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Thomas Wouters1b7f8912007-09-19 03:06:30 +00001------------------------------------------------------------------------
2-- ln.decTest -- decimal natural logarithm --
Benjamin Petersonf17ff4e2008-07-31 16:32:12 +00003-- Copyright (c) IBM Corporation, 2005, 2008. All rights reserved. --
Thomas Wouters1b7f8912007-09-19 03:06:30 +00004------------------------------------------------------------------------
5-- Please see the document "General Decimal Arithmetic Testcases" --
6-- at http://www2.hursley.ibm.com/decimal for the description of --
7-- these testcases. --
8-- --
9-- These testcases are experimental ('beta' versions), and they --
10-- may contain errors. They are offered on an as-is basis. In --
11-- particular, achieving the same results as the tests here is not --
12-- a guarantee that an implementation complies with any Standard --
13-- or specification. The tests are not exhaustive. --
14-- --
15-- Please send comments, suggestions, and corrections to the author: --
16-- Mike Cowlishaw, IBM Fellow --
17-- IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK --
18-- mfc@uk.ibm.com --
19------------------------------------------------------------------------
Mark Dickinson8a546532009-10-08 16:30:38 +000020version: 2.59
Thomas Wouters1b7f8912007-09-19 03:06:30 +000021
22extended: 1
23precision: 16
24rounding: half_even
25maxExponent: 384
26minexponent: -383
27
28-- basics (examples in specification)
29precision: 9
30lnxs001 ln 0 -> -Infinity
31lnxs002 ln 1.000 -> 0
32lnxs003 ln 2.71828183 -> 1.00000000 Inexact Rounded
33lnxs004 ln 10 -> 2.30258509 Inexact Rounded
34lnxs005 ln +Infinity -> Infinity
35
36
37-- basics
38precision: 16
39lnx0001 ln 0 -> -Infinity
40lnx0002 ln 1E-9 -> -20.72326583694641 Inexact Rounded
41lnx0003 ln 0.0007 -> -7.264430222920869 Inexact Rounded
42lnx0004 ln 0.1 -> -2.302585092994046 Inexact Rounded
43lnx0005 ln 0.7 -> -0.3566749439387324 Inexact Rounded
44lnx0006 ln 1 -> 0
45lnx0007 ln 1.000 -> 0
46lnx0008 ln 1.5 -> 0.4054651081081644 Inexact Rounded
47lnx0009 ln 2 -> 0.6931471805599453 Inexact Rounded
48lnx0010 ln 2.718281828459045 -> 0.9999999999999999 Inexact Rounded
49lnx0011 ln 2.718281828459046 -> 1.000000000000000 Inexact Rounded
50lnx0012 ln 2.718281828459047 -> 1.000000000000001 Inexact Rounded
51lnx0013 ln 10 -> 2.302585092994046 Inexact Rounded
52lnx0014 ln 10.5 -> 2.351375257163478 Inexact Rounded
53lnx0015 ln 9999 -> 9.210240366975849 Inexact Rounded
54lnx0016 ln 1E6 -> 13.81551055796427 Inexact Rounded
55lnx0017 ln 1E+9 -> 20.72326583694641 Inexact Rounded
56lnx0018 ln +Infinity -> Infinity
57
58-- notable cases
59-- negatives
60lnx0021 ln -1E-9 -> NaN Invalid_operation
61lnx0022 ln -0.0007 -> NaN Invalid_operation
62lnx0023 ln -0.1 -> NaN Invalid_operation
63lnx0024 ln -0.7 -> NaN Invalid_operation
64lnx0025 ln -1 -> NaN Invalid_operation
65lnx0026 ln -1.5 -> NaN Invalid_operation
66lnx0027 ln -2 -> NaN Invalid_operation
67lnx0029 ln -10.5 -> NaN Invalid_operation
68lnx0028 ln -9999 -> NaN Invalid_operation
69lnx0030 ln -2.718281828459045 -> NaN Invalid_operation
70lnx0031 ln -2.718281828459046 -> NaN Invalid_operation
71lnx0032 ln -0 -> -Infinity
72lnx0033 ln -0E+17 -> -Infinity
73lnx0034 ln -0E-17 -> -Infinity
74-- other zeros
75lnx0041 ln 0 -> -Infinity
76lnx0042 ln 0E+17 -> -Infinity
77lnx0043 ln 0E-17 -> -Infinity
78-- infinities
79lnx0045 ln -Infinity -> NaN Invalid_operation
80lnx0046 ln +Infinity -> Infinity
81-- ones
82lnx0050 ln 1 -> 0
83lnx0051 ln 1.0 -> 0
84lnx0052 ln 1.000000000000000 -> 0
85lnx0053 ln 1.000000000000000000 -> 0
86
87-- lower precision basics
88Precision: 7
89lnx0101 ln 0 -> -Infinity
90lnx0102 ln 1E-9 -> -20.72327 Inexact Rounded
91lnx0103 ln 0.0007 -> -7.264430 Inexact Rounded
92lnx0104 ln 0.1 -> -2.302585 Inexact Rounded
93lnx0105 ln 0.7 -> -0.3566749 Inexact Rounded
94lnx0106 ln 1 -> 0
95lnx0107 ln 1.5 -> 0.4054651 Inexact Rounded
96lnx0108 ln 2 -> 0.6931472 Inexact Rounded
97lnx0109 ln 2.718281828459045 -> 1.000000 Inexact Rounded
98lnx0110 ln 2.718281828459046 -> 1.000000 Inexact Rounded
99lnx0111 ln 2.718281828459047 -> 1.000000 Inexact Rounded
