1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
|
var tanh_data = [
[-0.9999983310699463, -6.998237084679027],
[-0.9999978542327881, -6.87257975132917],
[-0.999992847442627, -6.2705920974657525],
[-0.9999861717224121, -5.940967614084813],
[-0.9999828338623047, -5.832855225378502],
[-0.9999399185180664, -5.20646301208756],
[-0.9998834133148193, -4.8749821841810785],
[-0.9998509883880615, -4.752279497280338],
[-0.9996016025543213, -4.260504202858904],
[-0.9993612766265869, -4.0244334353203115],
[-0.9989283084869385, -3.7655641082999236],
[-0.9969782829284668, -3.246782610980921],
[-0.9950058460235596, -2.9950671179940938],
[-0.9942638874053955, -2.9256242749609536],
[-0.990715742111206, -2.6839646283308363],
[-0.9903340339660645, -2.663723350226518],
[-0.9760982990264893, -2.207464998348322],
[-0.975830078125, -2.201817459680556],
[-0.9728245735168457, -2.1424542308291437],
[-0.9643559455871582, -2.0046686756020917],
[-0.9377224445343018, -1.7188337346177065],
[-0.9362406730651855, -1.7066940482565154],
[-0.9310147762298584, -1.6659543005533146],
[-0.9284839630126953, -1.6472838718760747],
[-0.9270248413085938, -1.6368067340881562],
[-0.9075665473937988, -1.5135473477311114],
[-0.897477388381958, -1.4590986086331497],
[-0.8920106887817383, -1.431681573516303],
[-0.8776559829711914, -1.365471286049011],
[-0.864722728729248, -1.3117705583444539],
[-0.8482067584991455, -1.249725893334944],
[-0.8056559562683105, -1.1145246028592257],
[-0.8048388957977295, -1.112200609756455],
[-0.7801985740661621, -1.0458778330822556],
[-0.7749934196472168, -1.032711173436253],
[-0.7619285583496094, -1.0007967281362184],
[-0.7504425048828125, -0.9739672824457072],
[-0.7495596408843994, -0.9719492983286864],
[-0.7481319904327393, -0.968698942014487],
[-0.7459518909454346, -0.9637657636705832],
[-0.7401137351989746, -0.9507308314464193],
[-0.7289731502532959, -0.9265325319867653],
[-0.7226788997650146, -0.9132299082876396],
[-0.7161557674407959, -0.8997082193533088],
[-0.7017018795013428, -0.8706453720344796],
[-0.7013418674468994, -0.86993650130945],
[-0.691054105758667, -0.8499705913361888],
[-0.6847054958343506, -0.837919455842005],
[-0.6838164329528809, -0.8362476144993315],
[-0.6747090816497803, -0.8193374156276964],
[-0.6575610637664795, -0.7885046044142132],
[-0.6522045135498047, -0.7791255597799839],
[-0.6261923313140869, -0.7351275788820003],
[-0.623173713684082, -0.7301771459970386],
[-0.6067488193511963, -0.7037597526130627],
[-0.5838055610656738, -0.6682166303197608],
[-0.579524040222168, -0.6617457665293066],
[-0.5760939121246338, -0.656596458857398],
[-0.5654678344726562, -0.6408350116350283],
[-0.5578761100769043, -0.6297442839791668],
[-0.5523209571838379, -0.6217149641475687],
[-0.5396339893341064, -0.6036390747171698],
[-0.5128989219665527, -0.5666556256064771],
[-0.5087778568267822, -0.5610793900942042],
[-0.4977825880050659, -0.546353950571504],
[-0.4913865327835083, -0.5378865967606703],
[-0.48976075649261475, -0.5357455496477738],
[-0.48493504524230957, -0.5294166456244711],
[-0.4479050636291504, -0.4820764946679979],
[-0.4461095333099365, -0.4798325976916711],
[-0.4429593086242676, -0.47590653371561276],
[-0.42827916145324707, -0.45778739362936793],
[-0.40590059757232666, -0.4306933608076879],
[-0.40029656887054443, -0.4240020382545707],
[-0.3961341381072998, -0.4190551379319939],
[-0.3836275339126587, -0.40430627175908734],
[-0.36686253547668457, -0.3847928551425507],
[-0.3657644987106323, -0.38352464227459343],
[-0.33507001399993896, -0.3485286317501442],
[-0.32572221755981445, -0.3380352468276522],
[-0.3191967010498047, -0.3307524237890151],
[-0.3000025749206543, -0.3095224337886503],
[-0.29665136337280273, -0.3058438250228025],
[-0.2944457530975342, -0.3034271164344305],
[-0.2872810363769531, -0.29560018347246825],
[-0.27738428115844727, -0.28484608203169437],
[-0.2390844225883484, -0.2438028008332661],
[-0.23685944080352783, -0.24144425169391517],
[-0.2253856658935547, -0.2293228153248168],
[-0.22283810377120972, -0.22664053064745143],
