1 ------------------------------------------------------------------------ 2 -- ln.decTest -- decimal natural logarithm -- 3 -- Copyright (c) IBM Corporation, 2005, 2008. All rights reserved. -- 4 ------------------------------------------------------------------------ 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 (a] uk.ibm.com -- 19 ------------------------------------------------------------------------ 20 version: 2.59 21 22 extended: 1 23 precision: 16 24 rounding: half_even 25 maxExponent: 384 26 minexponent: -383 27 28 -- basics (examples in specification) 29 precision: 9 30 lnxs001 ln 0 -> -Infinity 31 lnxs002 ln 1.000 -> 0 32 lnxs003 ln 2.71828183 -> 1.00000000 Inexact Rounded 33 lnxs004 ln 10 -> 2.30258509 Inexact Rounded 34 lnxs005 ln +Infinity -> Infinity 35 36 37 -- basics 38 precision: 16 39 lnx0001 ln 0 -> -Infinity 40 lnx0002 ln 1E-9 -> -20.72326583694641 Inexact Rounded 41 lnx0003 ln 0.0007 -> -7.264430222920869 Inexact Rounded 42 lnx0004 ln 0.1 -> -2.302585092994046 Inexact Rounded 43 lnx0005 ln 0.7 -> -0.3566749439387324 Inexact Rounded 44 lnx0006 ln 1 -> 0 45 lnx0007 ln 1.000 -> 0 46 lnx0008 ln 1.5 -> 0.4054651081081644 Inexact Rounded 47 lnx0009 ln 2 -> 0.6931471805599453 Inexact Rounded 48 lnx0010 ln 2.718281828459045 -> 0.9999999999999999 Inexact Rounded 49 lnx0011 ln 2.718281828459046 -> 1.000000000000000 Inexact Rounded 50 lnx0012 ln 2.718281828459047 -> 1.000000000000001 Inexact Rounded 51 lnx0013 ln 10 -> 2.302585092994046 Inexact Rounded 52 lnx0014 ln 10.5 -> 2.351375257163478 Inexact Rounded 53 lnx0015 ln 9999 -> 9.210240366975849 Inexact Rounded 54 lnx0016 ln 1E6 -> 13.81551055796427 Inexact Rounded 55 lnx0017 ln 1E+9 -> 20.72326583694641 Inexact Rounded 56 lnx0018 ln +Infinity -> Infinity 57 58 -- notable cases 59 -- negatives 60 lnx0021 ln -1E-9 -> NaN Invalid_operation 61 lnx0022 ln -0.0007 -> NaN Invalid_operation 62 lnx0023 ln -0.1 -> NaN Invalid_operation 63 lnx0024 ln -0.7 -> NaN Invalid_operation 64 lnx0025 ln -1 -> NaN Invalid_operation 65 lnx0026 ln -1.5 -> NaN Invalid_operation 66 lnx0027 ln -2 -> NaN Invalid_operation 67 lnx0029 ln -10.5 -> NaN Invalid_operation 68 lnx0028 ln -9999 -> NaN Invalid_operation 69 lnx0030 ln -2.718281828459045 -> NaN Invalid_operation 70 lnx0031 ln -2.718281828459046 -> NaN Invalid_operation 71 lnx0032 ln -0 -> -Infinity 72 lnx0033 ln -0E+17 -> -Infinity 73 lnx0034 ln -0E-17 -> -Infinity 74 -- other zeros 75 lnx0041 ln 0 -> -Infinity 76 lnx0042 ln 0E+17 -> -Infinity 77 lnx0043 ln 0E-17 -> -Infinity 78 -- infinities 79 lnx0045 ln -Infinity -> NaN Invalid_operation 80 lnx0046 ln +Infinity -> Infinity 81 -- ones 82 lnx0050 ln 1 -> 0 83 lnx0051 ln 1.0 -> 0 84 lnx0052 ln 1.000000000000000 -> 0 85 lnx0053 ln 1.000000000000000000 -> 0 86 87 -- lower precision basics 88 Precision: 7 89 lnx0101 ln 0 -> -Infinity 90 lnx0102 ln 1E-9 -> -20.72327 Inexact Rounded 91 lnx0103 ln 0.0007 -> -7.264430 Inexact Rounded 92 lnx0104 ln 0.1 -> -2.302585 Inexact Rounded 93 lnx0105 ln 0.7 -> -0.3566749 Inexact Rounded 94 lnx0106 ln 1 -> 0 95 lnx0107 ln 1.5 -> 0.4054651 Inexact Rounded 96 lnx0108 ln 2 -> 0.6931472 Inexact Rounded 97 lnx0109 ln 2.718281828459045 -> 1.000000 Inexact Rounded 98 lnx0110 ln 2.718281828459046 -> 1.000000 Inexact Rounded 99 lnx0111 ln 2.718281828459047 -> 1.000000 Inexact Rounded 100 lnx0112 ln 10 -> 2.302585 Inexact Rounded 101 lnx0113 ln 10.5 -> 2.351375 Inexact Rounded 102 lnx0114 ln 9999 -> 9.210240 Inexact Rounded 103 lnx0115 ln 1E6 -> 13.81551 Inexact Rounded 104 lnx0116 ln 1E+9 -> 20.72327 Inexact Rounded 105 lnx0117 ln +Infinity -> Infinity 106 Precision: 2 107 lnx0121 ln 0 -> -Infinity 108 lnx0122 ln 1E-9 -> -21 Inexact Rounded 109 lnx0123 ln 0.0007 -> -7.3 Inexact Rounded 110 lnx0124 ln 0.1 -> -2.3 Inexact Rounded 111 lnx0125 ln 0.7 -> -0.36 Inexact Rounded 112 lnx0126 ln 1 -> 0 113 lnx0127 ln 1.5 -> 0.41 Inexact Rounded 114 lnx0128 ln 2 -> 0.69 Inexact Rounded 115 lnx0129 ln 2.718281828459045 -> 1.0 Inexact Rounded 116 lnx0130 ln 2.718281828459046 -> 1.0 Inexact Rounded 117 lnx0131 ln 2.718281828459047 -> 1.0 Inexact Rounded 118 