100lnx0112 ln 10 -> 2.302585 Inexact Rounded
101lnx0113 ln 10.5 -> 2.351375 Inexact Rounded
102lnx0114 ln 9999 -> 9.210240 Inexact Rounded
103lnx0115 ln 1E6 -> 13.81551 Inexact Rounded
104lnx0116 ln 1E+9 -> 20.72327 Inexact Rounded
105lnx0117 ln +Infinity -> Infinity
106Precision: 2
107lnx0121 ln 0 -> -Infinity
108lnx0122 ln 1E-9 -> -21 Inexact Rounded
109lnx0123 ln 0.0007 -> -7.3 Inexact Rounded
110lnx0124 ln 0.1 -> -2.3 Inexact Rounded
111lnx0125 ln 0.7 -> -0.36 Inexact Rounded
112lnx0126 ln 1 -> 0
113lnx0127 ln 1.5 -> 0.41 Inexact Rounded
114lnx0128 ln 2 -> 0.69 Inexact Rounded
115lnx0129 ln 2.718281828459045 -> 1.0 Inexact Rounded
116lnx0130 ln 2.718281828459046 -> 1.0 Inexact Rounded
117lnx0131 ln 2.718281828459047 -> 1.0 Inexact Rounded
118lnx0132 ln 10 -> 2.3 Inexact Rounded
119lnx0133 ln 10.5 -> 2.4 Inexact Rounded
120lnx0134 ln 9999 -> 9.2 Inexact Rounded
121lnx0135 ln 1E6 -> 14 Inexact Rounded
122lnx0136 ln 1E+9 -> 21 Inexact Rounded
123lnx0137 ln +Infinity -> Infinity
124Precision: 1
125lnx0141 ln 0 -> -Infinity
126lnx0142 ln 1E-9 -> -2E+1 Inexact Rounded
127lnx0143 ln 0.0007 -> -7 Inexact Rounded
128lnx0144 ln 0.1 -> -2 Inexact Rounded
129lnx0145 ln 0.7 -> -0.4 Inexact Rounded
130lnx0146 ln 1 -> 0
131lnx0147 ln 1.5 -> 0.4 Inexact Rounded
132lnx0148 ln 2 -> 0.7 Inexact Rounded
133lnx0149 ln 2.718281828459045 -> 1 Inexact Rounded
134lnx0150 ln 2.718281828459046 -> 1 Inexact Rounded
135lnx0151 ln 2.718281828459047 -> 1 Inexact Rounded
136lnx0152 ln 10 -> 2 Inexact Rounded
137lnx0153 ln 10.5 -> 2 Inexact Rounded
138lnx0154 ln 9999 -> 9 Inexact Rounded
139lnx0155 ln 1E6 -> 1E+1 Inexact Rounded
140lnx0156 ln 1E+9 -> 2E+1 Inexact Rounded
141lnx0157 ln +Infinity -> Infinity
142
143-- group low-precision ln(1)s:
144precision: 1
145lnx0161 ln 1 -> 0
146precision: 2
147lnx0162 ln 1 -> 0
148precision: 3
149lnx0163 ln 1 -> 0
150precision: 4
151lnx0164 ln 1 -> 0
152precision: 5
153lnx0165 ln 1 -> 0
154precision: 6
155lnx0166 ln 1 -> 0
156precision: 7
157lnx0167 ln 1 -> 0
158precision: 8
159lnx0168 ln 1 -> 0
160
161-- edge-test ln(2) and ln(10) in case of lookasides
162precision: 45
163lnx201 ln 2 -> 0.693147180559945309417232121458176568075500134 Inexact Rounded
164lnx202 ln 10 -> 2.30258509299404568401799145468436420760110149 Inexact Rounded
165precision: 44
166lnx203 ln 2 -> 0.69314718055994530941723212145817656807550013 Inexact Rounded
167lnx204 ln 10 -> 2.3025850929940456840179914546843642076011015 Inexact Rounded
168precision: 43
169lnx205 ln 2 -> 0.6931471805599453094172321214581765680755001 Inexact Rounded
170lnx206 ln 10 -> 2.302585092994045684017991454684364207601101 Inexact Rounded
171precision: 42
172lnx207 ln 2 -> 0.693147180559945309417232121458176568075500 Inexact Rounded
173lnx208 ln 10 -> 2.30258509299404568401799145468436420760110 Inexact Rounded
174precision: 41
175lnx209 ln 2 -> 0.69314718055994530941723212145817656807550 Inexact Rounded
176lnx210 ln 10 -> 2.3025850929940456840179914546843642076011 Inexact Rounded
177precision: 40
178lnx211 ln 2 -> 0.6931471805599453094172321214581765680755 Inexact Rounded
179lnx212 ln 10 -> 2.302585092994045684017991454684364207601 Inexact Rounded
180precision: 39
181lnx213 ln 2 -> 0.693147180559945309417232121458176568076 Inexact Rounded
182lnx214 ln 10 -> 2.30258509299404568401799145468436420760 Inexact Rounded
183precision: 38
184lnx215 ln 2 -> 0.69314718055994530941723212145817656808 Inexact Rounded
185lnx216 ln 10 -> 2.3025850929940456840179914546843642076 Inexact Rounded
186precision: 37
187lnx217 ln 2 -> 0.6931471805599453094172321214581765681 Inexact Rounded
188lnx218 ln 10 -> 2.302585092994045684017991454684364208 Inexact Rounded
189precision: 36
190lnx219 ln 2 -> 0.693147180559945309417232121458176568 Inexact Rounded
191lnx220 ln 10 -> 2.30258509299404568401799145468436421 Inexact Rounded
192precision: 35
193lnx221 ln 2 -> 0.69314718055994530941723212145817657 Inexact Rounded
194lnx222 ln 10 -> 2.3025850929940456840179914546843642 Inexact Rounded
195precision: 34
196lnx223 ln 2 -> 0.6931471805599453094172321214581766 Inexact Rounded
197lnx224 ln 10 -> 2.302585092994045684017991454684364 Inexact Rounded
