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-rw-r--r--src/math/cmplx/cmath_test.go1589
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diff --git a/src/math/cmplx/cmath_test.go b/src/math/cmplx/cmath_test.go
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+++ b/src/math/cmplx/cmath_test.go
@@ -0,0 +1,1589 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cmplx
+
+import (
+ "math"
+ "testing"
+)
+
+// The higher-precision values in vc26 were used to derive the
+// input arguments vc (see also comment below). For reference
+// only (do not delete).
+var vc26 = []complex128{
+ (4.97901192488367350108546816 + 7.73887247457810456552351752i),
+ (7.73887247457810456552351752 - 0.27688005719200159404635997i),
+ (-0.27688005719200159404635997 - 5.01060361827107492160848778i),
+ (-5.01060361827107492160848778 + 9.63629370719841737980004837i),
+ (9.63629370719841737980004837 + 2.92637723924396464525443662i),
+ (2.92637723924396464525443662 + 5.22908343145930665230025625i),
+ (5.22908343145930665230025625 + 2.72793991043601025126008608i),
+ (2.72793991043601025126008608 + 1.82530809168085506044576505i),
+ (1.82530809168085506044576505 - 8.68592476857560136238589621i),
+ (-8.68592476857560136238589621 + 4.97901192488367350108546816i),
+}
+
+var vc = []complex128{
+ (4.9790119248836735e+00 + 7.7388724745781045e+00i),
+ (7.7388724745781045e+00 - 2.7688005719200159e-01i),
+ (-2.7688005719200159e-01 - 5.0106036182710749e+00i),
+ (-5.0106036182710749e+00 + 9.6362937071984173e+00i),
+ (9.6362937071984173e+00 + 2.9263772392439646e+00i),
+ (2.9263772392439646e+00 + 5.2290834314593066e+00i),
+ (5.2290834314593066e+00 + 2.7279399104360102e+00i),
+ (2.7279399104360102e+00 + 1.8253080916808550e+00i),
+ (1.8253080916808550e+00 - 8.6859247685756013e+00i),
+ (-8.6859247685756013e+00 + 4.9790119248836735e+00i),
+}
+
+// The expected results below were computed by the high precision calculators
+// at https://keisan.casio.com/. More exact input values (array vc[], above)
+// were obtained by printing them with "%.26f". The answers were calculated
+// to 26 digits (by using the "Digit number" drop-down control of each
+// calculator).
+
+var abs = []float64{
+ 9.2022120669932650313380972e+00,
+ 7.7438239742296106616261394e+00,
+ 5.0182478202557746902556648e+00,
+ 1.0861137372799545160704002e+01,
+ 1.0070841084922199607011905e+01,
+ 5.9922447613166942183705192e+00,
+ 5.8978784056736762299945176e+00,
+ 3.2822866700678709020367184e+00,
+ 8.8756430028990417290744307e+00,
+ 1.0011785496777731986390856e+01,
+}
+
+var acos = []complex128{
+ (1.0017679804707456328694569 - 2.9138232718554953784519807i),
+ (0.03606427612041407369636057 + 2.7358584434576260925091256i),
+ (1.6249365462333796703711823 + 2.3159537454335901187730929i),
+ (2.0485650849650740120660391 - 3.0795576791204117911123886i),
+ (0.29621132089073067282488147 - 3.0007392508200622519398814i),
+ (1.0664555914934156601503632 - 2.4872865024796011364747111i),
+ (0.48681307452231387690013905 - 2.463655912283054555225301i),
+ (0.6116977071277574248407752 - 1.8734458851737055262693056i),
+ (1.3649311280370181331184214 + 2.8793528632328795424123832i),
+ (2.6189310485682988308904501 - 2.9956543302898767795858704i),
+}
+var acosh = []complex128{
+ (2.9138232718554953784519807 + 1.0017679804707456328694569i),
+ (2.7358584434576260925091256 - 0.03606427612041407369636057i),
+ (2.3159537454335901187730929 - 1.6249365462333796703711823i),
+ (3.0795576791204117911123886 + 2.0485650849650740120660391i),
+ (3.0007392508200622519398814 + 0.29621132089073067282488147i),
+ (2.4872865024796011364747111 + 1.0664555914934156601503632i),
+ (2.463655912283054555225301 + 0.48681307452231387690013905i),
+ (1.8734458851737055262693056 + 0.6116977071277574248407752i),
+ (2.8793528632328795424123832 - 1.3649311280370181331184214i),
+ (2.9956543302898767795858704 + 2.6189310485682988308904501i),
+}
+var asin = []complex128{
+ (0.56902834632415098636186476 + 2.9138232718554953784519807i),
+ (1.5347320506744825455349611 - 2.7358584434576260925091256i),
+ (-0.054140219438483051139860579 - 2.3159537454335901187730929i),
+ (-0.47776875817017739283471738 + 3.0795576791204117911123886i),
+ (1.2745850059041659464064402 + 3.0007392508200622519398814i),
+ (0.50434073530148095908095852 + 2.4872865024796011364747111i),
+ (1.0839832522725827423311826 + 2.463655912283054555225301i),
+ (0.9590986196671391943905465 + 1.8734458851737055262693056i),
+ (0.20586519875787848611290031 - 2.8793528632328795424123832i),
+ (-1.0481347217734022116591284 + 2.9956543302898767795858704i),
+}
+var asinh = []complex128{
+ (2.9113760469415295679342185 + 0.99639459545704326759805893i),
+ (2.7441755423994259061579029 - 0.035468308789000500601119392i),
+ (-2.2962136462520690506126678 - 1.5144663565690151885726707i),
+ (-3.0771233459295725965402455 + 1.0895577967194013849422294i),
+ (3.0048366100923647417557027 + 0.29346979169819220036454168i),
+ (2.4800059370795363157364643 + 1.0545868606049165710424232i),
+ (2.4718773838309585611141821 + 0.47502344364250803363708842i),
+ (1.8910743588080159144378396 + 0.56882925572563602341139174i),
+ (2.8735426423367341878069406 - 1.362376149648891420997548i),
+ (-2.9981750586172477217567878 + 0.5183571985225367505624207i),
+}
+var atan = []complex128{
+ (1.5115747079332741358607654 + 0.091324403603954494382276776i),
+ (1.4424504323482602560806727 - 0.0045416132642803911503770933i),
+ (-1.5593488703630532674484026 - 0.20163295409248362456446431i),