lnx0132 ln 10 -> 2.3 Inexact Rounded 119 lnx0133 ln 10.5 -> 2.4 Inexact Rounded 120 lnx0134 ln 9999 -> 9.2 Inexact Rounded 121 lnx0135 ln 1E6 -> 14 Inexact Rounded 122 lnx0136 ln 1E+9 -> 21 Inexact Rounded 123 lnx0137 ln +Infinity -> Infinity 124 Precision: 1 125 lnx0141 ln 0 -> -Infinity 126 lnx0142 ln 1E-9 -> -2E+1 Inexact Rounded 127 lnx0143 ln 0.0007 -> -7 Inexact Rounded 128 lnx0144 ln 0.1 -> -2 Inexact Rounded 129 lnx0145 ln 0.7 -> -0.4 Inexact Rounded 130 lnx0146 ln 1 -> 0 131 lnx0147 ln 1.5 -> 0.4 Inexact Rounded 132 lnx0148 ln 2 -> 0.7 Inexact Rounded 133 lnx0149 ln 2.718281828459045 -> 1 Inexact Rounded 134 lnx0150 ln 2.718281828459046 -> 1 Inexact Rounded 135 lnx0151 ln 2.718281828459047 -> 1 Inexact Rounded 136 lnx0152 ln 10 -> 2 Inexact Rounded 137 lnx0153 ln 10.5 -> 2 Inexact Rounded 138 lnx0154 ln 9999 -> 9 Inexact Rounded 139 lnx0155 ln 1E6 -> 1E+1 Inexact Rounded 140 lnx0156 ln 1E+9 -> 2E+1 Inexact Rounded 141 lnx0157 ln +Infinity -> Infinity 142 143 -- group low-precision ln(1)s: 144 precision: 1 145 lnx0161 ln 1 -> 0 146 precision: 2 147 lnx0162 ln 1 -> 0 148 precision: 3 149 lnx0163 ln 1 -> 0 150 precision: 4 151 lnx0164 ln 1 -> 0 152 precision: 5 153 lnx0165 ln 1 -> 0 154 precision: 6 155 lnx0166 ln 1 -> 0 156 precision: 7 157 lnx0167 ln 1 -> 0 158 precision: 8 159 lnx0168 ln 1 -> 0 160 161 -- edge-test ln(2) and ln(10) in case of lookasides 162 precision: 45 163 lnx201 ln 2 -> 0.693147180559945309417232121458176568075500134 Inexact Rounded 164 lnx202 ln 10 -> 2.30258509299404568401799145468436420760110149 Inexact Rounded 165 precision: 44 166 lnx203 ln 2 -> 0.69314718055994530941723212145817656807550013 Inexact Rounded 167 lnx204 ln 10 -> 2.3025850929940456840179914546843642076011015 Inexact Rounded 168 precision: 43 169 lnx205 ln 2 -> 0.6931471805599453094172321214581765680755001 Inexact Rounded 170 lnx206 ln 10 -> 2.302585092994045684017991454684364207601101 Inexact Rounded 171 precision: 42 172 lnx207 ln 2 -> 0.693147180559945309417232121458176568075500 Inexact Rounded 173 lnx208 ln 10 -> 2.30258509299404568401799145468436420760110 Inexact Rounded 174 precision: 41 175 lnx209 ln 2 -> 0.69314718055994530941723212145817656807550 Inexact Rounded 176 lnx210 ln 10 -> 2.3025850929940456840179914546843642076011 Inexact Rounded 177 precision: 40 178 lnx211 ln 2 -> 0.6931471805599453094172321214581765680755 Inexact Rounded 179 lnx212 ln 10 -> 2.302585092994045684017991454684364207601 Inexact Rounded 180 precision: 39 181 lnx213 ln 2 -> 0.693147180559945309417232121458176568076 Inexact Rounded 182 lnx214 ln 10 -> 2.30258509299404568401799145468436420760 Inexact Rounded 183 precision: 38 184 lnx215 ln 2 -> 0.69314718055994530941723212145817656808 Inexact Rounded 185 lnx216 ln 10 -> 2.3025850929940456840179914546843642076 Inexact Rounded 186 precision: 37 187 lnx217 ln 2 -> 0.6931471805599453094172321214581765681 Inexact Rounded 188 lnx218 ln 10 -> 2.302585092994045684017991454684364208 Inexact Rounded 189 precision: 36 190 lnx219 ln 2 -> 0.693147180559945309417232121458176568 Inexact Rounded 191 lnx220 ln 10 -> 2.30258509299404568401799145468436421 Inexact Rounded 192 precision: 35 193 lnx221 ln 2 -> 0.69314718055994530941723212145817657 Inexact Rounded 194 lnx222 ln 10 -> 2.3025850929940456840179914546843642 Inexact Rounded 195 precision: 34 196 lnx223 ln 2 -> 0.6931471805599453094172321214581766 Inexact Rounded 197 lnx224 ln 10 -> 2.302585092994045684017991454684364 Inexact Rounded 198 precision: 33 199 lnx225 ln 2 -> 0.693147180559945309417232121458177 Inexact Rounded 200 lnx226 ln 10 -> 2.30258509299404568401799145468436 Inexact Rounded 201 precision: 32 202 lnx227 ln 2 -> 0.69314718055994530941723212145818 Inexact Rounded 203 lnx228 ln 10 -> 2.3025850929940456840179914546844 Inexact Rounded 204 precision: 31 205 lnx229 ln 2 -> 0.6931471805599453094172321214582 Inexact Rounded 206 lnx230 ln 10 -> 2.302585092994045684017991454684 Inexact Rounded 207 precision: 30 208 lnx231 ln 2 -> 0.693147180559945309417232121458 Inexact Rounded 209 lnx232 ln 10 -> 2.30258509299404568401799145468 Inexact Rounded 