test_spec_functions_data.hpp 88 KB

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  1. // complex(z), n, complex(D1(n,z)), abs_err_real, abs_err_imag
  2. std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
  3. D1_test_16digits
  4. = {
  5. {{0.07425,0.0},0,{13.44325436668153,0.0},1.3e-15,0.0},
  6. {{0.07425,0.0},1,{26.92117459633998,0.0},2.7e-15,0.0},
  7. {{0.07425,0.0},2,{40.39343233283062,0.0},4.0e-15,0.0},
  8. {{0.07425,0.0},3,{53.8638034125887,0.0},5.4e-15,0.0},
  9. {{0.07425,0.0},4,{67.33331707981798,0.0},6.7e-15,0.0},
  10. {{0.07575,0.0},0,{13.17606046765979,0.0},1.3e-15,0.0},
  11. {{0.07575,0.0},1,{26.38748777963147,0.0},2.6e-15,0.0},
  12. {{0.07575,0.0},2,{39.59313798170167,0.0},4.0e-15,0.0},
  13. {{0.07575,0.0},3,{52.79686337350637,0.0},5.3e-15,0.0},
  14. {{0.07575,0.0},4,{65.99971402008605,0.0},6.6e-15,0.0},
  15. {{7.5,0.0},0,{0.3695472563090164,0.0},3.7e-17,0.0},
  16. {{7.5,0.0},1,{-4.366784043615744,0.0},4.4e-16,0.0},
  17. {{7.5,0.0},2,{-0.05084479598595977,0.0},5.1e-18,0.0},
  18. {{7.5,0.0},3,{1.818058207399475,0.0},1.8e-16,0.0},
  19. {{7.5,0.0},4,{-1.311710105034662,0.0},1.3e-16,0.0},
  20. {{7.5,0.0},5,{-0.1612017752951218,0.0},1.6e-17,0.0},
  21. {{7.5,0.0},6,{0.2403642873973738,0.0},2.4e-17,0.0},
  22. {{7.5,0.0},7,{0.509732566745001,0.0},5.1e-17,0.0},
  23. {{7.5,0.0},8,{0.7288779051967778,0.0},7.3e-17,0.0},
  24. {{7.5,0.0},9,{0.9225920223879098,0.0},9.2e-17,0.0},
  25. {{7.5,0.0},10,{1.101289075837662,0.0},1.1e-16,0.0},
  26. {{7.5,0.0},11,{1.270228055670032,0.0},1.3e-16,0.0},
  27. {{7.5,0.0},12,{1.432398653656861,0.0},1.4e-16,0.0},
  28. {{7.5,0.0},13,{1.589646926286713,0.0},1.6e-16,0.0},
  29. {{7.5,0.0},14,{1.743184380873933,0.0},1.7e-16,0.0},
  30. {{7.5,0.0},16,{2.042220854428171,0.0},2.0e-16,0.0},
  31. {{7.5,0.0},17,{2.188751725980377,0.0},2.2e-16,0.0},
  32. {{7.5,0.0},18,{2.33376648704411,0.0},2.3e-16,0.0},
  33. {{7.5,0.0},19,{2.477519013106746,0.0},2.5e-16,0.0},
  34. {{7.5,0.0},21,{2.761992897922038,0.0},2.8e-16,0.0},
  35. {{7.5,0.0},22,{2.90300061550683,0.0},2.9e-16,0.0},
  36. {{7.5,0.0},24,{3.183085123876985,0.0},3.2e-16,0.0},
  37. {{7.5,0.0},26,{3.461101068633011,0.0},3.5e-16,0.0},
  38. {{7.5,0.0},27,{3.599479435575162,0.0},3.6e-16,0.0},
  39. {{7.5,0.0},30,{4.012605389511785,0.0},4.0e-16,0.0},
  40. {{750.0,0.0},0,{-0.8951915139149222,0.0},9.0e-17,0.0},
  41. {{750.0,0.0},1,{1.114084720130935,0.0},1.1e-16,0.0},
  42. {{750.0,0.0},2,{-0.9024181120233614,0.0},9.0e-17,0.0},
  43. {{750.0,0.0},3,{1.099243620946342,0.0},1.1e-16,0.0},
  44. {{750.0,0.0},4,{-0.9194850798920686,0.0},9.2e-17,0.0},
  45. {{750.0,0.0},5,{1.073070000370522,0.0},1.1e-16,0.0},
  46. {{750.0,0.0},6,{-0.9469054237300034,0.0},9.5e-17,0.0},
  47. {{750.0,0.0},7,{1.036430596034115,0.0},1.0e-16,0.0},
  48. {{750.0,0.0},9,{0.990456172692469,0.0},9.9e-17,0.0},
  49. {{750.0,0.0},10,{-1.036746111869826,0.0},1.0e-16,0.0},
  50. {{750.0,0.0},11,{0.9364345757891685,0.0},9.4e-17,0.0},
  51. {{750.0,0.0},13,{0.875701892481254,0.0},8.8e-17,0.0},
  52. {{750.0,0.0},15,{0.8095451807506758,0.0},8.1e-17,0.0},