+ (-1.5280619472445889867794105 + 0.081721556230672003746956324i),
+ (1.4759909163240799678221039 + 0.028602969320691644358773586i),
+ (1.4877353772046548932715555 + 0.14566877153207281663773599i),
+ (1.4206983927779191889826 + 0.076830486127880702249439993i),
+ (1.3162236060498933364869556 + 0.16031313000467530644933363i),
+ (1.5473450684303703578810093 - 0.11064907507939082484935782i),
+ (-1.4841462340185253987375812 + 0.049341850305024399493142411i),
+}
+var atanh = []complex128{
+ (0.058375027938968509064640438 + 1.4793488495105334458167782i),
+ (0.12977343497790381229915667 - 1.5661009410463561327262499i),
+ (-0.010576456067347252072200088 - 1.3743698658402284549750563i),
+ (-0.042218595678688358882784918 + 1.4891433968166405606692604i),
+ (0.095218997991316722061828397 + 1.5416884098777110330499698i),
+ (0.079965459366890323857556487 + 1.4252510353873192700350435i),
+ (0.15051245471980726221708301 + 1.4907432533016303804884461i),
+ (0.25082072933993987714470373 + 1.392057665392187516442986i),
+ (0.022896108815797135846276662 - 1.4609224989282864208963021i),
+ (-0.08665624101841876130537396 + 1.5207902036935093480142159i),
+}
+var conj = []complex128{
+ (4.9790119248836735e+00 - 7.7388724745781045e+00i),
+ (7.7388724745781045e+00 + 2.7688005719200159e-01i),
+ (-2.7688005719200159e-01 + 5.0106036182710749e+00i),
+ (-5.0106036182710749e+00 - 9.6362937071984173e+00i),
+ (9.6362937071984173e+00 - 2.9263772392439646e+00i),
+ (2.9263772392439646e+00 - 5.2290834314593066e+00i),
+ (5.2290834314593066e+00 - 2.7279399104360102e+00i),
+ (2.7279399104360102e+00 - 1.8253080916808550e+00i),
+ (1.8253080916808550e+00 + 8.6859247685756013e+00i),
+ (-8.6859247685756013e+00 - 4.9790119248836735e+00i),
+}
+var cos = []complex128{
+ (3.024540920601483938336569e+02 + 1.1073797572517071650045357e+03i),
+ (1.192858682649064973252758e-01 + 2.7857554122333065540970207e-01i),
+ (7.2144394304528306603857962e+01 - 2.0500129667076044169954205e+01i),
+ (2.24921952538403984190541e+03 - 7.317363745602773587049329e+03i),
+ (-9.148222970032421760015498e+00 + 1.953124661113563541862227e+00i),
+ (-9.116081175857732248227078e+01 - 1.992669213569952232487371e+01i),
+ (3.795639179042704640002918e+00 + 6.623513350981458399309662e+00i),
+ (-2.9144840732498869560679084e+00 - 1.214620271628002917638748e+00i),
+ (-7.45123482501299743872481e+02 + 2.8641692314488080814066734e+03i),
+ (-5.371977967039319076416747e+01 + 4.893348341339375830564624e+01i),
+}
+var cosh = []complex128{
+ (8.34638383523018249366948e+00 + 7.2181057886425846415112064e+01i),
+ (1.10421967379919366952251e+03 - 3.1379638689277575379469861e+02i),
+ (3.051485206773701584738512e-01 - 2.6805384730105297848044485e-01i),
+ (-7.33294728684187933370938e+01 + 1.574445942284918251038144e+01i),
+ (-7.478643293945957535757355e+03 + 1.6348382209913353929473321e+03i),
+ (4.622316522966235701630926e+00 - 8.088695185566375256093098e+00i),
+ (-8.544333183278877406197712e+01 + 3.7505836120128166455231717e+01i),
+ (-1.934457815021493925115198e+00 + 7.3725859611767228178358673e+00i),
+ (-2.352958770061749348353548e+00 - 2.034982010440878358915409e+00i),
+ (7.79756457532134748165069e+02 + 2.8549350716819176560377717e+03i),
+}
+var exp = []complex128{
+ (1.669197736864670815125146e+01 + 1.4436895109507663689174096e+02i),
+ (2.2084389286252583447276212e+03 - 6.2759289284909211238261917e+02i),
+ (2.227538273122775173434327e-01 + 7.2468284028334191250470034e-01i),
+ (-6.5182985958153548997881627e-03 - 1.39965837915193860879044e-03i),
+ (-1.4957286524084015746110777e+04 + 3.269676455931135688988042e+03i),
+ (9.218158701983105935659273e+00 - 1.6223985291084956009304582e+01i),
+ (-1.7088175716853040841444505e+02 + 7.501382609870410713795546e+01i),
+ (-3.852461315830959613132505e+00 + 1.4808420423156073221970892e+01i),
+ (-4.586775503301407379786695e+00 - 4.178501081246873415144744e+00i),
+ (4.451337963005453491095747e-05 - 1.62977574205442915935263e-04i),
+}
+var log = []complex128{
+ (2.2194438972179194425697051e+00 + 9.9909115046919291062461269e-01i),
+ (2.0468956191154167256337289e+00 - 3.5762575021856971295156489e-02i),
+ (1.6130808329853860438751244e+00 - 1.6259990074019058442232221e+00i),
+ (2.3851910394823008710032651e+00 + 2.0502936359659111755031062e+00i),
+ (2.3096442270679923004800651e+00 + 2.9483213155446756211881774e-01i),
+ (1.7904660933974656106951860e+00 + 1.0605860367252556281902109e+00i),
+ (1.7745926939841751666177512e+00 + 4.8084556083358307819310911e-01i),
+ (1.1885403350045342425648780e+00 + 5.8969634164776659423195222e-01i),
+ (2.1833107837679082586772505e+00 - 1.3636647724582455028314573e+00i),
+ (2.3037629487273259170991671e+00 + 2.6210913895386013290915234e+00i),
+}
+var log10 = []complex128{
+ (9.6389223745559042474184943e-01 + 4.338997735671419492599631e-01i),
+ (8.8895547241376579493490892e-01 - 1.5531488990643548254864806e-02i),
+ (7.0055210462945412305244578e-01 - 7.0616239649481243222248404e-01i),
+ (1.0358753067322445311676952e+00 + 8.9043121238134980156490909e-01i),
+ (1.003065742975330237172029e+00 + 1.2804396782187887479857811e-01i),
+ (7.7758954439739162532085157e-01 + 4.6060666333341810869055108e-01i),
+ (7.7069581462315327037689152e-01 + 2.0882857371769952195512475e-01i),
+ (5.1617650901191156135137239e-01 + 2.5610186717615977620363299e-01i),
+ (9.4819982567026639742663212e-01 - 5.9223208584446952284914289e-01i),
+ (1.0005115362454417135973429e+00 + 1.1383255270407412817250921e+00i),
+}
+
+type ff struct {
+ r, theta float64
+}
+
+var polar = []ff{
