenchmarkAtanh(b *testing.B) {
   864  	for i := 0; i < b.N; i++ {
   865  		Atanh(complex(2.5, 3.5))
   866  	}
   867  }
   868  func BenchmarkConj(b *testing.B) {
   869  	for i := 0; i < b.N; i++ {
   870  		Conj(complex(2.5, 3.5))
   871  	}
   872  }
   873  func BenchmarkCos(b *testing.B) {
   874  	for i := 0; i < b.N; i++ {
   875  		Cos(complex(2.5, 3.5))
   876  	}
   877  }
   878  func BenchmarkCosh(b *testing.B) {
   879  	for i := 0; i < b.N; i++ {
   880  		Cosh(complex(2.5, 3.5))
   881  	}
   882  }
   883  func BenchmarkExp(b *testing.B) {
   884  	for i := 0; i < b.N; i++ {
   885  		Exp(complex(2.5, 3.5))
   886  	}
   887  }
   888  func BenchmarkLog(b *testing.B) {
   889  	for i := 0; i < b.N; i++ {
   890  		Log(complex(2.5, 3.5))
   891  	}
   892  }
   893  func BenchmarkLog10(b *testing.B) {
   894  	for i := 0; i < b.N; i++ {
   895  		Log10(complex(2.5, 3.5))
   896  	}
   897  }
   898  func BenchmarkPhase(b *testing.B) {
   899  	for i := 0; i < b.N; i++ {
   900  		Phase(complex(2.5, 3.5))
   901  	}
   902  }
   903  func BenchmarkPolar(b *testing.B) {
   904  	for i := 0; i < b.N; i++ {
   905  		Polar(complex(2.5, 3.5))
   906  	}
   907  }
   908  func BenchmarkPow(b *testing.B) {
   909  	for i := 0; i < b.N; i++ {
   910  		Pow(complex(2.5, 3.5), complex(2.5, 3.5))
   911  	}
   912  }
   913  func BenchmarkRect(b *testing.B) {
   914  	for i := 0; i < b.N; i++ {
   915  		Rect(2.5, 1.5)
   916  	}
   917  }
   918  func BenchmarkSin(b *testing.B) {
   919  	for i := 0; i < b.N; i++ {
   920  		Sin(complex(2.5, 3.5))
   921  	}
   922  }
   923  func BenchmarkSinh(b *testing.B) {
   924  	for i := 0; i < b.N; i++ {
   925  		Sinh(complex(2.5, 3.5))
   926  	}
   927  }
   928  func BenchmarkSqrt(b *testing.B) {
   929  	for i := 0; i < b.N; i++ {
   930  		Sqrt(complex(2.5, 3.5))
   931  	}
   932  }
   933  func BenchmarkTan(b *testing.B) {
   934  	for i := 0; i < b.N; i++ {
   935  		Tan(complex(2.5, 3.5))
   936  	}
   937  }
   938  func BenchmarkTanh(b *testing.B) {
   939  	for i := 0; i < b.N; i++ {
   940  		Tanh(complex(2.5, 3.5))
   941  	}
   942  }
   943  

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