198precision: 33
199lnx225 ln 2 -> 0.693147180559945309417232121458177 Inexact Rounded
200lnx226 ln 10 -> 2.30258509299404568401799145468436 Inexact Rounded
201precision: 32
202lnx227 ln 2 -> 0.69314718055994530941723212145818 Inexact Rounded
203lnx228 ln 10 -> 2.3025850929940456840179914546844 Inexact Rounded
204precision: 31
205lnx229 ln 2 -> 0.6931471805599453094172321214582 Inexact Rounded
206lnx230 ln 10 -> 2.302585092994045684017991454684 Inexact Rounded
207precision: 30
208lnx231 ln 2 -> 0.693147180559945309417232121458 Inexact Rounded
209lnx232 ln 10 -> 2.30258509299404568401799145468 Inexact Rounded
210
211-- extreme input range values
212maxExponent: 384
213minExponent: -383
214Precision: 16
215
216lnx0901 ln 1e-400 -> -921.0340371976183 Inexact Rounded
217lnx0902 ln 1e+400 -> 921.0340371976183 Inexact Rounded
218lnx0903 ln 1e-999999 -> -2302582.790408953 Inexact Rounded
219lnx0904 ln 1e+999999 -> 2302582.790408953 Inexact Rounded
220lnx0905 ln 1e-1000013 -> -2302615.026600255 Inexact Rounded
221lnx0906 ln 2e-1000013 -> -2302614.333453074 Inexact Rounded
222
223lnx0910 ln 9.999999e+999999 -> 2302585.092993946 Inexact Rounded
224lnx0911 ln 9.9999999e+999999 -> 2302585.092994036 Inexact Rounded
225lnx0912 ln 9.99999999e+999999 -> 2302585.092994045 Inexact Rounded
226lnx0913 ln 9.999999999e+999999 -> 2302585.092994046 Inexact Rounded
227lnx0914 ln 9.999999999999e+999999 -> 2302585.092994046 Inexact Rounded
228lnx0915 ln 9.999999999999999e+999999 -> 2302585.092994046 Inexact Rounded
229lnx0916 ln 9.999999999999999999999999e+999999 -> 2302585.092994046 Inexact Rounded
230
231-- randoms
232-- P=50, within 0-999
233Precision: 50
234maxExponent: 384
235minExponent: -383
236lnx1501 ln 0.00098800906574486388604608477869812518857023768951 -> -6.9198186844033787995945147836955586009548513043689 Inexact Rounded
237lnx1502 ln 158.15866624664623070184595045304145949900714987827 -> 5.0635987458895647454907806507503825602758392287684 Inexact Rounded
238lnx1503 ln 0.00565661412059571925040285814021799775249288309321 -> -5.1749297776760632102047540300491550931651318975237 Inexact Rounded
239lnx1504 ln 0.00000006914232532620489602008402091666547903180607 -> -16.487098770877825308138976818688771638172333034347 Inexact Rounded
240lnx1505 ln 0.00025380374621297657504661540749355251231770070723 -> -8.2789492423005003205242162741569033124260321954589 Inexact Rounded
241lnx1506 ln 83.033654063877426261108592599182418953442677554806 -> 4.4192459962647137976949249810815698465031609843669 Inexact Rounded
242lnx1507 ln 0.00000000416863228092481651627734668440663678118729 -> -19.295677845122141772791294599714950175284915666430 Inexact Rounded
243lnx1508 ln 0.00000140847873187820570181214271960511080523457669 -> -13.473000349581967189668305314384952251556809480339 Inexact Rounded
244lnx1509 ln 66.176106555181527101630351127583944689752069132522 -> 4.1923194696232505883666171116966137694013431504252 Inexact Rounded
245lnx1510 ln 0.00000000000009899043487403590900111602024562297908 -> -29.943753166877840985821508112917991506656545174163 Inexact Rounded
246lnx1511 ln 0.00000000000324618296721747097510453388683912733569 -> -26.453541281444586819009546418577507163362590139422 Inexact Rounded
247lnx1512 ln 72.646968818463546449499147579023555008392860423385 -> 4.2856116660689646882852128853423566276718230426479 Inexact Rounded
248lnx1513 ln 0.00000000000000066755483124635612574263153825990523 -> -34.942910142802769319262875080398852491588707172483 Inexact Rounded
249lnx1514 ln 61.002910447202398204114909451851111424657671911002 -> 4.1109215752843377323363182051446177066434038096529 Inexact Rounded
250lnx1515 ln 917.06917611331980999227893584010544542312239174774 -> 6.8211829068303114128752453661946446979787826282907 Inexact Rounded
251lnx1516 ln 0.00000000170823794883673083358549749078972003965194 -> -20.187803436976150477297246666771626827057191023004 Inexact Rounded
252lnx1517 ln 0.53731767845358224445809761315159249898566542910649 -> -0.62116577939968409211736413628236285160048357000961 Inexact Rounded