+ {9.2022120669932650313380972e+00, 9.9909115046919291062461269e-01},
+ {7.7438239742296106616261394e+00, -3.5762575021856971295156489e-02},
+ {5.0182478202557746902556648e+00, -1.6259990074019058442232221e+00},
+ {1.0861137372799545160704002e+01, 2.0502936359659111755031062e+00},
+ {1.0070841084922199607011905e+01, 2.9483213155446756211881774e-01},
+ {5.9922447613166942183705192e+00, 1.0605860367252556281902109e+00},
+ {5.8978784056736762299945176e+00, 4.8084556083358307819310911e-01},
+ {3.2822866700678709020367184e+00, 5.8969634164776659423195222e-01},
+ {8.8756430028990417290744307e+00, -1.3636647724582455028314573e+00},
+ {1.0011785496777731986390856e+01, 2.6210913895386013290915234e+00},
+}
+var pow = []complex128{
+ (-2.499956739197529585028819e+00 + 1.759751724335650228957144e+00i),
+ (7.357094338218116311191939e+04 - 5.089973412479151648145882e+04i),
+ (1.320777296067768517259592e+01 - 3.165621914333901498921986e+01i),
+ (-3.123287828297300934072149e-07 - 1.9849567521490553032502223e-7i),
+ (8.0622651468477229614813e+04 - 7.80028727944573092944363e+04i),
+ (-1.0268824572103165858577141e+00 - 4.716844738244989776610672e-01i),
+ (-4.35953819012244175753187e+01 + 2.2036445974645306917648585e+02i),
+ (8.3556092283250594950239e-01 - 1.2261571947167240272593282e+01i),
+ (1.582292972120769306069625e+03 + 1.273564263524278244782512e+04i),
+ (6.592208301642122149025369e-08 + 2.584887236651661903526389e-08i),
+}
+var sin = []complex128{
+ (-1.1073801774240233539648544e+03 + 3.024539773002502192425231e+02i),
+ (1.0317037521400759359744682e+00 - 3.2208979799929570242818e-02i),
+ (-2.0501952097271429804261058e+01 - 7.2137981348240798841800967e+01i),
+ (7.3173638080346338642193078e+03 + 2.249219506193664342566248e+03i),
+ (-1.964375633631808177565226e+00 - 9.0958264713870404464159683e+00i),
+ (1.992783647158514838337674e+01 - 9.11555769410191350416942e+01i),
+ (-6.680335650741921444300349e+00 + 3.763353833142432513086117e+00i),
+ (1.2794028166657459148245993e+00 - 2.7669092099795781155109602e+00i),
+ (2.8641693949535259594188879e+03 + 7.451234399649871202841615e+02i),
+ (-4.893811726244659135553033e+01 - 5.371469305562194635957655e+01i),
+}
+var sinh = []complex128{
+ (8.34559353341652565758198e+00 + 7.2187893208650790476628899e+01i),
+ (1.1042192548260646752051112e+03 - 3.1379650595631635858792056e+02i),
+ (-8.239469336509264113041849e-02 + 9.9273668758439489098514519e-01i),
+ (7.332295456982297798219401e+01 - 1.574585908122833444899023e+01i),
+ (-7.4786432301380582103534216e+03 + 1.63483823493980029604071e+03i),
+ (4.595842179016870234028347e+00 - 8.135290105518580753211484e+00i),
+ (-8.543842533574163435246793e+01 + 3.750798997857594068272375e+01i),
+ (-1.918003500809465688017307e+00 + 7.4358344619793504041350251e+00i),
+ (-2.233816733239658031433147e+00 - 2.143519070805995056229335e+00i),
+ (-7.797564130187551181105341e+02 - 2.8549352346594918614806877e+03i),
+}
+var sqrt = []complex128{
+ (2.6628203086086130543813948e+00 + 1.4531345674282185229796902e+00i),
+ (2.7823278427251986247149295e+00 - 4.9756907317005224529115567e-02i),
+ (1.5397025302089642757361015e+00 - 1.6271336573016637535695727e+00i),
+ (1.7103411581506875260277898e+00 + 2.8170677122737589676157029e+00i),
+ (3.1390392472953103383607947e+00 + 4.6612625849858653248980849e-01i),
+ (2.1117080764822417640789287e+00 + 1.2381170223514273234967850e+00i),
+ (2.3587032281672256703926939e+00 + 5.7827111903257349935720172e-01i),
+ (1.7335262588873410476661577e+00 + 5.2647258220721269141550382e-01i),
+ (2.3131094974708716531499282e+00 - 1.8775429304303785570775490e+00i),
+ (8.1420535745048086240947359e-01 + 3.0575897587277248522656113e+00i),
+}
+var tan = []complex128{
+ (-1.928757919086441129134525e-07 + 1.0000003267499169073251826e+00i),
+ (1.242412685364183792138948e+00 - 3.17149693883133370106696e+00i),
+ (-4.6745126251587795225571826e-05 - 9.9992439225263959286114298e-01i),
+ (4.792363401193648192887116e-09 + 1.0000000070589333451557723e+00i),
+ (2.345740824080089140287315e-03 + 9.947733046570988661022763e-01i),
+ (-2.396030789494815566088809e-05 + 9.9994781345418591429826779e-01i),
+ (-7.370204836644931340905303e-03 + 1.0043553413417138987717748e+00i),
+ (-3.691803847992048527007457e-02 + 9.6475071993469548066328894e-01i),
+ (-2.781955256713729368401878e-08 - 1.000000049848910609006646e+00i),
+ (9.4281590064030478879791249e-05 + 9.9999119340863718183758545e-01i),
+}
+var tanh = []complex128{
+ (1.0000921981225144748819918e+00 + 2.160986245871518020231507e-05i),
+ (9.9999967727531993209562591e-01 - 1.9953763222959658873657676e-07i),
+ (-1.765485739548037260789686e+00 + 1.7024216325552852445168471e+00i),
+ (-9.999189442732736452807108e-01 + 3.64906070494473701938098e-05i),
+ (9.9999999224622333738729767e-01 - 3.560088949517914774813046e-09i),
+ (1.0029324933367326862499343e+00 - 4.948790309797102353137528e-03i),
+ (9.9996113064788012488693567e-01 - 4.226995742097032481451259e-05i),
+ (1.0074784189316340029873945e+00 - 4.194050814891697808029407e-03i),
+ (9.9385534229718327109131502e-01 + 5.144217985914355502713437e-02i),
+ (-1.0000000491604982429364892e+00 - 2.901873195374433112227349e-08i),
+}
+
+// huge values along the real axis for testing reducePi in Tan
+var hugeIn = []complex128{
+ 1 << 28,
+ 1 << 29,
+ 1 << 30,
+ 1 << 35,
+ -1 << 120,
+ 1 << 240,
+ 1 << 300,
+ -1 << 480,
+ 1234567891234567 << 180,
+ -1234567891234567 << 300,
+}
+
+// Results for tanHuge[i] calculated with https://github.com/robpike/ivy
+// using 4096 bits of working precision.
