ipiq: Add simple IPI latency measure sysctls (2)
[dragonfly.git] / lib / libm / bsdsrc / b_log.c
CommitLineData
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1/*
2 * Copyright (c) 1992, 1993
3 * The Regents of the University of California. All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
6ff43c94 13 * 3. Neither the name of the University nor the names of its contributors
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14 * may be used to endorse or promote products derived from this software
15 * without specific prior written permission.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
18 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
19 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
21 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
22 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
23 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
24 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
25 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
26 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
27 * SUCH DAMAGE.
28 *
6ff43c94
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29 * @(#)log.c 8.2 (Berkeley) 11/30/93
30 * $FreeBSD: head/lib/msun/bsdsrc/b_log.c 176449 2008-02-22 02:26:51Z das $
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31 */
32
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33#include <math.h>
34#include <errno.h>
35
36#include "mathimpl.h"
37
38/* Table-driven natural logarithm.
39 *
40 * This code was derived, with minor modifications, from:
41 * Peter Tang, "Table-Driven Implementation of the
42 * Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
43 * Math Software, vol 16. no 4, pp 378-400, Dec 1990).
44 *
45 * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
46 * where F = j/128 for j an integer in [0, 128].
47 *
48 * log(2^m) = log2_hi*m + log2_tail*m
49 * since m is an integer, the dominant term is exact.
50 * m has at most 10 digits (for subnormal numbers),
51 * and log2_hi has 11 trailing zero bits.
52 *
53 * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
54 * logF_hi[] + 512 is exact.
55 *
56 * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
57 * the leading term is calculated to extra precision in two
58 * parts, the larger of which adds exactly to the dominant
59 * m and F terms.
60 * There are two cases:
61 * 1. when m, j are non-zero (m | j), use absolute
62 * precision for the leading term.
63 * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
64 * In this case, use a relative precision of 24 bits.
65 * (This is done differently in the original paper)
66 *
67 * Special cases:
68 * 0 return signalling -Inf
69 * neg return signalling NaN
70 * +Inf return +Inf
71*/
72
73#define N 128
74
75/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
76 * Used for generation of extend precision logarithms.
77 * The constant 35184372088832 is 2^45, so the divide is exact.
78 * It ensures correct reading of logF_head, even for inaccurate
79 * decimal-to-binary conversion routines. (Everybody gets the
80 * right answer for integers less than 2^53.)
81 * Values for log(F) were generated using error < 10^-57 absolute
82 * with the bc -l package.
83*/
84static double A1 = .08333333333333178827;
85static double A2 = .01250000000377174923;
86static double A3 = .002232139987919447809;
87static double A4 = .0004348877777076145742;
88
89static double logF_head[N+1] = {
90 0.,
91 .007782140442060381246,
92 .015504186535963526694,
93 .023167059281547608406,
94 .030771658666765233647,
95 .038318864302141264488,
96 .045809536031242714670,
97 .053244514518837604555,
98 .060624621816486978786,
99 .067950661908525944454,
100 .075223421237524235039,
101 .082443669210988446138,
102 .089612158689760690322,
103 .096729626458454731618,
104 .103796793681567578460,
105 .110814366340264314203,
106 .117783035656430001836,
107 .124703478501032805070,
108 .131576357788617315236,
109 .138402322859292326029,
110 .145182009844575077295,
111 .151916042025732167530,
112 .158605030176659056451,
113 .165249572895390883786,
114 .171850256926518341060,
115 .178407657472689606947,
116 .184922338493834104156,
117 .191394852999565046047,
118 .197825743329758552135,
119 .204215541428766300668,
120 .210564769107350002741,