  53. {{750.0,0.0},18,{-1.422356478541503,0.0},1.4e-16,0.0},
  54. {{750.0,0.0},20,{-1.592210408225887,0.0},1.6e-16,0.0},
  55. {{750.0,0.0},23,{0.5110077375181897,0.0},5.1e-17,0.0},
  56. {{750.0,0.0},27,{0.3496666467211573,0.0},3.5e-17,0.0},
  57. {{750.0,0.0},31,{0.1809968576664919,0.0},1.8e-17,0.0},
  58. {{750.0,0.0},35,{0.0004860079342239934,0.0},4.9e-20,0.0},
  59. {{750.0,0.0},41,{-0.317251336807483,0.0},3.2e-17,0.0},
  60. {{750.0,0.0},47,{-0.7807372174284117,0.0},7.8e-17,0.0},
  61. {{750.0,0.0},54,{0.4580930397540441,0.0},4.6e-17,0.0},
  62. {{750.0,0.0},62,{-0.1958618028998245,0.0},2.0e-17,0.0},
  63. {{750.0,0.0},71,{0.6403656124320398,0.0},6.4e-17,0.0},
  64. {{750.0,0.0},81,{-0.4803642218027248,0.0},4.8e-17,0.0},
  65. {{750.0,0.0},93,{3.417692358670104,0.0},3.4e-16,0.0},
  66. {{750.0,0.0},107,{-0.6675908137518288,0.0},6.7e-17,0.0},
  67. {{750.0,0.0},123,{0.07336983052954298,0.0},7.3e-18,0.0},
  68. {{750.0,0.0},141,{0.01864087618833894,0.0},1.9e-18,0.0},
  69. {{750.0,0.0},162,{0.4662167115741941,0.0},4.7e-17,0.0},
  70. {{750.0,0.0},186,{1.869792416792102,0.0},1.9e-16,0.0},
  71. {{750.0,0.0},214,{-0.1962317049357189,0.0},2.0e-17,0.0},
  72. {{750.0,0.0},246,{-0.9241109217019534,0.0},9.2e-17,0.0},
  73. {{750.0,0.0},282,{-2.278752089160206,0.0},2.3e-16,0.0},
  74. {{750.0,0.0},324,{0.1492340462699953,0.0},1.5e-17,0.0},
  75. {{750.0,0.0},372,{-1.501050800107926,0.0},1.5e-16,0.0},
  76. {{750.0,0.0},427,{1.251448627689853,0.0},1.3e-16,0.0},
  77. {{750.0,0.0},490,{-2.307846776579645,0.0},2.3e-16,0.0},
  78. {{750.0,0.0},562,{-0.6678454189015009,0.0},6.7e-17,0.0},
  79. {{750.0,0.0},645,{4.123866493958505,0.0},4.1e-16,0.0},
  80. {{750.0,0.0},740,{-0.04954886515946186,0.0},5.0e-18,0.0},
  81. {{750.0,0.0},850,{0.5377162125402363,0.0},5.4e-17,0.0},
  82. {{133.0,-0.001},0,{0.5694948983815571,0.001324324427352377},5.7e-17,1.3e-19},
  83. {{133.0,-0.001},1,{-1.786944015800289,0.004193067842684484},1.8e-16,4.2e-19},
  84. {{133.0,-0.001},2,{0.5399040215866582,0.001291157104802603},5.4e-17,1.3e-19},
  85. {{133.0,-0.001},3,{-1.955480625798034,0.004823242927232421},2.0e-16,4.8e-19},
  86. {{133.0,-0.001},4,{0.4735591560334697,0.001223127495142088},4.7e-17,1.2e-19},
  87. {{133.0,-0.001},5,{-2.331337152694187,0.006433469776449445},2.3e-16,6.4e-19},
  88. {{133.0,-0.001},6,{0.3756798707528821,0.00113876079036902},3.8e-17,1.1e-19},
  89. {{133.0,-0.001},7,{-3.148105562806491,0.01090750730183105},3.1e-16,1.1e-18},
  90. {{133.0,-0.001},8,{0.2515418522954845,0.001059202692643652},2.5e-17,1.1e-19},
  91. {{133.0,-0.001},9,{-5.506034746297112,0.03131226964093978},5.5e-16,3.1e-18},
  92. {{133.0,-0.001},10,{0.1039785994199451,0.001004592673307026},1.0e-17,1.0e-19},
  93. {{133.0,-0.001},11,{-46.98874438931292,2.213832762775254},4.7e-15,2.2e-16},
  94. {{133.0,-0.001},13,{5.89811290505382,0.03577867985992821},5.9e-16,3.6e-18},
  95. {{133.0,-0.001},14,{-0.2778831807551624,0.001065347008820747},2.8e-17,1.1e-19},
  96. {{133.0,-0.001},16,{-0.5501021158428141,0.001287235517159257},5.5e-17,1.3e-19},
