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 5package cmplx 6 7import ( 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). 15var 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 28var 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 https://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 47var 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 60var 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} 72var 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} 84var 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} 96var 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} 108var 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} 120var 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} 132var 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} 144var 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} 156var 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} 168var 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} 180var 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} 192var 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 205type ff struct { 206 r, theta float64 207} 208 209var 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} 221var 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} 233var 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} 245var 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} 257var 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} 269var 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} 281var 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 295var vcAbsSC = []complex128{ 296 NaN(), 297} 298var absSC = []float64{ 299 math.NaN(), 300} 301var vcAcosSC = []complex128{ 302 NaN(), 303} 304var acosSC = []complex128{ 305 NaN(), 306} 307var vcAcoshSC = []complex128{ 308 NaN(), 309} 310var acoshSC = []complex128{ 311 NaN(), 312} 313var vcAsinSC = []complex128{ 314 NaN(), 315} 316var asinSC = []complex128{ 317 NaN(), 318} 319var vcAsinhSC = []complex128{ 320 NaN(), 321} 322var asinhSC = []complex128{ 323 NaN(), 324} 325var vcAtanSC = []complex128{ 326 NaN(), 327} 328var atanSC = []complex128{ 329 NaN(), 330} 331var vcAtanhSC = []complex128{ 332 NaN(), 333} 334var atanhSC = []complex128{ 335 NaN(), 336} 337var vcConjSC = []complex128{ 338 NaN(), 339} 340var conjSC = []complex128{ 341 NaN(), 342} 343var vcCosSC = []complex128{ 344 NaN(), 345} 346var cosSC = []complex128{ 347 NaN(), 348} 349var vcCoshSC = []complex128{ 350 NaN(), 351} 352var coshSC = []complex128{ 353 NaN(), 354} 355var vcExpSC = []complex128{ 356 NaN(), 357} 358var expSC = []complex128{ 359 NaN(), 360} 361var 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} 372var isNaNSC = []bool{ 373 false, 374 false, 375 false, 376 true, 377 true, 378 false, 379 false, 380 false, 381 true, 382} 383var vcLogSC = []complex128{ 384 NaN(), 385} 386var logSC = []complex128{ 387 NaN(), 388} 389var vcLog10SC = []complex128{ 390 NaN(), 391} 392var log10SC = []complex128{ 393 NaN(), 394} 395var vcPolarSC = []complex128{ 396 NaN(), 397} 398var polarSC = []ff{ 399 {math.NaN(), math.NaN()}, 400} 401var vcPowSC = [][2]complex128{ 402 {NaN(), NaN()}, 403 {0, NaN()}, 404} 405var powSC = []complex128{ 406 NaN(), 407 NaN(), 408} 409var vcSinSC = []complex128{ 410 NaN(), 411} 412var sinSC = []complex128{ 413 NaN(), 414} 415var vcSinhSC = []complex128{ 416 NaN(), 417} 418var sinhSC = []complex128{ 419 NaN(), 420} 421var vcSqrtSC = []complex128{ 422 NaN(), 423} 424var sqrtSC = []complex128{ 425 NaN(), 426} 427var vcTanSC = []complex128{ 428 NaN(), 429} 430var tanSC = []complex128{ 431 NaN(), 432} 433var vcTanhSC = []complex128{ 434 NaN(), 435} 436var tanhSC = []complex128{ 437 NaN(), 438} 439 440// branch cut continuity checks 441// points on each axis at |z| > 1 are checked for one-sided continuity from both the positive and negative side 442// all possible branch cuts for the elementary functions are at one of these points 443 444var zero = 0.0 445var eps = 1.0 / (1 << 53) 446 447var branchPoints = [][2]complex128{ 448 {complex(2.0, zero), complex(2.0, eps)}, 449 {complex(2.0, -zero), complex(2.0, -eps)}, 450 {complex(-2.0, zero), complex(-2.0, eps)}, 451 {complex(-2.0, -zero), complex(-2.0, -eps)}, 452 {complex(zero, 2.0), complex(eps, 2.0)}, 453 {complex(-zero, 2.0), complex(-eps, 2.0)}, 454 {complex(zero, -2.0), complex(eps, -2.0)}, 455 {complex(-zero, -2.0), complex(-eps, -2.0)}, 456} 457 458// functions borrowed from pkg/math/all_test.go 459func tolerance(a, b, e float64) bool { 460 d := a - b 461 if d < 0 { 462 d = -d 463 } 464 465 // note: b is correct (expected) value, a is actual value. 466 // make error tolerance a fraction of b, not a. 467 if b != 0 { 468 e = e * b 469 if e < 0 { 470 e = -e 471 } 472 } 473 return d < e 474} 475func veryclose(a, b float64) bool { return tolerance(a, b, 4e-16) } 476func alike(a, b float64) bool { 477 switch { 478 case a != a && b != b: // math.IsNaN(a) && math.IsNaN(b): 479 return true 480 case a == b: 481 return math.Signbit(a) == math.Signbit(b) 482 } 483 return false 484} 485 486func cTolerance(a, b complex128, e float64) bool { 487 d := Abs(a - b) 488 if b != 0 { 489 e = e * Abs(b) 490 if e < 0 { 491 e = -e 492 } 493 } 494 return d < e 495} 496func cSoclose(a, b complex128, e float64) bool { return cTolerance(a, b, e) } 497func cVeryclose(a, b complex128) bool { return cTolerance(a, b, 4e-16) } 498func cAlike(a, b complex128) bool { 499 switch { 500 case IsNaN(a) && IsNaN(b): 501 return true 502 case a == b: 503 return math.Signbit(real(a)) == math.Signbit(real(b)) && math.Signbit(imag(a)) == math.Signbit(imag(b)) 504 } 505 return false 506} 507 508func TestAbs(t *testing.T) { 509 for i := 0; i < len(vc); i++ { 510 if f := Abs(vc[i]); !veryclose(abs[i], f) { 511 t.Errorf("Abs(%g) = %g, want %g", vc[i], f, abs[i]) 512 } 513 } 514 for i := 0; i < len(vcAbsSC); i++ { 515 if f := Abs(vcAbsSC[i]); !alike(absSC[i], f) { 516 t.Errorf("Abs(%g) = %g, want %g", vcAbsSC[i], f, absSC[i]) 517 } 518 } 519} 520func TestAcos(t *testing.T) { 521 for i := 0; i < len(vc); i++ { 522 if f := Acos(vc[i]); !cSoclose(acos[i], f, 1e-14) { 523 t.Errorf("Acos(%g) = %g, want %g", vc[i], f, acos[i]) 524 } 525 } 526 for i := 0; i < len(vcAcosSC); i++ { 527 if f := Acos(vcAcosSC[i]); !cAlike(acosSC[i], f) { 528 t.Errorf("Acos(%g) = %g, want %g", vcAcosSC[i], f, acosSC[i]) 529 } 530 } 531 for _, pt := range branchPoints { 532 if f0, f1 := Acos(pt[0]), Acos(pt[1]); !cVeryclose(f0, f1) { 533 t.Errorf("Acos(%g) not continuous, got %g want %g", pt[0], f0, f1) 534 } 535 } 536} 537func TestAcosh(t *testing.T) { 538 for i := 0; i < len(vc); i++ { 539 if f := Acosh(vc[i]); !cSoclose(acosh[i], f, 1e-14) { 540 t.Errorf("Acosh(%g) = %g, want %g", vc[i], f, acosh[i]) 541 } 542 } 543 for i := 0; i < len(vcAcoshSC); i++ { 544 if f := Acosh(vcAcoshSC[i]); !cAlike(acoshSC[i], f) { 545 t.Errorf("Acosh(%g) = %g, want %g", vcAcoshSC[i], f, acoshSC[i]) 546 } 547 } 548 for _, pt := range branchPoints { 549 if f0, f1 := Acosh(pt[0]), Acosh(pt[1]); !cVeryclose(f0, f1) { 550 t.Errorf("Acosh(%g) not continuous, got %g want %g", pt[0], f0, f1) 551 } 552 } 553} 554func TestAsin(t *testing.T) { 555 for i := 0; i < len(vc); i++ { 556 if f := Asin(vc[i]); !cSoclose(asin[i], f, 1e-14) { 557 t.Errorf("Asin(%g) = %g, want %g", vc[i], f, asin[i]) 558 } 559 } 560 for i := 0; i < len(vcAsinSC); i++ { 561 if f := Asin(vcAsinSC[i]); !cAlike(asinSC[i], f) { 562 t.Errorf("Asin(%g) = %g, want %g", vcAsinSC[i], f, asinSC[i]) 563 } 564 } 565 for _, pt := range branchPoints { 566 if f0, f1 := Asin(pt[0]), Asin(pt[1]); !cVeryclose(f0, f1) { 567 t.Errorf("Asin(%g) not continuous, got %g want %g", pt[0], f0, f1) 568 } 569 } 570} 571func TestAsinh(t *testing.T) { 572 for i := 0; i < len(vc); i++ { 573 if f := Asinh(vc[i]); !cSoclose(asinh[i], f, 4e-15) { 574 t.Errorf("Asinh(%g) = %g, want %g", vc[i], f, asinh[i]) 575 } 576 } 577 for i := 0; i < len(vcAsinhSC); i++ { 578 if f := Asinh(vcAsinhSC[i]); !cAlike(asinhSC[i], f) { 579 t.Errorf("Asinh(%g) = %g, want %g", vcAsinhSC[i], f, asinhSC[i]) 580 } 581 } 582 for _, pt := range branchPoints { 583 if f0, f1 := Asinh(pt[0]), Asinh(pt[1]); !cVeryclose(f0, f1) { 584 t.Errorf("Asinh(%g) not continuous, got %g want %g", pt[0], f0, f1) 585 } 586 } 587} 588func TestAtan(t *testing.T) { 589 for i := 0; i < len(vc); i++ { 590 if f := Atan(vc[i]); !cVeryclose(atan[i], f) { 591 t.Errorf("Atan(%g) = %g, want %g", vc[i], f, atan[i]) 592 } 593 } 594 for i := 0; i < len(vcAtanSC); i++ { 595 if f := Atan(vcAtanSC[i]); !cAlike(atanSC[i], f) { 596 t.Errorf("Atan(%g) = %g, want %g", vcAtanSC[i], f, atanSC[i]) 597 } 598 } 599 for _, pt := range branchPoints { 600 if f0, f1 := Atan(pt[0]), Atan(pt[1]); !cVeryclose(f0, f1) { 601 t.Errorf("Atan(%g) not continuous, got %g want %g", pt[0], f0, f1) 602 } 603 } 604} 605func TestAtanh(t *testing.T) { 606 for i := 0; i < len(vc); i++ { 607 if f := Atanh(vc[i]); !cVeryclose(atanh[i], f) { 608 t.Errorf("Atanh(%g) = %g, want %g", vc[i], f, atanh[i]) 609 } 610 } 611 for i := 0; i < len(vcAtanhSC); i++ { 612 if f := Atanh(vcAtanhSC[i]); !cAlike(atanhSC[i], f) { 613 t.Errorf("Atanh(%g) = %g, want %g", vcAtanhSC[i], f, atanhSC[i]) 614 } 615 } 616 for _, pt := range branchPoints { 617 if f0, f1 := Atanh(pt[0]), Atanh(pt[1]); !cVeryclose(f0, f1) { 