253lnx1518 ln 0.00000000000000008965291392882804161299758708033373 -> -36.950585970980857376081265073276303670820056916206 Inexact Rounded
254lnx1519 ln 0.00000000006990244916026429904498278982530170295668 -> -23.383920429244457578373523508427783144589480420753 Inexact Rounded
255lnx1520 ln 4.0312542977070300070506064666536478373801988540614 -> 1.3940775676592451945795752796421391871302024763305 Inexact Rounded
256lnx1521 ln 271.84991311551875601432518819562391699324632396423 -> 5.6052501239873862517916679747146539808077431873478 Inexact Rounded
257lnx1522 ln 7.4118671629373864667229445746862314443895404818689 -> 2.0030823863706344628239147639318289961917060121141 Inexact Rounded
258lnx1523 ln 0.00000000000002026311452625364905357321664186034258 -> -31.529974180054438792043856877314043794320951134754 Inexact Rounded
259lnx1524 ln 0.00000000000009563398651261756952398250624737809347 -> -29.978248130576972953141284136962670021368834792579 Inexact Rounded
260lnx1525 ln 0.00000000009556772669409858653026558223465197808991 -> -23.071185939748285541228206161472956661196956741186 Inexact Rounded
261lnx1526 ln 6.8441648298027301292342057248737326152250794026761 -> 1.9233964395801946597272589473417948024361005082908 Inexact Rounded
262lnx1527 ln 0.00000000000073059699884439979394945822035704264577 -> -27.944914388353724718836101828677771967128509603158 Inexact Rounded
263lnx1528 ln 0.00000000000000002610078280419082263138064745416787 -> -38.184566367516207885573773320135965798717120735115 Inexact Rounded
264lnx1529 ln 0.00000000000000000150259517166294243088546806083283 -> -41.039337946266676108538170837580051699618334928421 Inexact Rounded
265lnx1530 ln 0.00000000000000087919160541714580707181969708502091 -> -34.667528818827671507514319744047440696187358676848 Inexact Rounded
266lnx1531 ln 0.00000000000395726725120787763271849577708068584598 -> -26.255467416961357741818735787226671938678424748431 Inexact Rounded
267lnx1532 ln 0.00000000002014334901669366218018377213150715938355 -> -24.628146955635359035289123027319969201693737159108 Inexact Rounded
268lnx1533 ln 0.00000008097927101101093117753938766241442896030637 -> -16.329072628469715178637178365710373398203190937454 Inexact Rounded
269lnx1534 ln 0.00000000000017115834162632864392039668116243984176 -> -29.396187292434898225453626794459285157263177528034 Inexact Rounded
270lnx1535 ln 0.39168317593866334087305459933723864294857086105035 -> -0.93730199062757240485836637306785037368746737693029 Inexact Rounded
271lnx1536 ln 79.335036798971515026519630103325369729637514127617 -> 4.3736798570287828823772149735170431010616961976965 Inexact Rounded
272lnx1537 ln 0.00000000000000056004952129926137413602116591493625 -> -35.118506463181870020730685884333000241039028127213 Inexact Rounded
273lnx1538 ln 0.00000006006035907843890918832481099660639553666078 -> -16.627915795747112566532705974853114454405010472043 Inexact Rounded
274lnx1539 ln 0.00000000085242024937414906371333826574632450587590 -> -20.882941460268101080186482230657774997273494107221 Inexact Rounded
275lnx1540 ln 0.00000000000043671099499262350316173246550771951561 -> -28.459504757285639221776305968469058854558726593945 Inexact Rounded
276
277-- P=34, within 0-999
278Precision: 34
279lnx1201 ln 0.0086732880815927182997566810334394 -> -4.747507311920844752486938187973721 Inexact Rounded
280lnx1202 ln 0.0007104103693460260609792222569854 -> -7.249667769903503023005549250347695 Inexact Rounded
281lnx1203 ln 786.8398945385105190697541493392742 -> 6.668024790031836340471824147010546 Inexact Rounded
282lnx1204 ln 0.7723073620282687656895190171967399 -> -0.2583726708506850868786816238217326 Inexact Rounded
283lnx1205 ln 0.0061057951517197631287183938412200 -> -5.098516933918797347064454103742635 Inexact Rounded
284lnx1206 ln 0.6181379708184393730103917562498745 -> -0.4810435926903365087463387760350021 Inexact Rounded
285lnx1207 ln 09.13888261229039989110753389096760 -> 2.212538125507975574509563027696021 Inexact Rounded
286lnx1208 ln 802.0105417063143696497292158147174 -> 6.687121752052341737234832203350214 Inexact Rounded
287lnx1209 ln 778.7749710387773713523028497333058 -> 6.657722135126935472086625031413031 Inexact Rounded