  97. {{133.0,-0.001},18,{-0.9604617468736273,0.001903153851503216},9.6e-17,1.9e-19},
  98. {{133.0,-0.001},20,{-1.781366135936702,0.004149533558522542},1.8e-16,4.1e-19},
  99. {{133.0,-0.001},22,{-5.364106315522472,0.02974587750840188},5.4e-16,3.0e-18},
  100. {{133.0,-0.001},24,{5.606849372659069,0.03240384877063995},5.6e-16,3.2e-18},
  101. {{133.0,-0.001},27,{-0.9371713952326589,0.001835552825885577},9.4e-17,1.8e-19},
  102. {{133.0,-0.001},30,{0.1444928510146065,0.0009683028517003325},1.4e-17,9.7e-20},
  103. {{133.0,-0.001},34,{-1.077435738938742,0.002093596104973148},1.1e-16,2.1e-19},
  104. {{133.0,-0.001},38,{2.388603684198123,0.006621682434854192},2.4e-16,6.6e-19},
  105. {{133.0,-0.001},42,{-0.04594418870488948,0.0009000132524188679},4.6e-18,9.0e-20},
  106. {{133.0,-0.001},47,{-0.1928537665101976,0.0009096554574653678},1.9e-17,9.1e-20},
  107. {{133.0,-0.001},52,{-0.5759136780922404,0.001175873583204343},5.8e-17,1.2e-19},
  108. {{133.0,-0.001},58,{-0.001534349994635456,0.0008065485786972979},1.5e-19,8.1e-20},
  109. {{133.0,-0.001},65,{3.34959880398593,0.01197741989906779},3.3e-16,1.2e-18},
  110. {{133.0,-0.001},72,{-1.128245159231274,0.001975805382904386},1.1e-16,2.0e-19},
  111. {{133.0,-0.001},80,{0.3810052575576299,0.0007788355962317044},3.8e-17,7.8e-20},
  112. {{133.0,-0.001},89,{-1.389569631366617,0.002478084310925133},1.4e-16,2.5e-19},
  113. {{133.0,-0.001},99,{0.3062835121565152,0.0005341397085202431},3.1e-17,5.3e-20},
  114. {{133.0,-0.001},111,{-1.197963349765192,0.0017323088546027},1.2e-16,1.7e-19},
  115. {{133.0,-0.001},123,{19.56837074945142,0.3832056790545297},2.0e-15,3.8e-17},
  116. {{133.0,-0.001},137,{0.3055541934481533,2.456354568026977e-5},3.1e-17,2.5e-21},
  117. {{133.0,-0.001},153,{0.5906754727336102,1.688326789413069e-5},5.9e-17,1.7e-21},
  118. {{133.0,-0.001},170,{0.8115766470088518,1.526245423300269e-5},8.1e-17,1.5e-21},
  119. {{133.0,-0.001},190,{1.032740304150528,1.499507085033343e-5},1.0e-16,1.5e-21},
  120. {{13300.0,-0.1},0,{-0.06692914070761327,0.1001189584035135},6.7e-18,1.0e-17},
  121. {{13300.0,-0.1},1,{4.616651032403645,6.898387416052877},4.6e-16,6.9e-16},
  122. {{13300.0,-0.1},2,{-0.06715345623133977,0.1001219830819477},6.7e-18,1.0e-17},
  123. {{13300.0,-0.1},3,{4.626074281763076,6.874458933213065},4.6e-16,6.9e-16},
  124. {{13300.0,-0.1},4,{-0.06767688502979775,0.1001290804260918},6.8e-18,1.0e-17},
  125. {{13300.0,-0.1},5,{4.642643500855681,6.831476202578954},4.6e-16,6.8e-16},
  126. {{13300.0,-0.1},6,{-0.06849948986240052,0.1001403458942619},6.8e-18,1.0e-17},
  127. {{13300.0,-0.1},8,{-0.06962137099737601,0.1001559295836686},7.0e-18,1.0e-17},
  128. {{13300.0,-0.1},10,{-0.0710426684088035,0.1001760363552384},7.1e-18,1.0e-17},
  129. {{13300.0,-0.1},12,{-0.07276356477625575,0.1002009260094824},7.3e-18,1.0e-17},
  130. {{13300.0,-0.1},15,{4.800736473590391,6.340163785321638},4.8e-16,6.3e-16},
  131. {{13300.0,-0.1},18,{-0.07972640059807958,0.1003077196914383},8.0e-18,1.0e-17},
  132. {{13300.0,-0.1},22,{-0.0858719620133543,0.1004100911573547},8.6e-18,1.0e-17},
  133. {{13300.0,-0.1},27,{4.963740562022939,5.241410780782546},5.0e-16,5.2e-16},