618 t.Errorf("Atanh(%g) not continuous, got %g want %g", pt[0], f0, f1) 619 } 620 } 621} 622func TestConj(t *testing.T) { 623 for i := 0; i < len(vc); i++ { 624 if f := Conj(vc[i]); !cVeryclose(conj[i], f) { 625 t.Errorf("Conj(%g) = %g, want %g", vc[i], f, conj[i]) 626 } 627 } 628 for i := 0; i < len(vcConjSC); i++ { 629 if f := Conj(vcConjSC[i]); !cAlike(conjSC[i], f) { 630 t.Errorf("Conj(%g) = %g, want %g", vcConjSC[i], f, conjSC[i]) 631 } 632 } 633} 634func TestCos(t *testing.T) { 635 for i := 0; i < len(vc); i++ { 636 if f := Cos(vc[i]); !cSoclose(cos[i], f, 3e-15) { 637 t.Errorf("Cos(%g) = %g, want %g", vc[i], f, cos[i]) 638 } 639 } 640 for i := 0; i < len(vcCosSC); i++ { 641 if f := Cos(vcCosSC[i]); !cAlike(cosSC[i], f) { 642 t.Errorf("Cos(%g) = %g, want %g", vcCosSC[i], f, cosSC[i]) 643 } 644 } 645} 646func TestCosh(t *testing.T) { 647 for i := 0; i < len(vc); i++ { 648 if f := Cosh(vc[i]); !cSoclose(cosh[i], f, 2e-15) { 649 t.Errorf("Cosh(%g) = %g, want %g", vc[i], f, cosh[i]) 650 } 651 } 652 for i := 0; i < len(vcCoshSC); i++ { 653 if f := Cosh(vcCoshSC[i]); !cAlike(coshSC[i], f) { 654 t.Errorf("Cosh(%g) = %g, want %g", vcCoshSC[i], f, coshSC[i]) 655 } 656 } 657} 658func TestExp(t *testing.T) { 659 for i := 0; i < len(vc); i++ { 660 if f := Exp(vc[i]); !cSoclose(exp[i], f, 1e-15) { 661 t.Errorf("Exp(%g) = %g, want %g", vc[i], f, exp[i]) 662 } 663 } 664 for i := 0; i < len(vcExpSC); i++ { 665 if f := Exp(vcExpSC[i]); !cAlike(expSC[i], f) { 666 t.Errorf("Exp(%g) = %g, want %g", vcExpSC[i], f, expSC[i]) 667 } 668 } 669} 670func TestIsNaN(t *testing.T) { 671 for i := 0; i < len(vcIsNaNSC); i++ { 672 if f := IsNaN(vcIsNaNSC[i]); isNaNSC[i] != f { 673 t.Errorf("IsNaN(%v) = %v, want %v", vcIsNaNSC[i], f, isNaNSC[i]) 674 } 675 } 676} 677func TestLog(t *testing.T) { 678 for i := 0; i < len(vc); i++ { 679 if f := Log(vc[i]); !cVeryclose(log[i], f) { 680 t.Errorf("Log(%g) = %g, want %g", vc[i], f, log[i]) 681 } 682 } 683 for i := 0; i < len(vcLogSC); i++ { 684 if f := Log(vcLogSC[i]); !cAlike(logSC[i], f) { 685 t.Errorf("Log(%g) = %g, want %g", vcLogSC[i], f, logSC[i]) 686 } 687 } 688 for _, pt := range branchPoints { 689 if f0, f1 := Log(pt[0]), Log(pt[1]); !cVeryclose(f0, f1) { 690 t.Errorf("Log(%g) not continuous, got %g want %g", pt[0], f0, f1) 691 } 692 } 693} 694func TestLog10(t *testing.T) { 695 for i := 0; i < len(vc); i++ { 696 if f := Log10(vc[i]); !cVeryclose(log10[i], f) { 697 t.Errorf("Log10(%g) = %g, want %g", vc[i], f, log10[i]) 698 } 699 } 700 for i := 0; i < len(vcLog10SC); i++ { 701 if f := Log10(vcLog10SC[i]); !cAlike(log10SC[i], f) { 702 t.Errorf("Log10(%g) = %g, want %g", vcLog10SC[i], f, log10SC[i]) 703 } 704 } 705} 706func TestPolar(t *testing.T) { 707 for i := 0; i < len(vc); i++ { 708 if r, theta := Polar(vc[i]); !veryclose(polar[i].r, r) && !veryclose(polar[i].theta, theta) { 709 t.Errorf("Polar(%g) = %g, %g want %g, %g", vc[i], r, theta, polar[i].r, polar[i].theta) 710 } 711 } 712 for i := 0; i < len(vcPolarSC); i++ { 713 if r, theta := Polar(vcPolarSC[i]); !alike(polarSC[i].r, r) && !alike(polarSC[i].theta, theta) { 714 t.Errorf("Polar(%g) = %g, %g, want %g, %g", vcPolarSC[i], r, theta, polarSC[i].r, polarSC[i].theta) 715 } 716 } 717} 718func TestPow(t *testing.T) { 719 // Special cases for Pow(0, c). 