1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25
26 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #include "libm_protos.h"
32
33 /*
34 * Table of constants for log, log2, and log10
35 * By K.C. Ng, November 21, 2004
36 *
37 * Y[j], 1/Y[j], log(Y[j]) for j = 0 to 255
38 * where HIWORD(Y[j]) ~ 0x3fb8400 + (j<<15)
39 * That is, 256 Y[j] space out logrithmically between 0.09375 and 24, and
40 * each is chosen so that 1/Y[j] and log(Y[j]) are very close to a IEEE
41 * double. In addition, each log(Y[j]) has 3 trailing zeros.
42 */
43 const double _TBL_log[] = {
44 9.47265623608246343e-02, 1.05567010464380857e+01,
45 -2.35676082856530300e+00, 9.66796869131412717e-02,
46 1.03434344062203838e+01, -2.33635196153499791e+00,
47 9.86328118117651004e-02, 1.01386139321308306e+01,
48 -2.31635129573594156e+00, 1.00585936733578435e-01,
49 9.94174764856737347e+00, -2.29674282498938709e+00,
50 1.02539062499949152e-01, 9.75238095238578850e+00,
51 -2.27751145544242561e+00, 1.04492186859904843e-01,
52 9.57009351656812157e+00, -2.25864297726331742e+00,
53 1.06445312294918631e-01, 9.39449543094380957e+00,
54 -2.24012392529694537e+00, 1.08398437050250693e-01,
55 9.22522526350104144e+00, -2.22194160843615762e+00,
56 1.10351562442130582e-01, 9.06194690740703912e+00,
57 -2.20408398741152212e+00, 1.12304686894746625e-01,
58 8.90434787407592943e+00, -2.18653968262558962e+00,
59 1.14257811990227776e-01, 8.75213679118525256e+00,
60 -2.16929787526329321e+00, 1.16210936696872255e-01,
61 8.60504207627572093e+00, -2.15234831939887172e+00,
62 1.18164061975360682e-01, 8.46280995492959498e+00,
63 -2.13568126444263484e+00, 1.20117187499996322e-01,
64 8.32520325203277523e+00, -2.11928745022706622e+00,
65 1.22070312499895098e-01, 8.19200000000703987e+00,
66 -2.10315806829801133e+00, 1.24023436774175100e-01,
67 8.06299217317146599e+00, -2.08728472499318229e+00,
68 1.26953123746900931e-01, 7.87692315467275872e+00,
69 -2.06393736501443570e+00, 1.30859374098123454e-01,
70 7.64179109744297769e+00, -2.03363201254049386e+00,
71 1.34765623780674720e-01, 7.42028992220936967e+00,
72 -2.00421812948999545e+00, 1.38671874242985771e-01,
73 7.21126764500034501e+00, -1.97564475345722457e+00,
74 1.42578124148616536e-01, 7.01369867201821506e+00,
75 -1.94786518986246371e+00, 1.46484374166731490e-01,
76 6.82666670549979404e+00, -1.92083651719164372e+00,
77 1.50390624434435488e-01, 6.64935067435644189e+00,
78 -1.89451920694646070e+00, 1.54296874339723084e-01,
79 6.48101268596180624e+00, -1.86887677685174936e+00,
80 1.58203124999987427e-01, 6.32098765432149001e+00,
81 -1.84387547036714849e+00, 1.62109374999815342e-01,
82 6.16867469880220742e+00, -1.81948401724404896e+00,
83 1.66015624243955634e-01, 6.02352943919619310e+00,
84 -1.79567337310324682e+00, 1.69921874302298687e-01,
85 5.88505749542848644e+00, -1.77241651049093640e+00,
86 1.73828124315277527e-01, 5.75280901142480605e+00,
87 -1.74968825924644555e+00, 1.77734374286237506e-01,
88 5.62637364896854919e+00, -1.72746512253855222e+00,
89 1.81640624146994889e-01, 5.50537636993989743e+00,
90 -1.70572513658236602e+00, 1.85546874316304788e-01,
91 5.38947370406942916e+00, -1.68444773712372431e+00,
92 1.89453124405085355e-01, 5.27835053203882509e+00,
93 -1.66361364967629299e+00, 1.93359374570531595e-01,
94 5.17171718320401652e+00, -1.64320477712600699e+00,
95 1.97265624263334577e-01, 5.06930694962380368e+00,
96 -1.62320411193263148e+00, 2.01171874086291030e-01,
97 4.97087380898513764e+00, -1.60359564135180399e+00,
98 2.05078123979995308e-01, 4.87619050044336610e+00,
99 -1.58436427985572159e+00, 2.08984373896073439e-01,
100 4.78504675424820736e+00, -1.56549579585994181e+00,