  134. {{13300.0,-0.1},32,{-0.1065312758569564,0.1008100053427372},1.1e-17,1.0e-17},
  135. {{13300.0,-0.1},40,{-0.1285658848011511,0.101331312547063},1.3e-17,1.0e-17},
  136. {{13300.0,-0.1},48,{-0.155597397912611,0.1021044995524675},1.6e-17,1.0e-17},
  137. {{13300.0,-0.1},59,{3.92606850470495,2.024234276214423},3.9e-16,2.0e-16},
  138. {{13300.0,-0.1},71,{3.266749502613612,1.325141142881345},3.3e-16,1.3e-16},
  139. {{13300.0,-0.1},87,{2.48855009697603,0.7680626670413273},2.5e-16,7.7e-17},
  140. {{13300.0,-0.1},105,{1.810033336881379,0.4412160521230632},1.8e-16,4.4e-17},
  141. {{13300.0,-0.1},128,{-0.8087709702171539,0.1659490518456605},8.1e-17,1.7e-17},
  142. {{13300.0,-0.1},155,{0.6659686332272149,0.1445045623007861},6.7e-17,1.4e-17},
  143. {{13300.0,-0.1},189,{0.1528980344747564,0.1020017803208432},1.5e-17,1.0e-17},
  144. {{13300.0,-0.1},229,{-0.5100291443011008,0.1258945028911659},5.1e-17,1.3e-17},
  145. {{13300.0,-0.1},279,{-4.714579612576236,3.50370615462884},4.7e-16,3.5e-16},
  146. {{13300.0,-0.1},338,{-2.613119300211035,0.8425696552260671},2.6e-16,8.4e-17},
  147. {{13300.0,-0.1},411,{4.556185151927977,3.088849941285113},4.6e-16,3.1e-16},
  148. {{13300.0,-0.1},499,{2.22274252736833,9.508151861627413},2.2e-16,9.5e-16},
  149. {{13300.0,-0.1},606,{-3.48249445021244,1.524850417565235},3.5e-16,1.5e-16},
  150. {{13300.0,-0.1},736,{3.705979656274174,8.373254202589672},3.7e-16,8.4e-16},
  151. {{13300.0,-0.1},894,{2.782768507188473,0.9519460681947263},2.8e-16,9.5e-17},
  152. {{0.0825,-0.055},0,{8.364112570866324,5.612760190811083},8.4e-16,5.6e-16},
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  456. {{6.2831853071795862319959269370884,-1.0},2,{0.2949375696085568,1.070592030672524},2.9e-17,1.1e-16},
  457. {{6.2831853071795862319959269370884,-1.0},3,{-0.2986322034569661,0.9008011017614757},3.0e-17,9.0e-17},
  458. {{6.2831853071795862319959269370884,-1.0},4,{-0.003223801583153805,0.4398947553395593},3.2e-19,4.4e-17},
  459. {{6.2831853071795862319959269370884,-1.0},5,{0.3254847904858648,0.3236711082223025},3.3e-17,3.2e-17},
  460. {{6.2831853071795862319959269370884,-1.0},6,{0.5915216297442743,0.2927648081692745},5.9e-17,2.9e-17},
  461. {{6.2831853071795862319959269370884,-1.0},7,{0.8216613358485906,0.2889872711150469},8.2e-17,2.9e-17},
  462. {{6.2831853071795862319959269370884,-1.0},8,{1.031011238016646,0.2965575908077732},1.0e-16,3.0e-17},
  463. {{6.2831853071795862319959269370884,-1.0},9,{1.227344826394146,0.3098261586314655},1.2e-16,3.1e-17},
  464. {{6.2831853071795862319959269370884,-1.0},10,{1.414970410777237,0.3263361380815797},1.4e-16,3.3e-17},
  465. {{6.2831853071795862319959269370884,-1.0},11,{1.596461936103797,0.3448619156356228},1.6e-16,3.4e-17},
  466. {{6.2831853071795862319959269370884,-1.0},12,{1.773455192293614,0.36472724630896},1.8e-16,3.6e-17},
  467. {{6.2831853071795862319959269370884,-1.0},13,{1.947042664720708,0.3855292662286455},1.9e-16,3.9e-17},
  468. {{6.2831853071795862319959269370884,-1.0},14,{2.117983884070411,0.4070131164963634},2.1e-16,4.1e-17},