720 var zero = complex(0, 0) 721 zeroPowers := [][2]complex128{ 722 {0, 1 + 0i}, 723 {1.5, 0 + 0i}, 724 {-1.5, complex(math.Inf(0), 0)}, 725 {-1.5 + 1.5i, Inf()}, 726 } 727 for _, zp := range zeroPowers { 728 if f := Pow(zero, zp[0]); f != zp[1] { 729 t.Errorf("Pow(%g, %g) = %g, want %g", zero, zp[0], f, zp[1]) 730 } 731 } 732 var a = complex(3.0, 3.0) 733 for i := 0; i < len(vc); i++ { 734 if f := Pow(a, vc[i]); !cSoclose(pow[i], f, 4e-15) { 735 t.Errorf("Pow(%g, %g) = %g, want %g", a, vc[i], f, pow[i]) 736 } 737 } 738 for i := 0; i < len(vcPowSC); i++ { 739 if f := Pow(vcPowSC[i][0], vcPowSC[i][1]); !cAlike(powSC[i], f) { 740 t.Errorf("Pow(%g, %g) = %g, want %g", vcPowSC[i][0], vcPowSC[i][1], f, powSC[i]) 741 } 742 } 743 for _, pt := range branchPoints { 744 if f0, f1 := Pow(pt[0], 0.1), Pow(pt[1], 0.1); !cVeryclose(f0, f1) { 745 t.Errorf("Pow(%g, 0.1) not continuous, got %g want %g", pt[0], f0, f1) 746 } 747 } 748} 749func TestRect(t *testing.T) { 750 for i := 0; i < len(vc); i++ { 751 if f := Rect(polar[i].r, polar[i].theta); !cVeryclose(vc[i], f) { 752 t.Errorf("Rect(%g, %g) = %g want %g", polar[i].r, polar[i].theta, f, vc[i]) 753 } 754 } 755 for i := 0; i < len(vcPolarSC); i++ { 756 if f := Rect(polarSC[i].r, polarSC[i].theta); !cAlike(vcPolarSC[i], f) { 757 t.Errorf("Rect(%g, %g) = %g, want %g", polarSC[i].r, polarSC[i].theta, f, vcPolarSC[i]) 758 } 759 } 760} 761func TestSin(t *testing.T) { 762 for i := 0; i < len(vc); i++ { 763 if f := Sin(vc[i]); !cSoclose(sin[i], f, 2e-15) { 764 t.Errorf("Sin(%g) = %g, want %g", vc[i], f, sin[i]) 765 } 766 } 767 for i := 0; i < len(vcSinSC); i++ { 768 if f := Sin(vcSinSC[i]); !cAlike(sinSC[i], f) { 769 t.Errorf("Sin(%g) = %g, want %g", vcSinSC[i], f, sinSC[i]) 770 } 771 } 772} 773func TestSinh(t *testing.T) { 774 for i := 0; i < len(vc); i++ { 775 if f := Sinh(vc[i]); !cSoclose(sinh[i], f, 2e-15) { 776 t.Errorf("Sinh(%g) = %g, want %g", vc[i], f, sinh[i]) 777 } 778 } 779 for i := 0; i < len(vcSinhSC); i++ { 780 if f := Sinh(vcSinhSC[i]); !cAlike(sinhSC[i], f) { 781 t.Errorf("Sinh(%g) = %g, want %g", vcSinhSC[i], f, sinhSC[i]) 782 } 783 } 784} 785func TestSqrt(t *testing.T) { 786 for i := 0; i < len(vc); i++ { 787 if f := Sqrt(vc[i]); !cVeryclose(sqrt[i], f) { 788 t.Errorf("Sqrt(%g) = %g, want %g", vc[i], f, sqrt[i]) 789 } 790 } 791 for i := 0; i < len(vcSqrtSC); i++ { 792 if f := Sqrt(vcSqrtSC[i]); !cAlike(sqrtSC[i], f) { 793 t.Errorf("Sqrt(%g) = %g, want %g", vcSqrtSC[i], f, sqrtSC[i]) 794 } 795 } 796 for _, pt := range branchPoints { 797 if f0, f1 := Sqrt(pt[0]), Sqrt(pt[1]); !cVeryclose(f0, f1) { 798 t.Errorf("Sqrt(%g) not continuous, got %g want %g", pt[0], f0, f1) 799 } 800 } 801} 802func TestTan(t *testing.T) { 803 for i := 0; i < len(vc); i++ { 804 if f := Tan(vc[i]); !cSoclose(tan[i], f, 3e-15) { 805 t.Errorf("Tan(%g) = %g, want %g", vc[i], f, tan[i]) 806 } 807 } 808 for i := 0; i < len(vcTanSC); i++ { 809 if f := Tan(vcTanSC[i]); !cAlike(tanSC[i], f) { 810 t.Errorf("Tan(%g) = %g, want %g", vcTanSC[i], f, tanSC[i]) 811 } 812 } 813} 814func TestTanh(t *testing.T) { 815 for i := 0; i < len(vc); i++ { 816 if f := Tanh(vc[i]); !cSoclose(tanh[i], f, 2e-15) { 817 t.Errorf("Tanh(%g) = %g, want %g", vc[i], f, tanh[i]) 818 } 819 } 820 for i := 0; i < len(vcTanhSC); i++ { 821 if f := Tanh(vcTanhSC[i]); !cAlike(tanhSC[i], f) { 822 t.Errorf("Tanh(%g) = %g, want %g", vcTanhSC[i], f, tanhSC[i]) 823 } 824 } 825} 826 827// See issue 17577 828func TestInfiniteLoopIntanSeries(t *testing.T) { 829 want := Inf() 830 if got := Cot(0); got != want { 831 t.Errorf("Cot(0): got %g, want %g", got, want) 832 } 833} 834 835func BenchmarkAbs(b *testing.B) { 836 for i := 0; i < b.N; i++ { 837 Abs(complex(2.5, 3.5)) 838 } 839} 840func BenchmarkAcos(b *testing.B) { 841 for i := 0; i < b.N; i++ { 842 Acos(complex(2.5, 3.5)) 843 } 844} 845func BenchmarkAcosh(b *testing.B) { 846 for i := 0; i < b.N; i++ { 847 Acosh(complex(2.5, 3.5)) 848 } 849} 850func BenchmarkAsin(b *testing.B) { 851 for i := 0; i < b.N; i++ { 852 Asin(complex(2.5, 3.5)) 853 } 854} 855func BenchmarkAsinh(b *testing.B) { 856 for i := 0; i < b.N; i++ { 857 Asinh(complex(2.5, 3.5)) 858 } 859} 860func BenchmarkAtan(b *testing.B) { 861 for i := 0; i < b.N; i++ { 862 Atan(complex(2.5, 3.5)) 863 } 864} 865func BenchmarkAtanh(b *testing.B) { 866 for i := 0; i < b.N; i++ { 867 Atanh(complex(2.5, 3.5)) 868 } 869} 870func BenchmarkConj(b *testing.B) { 871 for i := 0; i < b.N; i++ { 872 Conj(complex(2.5, 3.5)) 873 } 874} 875func BenchmarkCos(b *testing.B) { 876 for i := 0; i < b.N; i++ { 877 Cos(complex(2.5, 3.5)) 878 } 879} 880func BenchmarkCosh(b *testing.B) { 881 for i := 0; i < b.N; i++ { 882 Cosh(complex(2.5, 3.5)) 883 } 884} 885func BenchmarkExp(b *testing.B) { 886 for i := 0; i < b.N; i++ { 887 Exp(complex(2.5, 3.5)) 888 } 889} 890func BenchmarkLog(b *testing.B) { 891 for i := 0; i < b.N; i++ { 892 Log(complex(2.5, 3.5)) 893 } 894} 895func BenchmarkLog10(b *testing.B) { 896 for i := 0; i < b.N; i++ { 897 Log10(complex(2.5, 3.5)) 898 } 899} 900func BenchmarkPhase(b *testing.B) { 901 for i := 0; i < b.N; i++ { 902 Phase(complex(2.5, 3.5)) 903 } 904} 905func BenchmarkPolar(b *testing.B) { 906 for i := 0; i < b.N; i++ { 907 Polar(complex(2.5, 3.5)) 908 } 909} 910func BenchmarkPow(b *testing.B) { 911 for i := 0; i < b.N; i++ { 912 Pow(complex(2.5, 3.5), complex(2.5, 3.5)) 913 } 914} 915func BenchmarkRect(b *testing.B) { 916 for i := 0; i < b.N; i++ { 917 Rect(2.5, 1.5) 918 } 919} 920func BenchmarkSin(b *testing.B) { 921 for i := 0; i < b.N; i++ { 922 Sin(complex(2.5, 3.5)) 923 } 924} 925func BenchmarkSinh(b *testing.B) { 926 for i := 0; i < b.N; i++ { 927 Sinh(complex(2.5, 3.5)) 928 } 929} 930func BenchmarkSqrt(b *testing.B) { 931 for i := 0; i < b.N; i++ { 932 Sqrt(complex(2.5, 3.5)) 933 } 934} 935func BenchmarkTan(b *testing.B) { 936 for i := 0; i < b.N; i++ { 937 Tan(complex(2.5, 3.5)) 938 } 939} 940func BenchmarkTanh(b *testing.B) { 941 for i := 0; i < b.N; i++ { 942 Tanh(complex(2.5, 3.5)) 943 } 944} 945