+var tanHuge = []complex128{
+ 5.95641897939639421,
+ -0.34551069233430392,
+ -0.78469661331920043,
+ 0.84276385870875983,
+ 0.40806638884180424,
+ -0.37603456702698076,
+ 4.60901287677810962,
+ 3.39135965054779932,
+ -6.76813854009065030,
+ -0.76417695016604922,
+}
+
+// special cases conform to C99 standard appendix G.6 Complex arithmetic
+var inf, nan = math.Inf(1), math.NaN()
+
+var vcAbsSC = []complex128{
+ NaN(),
+}
+var absSC = []float64{
+ math.NaN(),
+}
+var acosSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.1.1
+ {complex(zero, zero),
+ complex(math.Pi/2, -zero)},
+ {complex(-zero, zero),
+ complex(math.Pi/2, -zero)},
+ {complex(zero, nan),
+ complex(math.Pi/2, nan)},
+ {complex(-zero, nan),
+ complex(math.Pi/2, nan)},
+ {complex(1.0, inf),
+ complex(math.Pi/2, -inf)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(-inf, 1.0),
+ complex(math.Pi, -inf)},
+ {complex(inf, 1.0),
+ complex(0.0, -inf)},
+ {complex(-inf, inf),
+ complex(3*math.Pi/4, -inf)},
+ {complex(inf, inf),
+ complex(math.Pi/4, -inf)},
+ {complex(inf, nan),
+ complex(nan, -inf)}, // imaginary sign unspecified
+ {complex(-inf, nan),
+ complex(nan, inf)}, // imaginary sign unspecified
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ complex(nan, -inf)},
+ {NaN(),
+ NaN()},
+}
+var acoshSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.2.1
+ {complex(zero, zero),
+ complex(zero, math.Pi/2)},
+ {complex(-zero, zero),
+ complex(zero, math.Pi/2)},
+ {complex(1.0, inf),
+ complex(inf, math.Pi/2)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(-inf, 1.0),
+ complex(inf, math.Pi)},
+ {complex(inf, 1.0),
+ complex(inf, zero)},
+ {complex(-inf, inf),
+ complex(inf, 3*math.Pi/4)},
+ {complex(inf, inf),
+ complex(inf, math.Pi/4)},
+ {complex(inf, nan),
+ complex(inf, nan)},
+ {complex(-inf, nan),
+ complex(inf, nan)},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ complex(inf, nan)},
+ {NaN(),
+ NaN()},
+}
+var asinSC = []struct {
+ in,
+ want complex128
+}{
+ // Derived from Asin(z) = -i * Asinh(i * z), G.6 #7
+ {complex(zero, zero),
+ complex(zero, zero)},
+ {complex(1.0, inf),
+ complex(0, inf)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, 1),
+ complex(math.Pi/2, inf)},
+ {complex(inf, inf),
+ complex(math.Pi/4, inf)},
+ {complex(inf, nan),
+ complex(nan, inf)}, // imaginary sign unspecified
+ {complex(nan, zero),
+ NaN()},
+ {complex(nan, 1),
+ NaN()},
+ {complex(nan, inf),
+ complex(nan, inf)},
+ {NaN(),
+ NaN()},
+}
+var asinhSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.2.2
+ {complex(zero, zero),
+ complex(zero, zero)},
+ {complex(1.0, inf),
+ complex(inf, math.Pi/2)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, 1.0),
+ complex(inf, zero)},
+ {complex(inf, inf),
+ complex(inf, math.Pi/4)},
+ {complex(inf, nan),
+ complex(inf, nan)},
+ {complex(nan, zero),
+ complex(nan, zero)},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ complex(inf, nan)}, // sign of real part unspecified
+ {NaN(),
+ NaN()},
+}
+var atanSC = []struct {
+ in,
+ want complex128
+}{
+ // Derived from Atan(z) = -i * Atanh(i * z), G.6 #7
+ {complex(0, zero),
+ complex(0, zero)},
+ {complex(0, nan),
+ NaN()},
+ {complex(1.0, zero),
+ complex(math.Pi/4, zero)},
+ {complex(1.0, inf),
+ complex(math.Pi/2, zero)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, 1),
+ complex(math.Pi/2, zero)},
+ {complex(inf, inf),
+ complex(math.Pi/2, zero)},
+ {complex(inf, nan),
+ complex(math.Pi/2, zero)},
+ {complex(nan, 1),
+ NaN()},
+ {complex(nan, inf),
+ complex(nan, zero)},
+ {NaN(),
+ NaN()},
+}
+var atanhSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.2.3
+ {complex(zero, zero),
+ complex(zero, zero)},
+ {complex(zero, nan),
+ complex(zero, nan)},
+ {complex(1.0, zero),
+ complex(inf, zero)},
+ {complex(1.0, inf),
+ complex(0, math.Pi/2)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, 1.0),
+ complex(zero, math.Pi/2)},
+ {complex(inf, inf),
+ complex(zero, math.Pi/2)},
+ {complex(inf, nan),
+ complex(0, nan)},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ complex(zero, math.Pi/2)}, // sign of real part not specified.
+ {NaN(),
+ NaN()},
+}
+var vcConjSC = []complex128{
+ NaN(),
+}
+var conjSC = []complex128{
+ NaN(),
+}
+var cosSC = []struct {
+ in,
+ want complex128
+}{
+ // Derived from Cos(z) = Cosh(i * z), G.6 #7
+ {complex(zero, zero),
+ complex(1.0, -zero)},
+ {complex(zero, inf),
+ complex(inf, -zero)},
+ {complex(zero, nan),
+ complex(nan, zero)}, // imaginary sign unspecified
+ {complex(1.0, inf),
+ complex(inf, -inf)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, zero),
+ complex(nan, -zero)},
+ {complex(inf, 1.0),
+ NaN()},
+ {complex(inf, inf),
+ complex(inf, nan)}, // real sign unspecified
+ {complex(inf, nan),
+ NaN()},
+ {complex(nan, zero),
+ complex(nan, -zero)}, // imaginary sign unspecified
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ complex(inf, nan)},
+ {NaN(),
+ NaN()},
+}
+var coshSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.2.4
+ {complex(zero, zero),
+ complex(1.0, zero)},
+ {complex(zero, inf),
+ complex(nan, zero)}, // imaginary sign unspecified
+ {complex(zero, nan),
+ complex(nan, zero)}, // imaginary sign unspecified
+ {complex(1.0, inf),
+ NaN()},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, zero),
+ complex(inf, zero)},
+ {complex(inf, 1.0),
+ complex(inf*math.Cos(1.0), inf*math.Sin(1.0))}, // +inf cis(y)
+ {complex(inf, inf),
+ complex(inf, nan)}, // real sign unspecified
+ {complex(inf, nan),
+ complex(inf, nan)},
+ {complex(nan, zero),
+ complex(nan, zero)}, // imaginary sign unspecified
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ NaN()},
+ {NaN(),
+ NaN()},
+}
+var expSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.3.1
+ {complex(zero, zero),
+ complex(1.0, zero)},
+ {complex(-zero, zero),
+ complex(1.0, zero)},
+ {complex(1.0, inf),
+ NaN()},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, zero),
+ complex(inf, zero)},
+ {complex(-inf, 1.0),
+ complex(math.Copysign(0.0, math.Cos(1.0)), math.Copysign(0.0, math.Sin(1.0)))}, // +0 cis(y)
+ {complex(inf, 1.0),
+ complex(inf*math.Cos(1.0), inf*math.Sin(1.0))}, // +inf cis(y)
+ {complex(-inf, inf),
+ complex(zero, zero)}, // real and imaginary sign unspecified
+ {complex(inf, inf),
+ complex(inf, nan)}, // real sign unspecified