  469. {{6.2831853071795862319959269370884,-1.0},15,{2.28682458641427,0.4290096105470636},2.3e-16,4.3e-17},
  470. {{6.2831853071795862319959269370884,-1.0},16,{2.453967796322013,0.4514019204534639},2.5e-16,4.5e-17},
  471. {{6.2831853071795862319959269370884,-1.0},18,{2.784310371123592,0.4970627630731119},2.8e-16,5.0e-17},
  472. {{6.2831853071795862319959269370884,-1.0},19,{2.947928703075273,0.5202242302820364},2.9e-16,5.2e-17},
  473. {{6.2831853071795862319959269370884,-1.0},20,{3.110719695447307,0.5435558939596922},3.1e-16,5.4e-17},
  474. {{6.2831853071795862319959269370884,-1.0},22,{3.434270806979098,0.590625695740279},3.4e-16,5.9e-17},
  475. {{6.2831853071795862319959269370884,-1.0},23,{3.595206946808026,0.6143246109772049},3.6e-16,6.1e-17},
  476. {{6.2831853071795862319959269370884,-1.0},25,{3.915734156142959,0.6619787064788887},3.9e-16,6.6e-17},
  477. {{6.2831853071795862319959269370884,-1.0},26,{4.075427821953628,0.6859125175106776},4.1e-16,6.9e-17},
  478. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},0,{-1.836418620170526e-18,-1.003741873197321},1.8e-34,1.0e-16},
  479. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},1,{0.01415314238170799,-0.9809158089497843},1.4e-18,9.8e-17},
  480. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},2,{0.05114736246509357,-0.9580400080884279},5.1e-18,9.6e-17},
  481. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},3,{0.09211316557854763,-0.9082339053736075},9.2e-18,9.1e-17},
  482. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},4,{0.1846022792219881,-0.8324588456241011},1.8e-17,8.3e-17},
  483. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},5,{0.3278509422643821,-0.7787308740926149},3.3e-17,7.8e-17},
  484. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},6,{0.490657891841003,-0.7594698540777983},4.9e-17,7.6e-17},
  485. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},7,{0.6556002657420997,-0.7661759616695461},6.6e-17,7.7e-17},
  486. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},8,{0.8170144707370777,-0.7897178762870168},8.2e-17,7.9e-17},
  487. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},9,{0.9738269711673275,-0.8240443504069009},9.7e-17,8.2e-17},
  488. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},10,{1.126363788598225,-0.8654702596325609},1.1e-16,8.7e-17},
  489. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},11,{1.275267657078007,-0.9117424236160586},1.3e-16,9.1e-17},
  490. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},12,{1.421169391490898,-0.9614426612842512},1.4e-16,9.6e-17},
  491. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},13,{1.564605168974907,-1.013646817955554},1.6e-16,1.0e-16},
  492. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},14,{1.70600982438213,-1.067731854089558},1.7e-16,1.1e-16},
  493. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},15,{1.845730814291544,-1.123264438028688},1.8e-16,1.1e-16},
  494. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},16,{1.984045299099804,-1.179934666313605},2.0e-16,1.2e-16},