210 211 -- extreme input range values 212 maxExponent: 384 213 minExponent: -383 214 Precision: 16 215 216 lnx0901 ln 1e-400 -> -921.0340371976183 Inexact Rounded 217 lnx0902 ln 1e+400 -> 921.0340371976183 Inexact Rounded 218 lnx0903 ln 1e-999999 -> -2302582.790408953 Inexact Rounded 219 lnx0904 ln 1e+999999 -> 2302582.790408953 Inexact Rounded 220 lnx0905 ln 1e-1000013 -> -2302615.026600255 Inexact Rounded 221 lnx0906 ln 2e-1000013 -> -2302614.333453074 Inexact Rounded 222 223 lnx0910 ln 9.999999e+999999 -> 2302585.092993946 Inexact Rounded 224 lnx0911 ln 9.9999999e+999999 -> 2302585.092994036 Inexact Rounded 225 lnx0912 ln 9.99999999e+999999 -> 2302585.092994045 Inexact Rounded 226 lnx0913 ln 9.999999999e+999999 -> 2302585.092994046 Inexact Rounded 227 lnx0914 ln 9.999999999999e+999999 -> 2302585.092994046 Inexact Rounded 228 lnx0915 ln 9.999999999999999e+999999 -> 2302585.092994046 Inexact Rounded 229 lnx0916 ln 9.999999999999999999999999e+999999 -> 2302585.092994046 Inexact Rounded 230 231 -- randoms 232 -- P=50, within 0-999 233 Precision: 50 234 maxExponent: 384 235 minExponent: -383 236 lnx1501 ln 0.00098800906574486388604608477869812518857023768951 -> -6.9198186844033787995945147836955586009548513043689 Inexact Rounded 237 lnx1502 ln 158.15866624664623070184595045304145949900714987827 -> 5.0635987458895647454907806507503825602758392287684 Inexact Rounded 238 lnx1503 ln 0.00565661412059571925040285814021799775249288309321 -> -5.1749297776760632102047540300491550931651318975237 Inexact Rounded 239 lnx1504 ln 0.00000006914232532620489602008402091666547903180607 -> -16.487098770877825308138976818688771638172333034347 Inexact Rounded 240 lnx1505 ln 0.00025380374621297657504661540749355251231770070723 -> -8.2789492423005003205242162741569033124260321954589 Inexact Rounded 241 lnx1506 ln 83.033654063877426261108592599182418953442677554806 -> 4.4192459962647137976949249810815698465031609843669 Inexact Rounded 242 lnx1507 ln 0.00000000416863228092481651627734668440663678118729 -> -19.295677845122141772791294599714950175284915666430 Inexact Rounded 243 lnx1508 ln 0.00000140847873187820570181214271960511080523457669 -> -13.473000349581967189668305314384952251556809480339 Inexact Rounded 244 lnx1509 ln 66.176106555181527101630351127583944689752069132522 -> 4.1923194696232505883666171116966137694013431504252 Inexact Rounded 245 lnx1510 ln 0.00000000000009899043487403590900111602024562297908 -> -29.943753166877840985821508112917991506656545174163 Inexact Rounded 246 lnx1511 ln 0.00000000000324618296721747097510453388683912733569 -> -26.453541281444586819009546418577507163362590139422 Inexact Rounded 247 lnx1512 ln 72.646968818463546449499147579023555008392860423385 -> 4.2856116660689646882852128853423566276718230426479 Inexact Rounded 248 lnx1513 ln 0.00000000000000066755483124635612574263153825990523 -> -34.942910142802769319262875080398852491588707172483 Inexact Rounded 249 lnx1514 ln 61.002910447202398204114909451851111424657671911002 -> 4.1109215752843377323363182051446177066434038096529 Inexact Rounded 250 lnx1515 ln 917.06917611331980999227893584010544542312239174774 -> 6.8211829068303114128752453661946446979787826282907 Inexact Rounded 251 lnx1516 ln 0.00000000170823794883673083358549749078972003965194 -> -20.187803436976150477297246666771626827057191023004 Inexact Rounded 252 lnx1517 ln 0.53731767845358224445809761315159249898566542910649 -> -0.62116577939968409211736413628236285160048357000961 Inexact Rounded 253 lnx1518 ln 0.00000000000000008965291392882804161299758708033373 -> -36.950585970980857376081265073276303670820056916206 Inexact Rounded 254 lnx1519 ln 0.00000000006990244916026429904498278982530170295668 -> -23.383920429244457578373523508427783144589480420753 Inexact Rounded 255 lnx1520 ln 4.0312542977070300070506064666536478373801988540614 -> 1.3940775676592451945795752796421391871302024763305 Inexact Rounded 256 lnx1521 ln 271.84991311551875601432518819562391699324632396423 -> 5.6052501239873862517916679747146539808077431873478 Inexact Rounded 257 lnx1522 ln 7.4118671629373864667229445746862314443895404818689 -> 2.0030823863706344628239147639318289961917060121141 Inexact Rounded 258 lnx1523 ln 0.00000000000002026311452625364905357321664186034258 -> -31.529974180054438792043856877314043794320951134754 Inexact Rounded 259 lnx1524 ln 0.00000000000009563398651261756952398250624737809347 -> -29.978248130576972953141284136962670021368834792579 Inexact Rounded 260 lnx1525 ln 0.00000000009556772669409858653026558223465197808991 -> -23.071185939748285541228206161472956661196956741186 Inexact Rounded 261 lnx1526 ln 6.8441648298027301292342057248737326152250794026761 -> 1.9233964395801946597272589473417948024361005082908 Inexact Rounded 262 lnx1527 ln 0.00000000000073059699884439979394945822035704264577 -> -27.944914388353724718836101828677771967128509603158 Inexact Rounded 263 lnx1528 ln 0.00000000000000002610078280419082263138064745416787 -> -38.184566367516207885573773320135965798717120735115 Inexact Rounded 264 lnx1529 ln 0.00000000000000000150259517166294243088546806083283 -> -41.039337946266676108538170837580051699618334928421 Inexact Rounded 265 lnx1530 ln 0.00000000000000087919160541714580707181969708502091 -> -34.667528818827671507514319744047440696187358676848 Inexact Rounded 266 lnx1531 ln 0.00000000000395726725120787763271849577708068584598 -> -26.255467416961357741818735787226671938678424748431 Inexact Rounded 267 lnx1532 ln 0.00000000002014334901669366218018377213150715938355 -> -24.628146955635359035289123027319969201693737159108 Inexact Rounded 268 lnx1533 ln 0.00000008097927101101093117753938766241442896030637 -> -16.329072628469715178637178365710373398203190937454 Inexact Rounded 269 lnx1534 ln 0.00000000000017115834162632864392039668116243984176 -> -29.396187292434898225453626794459285157263177528034 Inexact Rounded 270 lnx1535 ln 0.39168317593866334087305459933723864294857086105035 -> -0.93730199062757240485836637306785037368746737693029 Inexact Rounded 271 lnx1536 ln 79.335036798971515026519630103325369729637514127617 -> 4.3736798570287828823772149735170431010616961976965 Inexact Rounded 272 lnx1537 ln 0.00000000000000056004952129926137413602116591493625 -> -35.118506463181870020730685884333000241039028127213 Inexact Rounded 273 lnx1538 ln 0.00000006006035907843890918832481099660639553666078 -> -16.627915795747112566532705974853114454405010472043 Inexact Rounded 274 lnx1539 ln 0.00000000085242024937414906371333826574632450587590 -> -20.882941460268101080186482230657774997273494107221 Inexact Rounded 275 lnx1540 ln 0.00000000000043671099499262350316173246550771951561 -> -28.459504757285639221776305968469058854558726593945 Inexact Rounded 276 277 -- P=34, within 0-999 278 Precision: 34 279 lnx1201 ln 0.0086732880815927182997566810334394 -> -4.747507311920844752486938187973721 Inexact Rounded 280 lnx1202 ln 0.0007104103693460260609792222569854 -> -7.249667769903503023005549250347695 Inexact Rounded 281 lnx1203 ln 786.8398945385105190697541493392742 -> 6.668024790031836340471824147010546 Inexact Rounded 282 lnx1204 ln 0.7723073620282687656895190171967399 -> -0.2583726708506850868786816238217326 Inexact Rounded 283 lnx1205 ln 0.0061057951517197631287183938412200 -> -5.098516933918797347064454103742635 Inexact Rounded 284 lnx1206 ln 0.6181379708184393730103917562498745 -> -0.4810435926903365087463387760350021 Inexact Rounded 285 lnx1207 ln 09.13888261229039989110753389096760 -> 2.212538125507975574509563027696021 Inexact Rounded 286 lnx1208 ln 802.0105417063143696497292158147174 -> 6.687121752052341737234832203350214 Inexact Rounded 287 lnx1209 ln 778.7749710387773713523028497333058 -> 6.657722135126935472086625031413031 Inexact Rounded 288 lnx1210 ln 0.0024457295895346502513567679390616 -> -6.013411799940245345321348290398517 Inexact Rounded 289 lnx1211 ln 0.0000511296947872828310338864217860 -> -9.881145118237281798081573131711636 Inexact Rounded 290 lnx1212 ln 0.0000246803508602554924938685155658 -> -10.60950314264825661825360971430218 Inexact Rounded 291 lnx1213 ln 9.027898199253511668242977766616082 -> 2.200319582778899029786017830557293 Inexact Rounded 292 lnx1214 ln 0.0991812396542505631850692800904188 -> -2.310806398964672258823043180400384 Inexact Rounded 293 lnx1215 ln 0.0000000000070238810143028811223924 -> -25.68170519961636647174714538290075 Inexact Rounded 294 lnx1216 ln 2.630101665342826494730394729313167 -> 0.9670225014664367465128243039749559 Inexact Rounded 295 lnx1217 ln 0.0056878928594359587691526063254683 -> -5.169415422904037819736637399445096 Inexact Rounded 296 lnx1218 ln 567.3436047121057843908106573095590 -> 6.340965124964258486463444360787970 Inexact Rounded 297 lnx1219 ln 1.199291248124655996614605745649725 -> 0.1817307557425911805765087755675657 Inexact Rounded 298 lnx1220 ln 25.02050448582031098696267479135557 -> 3.219695668137659139544178905459317 Inexact Rounded 299 lnx1221 ln 0.0000000000009939597023558756961300 -> -27.63707972996537636504396558259058 Inexact Rounded 300 lnx1222 ln 0.0000007988551670159429716506430403 -> -14.04008617542597230988198612376415 Inexact Rounded 301 lnx1223 ln 4.681515800176129184873770605589795 -> 1.543621946415383338972124445445748 Inexact Rounded 302 lnx1224 ln 15.95126669161103011206658749345781 -> 2.769538242479483539275986395443539 Inexact Rounded 303 lnx1225 ln 0.0301626783922211213675457279076066 -> -3.501149933677283341023932281826341 Inexact Rounded 304 lnx1226 ln 000.0040544064881821770528475185674 -> -5.507950967557021671647165889608324 Inexact Rounded 305 lnx1227 ln 29.01617095935593792095913785100360 -> 3.367853293862745651888450004473297 Inexact Rounded 306 lnx1228 ln 78.01836167344736733024804243195323 -> 4.356944205055768575987781375003992 Inexact Rounded 307 lnx1229 ln 0.0000000096545319316965321158634893 -> -18.45583840160965814462095477365013 Inexact Rounded 308 lnx1230 ln 97.95475237720579752770587185074428 -> 4.584505661612812742208619358214729 Inexact Rounded 309 lnx1231 ln 528.0609262050423246402564228432371 -> 6.269211667589138113396583894315956 Inexact Rounded 310 lnx1232 ln 0.0000002250064349732969696660452972 -> -15.30713683526963996712167701738724 Inexact Rounded 311 lnx1233 ln 47.97063637767998658567199049725754 -> 3.870589081585660692195989854842372 Inexact Rounded 312 lnx1234 ln 0.0005394311344541432318853513414361 -> -7.524995428393925934087126702974121 Inexact Rounded 313 lnx1235 ln 0.0000000090973385649567471674972633 -> -18.51528393158931783447035004125791 Inexact Rounded 314 lnx1236 ln 0.0000000000238776490227576197317977 -> -24.45807828188389561331158879207262 Inexact Rounded 315 lnx1237 ln 0.0000236587000231921532145326218758 -> -10.65177964499823314952429277979034 Inexact Rounded 316 lnx1238 ln 499.1277448846130709827154556125942 -> 6.212862064761427967461188083514774 Inexact Rounded 317 lnx1239 ln 0.0000003960192300284787663712417647 -> -14.74180306619298548093697608293284 Inexact Rounded 318 lnx1240 ln 41.08268350829477451667228892495136 -> 3.715586706887278039173584859218960 Inexact Rounded 319 320 -- P=16, within 0-99 321 Precision: 16 322 lnx1101 ln 7.964875261033948 -> 2.075041282352241 Inexact Rounded 323 lnx1102 ln 13.54527396845394 -> 2.606037701870263 Inexact Rounded 324 lnx1103 ln 0.0008026554341331 -> -7.127585034321814 Inexact Rounded 325 lnx1104 ln 0.0000030582233261 -> -12.69767642300625 Inexact Rounded 326 lnx1105 ln 0.0004477497509672 -> -7.711276073210766 Inexact Rounded 327 lnx1106 ln 7.616268622474371 -> 2.030286567675148 Inexact Rounded 328 lnx1107 ln 51.58329925806381 -> 3.943197962309569 Inexact Rounded 329 lnx1108 ln 0.0018197497951263 -> -6.309056262549345 Inexact Rounded 330 lnx1109 ln 2.956282457072984 -> 1.083932552334575 Inexact Rounded 331 lnx1110 ln 0.3843325579189906 -> -0.9562470649400558 Inexact Rounded 332 lnx1111 ln 0.0074466329265663 -> -4.899993304919237 Inexact Rounded 333 lnx1112 ln 0.0003372478532993 -> -7.994692428206378 Inexact Rounded 334 lnx1113 ln 0.0084792263167809 -> -4.770136069569271 Inexact Rounded 335 lnx1114 ln 5.926756998151102 -> 1.779477182834305 Inexact Rounded 336 lnx1115 ln 9.025699152180897 -> 2.200075969604119 Inexact Rounded 337 lnx1116 ln 1.910124643533526 -> 0.6471684983238183 Inexact Rounded 338 lnx1117 ln 0.8158922711411020 -> -0.2034729533939387 Inexact