+ {complex(-inf, nan),
+ complex(zero, zero)}, // real and imaginary sign unspecified
+ {complex(inf, nan),
+ complex(inf, nan)}, // real sign unspecified
+ {complex(nan, zero),
+ complex(nan, zero)},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ NaN()},
+ {NaN(),
+ NaN()},
+}
+var vcIsNaNSC = []complex128{
+ complex(math.Inf(-1), math.Inf(-1)),
+ complex(math.Inf(-1), math.NaN()),
+ complex(math.NaN(), math.Inf(-1)),
+ complex(0, math.NaN()),
+ complex(math.NaN(), 0),
+ complex(math.Inf(1), math.Inf(1)),
+ complex(math.Inf(1), math.NaN()),
+ complex(math.NaN(), math.Inf(1)),
+ complex(math.NaN(), math.NaN()),
+}
+var isNaNSC = []bool{
+ false,
+ false,
+ false,
+ true,
+ true,
+ false,
+ false,
+ false,
+ true,
+}
+
+var logSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.3.2
+ {complex(zero, zero),
+ complex(-inf, zero)},
+ {complex(-zero, zero),
+ complex(-inf, math.Pi)},
+ {complex(1.0, inf),
+ complex(inf, math.Pi/2)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(-inf, 1.0),
+ complex(inf, math.Pi)},
+ {complex(inf, 1.0),
+ complex(inf, 0.0)},
+ {complex(-inf, inf),
+ complex(inf, 3*math.Pi/4)},
+ {complex(inf, inf),
+ complex(inf, math.Pi/4)},
+ {complex(-inf, nan),
+ complex(inf, nan)},
+ {complex(inf, nan),
+ complex(inf, nan)},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ complex(inf, nan)},
+ {NaN(),
+ NaN()},
+}
+var log10SC = []struct {
+ in,
+ want complex128
+}{
+ // derived from Log special cases via Log10(x) = math.Log10E*Log(x)
+ {complex(zero, zero),
+ complex(-inf, zero)},
+ {complex(-zero, zero),
+ complex(-inf, float64(math.Log10E)*float64(math.Pi))},
+ {complex(1.0, inf),
+ complex(inf, float64(math.Log10E)*float64(math.Pi/2))},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(-inf, 1.0),
+ complex(inf, float64(math.Log10E)*float64(math.Pi))},
+ {complex(inf, 1.0),
+ complex(inf, 0.0)},
+ {complex(-inf, inf),
+ complex(inf, float64(math.Log10E)*float64(3*math.Pi/4))},
+ {complex(inf, inf),
+ complex(inf, float64(math.Log10E)*float64(math.Pi/4))},
+ {complex(-inf, nan),
+ complex(inf, nan)},
+ {complex(inf, nan),
+ complex(inf, nan)},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ complex(inf, nan)},
+ {NaN(),
+ NaN()},
+}
+var vcPolarSC = []complex128{
+ NaN(),
+}
+var polarSC = []ff{
+ {math.NaN(), math.NaN()},
+}
+var vcPowSC = [][2]complex128{
+ {NaN(), NaN()},
+ {0, NaN()},
+}
+var powSC = []complex128{
+ NaN(),
+ NaN(),
+}
+var sinSC = []struct {
+ in,
+ want complex128
+}{
+ // Derived from Sin(z) = -i * Sinh(i * z), G.6 #7
+ {complex(zero, zero),
+ complex(zero, zero)},
+ {complex(zero, inf),
+ complex(zero, inf)},
+ {complex(zero, nan),
+ complex(zero, nan)},
+ {complex(1.0, inf),
+ complex(inf, inf)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, zero),
+ complex(nan, zero)},
+ {complex(inf, 1.0),
+ NaN()},
+ {complex(inf, inf),
+ complex(nan, inf)},
+ {complex(inf, nan),
+ NaN()},
+ {complex(nan, zero),
+ complex(nan, zero)},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ complex(nan, inf)},
+ {NaN(),
+ NaN()},
+}
+
+var sinhSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.2.5
+ {complex(zero, zero),
+ complex(zero, zero)},
+ {complex(zero, inf),
+ complex(zero, nan)}, // real sign unspecified
+ {complex(zero, nan),
+ complex(zero, nan)}, // real sign unspecified
+ {complex(1.0, inf),
+ NaN()},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, zero),
+ complex(inf, zero)},
+ {complex(inf, 1.0),
+ complex(inf*math.Cos(1.0), inf*math.Sin(1.0))}, // +inf cis(y)
+ {complex(inf, inf),
+ complex(inf, nan)}, // real sign unspecified
+ {complex(inf, nan),
+ complex(inf, nan)}, // real sign unspecified
+ {complex(nan, zero),
+ complex(nan, zero)},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ NaN()},
+ {NaN(),
+ NaN()},
+}
+
+var sqrtSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.4.2
+ {complex(zero, zero),
+ complex(zero, zero)},
+ {complex(-zero, zero),
+ complex(zero, zero)},
+ {complex(1.0, inf),
+ complex(inf, inf)},
+ {complex(nan, inf),
+ complex(inf, inf)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(-inf, 1.0),
+ complex(zero, inf)},
+ {complex(inf, 1.0),
+ complex(inf, zero)},
+ {complex(-inf, nan),
+ complex(nan, inf)}, // imaginary sign unspecified
+ {complex(inf, nan),
+ complex(inf, nan)},
+ {complex(nan, 1.0),
+ NaN()},
+ {NaN(),
+ NaN()},
+}
+var tanSC = []struct {
+ in,
+ want complex128
+}{
+ // Derived from Tan(z) = -i * Tanh(i * z), G.6 #7
+ {complex(zero, zero),
+ complex(zero, zero)},
+ {complex(zero, nan),
+ complex(zero, nan)},
+ {complex(1.0, inf),
+ complex(zero, 1.0)},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, 1.0),
+ NaN()},
+ {complex(inf, inf),
+ complex(zero, 1.0)},
+ {complex(inf, nan),
+ NaN()},
+ {complex(nan, zero),
+ NaN()},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ complex(zero, 1.0)},
+ {NaN(),
+ NaN()},
+}
+var tanhSC = []struct {
+ in,
+ want complex128
+}{
+ // G.6.2.6
+ {complex(zero, zero),
+ complex(zero, zero)},
+ {complex(1.0, inf),
+ NaN()},
+ {complex(1.0, nan),
+ NaN()},
+ {complex(inf, 1.0),
+ complex(1.0, math.Copysign(0.0, math.Sin(2*1.0)))}, // 1 + i 0 sin(2y)
+ {complex(inf, inf),
+ complex(1.0, zero)}, // imaginary sign unspecified
+ {complex(inf, nan),
+ complex(1.0, zero)}, // imaginary sign unspecified
+ {complex(nan, zero),
+ complex(nan, zero)},
+ {complex(nan, 1.0),
+ NaN()},
+ {complex(nan, inf),
+ NaN()},
+ {NaN(),
+ NaN()},
+}
+
+// branch cut continuity checks
+// points on each axis at |z| > 1 are checked for one-sided continuity from both the positive and negative side
+// all possible branch cuts for the elementary functions are at one of these points
+
+var zero = 0.0
+var eps = 1.0 / (1 << 53)
+
+var branchPoints = [][2]complex128{
+ {complex(2.0, zero), complex(2.0, eps)},
+ {complex(2.0, -zero), complex(2.0, -eps)},
+ {complex(-2.0, zero), complex(-2.0, eps)},
+ {complex(-2.0, -zero), complex(-2.0, -eps)},
+ {complex(zero, 2.0), complex(eps, 2.0)},
+ {complex(-zero, 2.0), complex(-eps, 2.0)},
+ {complex(zero, -2.0), complex(eps, -2.0)},
+ {complex(-zero, -2.0), complex(-eps, -2.0)},
+}
+
+// functions borrowed from pkg/math/all_test.go
+func tolerance(a, b, e float64) bool {
+ d := a - b
+ if d < 0 {
+ d = -d
+ }
+
+ // note: b is correct (expected) value, a is actual value.