101 2.12890623963011144e-01, 4.69724772930228163e+00,
102 -1.54697674768135762e+00, 2.16796874723889421e-01,
103 4.61261261848719517e+00, -1.52879442500076479e+00,
104 2.20703124198150608e-01, 4.53097346778917753e+00,
105 -1.51093680996032553e+00, 2.24609374375627030e-01,
106 4.45217392541970725e+00, -1.49339249945607477e+00,
107 2.28515625000094036e-01, 4.37606837606657528e+00,
108 -1.47615069024134016e+00, 2.32421873924349737e-01,
109 4.30252102831546246e+00, -1.45920113655598627e+00,
110 2.36328123935216378e-01, 4.23140497774241098e+00,
111 -1.44253408394829741e+00, 2.40234375000066919e-01,
112 4.16260162601510064e+00, -1.42614026966681173e+00,
113 2.44140623863132178e-01, 4.09600001907347711e+00,
114 -1.41001089239381727e+00, 2.48046874999894917e-01,
115 4.03149606299383390e+00, -1.39413753858134015e+00,
116 2.53906248590769879e-01, 3.93846156032078243e+00,
117 -1.37079018013412401e+00, 2.61718748558906533e-01,
118 3.82089554342693294e+00, -1.34048483059486401e+00,
119 2.69531249159214337e-01, 3.71014493910979404e+00,
120 -1.31107094300173976e+00, 2.77343749428383191e-01,
121 3.60563381024826013e+00, -1.28249756949928795e+00,
122 2.85156249289339359e-01, 3.50684932380819214e+00,
123 -1.25471800582335113e+00, 2.92968749999700462e-01,
124 3.41333333333682321e+00, -1.22768933094427446e+00,
125 3.00781248554318814e-01, 3.32467534065511261e+00,
126 -1.20137202743229921e+00, 3.08593748521894806e-01,
127 3.24050634463533127e+00, -1.17572959680235023e+00,
128 3.16406249999639899e-01, 3.16049382716409077e+00,
129 -1.15072828980826181e+00, 3.24218749999785061e-01,
130 3.08433734939963511e+00, -1.12633683668362750e+00,
131 3.32031248841858584e-01, 3.01176471638753718e+00,
132 -1.10252619147729547e+00, 3.39843749265406558e-01,
133 2.94252874199264314e+00, -1.07926932798654107e+00,
134 3.47656249999834799e-01, 2.87640449438338930e+00,
135 -1.05654107474789782e+00, 3.55468749999899247e-01,
136 2.81318681318761055e+00, -1.03431793796299587e+00,
137 3.63281249999864997e-01, 2.75268817204403371e+00,
138 -1.01257795132667816e+00, 3.71093749064121570e-01,
139 2.69473684890124421e+00, -9.91300555400967731e-01,
140 3.78906249999751032e-01, 2.63917525773369288e+00,
141 -9.70466465976836723e-01, 3.86718748879039009e-01,
142 2.58585859335407608e+00, -9.50057597243619156e-01,
143 3.94531249999987899e-01, 2.53465346534661240e+00,
144 -9.30056927638333697e-01, 4.02343749999485523e-01,
145 2.48543689320706163e+00, -9.10448456251205407e-01,
146 4.10156249578856991e-01, 2.43809524059864202e+00,
147 -8.91217095348825872e-01, 4.17968749447214571e-01,
148 2.39252336765021800e+00, -8.72348611340208357e-01,
149 4.25781248601723117e-01, 2.34862386092395203e+00,
150 -8.53829565534445223e-01, 4.33593749393073047e-01,
151 2.30630630953458038e+00, -8.35647244566987801e-01,
152 4.41406248572254134e-01, 2.26548673299152270e+00,
153 -8.17789629001761220e-01, 4.49218749348472501e-01,
154 2.22608695975035964e+00, -8.00245317566669279e-01,
155 4.57031249277175089e-01, 2.18803419149470768e+00,
156 -7.83003511263371976e-01, 4.64843748529596368e-01,
157 2.15126051100659366e+00, -7.66053954531254355e-01,
158 4.72656248830947701e-01, 2.11570248457175136e+00,
159 -7.49386901356188240e-01, 4.80468748609962581e-01,
160 2.08130081902951236e+00, -7.32993092000230995e-01,
161 4.88281249241778237e-01, 2.04800000318021258e+00,
162 -7.16863708730099525e-01, 4.96093748931098810e-01,
163 2.01574803583926521e+00, -7.00990360175606675e-01,
164 5.07812497779701388e-01, 1.96923077784079825e+00,
165 -6.77642998396260410e-01, 5.23437498033319737e-01,
166 1.91044776837204044e+00, -6.47337648285891021e-01,
167 5.39062498006593560e-01, 1.85507247062801328e+00,