Rounded 339 lnx1118 ln 0.0067080016475322 -> -5.004454189414139 Inexact Rounded 340 lnx1119 ln 0.0047583242092716 -> -5.347859729601094 Inexact Rounded 341 lnx1120 ln 0.0386647411641339 -> -3.252827175263113 Inexact Rounded 342 lnx1121 ln 0.0050226427841761 -> -5.293799032774131 Inexact Rounded 343 lnx1122 ln 6.927937541637261 -> 1.935562155866906 Inexact Rounded 344 lnx1123 ln 0.0000095745343513 -> -11.55640365579814 Inexact Rounded 345 lnx1124 ln 1.602465492956538 -> 0.4715433763243936 Inexact Rounded 346 lnx1125 ln 38.98415625087535 -> 3.663155313610213 Inexact Rounded 347 lnx1126 ln 5.343182042276734 -> 1.675821363568112 Inexact Rounded 348 lnx1127 ln 55.89763703245816 -> 4.023522107934110 Inexact Rounded 349 lnx1128 ln 0.7445257810280847 -> -0.2950077988101030 Inexact Rounded 350 lnx1129 ln 1.631407314946094 -> 0.4894430257201248 Inexact Rounded 351 lnx1130 ln 0.0005462451932602 -> -7.512442611116852 Inexact Rounded 352 lnx1131 ln 0.0000864173269362 -> -9.356322359017317 Inexact Rounded 353 lnx1132 ln 5.227161719132849 -> 1.653868438439637 Inexact Rounded 354 lnx1133 ln 60.57078466941998 -> 4.103812675662452 Inexact Rounded 355 lnx1134 ln 0.0992864325333160 -> -2.309746348350318 Inexact Rounded 356 lnx1135 ln 09.48564268447325 -> 2.249779359074983 Inexact Rounded 357 lnx1136 ln 0.0036106089355634 -> -5.623878840650787 Inexact Rounded 358 lnx1137 ln 1.805176865587172 -> 0.5906585734593707 Inexact Rounded 359 lnx1138 ln 62.59363259642255 -> 4.136663557220559 Inexact Rounded 360 lnx1139 ln 4.373828261137201 -> 1.475638657912000 Inexact Rounded 361 lnx1140 ln 0.994483524148738 -> -0.005531747794938690 Inexact Rounded 362 363 -- P=7, within 0-9 364 Precision: 7 365 lnx1001 ln 0.0912025 -> -2.394673 Inexact Rounded 366 lnx1002 ln 0.9728626 -> -0.02751242 Inexact Rounded 367 lnx1003 ln 0.3886032 -> -0.9451965 Inexact Rounded 368 lnx1004 ln 8.798639 -> 2.174597 Inexact Rounded 369 lnx1005 ln 2.459121 -> 0.8998040 Inexact Rounded 370 lnx1006 ln 2.013193 -> 0.6997220 Inexact Rounded 371 lnx1007 ln 9.064857 -> 2.204405 Inexact Rounded 372 lnx1008 ln 5.796417 -> 1.757240 Inexact Rounded 373 lnx1009 ln 0.1143471 -> -2.168517 Inexact Rounded 374 lnx1010 ln 0.5341542 -> -0.6270707 Inexact Rounded 375 lnx1011 ln 6.693781 -> 1.901179 Inexact Rounded 376 lnx1012 ln 0.0081779 -> -4.806320 Inexact Rounded 377 lnx1013 ln 8.313616 -> 2.117895 Inexact Rounded 378 lnx1014 ln 3.486925 -> 1.249020 Inexact Rounded 379 lnx1015 ln 0.1801401 -> -1.714020 Inexact Rounded 380 lnx1016 ln 0.5227148 -> -0.6487193 Inexact Rounded 381 lnx1017 ln 7.818111 -> 2.056443 Inexact Rounded 382 lnx1018 ln 0.0870671 -> -2.441076 Inexact Rounded 383 lnx1019 ln 8.153966 -> 2.098504 Inexact Rounded 384 lnx1020 ln 2.040975 -> 0.7134276 Inexact Rounded 385 lnx1021 ln 1.481642 -> 0.3931509 Inexact Rounded 386 lnx1022 ln 0.2610123 -> -1.343188 Inexact Rounded 387 lnx1023 ln 0.466723 -> -0.7620193 Inexact Rounded 388 lnx1024 ln 0.0518756 -> -2.958907 Inexact Rounded 389 lnx1025 ln 2.056410 -> 0.7209617 Inexact Rounded 390 lnx1026 ln 0.181522 -> -1.706378 Inexact Rounded 391 lnx1027 ln 0.515551 -> -0.6625190 Inexact Rounded 392 lnx1028 ln 8.425089 -> 2.131214 Inexact Rounded 393 lnx1029 ln 2.077091 -> 0.7309684 Inexact Rounded 394 lnx1030 ln 6.212705 -> 1.826596 Inexact Rounded 395 lnx1031 ln 5.729343 -> 1.745601 Inexact Rounded 396 lnx1032 ln 4.831251 -> 1.575105 Inexact Rounded 397 lnx1033 ln 2.029760 -> 0.7079176 Inexact Rounded 398 lnx1034 ln 8.615060 -> 2.153512 Inexact Rounded 399 lnx1035 ln 0.0611511 -> -2.794407 Inexact Rounded 400 lnx1036 ln 5.195269 -> 1.647748 Inexact Rounded 401 lnx1037 ln 9.617686 -> 2.263604 Inexact Rounded 402 lnx1038 ln 0.0049382 -> -5.310754 Inexact Rounded 403 lnx1039 ln 2.786840 -> 1.024908 Inexact Rounded 404 lnx1040 ln 0.0091073 -> -4.698679 Inexact Rounded 405 406 -- from here 3-digit tests are based on reverse exp tests 407 precision: 9 408 rounding: half_even 409 maxExponent: 384 410 minexponent: -383 411 412 lnx001 ln 0 -> -Infinity 413 lnx002 ln 0.367879441 -> -1.00000000 Inexact Rounded 414 lnx003 ln 1 -> 0 415 lnx005 ln 