libm & rtld: Ansify some remaining functions.
[dragonfly.git] / lib / libm / src / b_log.c
CommitLineData
1a3b704c
JM
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.
13 * 3. All advertising materials mentioning features or use of this software
14 * must display the following acknowledgement:
15 * This product includes software developed by the University of
16 * California, Berkeley and its contributors.
17 * 4. Neither the name of the University nor the names of its contributors
18 * may be used to endorse or promote products derived from this software
19 * without specific prior written permission.
20 *
21 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
22 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
23 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
24 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
25 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
26 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
27 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
28 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
29 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
30 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
31 * SUCH DAMAGE.
32 *
33 * FreeBSD SVN: 176449 (2008-02-22)
34 */
35
36/* @(#)log.c 8.2 (Berkeley) 11/30/93 */
37
38#include <math.h>
39#include <errno.h>
40
41#include "mathimpl.h"
42
43/* Table-driven natural logarithm.
44 *
45 * This code was derived, with minor modifications, from:
46 * Peter Tang, "Table-Driven Implementation of the
47 * Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
48 * Math Software, vol 16. no 4, pp 378-400, Dec 1990).
49 *
50 * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
51 * where F = j/128 for j an integer in [0, 128].
52 *
53 * log(2^m) = log2_hi*m + log2_tail*m
54 * since m is an integer, the dominant term is exact.
55 * m has at most 10 digits (for subnormal numbers),
56 * and log2_hi has 11 trailing zero bits.
57 *
58 * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
59 * logF_hi[] + 512 is exact.
60 *
61 * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
62 * the leading term is calculated to extra precision in two
63 * parts, the larger of which adds exactly to the dominant
64 * m and F terms.
65 * There are two cases:
66 * 1. when m, j are non-zero (m | j), use absolute
67 * precision for the leading term.
68 * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
69 * In this case, use a relative precision of 24 bits.
70 * (This is done differently in the original paper)
71 *
72 * Special cases:
73 * 0 return signalling -Inf
74 * neg return signalling NaN
75 * +Inf return +Inf
76*/
77
78#define N 128
79
80/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
81 * Used for generation of extend precision logarithms.
82 * The constant 35184372088832 is 2^45, so the divide is exact.
83 * It ensures correct reading of logF_head, even for inaccurate
84 * decimal-to-binary conversion routines. (Everybody gets the
85 * right answer for integers less than 2^53.)
86 * Values for log(F) were generated using error < 10^-57 absolute
87 * with the bc -l package.
88*/
89static double A1 = .08333333333333178827;
90static double A2 = .01250000000377174923;
91static double A3 = .002232139987919447809;
92static double A4 = .0004348877777076145742;
93
94static double logF_head[N+1] = {
95 0.,
96 .007782140442060381246,
97 .015504186535963526694,
98 .023167059281547608406,
99 .030771658666765233647,
100 .038318864302141264488,
101 .045809536031242714670,
102 .053244514518837604555,
103 .060624621816486978786,
104 .067950661908525944454,
105 .075223421237524235039,
106 .082443669210988446138,
107 .089612158689760690322,
108 .096729626458454731618,
109 .103796793681567578460,
110 .110814366340264314203,
111 .117783035656430001836,
112 .124703478501032805070,
113 .131576357788617315236,
114 .138402322859292326029,
115 .145182009844575077295,
116 .151916042025732167530,
117 .158605030176659056451,
118 .165249572895390883786,
119 .171850256926518341060,
120 .178407657472689606947,
121 .184922338493834104156,
122 .191394852999565046047,
123 .197825743329758552135,
124 .204215541428766300668,
125 .210564769107350002741,
126 .216873938300523150246,
127 .223143551314024080056,
128 .229374101064877322642,
129 .235566071312860003672,
130 .241719936886966024758,
131 .247836163904594286577,
132 .253915209980732470285,
133 .259957524436686071567,
134 .265963548496984003577,
135 .271933715484010463114,
136 .277868451003087102435,
137 .283768173130738432519,
138 .289633292582948342896,
139 .295464212893421063199,
140 .301261330578199704177,
141 .307025035294827830512,
142 .312755710004239517729,
143 .318453731118097493890,
144 .324119468654316733591,
145 .329753286372579168528,
146 .335355541920762334484,