  495. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},17,{2.121175274622946,-1.237515369840869},2.1e-16,1.2e-16},
  496. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},19,{2.392564196036499,-1.354767638565249},2.4e-16,1.4e-16},
  497. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},20,{2.527087793751678,-1.414208223835596},2.5e-16,1.4e-16},
  498. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},22,{2.794289611881632,-1.534314595034528},2.8e-16,1.5e-16},
  499. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},23,{2.927118403808978,-1.594865107779637},2.9e-16,1.6e-16},
  500. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},25,{3.191523552338415,-1.716747727625207},3.2e-16,1.7e-16},
  501. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},27,{3.454552595281413,-1.839467692756036},3.5e-16,1.8e-16},
  502. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},29,{3.716477216297216,-1.962842613985385},3.7e-16,2.0e-16},
  503. {{6.2831853071795862319959269370884,1.0},0,{-1.773439590975416e-16,-1.313035285499331},1.8e-32,1.3e-16},
  504. {{6.2831853071795862319959269370884,1.0},1,{-0.06304185943615409,-0.7403873087787056},6.3e-18,7.4e-17},
  505. {{6.2831853071795862319959269370884,1.0},2,{0.2949375696085568,-1.070592030672524},2.9e-17,1.1e-16},
  506. {{6.2831853071795862319959269370884,1.0},3,{-0.2986322034569661,-0.9008011017614757},3.0e-17,9.0e-17},
  507. {{6.2831853071795862319959269370884,1.0},4,{-0.003223801583153805,-0.4398947553395593},3.2e-19,4.4e-17},
  508. {{6.2831853071795862319959269370884,1.0},5,{0.3254847904858648,-0.3236711082223025},3.3e-17,3.2e-17},
  509. {{6.2831853071795862319959269370884,1.0},6,{0.5915216297442743,-0.2927648081692745},5.9e-17,2.9e-17},
  510. {{6.2831853071795862319959269370884,1.0},7,{0.8216613358485906,-0.2889872711150469},8.2e-17,2.9e-17},
  511. {{6.2831853071795862319959269370884,1.0},8,{1.031011238016646,-0.2965575908077732},1.0e-16,3.0e-17},
  512. {{6.2831853071795862319959269370884,1.0},9,{1.227344826394146,-0.3098261586314655},1.2e-16,3.1e-17},
  513. {{6.2831853071795862319959269370884,1.0},10,{1.414970410777237,-0.3263361380815797},1.4e-16,3.3e-17},
  514. {{6.2831853071795862319959269370884,1.0},11,{1.596461936103797,-0.3448619156356228},1.6e-16,3.4e-17},
  515. {{6.2831853071795862319959269370884,1.0},12,{1.773455192293614,-0.36472724630896},1.8e-16,3.6e-17},
  516. {{6.2831853071795862319959269370884,1.0},13,{1.947042664720708,-0.3855292662286455},1.9e-16,3.9e-17},
  517. {{6.2831853071795862319959269370884,1.0},14,{2.117983884070411,-0.4070131164963634},2.1e-16,4.1e-17},
  518. {{6.2831853071795862319959269370884,1.0},15,{2.28682458641427,-0.4290096105470636},2.3e-16,4.3e-17},
  519. {{6.2831853071795862319959269370884,1.0},16,{2.453967796322013,-0.4514019204534639},2.5e-16,4.5e-17},
  520. {{6.2831853071795862319959269370884,1.0},18,{2.784310371123592,-0.4970627630731119},2.8e-16,5.0e-17},
  521. {{6.2831853071795862319959269370884,1.0},19,{2.947928703075273,-0.5202242302820364},2.9e-16,5.2e-17},
  522. {{6.2831853071795862319959269370884,1.0},20,{3.110719695447307,-0.5435558939596922},3.1e-16,5.4e-17},