2.71828183 -> 1.00000000 Inexact Rounded 416 lnx006 ln 2.00000000 -> 0.693147181 Inexact Rounded 417 lnx007 ln +Infinity -> Infinity 418 419 -- tiny edge cases 420 precision: 7 421 lnx011 ln 1.105171 -> 0.1000001 Inexact Rounded 422 lnx012 ln 1.010050 -> 0.009999835 Inexact Rounded 423 lnx013 ln 1.000010 -> 0.000009999950 Inexact Rounded 424 lnx014 ln 1.000001 -> 9.999995E-7 Inexact Rounded 425 lnx015 ln 1.000000 -> 0 426 427 -- basic e=0, e=1, e=2, e=4, e>=8 cases 428 precision: 7 429 lnx041 ln 2.718282 -> 1.000000 Inexact Rounded 430 lnx042 ln 0.3678794 -> -1.000000 Inexact Rounded 431 lnx043 ln 22026.47 -> 10.00000 Inexact Rounded 432 lnx044 ln 0.00004539993 -> -10.00000 Inexact Rounded 433 lnx045 ln 2.688117E+43 -> 100.0000 Inexact Rounded 434 lnx046 ln 3.720076E-44 -> -100.0000 Inexact Rounded 435 lnx047 ln Infinity -> Infinity 436 lnx048 ln 0E-389 -> -Infinity 437 438 -- miscellanea 439 precision: 16 440 lnx055 ln 2.717658486884572E-236 -> -542.4103112874415 Inexact Rounded 441 precision: 17 442 lnx056 ln 2.7176584868845721E-236 -> -542.41031128744146 Inexact Rounded 443 precision: 18 444 lnx057 ln 2.71765848688457211E-236 -> -542.410311287441459 Inexact Rounded 445 precision: 19 446 lnx058 ln 2.717658486884572112E-236 -> -542.4103112874414592 Inexact Rounded 447 precision: 20 448 lnx059 ln 2.7176584868845721118E-236 -> -542.41031128744145917 Inexact Rounded 449 450 -- inputs ending in ..500.., ..499.., ..100.., ..999.. sequences 451 precision: 50 452 lnx102 ln 0.9999999100000040499998785000027 -> -9.0000000000000000000000033749953829996446124861750E-8 Inexact Rounded 453 precision: 30 454 lnx103 ln 0.999999910000004049999878500003 -> -8.99999999999999999999997337499E-8 Inexact Rounded 455 precision: 29 456 lnx104 ln 0.99999991000000404999987850000 -> -9.0000000000000000000002733750E-8 Inexact Rounded 457 precision: 28 458 lnx105 ln 0.9999999100000040499998785000 -> -9.000000000000000000000273375E-8 Inexact Rounded 459 precision: 27 460 lnx106 ln 0.999999910000004049999878500 -> -9.00000000000000000000027338E-8 Inexact Rounded 461 precision: 26 462 lnx107 ln 0.99999991000000404999987850 -> -9.0000000000000000000002734E-8 Inexact Rounded 463 precision: 25 464 lnx108 ln 0.9999999100000040499998785 -> -9.000000000000000000000273E-8 Inexact Rounded 465 precision: 24 466 lnx109 ln 0.999999910000004049999879 -> -8.99999999999999995000027E-8 Inexact Rounded 467 precision: 23 468 lnx110 ln 0.99999991000000404999988 -> -8.9999999999999998500003E-8 Inexact Rounded 469 precision: 22 470 lnx111 ln 0.9999999100000040499999 -> -8.999999999999997850000E-8 Inexact Rounded 471 precision: 21 472 lnx112 ln 0.999999910000004050000 -> -8.99999999999998785000E-8 Inexact Rounded 473 precision: 20 474 lnx113 ln 0.99999991000000405000 -> -8.9999999999999878500E-8 Inexact Rounded 475 precision: 19 476 lnx114 ln 0.9999999100000040500 -> -8.999999999999987850E-8 Inexact Rounded 477 precision: 18 478 lnx115 ln 0.999999910000004050 -> -8.99999999999998785E-8 Inexact Rounded 479 -- next may be a > 0.5ulp case; a more precise answer is: 480 -- -8.99999999999998784999918E-8 481 precision: 17 482 lnx116 ln 0.99999991000000405 -> -8.9999999999999878E-8 Inexact Rounded 483 precision: 16 484 lnx117 ln 0.9999999100000040 -> -9.000000004999988E-8 Inexact Rounded 485 precision: 15 486 lnx118 ln 0.999999910000004 -> -9.00000000499999E-8 Inexact Rounded 487 precision: 14 488 lnx119 ln 0.99999991000000 -> -9.0000004050000E-8 Inexact Rounded 489 precision: 13 490 lnx120 ln 0.9999999100000 -> -9.000000405000E-8 Inexact Rounded 491 precision: 12 492 lnx121 ln 0.999999910000 -> -9.00000040500E-8 Inexact Rounded 493 precision: 11 494 lnx122 ln 0.99999991000 -> -9.0000004050E-8 Inexact Rounded 495 precision: 10 496 lnx123 ln 0.9999999100 -> -9.000000405E-8 Inexact Rounded 497 precision: 9 498 lnx124 ln 0.999999910 -> -9.00000041E-8 Inexact Rounded 499 precision: 8 500 lnx125 ln 0.99999991 -> -9.0000004E-8 Inexact Rounded 501 precision: 7 502 lnx126 ln 0.9999999 -> -1.000000E-7 Inexact Rounded 503 precision: 16 504 lnx126b ln 0.9999999 -> -1.000000050000003E-7 