288lnx1210 ln 0.0024457295895346502513567679390616 -> -6.013411799940245345321348290398517 Inexact Rounded
289lnx1211 ln 0.0000511296947872828310338864217860 -> -9.881145118237281798081573131711636 Inexact Rounded
290lnx1212 ln 0.0000246803508602554924938685155658 -> -10.60950314264825661825360971430218 Inexact Rounded
291lnx1213 ln 9.027898199253511668242977766616082 -> 2.200319582778899029786017830557293 Inexact Rounded
292lnx1214 ln 0.0991812396542505631850692800904188 -> -2.310806398964672258823043180400384 Inexact Rounded
293lnx1215 ln 0.0000000000070238810143028811223924 -> -25.68170519961636647174714538290075 Inexact Rounded
294lnx1216 ln 2.630101665342826494730394729313167 -> 0.9670225014664367465128243039749559 Inexact Rounded
295lnx1217 ln 0.0056878928594359587691526063254683 -> -5.169415422904037819736637399445096 Inexact Rounded
296lnx1218 ln 567.3436047121057843908106573095590 -> 6.340965124964258486463444360787970 Inexact Rounded
297lnx1219 ln 1.199291248124655996614605745649725 -> 0.1817307557425911805765087755675657 Inexact Rounded
298lnx1220 ln 25.02050448582031098696267479135557 -> 3.219695668137659139544178905459317 Inexact Rounded
299lnx1221 ln 0.0000000000009939597023558756961300 -> -27.63707972996537636504396558259058 Inexact Rounded
300lnx1222 ln 0.0000007988551670159429716506430403 -> -14.04008617542597230988198612376415 Inexact Rounded
301lnx1223 ln 4.681515800176129184873770605589795 -> 1.543621946415383338972124445445748 Inexact Rounded
302lnx1224 ln 15.95126669161103011206658749345781 -> 2.769538242479483539275986395443539 Inexact Rounded
303lnx1225 ln 0.0301626783922211213675457279076066 -> -3.501149933677283341023932281826341 Inexact Rounded
304lnx1226 ln 000.0040544064881821770528475185674 -> -5.507950967557021671647165889608324 Inexact Rounded
305lnx1227 ln 29.01617095935593792095913785100360 -> 3.367853293862745651888450004473297 Inexact Rounded
306lnx1228 ln 78.01836167344736733024804243195323 -> 4.356944205055768575987781375003992 Inexact Rounded
307lnx1229 ln 0.0000000096545319316965321158634893 -> -18.45583840160965814462095477365013 Inexact Rounded
308lnx1230 ln 97.95475237720579752770587185074428 -> 4.584505661612812742208619358214729 Inexact Rounded
309lnx1231 ln 528.0609262050423246402564228432371 -> 6.269211667589138113396583894315956 Inexact Rounded
310lnx1232 ln 0.0000002250064349732969696660452972 -> -15.30713683526963996712167701738724 Inexact Rounded
311lnx1233 ln 47.97063637767998658567199049725754 -> 3.870589081585660692195989854842372 Inexact Rounded
312lnx1234 ln 0.0005394311344541432318853513414361 -> -7.524995428393925934087126702974121 Inexact Rounded
313lnx1235 ln 0.0000000090973385649567471674972633 -> -18.51528393158931783447035004125791 Inexact Rounded
314lnx1236 ln 0.0000000000238776490227576197317977 -> -24.45807828188389561331158879207262 Inexact Rounded
315lnx1237 ln 0.0000236587000231921532145326218758 -> -10.65177964499823314952429277979034 Inexact Rounded
316lnx1238 ln 499.1277448846130709827154556125942 -> 6.212862064761427967461188083514774 Inexact Rounded
317lnx1239 ln 0.0000003960192300284787663712417647 -> -14.74180306619298548093697608293284 Inexact Rounded
318lnx1240 ln 41.08268350829477451667228892495136 -> 3.715586706887278039173584859218960 Inexact Rounded
319
320-- P=16, within 0-99
321Precision: 16
322lnx1101 ln 7.964875261033948 -> 2.075041282352241 Inexact Rounded
323lnx1102 ln 13.54527396845394 -> 2.606037701870263 Inexact Rounded
324lnx1103 ln 0.0008026554341331 -> -7.127585034321814 Inexact Rounded
325lnx1104 ln 0.0000030582233261 -> -12.69767642300625 Inexact Rounded
326lnx1105 ln 0.0004477497509672 -> -7.711276073210766 Inexact Rounded
327lnx1106 ln 7.616268622474371 -> 2.030286567675148 Inexact Rounded
328lnx1107 ln 51.58329925806381 -> 3.943197962309569 Inexact Rounded
329lnx1108 ln 0.0018197497951263 -> -6.309056262549345 Inexact Rounded
330lnx1109 ln 2.956282457072984 -> 1.083932552334575 Inexact Rounded
331lnx1110 ln 0.3843325579189906 -> -0.9562470649400558 Inexact Rounded
332lnx1111 ln 0.0074466329265663 -> -4.899993304919237 Inexact Rounded