147 .340926586970454081892,
148 .346466767346100823488,
149 .351976423156884266063,
150 .357455888922231679316,
151 .362905493689140712376,
152 .368325561158599157352,
153 .373716409793814818840,
154 .379078352934811846353,
155 .384411698910298582632,
156 .389716751140440464951,
157 .394993808240542421117,
158 .400243164127459749579,
159 .405465108107819105498,
160 .410659924985338875558,
161 .415827895143593195825,
162 .420969294644237379543,
163 .426084395310681429691,
164 .431173464818130014464,
165 .436236766774527495726,
166 .441274560805140936281,
167 .446287102628048160113,
168 .451274644139630254358,
169 .456237433481874177232,
170 .461175715122408291790,
171 .466089729924533457960,
172 .470979715219073113985,
173 .475845904869856894947,
174 .480688529345570714212,
175 .485507815781602403149,
176 .490303988045525329653,
177 .495077266798034543171,
178 .499827869556611403822,
179 .504556010751912253908,
180 .509261901790523552335,
181 .513945751101346104405,
182 .518607764208354637958,
183 .523248143765158602036,
184 .527867089620485785417,
185 .532464798869114019908,
186 .537041465897345915436,
187 .541597282432121573947,
188 .546132437597407260909,
189 .550647117952394182793,
190 .555141507540611200965,
191 .559615787935399566777,
192 .564070138285387656651,
193 .568504735352689749561,
194 .572919753562018740922,
195 .577315365035246941260,
196 .581691739635061821900,
197 .586049045003164792433,
198 .590387446602107957005,
199 .594707107746216934174,
200 .599008189645246602594,
201 .603290851438941899687,
202 .607555250224322662688,
203 .611801541106615331955,
204 .616029877215623855590,
205 .620240409751204424537,
206 .624433288012369303032,
207 .628608659422752680256,
208 .632766669570628437213,
209 .636907462236194987781,
210 .641031179420679109171,
211 .645137961373620782978,
212 .649227946625615004450,
213 .653301272011958644725,
214 .657358072709030238911,
215 .661398482245203922502,
216 .665422632544505177065,
217 .669430653942981734871,
218 .673422675212350441142,
219 .677398823590920073911,
220 .681359224807238206267,
221 .685304003098281100392,
222 .689233281238557538017,
223 .693147180560117703862
224};
225
226static double logF_tail[N+1] = {
227 0.,
228 -.00000000000000543229938420049,
229 .00000000000000172745674997061,
230 -.00000000000001323017818229233,
231 -.00000000000001154527628289872,
232 -.00000000000000466529469958300,
233 .00000000000005148849572685810,
234 -.00000000000002532168943117445,
235 -.00000000000005213620639136504,
236 -.00000000000001819506003016881,
237 .00000000000006329065958724544,
238 .00000000000008614512936087814,
239 -.00000000000007355770219435028,
240 .00000000000009638067658552277,
241 .00000000000007598636597194141,
242 .00000000000002579999128306990,
243 -.00000000000004654729747598444,
244 -.00000000000007556920687451336,
245 .00000000000010195735223708472,
246 -.00000000000017319034406422306,
247 -.00000000000007718001336828098,
248 .00000000000010980754099855238,
249 -.00000000000002047235780046195,
250 -.00000000000008372091099235912,
251 .00000000000014088127937111135,
252 .00000000000012869017157588257,
253 .00000000000017788850778198106,
254 .00000000000006440856150696891,
255 .00000000000016132822667240822,
256 -.00000000000007540916511956188,
257 -.00000000000000036507188831790,
258 .00000000000009120937249914984,
259 .00000000000018567570959796010,
260 -.00000000000003149265065191483,
261 -.00000000000009309459495196889,
262 .00000000000017914338601329117,
263 -.00000000000001302979717330866,
264 .00000000000023097385217586939,
265 .00000000000023999540484211737,
266 .00000000000015393776174455408,
267 -.00000000000036870428315837678,
268 .00000000000036920375082080089,
269 -.00000000000009383417223663699,
270 .00000000000009433398189512690,
271 .00000000000041481318704258568,
272 -.00000000000003792316480209314,
273 .00000000000008403156304792424,
274 -.00000000000034262934348285429,
275 .00000000000043712191957429145,
276 -.00000000000010475750058776541,
277 -.00000000000011118671389559323,
278 .00000000000037549577257259853,
279 .00000000000013912841212197565,
280 .00000000000010775743037572640,
281 .00000000000029391859187648000,
282 -.00000000000042790509060060774,
283 .00000000000022774076114039555,
284 .00000000000010849569622967912,
285 -.00000000000023073801945705758,
286 .00000000000015761203773969435,
287 .00000000000003345710269544082,
288 -.00000000000041525158063436123,
289 .00000000000032655698896907146,
290 -.00000000000044704265010452446,
291 .00000000000034527647952039772,
292 -.00000000000007048962392109746,
293 .00000000000011776978751369214,
294 -.00000000000010774341461609578,
295 .00000000000021863343293215910,
296 .00000000000024132639491333131,
297 .00000000000039057462209830700,
298 -.00000000000026570679203560751,