[-0.21552443504333496, -0.21895773601143995],
[-0.2153375744819641, -0.21876178107952995],
[-0.21016258001327515, -0.21334143320771737],
[-0.20250272750854492, -0.2053409277979887],
[-0.19156384468078613, -0.19396008474133075],
[-0.18251943588256836, -0.18458771439322938],
[-0.17464947700500488, -0.17645844608618066],
[-0.15646183490753174, -0.15775766677189154],
[-0.15580910444259644, -0.15708862621964176],
[-0.15365445613861084, -0.15488112515549593],
[-0.122499018907547, -0.12311733609904851],
[-0.1088167130947113, -0.10924929296737837],
[-0.08792558312416077, -0.08815322150790302],
[-0.08401328325271606, -0.08421178632314608],
[-0.06121261417865753, -0.06128924075509796],
[-0.05341699719429016, -0.05346789060550386],
[-0.05047759413719177, -0.05052053189238029],
[-0.02924579381942749, -0.029254136237332657],
[-0.02485968917608261, -0.02486481220617492],
[-0.020469173789024353, -0.02047203328100153],
[-0.01882001757621765, -0.018822240021756347],
[-0.016152501106262207, -0.016153906073109205],
[-0.0032715508714318275, -0.003271562543358962],
[1.6504814008555524e-12, 1.6504814008555524e-12],
[2.0654207510961697e-12, 2.0654207510961697e-12],
[6.933230031758164e-12, 6.933230031758164e-12],
[1.3351444949627478e-11, 1.3351444949627478e-11],
[1.6399812063916386e-11, 1.6399812063916386e-11],
[5.730159402528301e-11, 5.730159402528301e-11],
[1.113731329382972e-10, 1.113731329382972e-10],
[1.4214707189097453e-10, 1.4214707189097453e-10],
[3.8006320313144215e-10, 3.8006320313144215e-10],
[6.09162720266454e-10, 6.09162720266454e-10],
[1.0221641311147778e-9, 1.0221641311147778e-9],
[2.8819222563924995e-9, 2.8819222563924995e-9],
[4.7627768395841485e-9, 4.7627768395841485e-9],
[8.854133426439148e-9, 8.854133426439148e-9],
[2.3050326092288742e-8, 2.3050326092288745e-8],
[5.9392490925347374e-8, 5.939249092534745e-8],
[1.166764889148908e-7, 1.1667648891489133e-7],
[2.3799674409019644e-7, 2.3799674409020094e-7],
[4.684659415943315e-7, 4.684659415943658e-7],
[9.382699772686465e-7, 9.382699772689218e-7],
[0.00000110398559627356, 0.0000011039855962740086],
[0.0000032917760108830407, 0.0000032917760108949305],
[0.00000751721381675452, 0.000007517213816896115],
[0.000015114666894078255, 0.000015114666895229252],
[0.00002986399340443313, 0.00002986399341331128],
[0.00003387028118595481, 0.000033870281198906756],
[0.00009066011989489198, 0.00009066012014327826],
[0.00021949532674625516, 0.0002194953302712184],
[0.00043952150736004114, 0.0004395215356621756],
[0.0006333151832222939, 0.0006333152678940465],
[0.001115123275667429, 0.0011151237378863419],
[0.001962467096745968, 0.001962469616086656],
[0.005553754046559334, 0.005553811147953338],
[0.007324676960706711, 0.0073248079567425],
[0.008691128343343735, 0.008691347183450786],
[0.011912941932678223, 0.011913505535037906],
[0.02993336319923401, 0.029942308168570204],
[0.05124260485172272, 0.05128752666822782],
[0.05473744869232178, 0.05479221508125444],
[0.06158891320228577, 0.061666963819518306],
[0.09375360608100891, 0.09402975380882211],
[0.09442159533500671, 0.09470370926367391],
[0.09443172812461853, 0.09471393321406026],
[0.09943729639053345, 0.09976699249016487],
[0.11201295256614685, 0.11248498303558895],
[0.12310260534286499, 0.12373016402339168],
[0.13562965393066406, 0.13647060950861248],
[0.13763350248336792, 0.13851257866094746],
[0.14749455451965332, 0.14857829980464834],
[0.1618971824645996, 0.16333433166790448],
[0.17051106691360474, 0.17219298693637355],
[0.17051833868026733, 0.17220047646299907],
[0.18562912940979004, 0.18780647318150087],
[0.18898820877075195, 0.1912876932893582],
[0.23206615447998047, 0.23637212433914523],
[0.23480379581451416, 0.2392675448267427],
[0.2646920680999756, 0.27114729033023005],
[0.2794986963272095, 0.2871382059344433],
[0.28789305686950684, 0.2962673858386819],
[0.292596697807312, 0.30140373665239234],
[0.3101649284362793, 0.320727882769785],
[0.3109246492385864, 0.3215686893944558],
[0.31145012378692627, 0.3221505056451929],