333lnx1112 ln 0.0003372478532993 -> -7.994692428206378 Inexact Rounded
334lnx1113 ln 0.0084792263167809 -> -4.770136069569271 Inexact Rounded
335lnx1114 ln 5.926756998151102 -> 1.779477182834305 Inexact Rounded
336lnx1115 ln 9.025699152180897 -> 2.200075969604119 Inexact Rounded
337lnx1116 ln 1.910124643533526 -> 0.6471684983238183 Inexact Rounded
338lnx1117 ln 0.8158922711411020 -> -0.2034729533939387 Inexact Rounded
339lnx1118 ln 0.0067080016475322 -> -5.004454189414139 Inexact Rounded
340lnx1119 ln 0.0047583242092716 -> -5.347859729601094 Inexact Rounded
341lnx1120 ln 0.0386647411641339 -> -3.252827175263113 Inexact Rounded
342lnx1121 ln 0.0050226427841761 -> -5.293799032774131 Inexact Rounded
343lnx1122 ln 6.927937541637261 -> 1.935562155866906 Inexact Rounded
344lnx1123 ln 0.0000095745343513 -> -11.55640365579814 Inexact Rounded
345lnx1124 ln 1.602465492956538 -> 0.4715433763243936 Inexact Rounded
346lnx1125 ln 38.98415625087535 -> 3.663155313610213 Inexact Rounded
347lnx1126 ln 5.343182042276734 -> 1.675821363568112 Inexact Rounded
348lnx1127 ln 55.89763703245816 -> 4.023522107934110 Inexact Rounded
349lnx1128 ln 0.7445257810280847 -> -0.2950077988101030 Inexact Rounded
350lnx1129 ln 1.631407314946094 -> 0.4894430257201248 Inexact Rounded
351lnx1130 ln 0.0005462451932602 -> -7.512442611116852 Inexact Rounded
352lnx1131 ln 0.0000864173269362 -> -9.356322359017317 Inexact Rounded
353lnx1132 ln 5.227161719132849 -> 1.653868438439637 Inexact Rounded
354lnx1133 ln 60.57078466941998 -> 4.103812675662452 Inexact Rounded
355lnx1134 ln 0.0992864325333160 -> -2.309746348350318 Inexact Rounded
356lnx1135 ln 09.48564268447325 -> 2.249779359074983 Inexact Rounded
357lnx1136 ln 0.0036106089355634 -> -5.623878840650787 Inexact Rounded
358lnx1137 ln 1.805176865587172 -> 0.5906585734593707 Inexact Rounded
359lnx1138 ln 62.59363259642255 -> 4.136663557220559 Inexact Rounded
360lnx1139 ln 4.373828261137201 -> 1.475638657912000 Inexact Rounded
361lnx1140 ln 0.994483524148738 -> -0.005531747794938690 Inexact Rounded
362
363-- P=7, within 0-9
364Precision: 7
365lnx1001 ln 0.0912025 -> -2.394673 Inexact Rounded
366lnx1002 ln 0.9728626 -> -0.02751242 Inexact Rounded
367lnx1003 ln 0.3886032 -> -0.9451965 Inexact Rounded
368lnx1004 ln 8.798639 -> 2.174597 Inexact Rounded
369lnx1005 ln 2.459121 -> 0.8998040 Inexact Rounded
370lnx1006 ln 2.013193 -> 0.6997220 Inexact Rounded
371lnx1007 ln 9.064857 -> 2.204405 Inexact Rounded
372lnx1008 ln 5.796417 -> 1.757240 Inexact Rounded
373lnx1009 ln 0.1143471 -> -2.168517 Inexact Rounded
374lnx1010 ln 0.5341542 -> -0.6270707 Inexact Rounded
375lnx1011 ln 6.693781 -> 1.901179 Inexact Rounded
376lnx1012 ln 0.0081779 -> -4.806320 Inexact Rounded
377lnx1013 ln 8.313616 -> 2.117895 Inexact Rounded
378lnx1014 ln 3.486925 -> 1.249020 Inexact Rounded
379lnx1015 ln 0.1801401 -> -1.714020 Inexact Rounded
380lnx1016 ln 0.5227148 -> -0.6487193 Inexact Rounded
381lnx1017 ln 7.818111 -> 2.056443 Inexact Rounded
382lnx1018 ln 0.0870671 -> -2.441076 Inexact Rounded
383lnx1019 ln 8.153966 -> 2.098504 Inexact Rounded
384lnx1020 ln 2.040975 -> 0.7134276 Inexact Rounded
385lnx1021 ln 1.481642 -> 0.3931509 Inexact Rounded
386lnx1022 ln 0.2610123 -> -1.343188 Inexact Rounded
387lnx1023 ln 0.466723 -> -0.7620193 Inexact Rounded
388lnx1024 ln 0.0518756 -> -2.958907 Inexact Rounded
389lnx1025 ln 2.056410 -> 0.7209617 Inexact Rounded
390lnx1026 ln 0.181522 -> -1.706378 Inexact Rounded
391lnx1027 ln 0.515551 -> -0.6625190 Inexact Rounded
392lnx1028 ln 8.425089 -> 2.131214 Inexact Rounded
393lnx1029 ln 2.077091 -> 0.7309684 Inexact Rounded
394lnx1030 ln 6.212705 -> 1.826596 Inexact Rounded
395lnx1031 ln 5.729343 -> 1.745601 Inexact Rounded
396lnx1032 ln 4.831251 -> 1.575105 Inexact Rounded
397lnx1033 ln 2.029760 -> 0.7079176 Inexact Rounded
398lnx1034 ln 8.615060 -> 2.153512 Inexact Rounded
399lnx1035 ln 0.0611511 -> -2.794407 Inexact Rounded
400lnx1036 ln 5.195269 -> 1.647748 Inexact Rounded
401lnx1037 ln 9.617686 -> 2.263604 Inexact Rounded
402lnx1038 ln 0.0049382 -> -5.310754 Inexact Rounded
403lnx1039 ln 2.786840 -> 1.024908 Inexact Rounded
404lnx1040 ln 0.0091073 -> -4.698679 Inexact Rounded