168 -6.17923763020271188e-01, 5.54687498964024250e-01,
169 1.80281690477552603e+00, -5.89350388745976339e-01,
170 5.70312499806522322e-01, 1.75342465812909332e+00,
171 -5.61570823110474571e-01, 5.85937497921867001e-01,
172 1.70666667271966777e+00, -5.34542153929987052e-01,
173 6.01562498226483444e-01, 1.66233766723853860e+00,
174 -5.08224845014116688e-01, 6.17187498682654212e-01,
175 1.62025316801528496e+00, -4.82582413587029357e-01,
176 6.32812500000264566e-01, 1.58024691357958624e+00,
177 -4.57581109246760320e-01, 6.48437499353274216e-01,
178 1.54216867623689291e+00, -4.33189657120379490e-01,
179 6.64062498728508976e-01, 1.50588235582451335e+00,
180 -4.09379009344016609e-01, 6.79687498865382267e-01,
181 1.47126437027210688e+00, -3.86122146934356092e-01,
182 6.95312498728747119e-01, 1.43820224982050338e+00,
183 -3.63393896015796081e-01, 7.10937499999943157e-01,
184 1.40659340659351906e+00, -3.41170757402847080e-01,
185 7.26562499999845568e-01, 1.37634408602179792e+00,
186 -3.19430770766573779e-01, 7.42187500000120126e-01,
187 1.34736842105241350e+00, -2.98153372318914478e-01,
188 7.57812499999581890e-01, 1.31958762886670744e+00,
189 -2.77319285416786077e-01, 7.73437498602746576e-01,
190 1.29292929526503420e+00, -2.56910415591577124e-01,
191 7.89062500000142664e-01, 1.26732673267303819e+00,
192 -2.36909747078176913e-01, 8.04687500000259015e-01,
193 1.24271844660154174e+00, -2.17301275689659512e-01,
194 8.20312499999677036e-01, 1.21904761904809900e+00,
195 -1.98069913762487504e-01, 8.35937499999997113e-01,
196 1.19626168224299478e+00, -1.79201429457714445e-01,
197 8.51562499999758749e-01, 1.17431192660583728e+00,
198 -1.60682381690756770e-01, 8.67187500000204725e-01,
199 1.15315315315288092e+00, -1.42500062607046951e-01,
200 8.82812500000407896e-01, 1.13274336283133503e+00,
201 -1.24642445206814556e-01, 8.98437499999816813e-01,
202 1.11304347826109651e+00, -1.07098135556570995e-01,
203 9.14062499999708455e-01, 1.09401709401744296e+00,
204 -8.98563291221800009e-02, 9.29687500000063949e-01,
205 1.07563025210076635e+00, -7.29067708080189947e-02,
206 9.45312499999844014e-01, 1.05785123966959604e+00,
207 -5.62397183230410880e-02, 9.60937500000120459e-01,
208 1.04065040650393459e+00, -3.98459085470743157e-02,
209 9.76562499999976685e-01, 1.02400000000002445e+00,
210 -2.37165266173399170e-02, 9.92187500000169420e-01,
211 1.00787401574785940e+00, -7.84317746085513856e-03,
212 1.01562500000004907e+00, 9.84615384615337041e-01,
213 1.55041865360135717e-02, 1.04687500000009237e+00,
214 9.55223880596930641e-01, 4.58095360313824362e-02,
215 1.07812500000002154e+00, 9.27536231884039442e-01,
216 7.52234212376075018e-02, 1.10937499999982481e+00,
217 9.01408450704367703e-01, 1.03796793681485644e-01,
218 1.14062500000007416e+00, 8.76712328767066285e-01,
219 1.31576357788784293e-01, 1.17187500000009659e+00,
220 8.53333333333263000e-01, 1.58605030176721007e-01,
221 1.20312499999950173e+00, 8.31168831169175393e-01,
222 1.84922338493597849e-01, 1.23437500000022027e+00,
223 8.10126582278336449e-01, 2.10564769107528083e-01,
224 1.26562500000064615e+00, 7.90123456789720069e-01,
225 2.35566071313277448e-01, 1.29687500000144706e+00,
226 7.71084337348537208e-01, 2.59957524438041876e-01,
227 1.32812499999945932e+00, 7.52941176470894757e-01,
228 2.83768173130237500e-01, 1.35937500055846350e+00,
229 7.35632183605830825e-01, 3.07025035705735583e-01,
230 1.39062499999999467e+00, 7.19101123595508374e-01,
231 3.29753286372464149e-01, 1.42187500000017564e+00,
232 7.03296703296616421e-01, 3.51976423157301710e-01,
233 1.45312500161088876e+00, 6.88172042247866766e-01,
234 3.73716410902152685e-01, 1.48437500134602307e+00,