[0.3271782398223877, 0.3396649461699478],
[0.3574345111846924, 0.37394153436545424],
[0.3593693971633911, 0.37616159223090223],
[0.35960352420806885, 0.37643046596933716],
[0.3626827001571655, 0.3799714809649667],
[0.38961827754974365, 0.4113499159905353],
[0.3904266357421875, 0.41230330080214],
[0.3981136083602905, 0.4214052375603139],
[0.411507248878479, 0.43742438709579096],
[0.4120509624481201, 0.43807911823743495],
[0.41868770122528076, 0.4460997186945703],
[0.42136549949645996, 0.4493511447897729],
[0.4516327381134033, 0.48674948990473677],
[0.4538639783859253, 0.4895560176112375],
[0.4655507802963257, 0.5043748446613433],
[0.48124635219573975, 0.5246050193978663],
[0.48621630668640137, 0.5310932154891663],
[0.4898730516433716, 0.5358932909903701],
[0.5024838447570801, 0.5526234425942533],
[0.5074074268341064, 0.5592320547729962],
[0.5093221664428711, 0.5618140818296767],
[0.5143489837646484, 0.5686253097655146],
[0.5154285430908203, 0.5700943191671631],
[0.5234100818634033, 0.5810250825991418],
[0.5274472236633301, 0.5866018515043636],
[0.5309803485870361, 0.5915094458340507],
[0.5477793216705322, 0.6152030999229688],
[0.5577394962310791, 0.6295459624918965],
[0.5582785606384277, 0.6303287742357745],
[0.5843560695648193, 0.6690521906099505],
[0.5871362686157227, 0.6732844960442398],
[0.5878911018371582, 0.6744372167164567],
[0.5903406143188477, 0.6781887236623534],
[0.5945003032684326, 0.684597775489552],
[0.5957975387573242, 0.6866065102131665],
[0.5961520671844482, 0.6871563252400655],
[0.6005008220672607, 0.6939300827887145],
[0.6150004863739014, 0.7169242329194352],
[0.6162893772125244, 0.7189998055497108],
[0.6194069385528564, 0.7240422748778544],
[0.6285066604614258, 0.7389438896054792],
[0.6293842792510986, 0.7403958734869583],
[0.6416172981262207, 0.7609178886018204],
[0.6424276828765869, 0.7622965466812235],
[0.6437420845031738, 0.7645378650643101],
[0.6468508243560791, 0.769864795178161],
[0.6615910530090332, 0.7956379107512945],
[0.669950008392334, 0.8106524185805045],
[0.6813662052154541, 0.8316597473423232],
[0.6968657970428467, 0.8611812790659296],
[0.6981887817382812, 0.8637579113749143],
[0.7447831630706787, 0.9611360201710216],
[0.7518312931060791, 0.9771540941752986],
[0.7534394264221191, 0.9808634133542229],
[0.7567856311798096, 0.9886489208209699],
[0.7817282676696777, 1.0497991719828956],
[0.8115026950836182, 1.1314141444187586],
[0.814647912979126, 1.1406947755584418],
[0.8266689777374268, 1.1775230833699681],
[0.8313877582550049, 1.1926138225701433],
[0.8343038558959961, 1.2021323323039612],
[0.8416652679443359, 1.2268570644335162],
[0.8584413528442383, 1.2873896671573652],
[0.8678996562957764, 1.3245040433929398],
[0.8679344654083252, 1.3246451309261607],
[0.8800599575042725, 1.3760334877782177],
[0.9003539085388184, 1.4740852961194106],
[0.9099440574645996, 1.5271990851861994],
[0.9142425060272217, 1.5527768948273004],
[0.9149219989776611, 1.556931837197936],
[0.9184908866882324, 1.5792896628381612],
[0.9188928604125977, 1.5818663359427627],
[0.919395923614502, 1.5851082843320008],
[0.9296839237213135, 1.6560555223295368],
[0.9298396110534668, 1.6572041418041492],
[0.9352962970733643, 1.6990986433619266],
[0.9376416206359863, 1.718164398807965],
[0.9410912990570068, 1.7475084077246632],
[0.962122917175293, 1.9737180163455101],
[0.9748215675354004, 2.1811227771083783],
[0.9769454002380371, 2.2257214499698255],
[0.985663890838623, 2.4654635601650536],
[0.9880380630493164, 2.5565869228142004],
[0.9928233623504639, 2.8132383539094192],
[1e-300, 1e-300],
[0.00001, 0.000010000000000333334],
[0.3, 0.3095196042031117],
[1e-30, 1e-30],
[1e-10, 1e-10],
];
var sloppy_tolerance = 2; // FIXME
for (var [x, y] of tanh_data)
assertNear(Math.atanh(x), y, sloppy_tolerance);
assertNear(Math.atanh(+3 / 5), +Math.log(2), sloppy_tolerance);
assertNear(Math.atanh(-3 / 5), -Math.log(2), sloppy_tolerance);
for (var i = -1; i < 1; i += 0.05)
assertNear(Math.atanh(Math.tanh(i)), i, sloppy_tolerance);
reportCompare(0, 0, "ok");
|