405
406-- from here 3-digit tests are based on reverse exp tests
407precision: 9
408rounding: half_even
409maxExponent: 384
410minexponent: -383
411
412lnx001 ln 0 -> -Infinity
413lnx002 ln 0.367879441 -> -1.00000000 Inexact Rounded
414lnx003 ln 1 -> 0
415lnx005 ln 2.71828183 -> 1.00000000 Inexact Rounded
416lnx006 ln 2.00000000 -> 0.693147181 Inexact Rounded
417lnx007 ln +Infinity -> Infinity
418
419-- tiny edge cases
420precision: 7
421lnx011 ln 1.105171 -> 0.1000001 Inexact Rounded
422lnx012 ln 1.010050 -> 0.009999835 Inexact Rounded
423lnx013 ln 1.000010 -> 0.000009999950 Inexact Rounded
424lnx014 ln 1.000001 -> 9.999995E-7 Inexact Rounded
425lnx015 ln 1.000000 -> 0
426
427-- basic e=0, e=1, e=2, e=4, e>=8 cases
428precision: 7
429lnx041 ln 2.718282 -> 1.000000 Inexact Rounded
430lnx042 ln 0.3678794 -> -1.000000 Inexact Rounded
431lnx043 ln 22026.47 -> 10.00000 Inexact Rounded
432lnx044 ln 0.00004539993 -> -10.00000 Inexact Rounded
433lnx045 ln 2.688117E+43 -> 100.0000 Inexact Rounded
434lnx046 ln 3.720076E-44 -> -100.0000 Inexact Rounded
435lnx047 ln Infinity -> Infinity
436lnx048 ln 0E-389 -> -Infinity
437
438-- miscellanea
439precision: 16
440lnx055 ln 2.717658486884572E-236 -> -542.4103112874415 Inexact Rounded
441precision: 17
442lnx056 ln 2.7176584868845721E-236 -> -542.41031128744146 Inexact Rounded
443precision: 18
444lnx057 ln 2.71765848688457211E-236 -> -542.410311287441459 Inexact Rounded
445precision: 19
446lnx058 ln 2.717658486884572112E-236 -> -542.4103112874414592 Inexact Rounded
447precision: 20
448lnx059 ln 2.7176584868845721118E-236 -> -542.41031128744145917 Inexact Rounded
449
450-- inputs ending in ..500.., ..499.., ..100.., ..999.. sequences
451precision: 50
452lnx102 ln 0.9999999100000040499998785000027 -> -9.0000000000000000000000033749953829996446124861750E-8 Inexact Rounded
453precision: 30
454lnx103 ln 0.999999910000004049999878500003 -> -8.99999999999999999999997337499E-8 Inexact Rounded
455precision: 29
456lnx104 ln 0.99999991000000404999987850000 -> -9.0000000000000000000002733750E-8 Inexact Rounded
457precision: 28
458lnx105 ln 0.9999999100000040499998785000 -> -9.000000000000000000000273375E-8 Inexact Rounded
459precision: 27
460lnx106 ln 0.999999910000004049999878500 -> -9.00000000000000000000027338E-8 Inexact Rounded
461precision: 26
462lnx107 ln 0.99999991000000404999987850 -> -9.0000000000000000000002734E-8 Inexact Rounded
463precision: 25
464lnx108 ln 0.9999999100000040499998785 -> -9.000000000000000000000273E-8 Inexact Rounded
465precision: 24
466lnx109 ln 0.999999910000004049999879 -> -8.99999999999999995000027E-8 Inexact Rounded
467precision: 23
468lnx110 ln 0.99999991000000404999988 -> -8.9999999999999998500003E-8 Inexact Rounded
469precision: 22
470lnx111 ln 0.9999999100000040499999 -> -8.999999999999997850000E-8 Inexact Rounded
471precision: 21
472lnx112 ln 0.999999910000004050000 -> -8.99999999999998785000E-8 Inexact Rounded
473precision: 20
474lnx113 ln 0.99999991000000405000 -> -8.9999999999999878500E-8 Inexact Rounded
475precision: 19
476lnx114 ln 0.9999999100000040500 -> -8.999999999999987850E-8 Inexact Rounded
477precision: 18
478lnx115 ln 0.999999910000004050 -> -8.99999999999998785E-8 Inexact Rounded
479-- next may be a > 0.5ulp case; a more precise answer is:
480-- -8.99999999999998784999918E-8
481precision: 17
482lnx116 ln 0.99999991000000405 -> -8.9999999999999878E-8 Inexact Rounded
483precision: 16
484lnx117 ln 0.9999999100000040 -> -9.000000004999988E-8 Inexact Rounded
485precision: 15
486lnx118 ln 0.999999910000004 -> -9.00000000499999E-8 Inexact Rounded
487precision: 14
488lnx119 ln 0.99999991000000 -> -9.0000004050000E-8 Inexact Rounded
489precision: 13
490lnx120 ln 0.9999999100000 -> -9.000000405000E-8 Inexact Rounded
491precision: 12
492lnx121 ln 0.999999910000 -> -9.00000040500E-8 Inexact Rounded
493precision: 11
494lnx122 ln 0.99999991000 -> -9.0000004050E-8 Inexact Rounded
495precision: 10
496lnx123 ln 0.9999999100 -> -9.000000405E-8 Inexact Rounded
497precision: 9
498lnx124 ln 0.999999910 -> -9.00000041E-8 Inexact Rounded
499precision: 8
500lnx125 ln 0.99999991 -> -9.0000004E-8 Inexact Rounded