+ // make error tolerance a fraction of b, not a.
+ if b != 0 {
+ e = e * b
+ if e < 0 {
+ e = -e
+ }
+ }
+ return d < e
+}
+func veryclose(a, b float64) bool { return tolerance(a, b, 4e-16) }
+func alike(a, b float64) bool {
+ switch {
+ case a != a && b != b: // math.IsNaN(a) && math.IsNaN(b):
+ return true
+ case a == b:
+ return math.Signbit(a) == math.Signbit(b)
+ }
+ return false
+}
+
+func cTolerance(a, b complex128, e float64) bool {
+ d := Abs(a - b)
+ if b != 0 {
+ e = e * Abs(b)
+ if e < 0 {
+ e = -e
+ }
+ }
+ return d < e
+}
+func cSoclose(a, b complex128, e float64) bool { return cTolerance(a, b, e) }
+func cVeryclose(a, b complex128) bool { return cTolerance(a, b, 4e-16) }
+func cAlike(a, b complex128) bool {
+ var realAlike, imagAlike bool
+ if isExact(real(b)) {
+ realAlike = alike(real(a), real(b))
+ } else {
+ // Allow non-exact special cases to have errors in ULP.
+ realAlike = veryclose(real(a), real(b))
+ }
+ if isExact(imag(b)) {
+ imagAlike = alike(imag(a), imag(b))
+ } else {
+ // Allow non-exact special cases to have errors in ULP.
+ imagAlike = veryclose(imag(a), imag(b))
+ }
+ return realAlike && imagAlike
+}
+func isExact(x float64) bool {
+ // Special cases that should match exactly. Other cases are multiples
+ // of Pi that may not be last bit identical on all platforms.
+ return math.IsNaN(x) || math.IsInf(x, 0) || x == 0 || x == 1 || x == -1
+}
+
+func TestAbs(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Abs(vc[i]); !veryclose(abs[i], f) {
+ t.Errorf("Abs(%g) = %g, want %g", vc[i], f, abs[i])
+ }
+ }
+ for i := 0; i < len(vcAbsSC); i++ {
+ if f := Abs(vcAbsSC[i]); !alike(absSC[i], f) {
+ t.Errorf("Abs(%g) = %g, want %g", vcAbsSC[i], f, absSC[i])
+ }
+ }
+}
+func TestAcos(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Acos(vc[i]); !cSoclose(acos[i], f, 1e-14) {
+ t.Errorf("Acos(%g) = %g, want %g", vc[i], f, acos[i])
+ }
+ }
+ for _, v := range acosSC {
+ if f := Acos(v.in); !cAlike(v.want, f) {
+ t.Errorf("Acos(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Acos(Conj(z)) == Conj(Acos(z))
+ if f := Acos(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Acos(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ }
+ for _, pt := range branchPoints {
+ if f0, f1 := Acos(pt[0]), Acos(pt[1]); !cVeryclose(f0, f1) {
+ t.Errorf("Acos(%g) not continuous, got %g want %g", pt[0], f0, f1)
+ }
+ }
+}
+func TestAcosh(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Acosh(vc[i]); !cSoclose(acosh[i], f, 1e-14) {
+ t.Errorf("Acosh(%g) = %g, want %g", vc[i], f, acosh[i])
+ }
+ }
+ for _, v := range acoshSC {
+ if f := Acosh(v.in); !cAlike(v.want, f) {
+ t.Errorf("Acosh(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Acosh(Conj(z)) == Conj(Acosh(z))
+ if f := Acosh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Acosh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+
+ }
+ for _, pt := range branchPoints {
+ if f0, f1 := Acosh(pt[0]), Acosh(pt[1]); !cVeryclose(f0, f1) {
+ t.Errorf("Acosh(%g) not continuous, got %g want %g", pt[0], f0, f1)
+ }
+ }
+}
+func TestAsin(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Asin(vc[i]); !cSoclose(asin[i], f, 1e-14) {
+ t.Errorf("Asin(%g) = %g, want %g", vc[i], f, asin[i])
+ }
+ }
+ for _, v := range asinSC {
+ if f := Asin(v.in); !cAlike(v.want, f) {
+ t.Errorf("Asin(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Asin(Conj(z)) == Asin(Sinh(z))
+ if f := Asin(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Asin(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Asin(-z) == -Asin(z)
+ if f := Asin(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Asin(%g) = %g, want %g", -v.in, f, -v.want)
+ }
+ }
+ for _, pt := range branchPoints {
+ if f0, f1 := Asin(pt[0]), Asin(pt[1]); !cVeryclose(f0, f1) {
+ t.Errorf("Asin(%g) not continuous, got %g want %g", pt[0], f0, f1)
+ }
+ }
+}
+func TestAsinh(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Asinh(vc[i]); !cSoclose(asinh[i], f, 4e-15) {
+ t.Errorf("Asinh(%g) = %g, want %g", vc[i], f, asinh[i])
+ }
+ }
+ for _, v := range asinhSC {
+ if f := Asinh(v.in); !cAlike(v.want, f) {
+ t.Errorf("Asinh(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Asinh(Conj(z)) == Asinh(Sinh(z))
+ if f := Asinh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Asinh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Asinh(-z) == -Asinh(z)
+ if f := Asinh(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Asinh(%g) = %g, want %g", -v.in, f, -v.want)
+ }
+ }
+ for _, pt := range branchPoints {
+ if f0, f1 := Asinh(pt[0]), Asinh(pt[1]); !cVeryclose(f0, f1) {
+ t.Errorf("Asinh(%g) not continuous, got %g want %g", pt[0], f0, f1)
+ }
+ }
+}
+func TestAtan(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Atan(vc[i]); !cVeryclose(atan[i], f) {
+ t.Errorf("Atan(%g) = %g, want %g", vc[i], f, atan[i])
+ }
+ }
+ for _, v := range atanSC {
+ if f := Atan(v.in); !cAlike(v.want, f) {
+ t.Errorf("Atan(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Atan(Conj(z)) == Conj(Atan(z))
+ if f := Atan(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Atan(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Atan(-z) == -Atan(z)