235 6.73684209915422660e-01, 3.94993809147663466e-01,
236 1.51562499999932343e+00, 6.59793814433284220e-01,
237 4.15827895143264570e-01, 1.54687500000028200e+00,
238 6.46464646464528614e-01, 4.36236766775100371e-01,
239 1.57812500000061906e+00, 6.33663366336385092e-01,
240 4.56237433481979870e-01, 1.60937500243255216e+00,
241 6.21359222361793417e-01, 4.75845906381452632e-01,
242 1.64062500000026312e+00, 6.09523809523711768e-01,
243 4.95077266798011895e-01, 1.67187500000027911e+00,
244 5.98130841121395473e-01, 5.13945751102401260e-01,
245 1.70312500224662178e+00, 5.87155962528224662e-01,
246 5.32464800188589216e-01, 1.73437500283893620e+00,
247 5.76576575632799071e-01, 5.50647119589526390e-01,
248 1.76562500399259092e+00, 5.66371680135198341e-01,
249 5.68504737613959144e-01, 1.79687500443862880e+00,
250 5.56521737755718449e-01, 5.86049047473771623e-01,
251 1.82812500114411280e+00, 5.47008546666207462e-01,
252 6.03290852063923744e-01, 1.85937500250667465e+00,
253 5.37815125325376786e-01, 6.20240411099985067e-01,
254 1.89062500504214515e+00, 5.28925618424108568e-01,
255 6.36907464903988974e-01, 1.92187500371610143e+00,
256 5.20325202245941476e-01, 6.53301273946326866e-01,
257 1.95312500494870611e+00, 5.11999998702726389e-01,
258 6.69430656476366792e-01, 1.98437500351688123e+00,
259 5.03937006980894941e-01, 6.85304004871206018e-01,
260 2.03125000000003997e+00, 4.92307692307682621e-01,
261 7.08651367095930240e-01, 2.09375000579615866e+00,
262 4.77611938976327366e-01, 7.38956719359554093e-01,
263 2.15625000000061062e+00, 4.63768115941897652e-01,
264 7.68370601797816022e-01, 2.21875000323311955e+00,
265 4.50704224695355204e-01, 7.96943975698769513e-01,
266 2.28125000853738547e+00, 4.38356162743050726e-01,
267 8.24723542091080120e-01, 2.34374999999916556e+00,
268 4.26666666666818573e-01, 8.51752210736227866e-01,
269 2.40625000438447856e+00, 4.15584414827170512e-01,
270 8.78069520876078258e-01, 2.46875000884389584e+00,
271 4.05063289688167072e-01, 9.03711953249632494e-01,
272 2.53124999999940403e+00, 3.95061728395154743e-01,
273 9.28713251872476775e-01, 2.59375000434366632e+00,
274 3.85542168029044230e-01, 9.53104706671537905e-01,
275 2.65625000734081196e+00, 3.76470587194880080e-01,
276 9.76915356454189698e-01, 2.71875000787161980e+00,
277 3.67816090889081959e-01, 1.00017221875016560e+00,
278 2.78125001557333462e+00, 3.59550559784484969e-01,
279 1.02290047253181449e+00, 2.84375001147093220e+00,
280 3.51648350229895601e-01, 1.04512360775085789e+00,
281 2.90625000771072894e+00, 3.44086020592463127e-01,
282 1.06686359300668343e+00, 2.96875001371853831e+00,
283 3.36842103706616824e-01, 1.08814099342179560e+00,
284 3.03125000512624965e+00, 3.29896906658595002e-01,
285 1.10897507739479018e+00, 3.09375001373132807e+00,
286 3.23232321797685962e-01, 1.12938395177327244e+00,
287 3.15625001204422961e+00, 3.16831681959289180e-01,
288 1.14938461785752644e+00, 3.21875000888250318e+00,
289 3.10679610793130057e-01, 1.16899308818952186e+00,
290 3.28125000000102052e+00, 3.04761904761809976e-01,
291 1.18822444735810784e+00, 3.34375001587649123e+00,
292 2.99065419140752298e-01, 1.20709293641028914e+00,
293 3.40625000791328070e+00, 2.93577980969346064e-01,
294 1.22561198175258212e+00, 3.46875000615970519e+00,
295 2.88288287776354346e-01, 1.24379430028837845e+00,
296 3.53125000516822674e+00, 2.83185840293502689e-01,
297 1.26165191737618265e+00, 3.59375001425228779e+00,
298 2.78260868461675415e-01, 1.27919622952937750e+00,
299 3.65625001719730669e+00, 2.73504272217836075e-01,
300 1.29643803670156643e+00, 3.71875000856489324e+00,
301 2.68907562405871714e-01, 1.31338759261496740e+00,
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