  523. {{6.2831853071795862319959269370884,1.0},22,{3.434270806979098,-0.590625695740279},3.4e-16,5.9e-17},
  524. {{6.2831853071795862319959269370884,1.0},23,{3.595206946808026,-0.6143246109772049},3.6e-16,6.1e-17},
  525. {{6.2831853071795862319959269370884,1.0},25,{3.915734156142959,-0.6619787064788887},3.9e-16,6.6e-17},
  526. {{6.2831853071795862319959269370884,1.0},26,{4.075427821953628,-0.6859125175106776},4.1e-16,6.9e-17},
  527. {{3.1415926535897932384626433832795,0.0},0,{-2.704418609247059e+282,0.0},2.7e+266,0.0},
  528. {{3.1415926535897932384626433832795,0.0},1,{-0.3183098861837907,0.0},3.2e-17,0.0},
  529. {{3.1415926535897932384626433832795,0.0},2,{0.4105777788290164,0.0},4.1e-17,0.0},
  530. {{3.1415926535897932384626433832795,0.0},3,{0.8821173642494784,0.0},8.8e-17,0.0},
  531. {{3.1415926535897932384626433832795,0.0},4,{1.283506275095942,0.0},1.3e-16,0.0},
  532. {{3.1415926535897932384626433832795,0.0},5,{1.654748956488027,0.0},1.7e-16,0.0},
  533. {{3.1415926535897932384626433832795,0.0},6,{2.010012841716631,0.0},2.0e-16,0.0},
  534. {{3.1415926535897932384626433832795,0.0},7,{2.355698958080709,0.0},2.4e-16,0.0},
  535. {{3.1415926535897932384626433832795,0.0},8,{2.695156885492767,0.0},2.7e-16,0.0},
  536. {{3.1415926535897932384626433832795,0.0},9,{3.030322020436486,0.0},3.0e-16,0.0},
  537. {{3.1415926535897932384626433832795,0.0},10,{3.362395801011574,0.0},3.4e-16,0.0},
  538. {{3.1415926535897932384626433832795,0.0},11,{3.692165818289568,0.0},3.7e-16,0.0},
  539. {{3.1415926535897932384626433832795,0.0},12,{4.02017100538644,0.0},4.0e-16,0.0},
  540. {{3.1415926535897932384626433832795,0.0},13,{4.346793172787544,0.0},4.3e-16,0.0},
  541. {{3.1415926535897932384626433832795,0.0},14,{4.672310695202237,0.0},4.7e-16,0.0},
  542. {{3.1415926535897932384626433832795,0.0},15,{4.996931497029032,0.0},5.0e-16,0.0},
  543. {{3.1415926535897932384626433832795,0.0},16,{5.320814119475183,0.0},5.3e-16,0.0},
  544. {{3.1415926535897932384626433832795,0.0},17,{5.644081624955091,0.0},5.6e-16,0.0},
  545. {{3.1415926535897932384626433832795,0.0},18,{5.966831036716778,0.0},6.0e-16,0.0},
  546. {{3.1415926535897932384626433832795,0.0},20,{6.611070983143532,0.0},6.6e-16,0.0},
  547. //{{3.141592653589793,0.0},0,{-4193528956200935.0,0.0},0.42,0.0}, // TODO fails for pi truncated to double precision
  548. {{3.141592653589793,0.0},1,{-0.3183098861837905,0.0},3.2e-17,0.0},
  549. {{3.141592653589793,0.0},2,{0.4105777788290165,0.0},4.1e-17,0.0},
  550. {{3.141592653589793,0.0},3,{0.8821173642494785,0.0},8.8e-17,0.0},
  551. {{3.141592653589793,0.0},4,{1.283506275095942,0.0},1.3e-16,0.0},
  552. {{3.141592653589793,0.0},5,{1.654748956488027,0.0},1.7e-16,0.0},
  553. {{3.141592653589793,0.0},6,{2.010012841716632,0.0},2.0e-16,0.0},
  554. {{3.141592653589793,0.0},7,{2.355698958080709,0.0},2.4e-16,0.0},
  555. {{3.141592653589793,0.0},8,{2.695156885492767,0.0},2.7e-16,0.0},
  556. {{3.141592653589793,0.0},9,{3.030322020436486,0.0},3.0e-16,0.0},
  557. {{3.141592653589793,0.0},10,{3.362395801011574,0.0},3.4e-16,0.0},