+ if f := Atan(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Atan(%g) = %g, want %g", -v.in, f, -v.want)
+ }
+ }
+ for _, pt := range branchPoints {
+ if f0, f1 := Atan(pt[0]), Atan(pt[1]); !cVeryclose(f0, f1) {
+ t.Errorf("Atan(%g) not continuous, got %g want %g", pt[0], f0, f1)
+ }
+ }
+}
+func TestAtanh(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Atanh(vc[i]); !cVeryclose(atanh[i], f) {
+ t.Errorf("Atanh(%g) = %g, want %g", vc[i], f, atanh[i])
+ }
+ }
+ for _, v := range atanhSC {
+ if f := Atanh(v.in); !cAlike(v.want, f) {
+ t.Errorf("Atanh(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Atanh(Conj(z)) == Conj(Atanh(z))
+ if f := Atanh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Atanh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Atanh(-z) == -Atanh(z)
+ if f := Atanh(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Atanh(%g) = %g, want %g", -v.in, f, -v.want)
+ }
+ }
+ for _, pt := range branchPoints {
+ if f0, f1 := Atanh(pt[0]), Atanh(pt[1]); !cVeryclose(f0, f1) {
+ t.Errorf("Atanh(%g) not continuous, got %g want %g", pt[0], f0, f1)
+ }
+ }
+}
+func TestConj(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Conj(vc[i]); !cVeryclose(conj[i], f) {
+ t.Errorf("Conj(%g) = %g, want %g", vc[i], f, conj[i])
+ }
+ }
+ for i := 0; i < len(vcConjSC); i++ {
+ if f := Conj(vcConjSC[i]); !cAlike(conjSC[i], f) {
+ t.Errorf("Conj(%g) = %g, want %g", vcConjSC[i], f, conjSC[i])
+ }
+ }
+}
+func TestCos(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Cos(vc[i]); !cSoclose(cos[i], f, 3e-15) {
+ t.Errorf("Cos(%g) = %g, want %g", vc[i], f, cos[i])
+ }
+ }
+ for _, v := range cosSC {
+ if f := Cos(v.in); !cAlike(v.want, f) {
+ t.Errorf("Cos(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Cos(Conj(z)) == Cos(Cosh(z))
+ if f := Cos(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Cos(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Cos(-z) == Cos(z)
+ if f := Cos(-v.in); !cAlike(v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Cos(%g) = %g, want %g", -v.in, f, v.want)
+ }
+ }
+}
+func TestCosh(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Cosh(vc[i]); !cSoclose(cosh[i], f, 2e-15) {
+ t.Errorf("Cosh(%g) = %g, want %g", vc[i], f, cosh[i])
+ }
+ }
+ for _, v := range coshSC {
+ if f := Cosh(v.in); !cAlike(v.want, f) {
+ t.Errorf("Cosh(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Cosh(Conj(z)) == Conj(Cosh(z))
+ if f := Cosh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Cosh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Cosh(-z) == Cosh(z)
+ if f := Cosh(-v.in); !cAlike(v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Cosh(%g) = %g, want %g", -v.in, f, v.want)
+ }
+ }
+}
+func TestExp(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Exp(vc[i]); !cSoclose(exp[i], f, 1e-15) {
+ t.Errorf("Exp(%g) = %g, want %g", vc[i], f, exp[i])
+ }
+ }
+ for _, v := range expSC {
+ if f := Exp(v.in); !cAlike(v.want, f) {
+ t.Errorf("Exp(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Exp(Conj(z)) == Exp(Cosh(z))
+ if f := Exp(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Exp(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ }
+}
+func TestIsNaN(t *testing.T) {
+ for i := 0; i < len(vcIsNaNSC); i++ {
+ if f := IsNaN(vcIsNaNSC[i]); isNaNSC[i] != f {
+ t.Errorf("IsNaN(%v) = %v, want %v", vcIsNaNSC[i], f, isNaNSC[i])
+ }
+ }
+}
+func TestLog(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Log(vc[i]); !cVeryclose(log[i], f) {
+ t.Errorf("Log(%g) = %g, want %g", vc[i], f, log[i])
+ }
+ }
+ for _, v := range logSC {
+ if f := Log(v.in); !cAlike(v.want, f) {
+ t.Errorf("Log(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Log(Conj(z)) == Conj(Log(z))
+ if f := Log(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Log(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ }
+ for _, pt := range branchPoints {
+ if f0, f1 := Log(pt[0]), Log(pt[1]); !cVeryclose(f0, f1) {
+ t.Errorf("Log(%g) not continuous, got %g want %g", pt[0], f0, f1)
+ }
+ }
+}
+func TestLog10(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Log10(vc[i]); !cVeryclose(log10[i], f) {
+ t.Errorf("Log10(%g) = %g, want %g", vc[i], f, log10[i])
+ }
+ }
+ for _, v := range log10SC {
+ if f := Log10(v.in); !cAlike(v.want, f) {
+ t.Errorf("Log10(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Log10(Conj(z)) == Conj(Log10(z))
+ if f := Log10(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Log10(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ }
+}
+func TestPolar(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if r, theta := Polar(vc[i]); !veryclose(polar[i].r, r) && !veryclose(polar[i].theta, theta) {
+ t.Errorf("Polar(%g) = %g, %g want %g, %g", vc[i], r, theta, polar[i].r, polar[i].theta)
+ }
+ }
+ for i := 0; i < len(vcPolarSC); i++ {
+ if r, theta := Polar(vcPolarSC[i]); !alike(polarSC[i].r, r) && !alike(polarSC[i].theta, theta) {
+ t.Errorf("Polar(%g) = %g, %g, want %g, %g", vcPolarSC[i], r, theta, polarSC[i].r, polarSC[i].theta)
+ }
+ }
+}
+func TestPow(t *testing.T) {
+ // Special cases for Pow(0, c).