501precision: 7
502lnx126 ln 0.9999999 -> -1.000000E-7 Inexact Rounded
503precision: 16
504lnx126b ln 0.9999999 -> -1.000000050000003E-7 Inexact Rounded
505precision: 6
506lnx127 ln 0.999999 -> -0.00000100000 Inexact Rounded
507precision: 5
508lnx128 ln 0.99999 -> -0.000010000 Inexact Rounded
509precision: 4
510lnx129 ln 0.9999 -> -0.0001000 Inexact Rounded
511precision: 3
512lnx130 ln 0.999 -> -0.00100 Inexact Rounded
513precision: 2
514lnx131 ln 0.99 -> -0.010 Inexact Rounded
515precision: 1
516lnx132 ln 0.9 -> -0.1 Inexact Rounded
517
518
519-- cases near 1 -- 1 2345678901234567890
520precision: 20
521lnx401 ln 2.7182818284589365041 -> 0.99999999999996000000 Inexact Rounded
522lnx402 ln 2.7182818284589636869 -> 0.99999999999997000000 Inexact Rounded
523lnx403 ln 2.7182818284589908697 -> 0.99999999999997999999 Inexact Rounded
524lnx404 ln 2.7182818284590180525 -> 0.99999999999998999998 Inexact Rounded
525lnx405 ln 2.7182818284590452354 -> 1.0000000000000000000 Inexact Rounded
526lnx406 ln 2.7182818284593170635 -> 1.0000000000001000000 Inexact Rounded
527lnx407 ln 2.7182818284595888917 -> 1.0000000000002000000 Inexact Rounded
528precision: 14
529lnx411 ln 2.7182818284589 -> 0.99999999999995 Inexact Rounded
530lnx413 ln 2.7182818284590 -> 0.99999999999998 Inexact Rounded
531lnx416 ln 2.7182818284591 -> 1.0000000000000 Inexact Rounded
532lnx417 ln 2.7182818284592 -> 1.0000000000001 Inexact Rounded
533
534-- overflows, including some exp overprecise borderlines
535precision: 7
536maxExponent: 384
537minExponent: -383
538lnx709 ln 9.999999E+384 -> 886.4953 Inexact Rounded
539lnx711 ln 9.999992E+384 -> 886.4953 Inexact Rounded
540precision: 16
541lnx722 ln 9.999999999999999E+384 -> 886.4952608027076 Inexact Rounded
542lnx724 ln 9.999999999999917E+384 -> 886.4952608027076 Inexact Rounded
543lnx726 ln 9.999999999999117E+384 -> 886.4952608027075 Inexact Rounded
544-- and more...
545precision: 15
546maxExponent: 999
547minExponent: -999
548lnx731 ln 9.99999999999999E+999 -> 2302.58509299405 Inexact Rounded
549-- next may be a > 0.5ulp case; a more precise answer is:
550-- 2302.58509299404495001799145442
551lnx732 ln 9.99999999999266E+999 -> 2302.58509299404 Inexact Rounded
552lnx733 ln 9.99999999999265E+999 -> 2302.58509299404 Inexact Rounded
553lnx734 ln 9.99999999999264E+999 -> 2302.58509299404 Inexact Rounded
554
555-- subnormals and underflows for exp, including underflow-to-zero edge point
556precision: 7
557maxExponent: 384
558minExponent: -383
559lnx751 ln 0E-389 -> -Infinity
560lnx758 ln 1.000001E-383 -> -881.8901 Inexact Rounded
561lnx759 ln 9.99991E-384 -> -881.8901 Inexact Rounded
562lnx760 ln 4.4605E-385 -> -885.0000 Inexact Rounded
563lnx761 ln 2.221E-386 -> -887.9999 Inexact Rounded
564lnx762 ln 3.01E-387 -> -889.9985 Inexact Rounded
565lnx763 ln 1.7E-388 -> -892.8724 Inexact Rounded
566lnx764 ln 1.5E-388 -> -892.9976 Inexact Rounded
567lnx765 ln 9E-389 -> -893.5084 Inexact Rounded
568lnx766 ln 1E-389 -> -895.7056 Inexact Rounded
569lnx774 ln 0E-389 -> -Infinity
570
571-- special values
572lnx820 ln Infinity -> Infinity
573lnx821 ln 0 -> -Infinity
574lnx822 ln NaN -> NaN
575lnx823 ln sNaN -> NaN Invalid_operation
576-- propagating NaNs
577lnx824 ln sNaN123 -> NaN123 Invalid_operation
578lnx825 ln -sNaN321 -> -NaN321 Invalid_operation
579lnx826 ln NaN456 -> NaN456
580lnx827 ln -NaN654 -> -NaN654
581lnx828 ln NaN1 -> NaN1
582
583-- Invalid operations due to restrictions
584-- [next two probably skipped by most test harnesses]
585precision: 100000000
586lnx901 ln 1 -> NaN Invalid_context
587precision: 99999999
588lnx902 ln 0 -> NaN Invalid_context
589
590precision: 9
591maxExponent: 1000000
592minExponent: -999999
593lnx903 ln 1 -> NaN Invalid_context
594maxExponent: 999999
595minExponent: -999999
596lnx904 ln 0 -> -Infinity
597maxExponent: 999999
598minExponent: -1000000
599lnx905 ln 1 -> NaN Invalid_context
600maxExponent: 999999
601minExponent: -999998
602lnx906 ln 0 -> -Infinity
603
604-- payload decapitate
605precision: 5
606lnx910 ln -sNaN1234567890 -> -NaN67890 Invalid_operation
607
608-- Null test
609lnx900 ln # -> NaN Invalid_operation
610
611