  558. {{3.141592653589793,0.0},11,{3.692165818289568,0.0},3.7e-16,0.0},
  559. {{3.141592653589793,0.0},12,{4.02017100538644,0.0},4.0e-16,0.0},
  560. {{3.141592653589793,0.0},13,{4.346793172787545,0.0},4.3e-16,0.0},
  561. {{3.141592653589793,0.0},14,{4.672310695202237,0.0},4.7e-16,0.0},
  562. {{3.141592653589793,0.0},15,{4.996931497029033,0.0},5.0e-16,0.0},
  563. {{3.141592653589793,0.0},16,{5.320814119475183,0.0},5.3e-16,0.0},
  564. {{3.141592653589793,0.0},17,{5.644081624955091,0.0},5.6e-16,0.0},
  565. {{3.141592653589793,0.0},18,{5.966831036716779,0.0},6.0e-16,0.0},
  566. {{3.141592653589793,0.0},20,{6.611070983143533,0.0},6.6e-16,0.0},
  567. };
  568. // complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
  569. std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
  570. D2_test_16digits
  571. = {
  572. {{0.07425,0.0},0,{-0.07438674986902373,0.0},7.4e-18,0.0},
  573. {{0.07425,0.0},1,{-13.39417131419206,0.0},1.3e-15,0.0},
  574. {{0.07425,0.0},2,{-26.91123162027382,0.0},2.7e-15,0.0},
  575. {{0.07425,0.0},3,{-40.3891849341013,0.0},4.0e-15,0.0},
  576. {{0.07425,0.0},4,{-53.86144505752241,0.0},5.4e-15,0.0},
  577. {{0.07575,0.0},0,{-0.07589521939842851,0.0},7.6e-18,0.0},
  578. {{0.07575,0.0},1,{-13.12600313416894,0.0},1.3e-15,0.0},
  579. {{0.07575,0.0},2,{-26.37734215323807,0.0},2.6e-15,0.0},
  580. {{0.07575,0.0},3,{-39.58880458732769,0.0},4.0e-15,0.0},
  581. {{0.07575,0.0},4,{-52.79445732439479,0.0},5.3e-15,0.0},
  582. {{7.5,0.0},0,{-2.706013866772691,0.0},2.7e-16,0.0},
  583. {{7.5,0.0},1,{0.2188602976402436,0.0},2.2e-17,0.0},
  584. {{7.5,0.0},2,{20.65104828146692,0.0},2.1e-15,0.0},
  585. {{7.5,0.0},3,{-0.4493801597873413,0.0},4.5e-17,0.0},
  586. {{7.5,0.0},4,{0.4842572533435941,0.0},4.8e-17,0.0},
  587. {{7.5,0.0},5,{4.81550654897139,0.0},4.8e-16,0.0},
  588. {{7.5,0.0},6,{-1.049034583259778,0.0},1.0e-16,0.0},
  589. {{7.5,0.0},7,{-0.4288861055358842,0.0},4.3e-17,0.0},
  590. {{7.5,0.0},8,{-0.3980175767871659,0.0},4.0e-17,0.0},
  591. {{7.5,0.0},9,{-0.5742246552691164,0.0},5.7e-17,0.0},
  592. {{7.5,0.0},10,{-0.809102874298828,0.0},8.1e-17,0.0},
  593. {{7.5,0.0},11,{-1.027254862439886,0.0},1.0e-16,0.0},
  594. {{7.5,0.0},12,{-1.219374574466933,0.0},1.2e-16,0.0},
  595. {{7.5,0.0},13,{-1.39466116147432,0.0},1.4e-16,0.0},
  596. {{7.5,0.0},14,{-1.560043091026306,0.0},1.6e-16,0.0},
  597. {{7.5,0.0},16,{-1.873757439540259,0.0},1.9e-16,0.0},
  598. {{7.5,0.0},17,{-2.025145514642434,0.0},2.0e-16,0.0},
  599. {{7.5,0.0},18,{-2.174018730753354,0.0},2.2e-16,0.0},
  600. {{7.5,0.0},19,{-2.320899679256512,0.0},2.3e-16,0.0},
  601. {{7.5,0.0},21,{-2.610108605596247,0.0},2.6e-16,0.0},
  602. {{7.5,0.0},22,{-2.752939994498599,0.0},2.8e-16,0.0},
  603. {{7.5,0.0},24,{-3.035926615655057,0.0},3.0e-16,0.0},
  604. {{7.5,0.0},26,{-3.316132176384959,0.0},3.3e-16,0.0},
  605. {{7.5,0.0},27,{-3.455410513492717,0.0},3.5e-16,0.0},
  606. {{7.5,0.0},30,{-3.870677968225079,0.0},3.9e-16,0.0},
  607. {{750.0,0.0},0,{1.117079400838733,0.0},1.1e-16,0.0},
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