+ var zero = complex(0, 0)
+ zeroPowers := [][2]complex128{
+ {0, 1 + 0i},
+ {1.5, 0 + 0i},
+ {-1.5, complex(math.Inf(0), 0)},
+ {-1.5 + 1.5i, Inf()},
+ }
+ for _, zp := range zeroPowers {
+ if f := Pow(zero, zp[0]); f != zp[1] {
+ t.Errorf("Pow(%g, %g) = %g, want %g", zero, zp[0], f, zp[1])
+ }
+ }
+ var a = complex(3.0, 3.0)
+ for i := 0; i < len(vc); i++ {
+ if f := Pow(a, vc[i]); !cSoclose(pow[i], f, 4e-15) {
+ t.Errorf("Pow(%g, %g) = %g, want %g", a, vc[i], f, pow[i])
+ }
+ }
+ for i := 0; i < len(vcPowSC); i++ {
+ if f := Pow(vcPowSC[i][0], vcPowSC[i][1]); !cAlike(powSC[i], f) {
+ t.Errorf("Pow(%g, %g) = %g, want %g", vcPowSC[i][0], vcPowSC[i][1], f, powSC[i])
+ }
+ }
+ for _, pt := range branchPoints {
+ if f0, f1 := Pow(pt[0], 0.1), Pow(pt[1], 0.1); !cVeryclose(f0, f1) {
+ t.Errorf("Pow(%g, 0.1) not continuous, got %g want %g", pt[0], f0, f1)
+ }
+ }
+}
+func TestRect(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Rect(polar[i].r, polar[i].theta); !cVeryclose(vc[i], f) {
+ t.Errorf("Rect(%g, %g) = %g want %g", polar[i].r, polar[i].theta, f, vc[i])
+ }
+ }
+ for i := 0; i < len(vcPolarSC); i++ {
+ if f := Rect(polarSC[i].r, polarSC[i].theta); !cAlike(vcPolarSC[i], f) {
+ t.Errorf("Rect(%g, %g) = %g, want %g", polarSC[i].r, polarSC[i].theta, f, vcPolarSC[i])
+ }
+ }
+}
+func TestSin(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Sin(vc[i]); !cSoclose(sin[i], f, 2e-15) {
+ t.Errorf("Sin(%g) = %g, want %g", vc[i], f, sin[i])
+ }
+ }
+ for _, v := range sinSC {
+ if f := Sin(v.in); !cAlike(v.want, f) {
+ t.Errorf("Sin(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Sin(Conj(z)) == Conj(Sin(z))
+ if f := Sin(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Sinh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Sin(-z) == -Sin(z)
+ if f := Sin(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Sinh(%g) = %g, want %g", -v.in, f, -v.want)
+ }
+ }
+}
+func TestSinh(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Sinh(vc[i]); !cSoclose(sinh[i], f, 2e-15) {
+ t.Errorf("Sinh(%g) = %g, want %g", vc[i], f, sinh[i])
+ }
+ }
+ for _, v := range sinhSC {
+ if f := Sinh(v.in); !cAlike(v.want, f) {
+ t.Errorf("Sinh(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Sinh(Conj(z)) == Conj(Sinh(z))
+ if f := Sinh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Sinh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Sinh(-z) == -Sinh(z)
+ if f := Sinh(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Sinh(%g) = %g, want %g", -v.in, f, -v.want)
+ }
+ }
+}
+func TestSqrt(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Sqrt(vc[i]); !cVeryclose(sqrt[i], f) {
+ t.Errorf("Sqrt(%g) = %g, want %g", vc[i], f, sqrt[i])
+ }
+ }
+ for _, v := range sqrtSC {
+ if f := Sqrt(v.in); !cAlike(v.want, f) {
+ t.Errorf("Sqrt(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Sqrt(Conj(z)) == Conj(Sqrt(z))
+ if f := Sqrt(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Sqrt(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ }
+ for _, pt := range branchPoints {
+ if f0, f1 := Sqrt(pt[0]), Sqrt(pt[1]); !cVeryclose(f0, f1) {
+ t.Errorf("Sqrt(%g) not continuous, got %g want %g", pt[0], f0, f1)
+ }
+ }
+}
+func TestTan(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Tan(vc[i]); !cSoclose(tan[i], f, 3e-15) {
+ t.Errorf("Tan(%g) = %g, want %g", vc[i], f, tan[i])
+ }
+ }
+ for _, v := range tanSC {
+ if f := Tan(v.in); !cAlike(v.want, f) {
+ t.Errorf("Tan(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Tan(Conj(z)) == Conj(Tan(z))
+ if f := Tan(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Tan(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Tan(-z) == -Tan(z)
+ if f := Tan(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Tan(%g) = %g, want %g", -v.in, f, -v.want)
+ }
+ }
+}
+func TestTanh(t *testing.T) {
+ for i := 0; i < len(vc); i++ {
+ if f := Tanh(vc[i]); !cSoclose(tanh[i], f, 2e-15) {
+ t.Errorf("Tanh(%g) = %g, want %g", vc[i], f, tanh[i])
+ }
+ }
+ for _, v := range tanhSC {
+ if f := Tanh(v.in); !cAlike(v.want, f) {
+ t.Errorf("Tanh(%g) = %g, want %g", v.in, f, v.want)
+ }
+ if math.IsNaN(imag(v.in)) || math.IsNaN(imag(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Tanh(Conj(z)) == Conj(Tanh(z))
+ if f := Tanh(Conj(v.in)); !cAlike(Conj(v.want), f) && !cAlike(v.in, Conj(v.in)) {
+ t.Errorf("Tanh(%g) = %g, want %g", Conj(v.in), f, Conj(v.want))
+ }
+ if math.IsNaN(real(v.in)) || math.IsNaN(real(v.want)) {
+ // Negating NaN is undefined with regard to the sign bit produced.
+ continue
+ }
+ // Tanh(-z) == -Tanh(z)
+ if f := Tanh(-v.in); !cAlike(-v.want, f) && !cAlike(v.in, -v.in) {
+ t.Errorf("Tanh(%g) = %g, want %g", -v.in, f, -v.want)
+ }
+ }
+}
+
+// See issue 17577
+func TestInfiniteLoopIntanSeries(t *testing.T) {
+ want := Inf()
+ if got := Cot(0); got != want {
+ t.Errorf("Cot(0): got %g, want %g", got, want)
+ }
+}
+
+func BenchmarkAbs(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Abs(complex(2.5, 3.5))
+ }
+}
+func BenchmarkAcos(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Acos(complex(2.5, 3.5))
+ }
+}
+func BenchmarkAcosh(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Acosh(complex(2.5, 3.5))
+ }
+}
+func BenchmarkAsin(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Asin(complex(2.5, 3.5))
+ }
+}
+func BenchmarkAsinh(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Asinh(complex(2.5, 3.5))
+ }
+}
+func BenchmarkAtan(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Atan(complex(2.5, 3.5))
+ }
+}
+func BenchmarkAtanh(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Atanh(complex(2.5, 3.5))
+ }
+}
+func BenchmarkConj(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Conj(complex(2.5, 3.5))
+ }
+}
+func BenchmarkCos(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Cos(complex(2.5, 3.5))
+ }
+}
+func BenchmarkCosh(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Cosh(complex(2.5, 3.5))
+ }
+}
+func BenchmarkExp(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Exp(complex(2.5, 3.5))
+ }
+}
+func BenchmarkLog(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Log(complex(2.5, 3.5))
+ }
+}
+func BenchmarkLog10(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Log10(complex(2.5, 3.5))
+ }
+}
+func BenchmarkPhase(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Phase(complex(2.5, 3.5))
+ }
+}
+func BenchmarkPolar(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Polar(complex(2.5, 3.5))
+ }
+}
+func BenchmarkPow(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Pow(complex(2.5, 3.5), complex(2.5, 3.5))
+ }
+}
+func BenchmarkRect(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Rect(2.5, 1.5)
+ }
+}
+func BenchmarkSin(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Sin(complex(2.5, 3.5))
+ }
+}
+func BenchmarkSinh(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Sinh(complex(2.5, 3.5))
+ }
+}
+func BenchmarkSqrt(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Sqrt(complex(2.5, 3.5))
+ }
+}
+func BenchmarkTan(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Tan(complex(2.5, 3.5))
+ }
+}
+func BenchmarkTanh(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Tanh(complex(2.5, 3.5))
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-29 04:07:40 +0000