Inexact Rounded 505 precision: 6 506 lnx127 ln 0.999999 -> -0.00000100000 Inexact Rounded 507 precision: 5 508 lnx128 ln 0.99999 -> -0.000010000 Inexact Rounded 509 precision: 4 510 lnx129 ln 0.9999 -> -0.0001000 Inexact Rounded 511 precision: 3 512 lnx130 ln 0.999 -> -0.00100 Inexact Rounded 513 precision: 2 514 lnx131 ln 0.99 -> -0.010 Inexact Rounded 515 precision: 1 516 lnx132 ln 0.9 -> -0.1 Inexact Rounded 517 518 519 -- cases near 1 -- 1 2345678901234567890 520 precision: 20 521 lnx401 ln 2.7182818284589365041 -> 0.99999999999996000000 Inexact Rounded 522 lnx402 ln 2.7182818284589636869 -> 0.99999999999997000000 Inexact Rounded 523 lnx403 ln 2.7182818284589908697 -> 0.99999999999997999999 Inexact Rounded 524 lnx404 ln 2.7182818284590180525 -> 0.99999999999998999998 Inexact Rounded 525 lnx405 ln 2.7182818284590452354 -> 1.0000000000000000000 Inexact Rounded 526 lnx406 ln 2.7182818284593170635 -> 1.0000000000001000000 Inexact Rounded 527 lnx407 ln 2.7182818284595888917 -> 1.0000000000002000000 Inexact Rounded 528 precision: 14 529 lnx411 ln 2.7182818284589 -> 0.99999999999995 Inexact Rounded 530 lnx413 ln 2.7182818284590 -> 0.99999999999998 Inexact Rounded 531 lnx416 ln 2.7182818284591 -> 1.0000000000000 Inexact Rounded 532 lnx417 ln 2.7182818284592 -> 1.0000000000001 Inexact Rounded 533 534 -- overflows, including some exp overprecise borderlines 535 precision: 7 536 maxExponent: 384 537 minExponent: -383 538 lnx709 ln 9.999999E+384 -> 886.4953 Inexact Rounded 539 lnx711 ln 9.999992E+384 -> 886.4953 Inexact Rounded 540 precision: 16 541 lnx722 ln 9.999999999999999E+384 -> 886.4952608027076 Inexact Rounded 542 lnx724 ln 9.999999999999917E+384 -> 886.4952608027076 Inexact Rounded 543 lnx726 ln 9.999999999999117E+384 -> 886.4952608027075 Inexact Rounded 544 -- and more... 545 precision: 15 546 maxExponent: 999 547 minExponent: -999 548 lnx731 ln 9.99999999999999E+999 -> 2302.58509299405 Inexact Rounded 549 -- next may be a > 0.5ulp case; a more precise answer is: 550 -- 2302.58509299404495001799145442 551 lnx732 ln 9.99999999999266E+999 -> 2302.58509299404 Inexact Rounded 552 lnx733 ln 9.99999999999265E+999 -> 2302.58509299404 Inexact Rounded 553 lnx734 ln 9.99999999999264E+999 -> 2302.58509299404 Inexact Rounded 554 555 -- subnormals and underflows for exp, including underflow-to-zero edge point 556 precision: 7 557 maxExponent: 384 558 minExponent: -383 559 lnx751 ln 0E-389 -> -Infinity 560 lnx758 ln 1.000001E-383 -> -881.8901 Inexact Rounded 561 lnx759 ln 9.99991E-384 -> -881.8901 Inexact Rounded 562 lnx760 ln 4.4605E-385 -> -885.0000 Inexact Rounded 563 lnx761 ln 2.221E-386 -> -887.9999 Inexact Rounded 564 lnx762 ln 3.01E-387 -> -889.9985 Inexact Rounded 565 lnx763 ln 1.7E-388 -> -892.8724 Inexact Rounded 566 lnx764 ln 1.5E-388 -> -892.9976 Inexact Rounded 567 lnx765 ln 9E-389 -> -893.5084 Inexact Rounded 568 lnx766 ln 1E-389 -> -895.7056 Inexact Rounded 569 lnx774 ln 0E-389 -> -Infinity 570 571 -- special values 572 lnx820 ln Infinity -> Infinity 573 lnx821 ln 0 -> -Infinity 574 lnx822 ln NaN -> NaN 575 lnx823 ln sNaN -> NaN Invalid_operation 576 -- propagating NaNs 577 lnx824 ln sNaN123 -> NaN123 Invalid_operation 578 lnx825 ln -sNaN321 -> -NaN321 Invalid_operation 579 lnx826 ln NaN456 -> NaN456 580 lnx827 ln -NaN654 -> -NaN654 581 lnx828 ln NaN1 -> NaN1 582 583 -- Invalid operations due to restrictions 584 -- [next two probably skipped by most test harnesses] 585 precision: 100000000 586 lnx901 ln 1 -> NaN Invalid_context 587 precision: 99999999 588 lnx902 ln 0 -> NaN Invalid_context 589 590 precision: 9 591 maxExponent: 1000000 592 minExponent: -999999 593 lnx903 ln 1 -> NaN Invalid_context 594 maxExponent: 999999 595 minExponent: -999999 596 lnx904 ln 0 -> -Infinity 597 maxExponent: 999999 598 minExponent: -1000000 599 lnx905 ln 1 -> NaN Invalid_context 600 maxExponent: 999999 601 minExponent: -999998 602 lnx906 ln 0 -> -Infinity 603 604 -- payload decapitate 605 precision: 5 606 lnx910 ln -sNaN1234567890 -> -NaN67890 Invalid_operation 607 608 -- Null test 609 lnx900 ln # -> NaN Invalid_operation 610 611 612