121 .216873938300523150246,
122 .223143551314024080056,
123 .229374101064877322642,
124 .235566071312860003672,
125 .241719936886966024758,
126 .247836163904594286577,
127 .253915209980732470285,
128 .259957524436686071567,
129 .265963548496984003577,
130 .271933715484010463114,
131 .277868451003087102435,
132 .283768173130738432519,
133 .289633292582948342896,
134 .295464212893421063199,
135 .301261330578199704177,
136 .307025035294827830512,
137 .312755710004239517729,
138 .318453731118097493890,
139 .324119468654316733591,
140 .329753286372579168528,
141 .335355541920762334484,
142 .340926586970454081892,
143 .346466767346100823488,
144 .351976423156884266063,
145 .357455888922231679316,
146 .362905493689140712376,
147 .368325561158599157352,
148 .373716409793814818840,
149 .379078352934811846353,
150 .384411698910298582632,
151 .389716751140440464951,
152 .394993808240542421117,
153 .400243164127459749579,
154 .405465108107819105498,
155 .410659924985338875558,
156 .415827895143593195825,
157 .420969294644237379543,
158 .426084395310681429691,
159 .431173464818130014464,
160 .436236766774527495726,
161 .441274560805140936281,
162 .446287102628048160113,
163 .451274644139630254358,
164 .456237433481874177232,
165 .461175715122408291790,
166 .466089729924533457960,
167 .470979715219073113985,
168 .475845904869856894947,
169 .480688529345570714212,
170 .485507815781602403149,
171 .490303988045525329653,
172 .495077266798034543171,
173 .499827869556611403822,
174 .504556010751912253908,
175 .509261901790523552335,
176 .513945751101346104405,
177 .518607764208354637958,
178 .523248143765158602036,
179 .527867089620485785417,
180 .532464798869114019908,
181 .537041465897345915436,
182 .541597282432121573947,
183 .546132437597407260909,
184 .550647117952394182793,
185 .555141507540611200965,
186 .559615787935399566777,
187 .564070138285387656651,
188 .568504735352689749561,
189 .572919753562018740922,
190 .577315365035246941260,
191 .581691739635061821900,
192 .586049045003164792433,
193 .590387446602107957005,
194 .594707107746216934174,
195 .599008189645246602594,
196 .603290851438941899687,
197 .607555250224322662688,
198 .611801541106615331955,
199 .616029877215623855590,
200 .620240409751204424537,
201 .624433288012369303032,
202 .628608659422752680256,
203 .632766669570628437213,
204 .636907462236194987781,
205 .641031179420679109171,
206 .645137961373620782978,
207 .649227946625615004450,
208 .653301272011958644725,
209 .657358072709030238911,
210 .661398482245203922502,
211 .665422632544505177065,
212 .669430653942981734871,
213 .673422675212350441142,
214 .677398823590920073911,
215 .681359224807238206267,
216 .685304003098281100392,
217 .689233281238557538017,
218 .693147180560117703862
219};
220
221static double logF_tail[N+1] = {
222 0.,
223 -.00000000000000543229938420049,
224 .00000000000000172745674997061,
225 -.00000000000001323017818229233,
226 -.00000000000001154527628289872,
227 -.00000000000000466529469958300,
228 .00000000000005148849572685810,
229 -.00000000000002532168943117445,
230 -.00000000000005213620639136504,
231 -.00000000000001819506003016881,
232 .00000000000006329065958724544,
233 .00000000000008614512936087814,
234 -.00000000000007355770219435028,
235 .00000000000009638067658552277,
236 .00000000000007598636597194141,
237 .00000000000002579999128306990,
238 -.00000000000004654729747598444,
239 -.00000000000007556920687451336,
240 .00000000000010195735223708472,
241 -.00000000000017319034406422306,
242 -.00000000000007718001336828098,
243 .00000000000010980754099855238,
244 -.00000000000002047235780046195,
245 -.00000000000008372091099235912,
246 .00000000000014088127937111135,
247 .00000000000012869017157588257,
248 .00000000000017788850778198106,
249 .00000000000006440856150696891,
250 .00000000000016132822667240822,
251 -.00000000000007540916511956188,
252 -.00000000000000036507188831790,
253 .00000000000009120937249914984,
254 .00000000000018567570959796010,
255 -.00000000000003149265065191483,
256 -.00000000000009309459495196889,
257 .00000000000017914338601329117,
258 -.00000000000001302979717330866,
259 .00000000000023097385217586939,
260 .00000000000023999540484211737,
261 .00000000000015393776174455408,
262 -.00000000000036870428315837678,
263 .00000000000036920375082080089,