299 .00000000000037135141919592021,
300 -.00000000000017166921336082431,
301 -.00000000000028658285157914353,
302 -.00000000000023812542263446809,
303 .00000000000006576659768580062,
304 -.00000000000028210143846181267,
305 .00000000000010701931762114254,
306 .00000000000018119346366441110,
307 .00000000000009840465278232627,
308 -.00000000000033149150282752542,
309 -.00000000000018302857356041668,
310 -.00000000000016207400156744949,
311 .00000000000048303314949553201,
312 -.00000000000071560553172382115,
313 .00000000000088821239518571855,
314 -.00000000000030900580513238244,
315 -.00000000000061076551972851496,
316 .00000000000035659969663347830,
317 .00000000000035782396591276383,
318 -.00000000000046226087001544578,
319 .00000000000062279762917225156,
320 .00000000000072838947272065741,
321 .00000000000026809646615211673,
322 -.00000000000010960825046059278,
323 .00000000000002311949383800537,
324 -.00000000000058469058005299247,
325 -.00000000000002103748251144494,
326 -.00000000000023323182945587408,
327 -.00000000000042333694288141916,
328 -.00000000000043933937969737844,
329 .00000000000041341647073835565,
330 .00000000000006841763641591466,
331 .00000000000047585534004430641,
332 .00000000000083679678674757695,
333 -.00000000000085763734646658640,
334 .00000000000021913281229340092,
335 -.00000000000062242842536431148,
336 -.00000000000010983594325438430,
337 .00000000000065310431377633651,
338 -.00000000000047580199021710769,
339 -.00000000000037854251265457040,
340 .00000000000040939233218678664,
341 .00000000000087424383914858291,
342 .00000000000025218188456842882,
343 -.00000000000003608131360422557,
344 -.00000000000050518555924280902,
345 .00000000000078699403323355317,
346 -.00000000000067020876961949060,
347 .00000000000016108575753932458,
348 .00000000000058527188436251509,
349 -.00000000000035246757297904791,
350 -.00000000000018372084495629058,
351 .00000000000088606689813494916,
352 .00000000000066486268071468700,
353 .00000000000063831615170646519,
354 .00000000000025144230728376072,
355 -.00000000000017239444525614834
356};
357
358#if 0
359double
360#ifdef _ANSI_SOURCE
361log(double x)
362#else
363log(x) double x;
364#endif
365{
366 int m, j;
367 double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0;
368 volatile double u1;
369
370 /* Catch special cases */
371 if (x <= 0)
372 if (x == zero) /* log(0) = -Inf */
373 return (-one/zero);
374 else /* log(neg) = NaN */
375 return (zero/zero);
376 else if (!finite(x))
377 return (x+x); /* x = NaN, Inf */
378
379 /* Argument reduction: 1 <= g < 2; x/2^m = g; */
380 /* y = F*(1 + f/F) for |f| <= 2^-8 */
381
382 m = logb(x);
383 g = ldexp(x, -m);
384 if (m == -1022) {
385 j = logb(g), m += j;
386 g = ldexp(g, -j);
387 }
388 j = N*(g-1) + .5;
389 F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */
390 f = g - F;
391
392 /* Approximate expansion for log(1+f/F) ~= u + q */
393 g = 1/(2*F+f);
394 u = 2*f*g;
395 v = u*u;
396 q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
397
398 /* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8,
399 * u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits.
400 * It also adds exactly to |m*log2_hi + log_F_head[j] | < 750
401 */
402 if (m | j)
403 u1 = u + 513, u1 -= 513;
404
405 /* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero;
406 * u1 = u to 24 bits.
407 */
408 else
409 u1 = u, TRUNC(u1);
410 u2 = (2.0*(f - F*u1) - u1*f) * g;
411 /* u1 + u2 = 2f/(2F+f) to extra precision. */
412
413 /* log(x) = log(2^m*F*(1+f/F)) = */
414 /* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */
415 /* (exact) + (tiny) */
416
417 u1 += m*logF_head[N] + logF_head[j]; /* exact */
418 u2 = (u2 + logF_tail[j]) + q; /* tiny */
419 u2 += logF_tail[N]*m;
420 return (u1 + u2);
421}
422#endif
423
424/*
425 * Extra precision variant, returning struct {double a, b;};
426 * log(x) = a+b to 63 bits, with a rounded to 26 bits.
427 */
428struct Double
1a3b704c 429__log__D(double x)
1a3b704c
JM
430{
431 int m, j;
432 double F, f, g, q, u, v, u2;
433 volatile double u1;
434 struct Double r;
435
436 /* Argument reduction: 1 <= g < 2; x/2^m = g; */
437 /* y = F*(1 + f/F) for |f| <= 2^-8 */
438
439 m = logb(x);
440 g = ldexp(x, -m);
441 if (m == -1022) {
442 j = logb(g), m += j;
443 g = ldexp(g, -j);
444 }
445 j = N*(g-1) + .5;
446 F = (1.0/N) * j + 1;
447 f = g - F;
448
449 g = 1/(2*F+f);
450 u = 2*f*g;
451 v = u*u;
452 q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
453 if (m | j)
454 u1 = u + 513, u1 -= 513;
455 else
456 u1 = u, TRUNC(u1);
457 u2 = (2.0*(f - F*u1) - u1*f) * g;
458
459 u1 += m*logF_head[N] + logF_head[j];
460
461 u2 += logF_tail[j]; u2 += q;
462 u2 += logF_tail[N]*m;
463 r.a = u1 + u2; /* Only difference is here */
464 TRUNC(r.a);
465 r.b = (u1 - r.a) + u2;
466 return (r);
467}