264 -.00000000000009383417223663699,
265 .00000000000009433398189512690,
266 .00000000000041481318704258568,
267 -.00000000000003792316480209314,
268 .00000000000008403156304792424,
269 -.00000000000034262934348285429,
270 .00000000000043712191957429145,
271 -.00000000000010475750058776541,
272 -.00000000000011118671389559323,
273 .00000000000037549577257259853,
274 .00000000000013912841212197565,
275 .00000000000010775743037572640,
276 .00000000000029391859187648000,
277 -.00000000000042790509060060774,
278 .00000000000022774076114039555,
279 .00000000000010849569622967912,
280 -.00000000000023073801945705758,
281 .00000000000015761203773969435,
282 .00000000000003345710269544082,
283 -.00000000000041525158063436123,
284 .00000000000032655698896907146,
285 -.00000000000044704265010452446,
286 .00000000000034527647952039772,
287 -.00000000000007048962392109746,
288 .00000000000011776978751369214,
289 -.00000000000010774341461609578,
290 .00000000000021863343293215910,
291 .00000000000024132639491333131,
292 .00000000000039057462209830700,
293 -.00000000000026570679203560751,
294 .00000000000037135141919592021,
295 -.00000000000017166921336082431,
296 -.00000000000028658285157914353,
297 -.00000000000023812542263446809,
298 .00000000000006576659768580062,
299 -.00000000000028210143846181267,
300 .00000000000010701931762114254,
301 .00000000000018119346366441110,
302 .00000000000009840465278232627,
303 -.00000000000033149150282752542,
304 -.00000000000018302857356041668,
305 -.00000000000016207400156744949,
306 .00000000000048303314949553201,
307 -.00000000000071560553172382115,
308 .00000000000088821239518571855,
309 -.00000000000030900580513238244,
310 -.00000000000061076551972851496,
311 .00000000000035659969663347830,
312 .00000000000035782396591276383,
313 -.00000000000046226087001544578,
314 .00000000000062279762917225156,
315 .00000000000072838947272065741,
316 .00000000000026809646615211673,
317 -.00000000000010960825046059278,
318 .00000000000002311949383800537,
319 -.00000000000058469058005299247,
320 -.00000000000002103748251144494,
321 -.00000000000023323182945587408,
322 -.00000000000042333694288141916,
323 -.00000000000043933937969737844,
324 .00000000000041341647073835565,
325 .00000000000006841763641591466,
326 .00000000000047585534004430641,
327 .00000000000083679678674757695,
328 -.00000000000085763734646658640,
329 .00000000000021913281229340092,
330 -.00000000000062242842536431148,
331 -.00000000000010983594325438430,
332 .00000000000065310431377633651,
333 -.00000000000047580199021710769,
334 -.00000000000037854251265457040,
335 .00000000000040939233218678664,
336 .00000000000087424383914858291,
337 .00000000000025218188456842882,
338 -.00000000000003608131360422557,
339 -.00000000000050518555924280902,
340 .00000000000078699403323355317,
341 -.00000000000067020876961949060,
342 .00000000000016108575753932458,
343 .00000000000058527188436251509,
344 -.00000000000035246757297904791,
345 -.00000000000018372084495629058,
346 .00000000000088606689813494916,
347 .00000000000066486268071468700,
348 .00000000000063831615170646519,
349 .00000000000025144230728376072,
350 -.00000000000017239444525614834
351};
352
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353
354/*
355 * Extra precision variant, returning struct {double a, b;};
356 * log(x) = a+b to 63 bits, with a rounded to 26 bits.
357 */
358struct Double
1a3b704c 359__log__D(double x)
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360{
361 int m, j;
362 double F, f, g, q, u, v, u2;
363 volatile double u1;
364 struct Double r;
365
366 /* Argument reduction: 1 <= g < 2; x/2^m = g; */
367 /* y = F*(1 + f/F) for |f| <= 2^-8 */
368
369 m = logb(x);
370 g = ldexp(x, -m);
371 if (m == -1022) {
372 j = logb(g), m += j;
373 g = ldexp(g, -j);
374 }
375 j = N*(g-1) + .5;
376 F = (1.0/N) * j + 1;
377 f = g - F;
378
379 g = 1/(2*F+f);
380 u = 2*f*g;
381 v = u*u;
382 q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
383 if (m | j)
384 u1 = u + 513, u1 -= 513;
385 else
386 u1 = u, TRUNC(u1);
387 u2 = (2.0*(f - F*u1) - u1*f) * g;
388
389 u1 += m*logF_head[N] + logF_head[j];
390
391 u2 += logF_tail[j]; u2 += q;
392 u2 += logF_tail[N]*m;
393 r.a = u1 + u2; /* Only difference is here */
394 TRUNC(r.a);
395 r.b = (u1 - r.a) + u2;
396 return (r);
397}