1 #include "FEATURE/uwin"
2
3 #if !_UWIN
4
_STUB_log()5 void _STUB_log(){}
6
7 #else
8
9 /*
10 * Copyright (c) 1992, 1993
11 * The Regents of the University of California. All rights reserved.
12 *
13 * Redistribution and use in source and binary forms, with or without
14 * modification, are permitted provided that the following conditions
15 * are met:
16 * 1. Redistributions of source code must retain the above copyright
17 * notice, this list of conditions and the following disclaimer.
18 * 2. Redistributions in binary form must reproduce the above copyright
19 * notice, this list of conditions and the following disclaimer in the
20 * documentation and/or other materials provided with the distribution.
21 * 3. Neither the name of the University nor the names of its contributors
22 * may be used to endorse or promote products derived from this software
23 * without specific prior written permission.
24 *
25 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35 * SUCH DAMAGE.
36 */
37
38 #ifndef lint
39 static char sccsid[] = "@(#)log.c 8.2 (Berkeley) 11/30/93";
40 #endif /* not lint */
41
42 #include <math.h>
43 #include <errno.h>
44
45 #include "mathimpl.h"
46
47 /* Table-driven natural logarithm.
48 *
49 * This code was derived, with minor modifications, from:
50 * Peter Tang, "Table-Driven Implementation of the
51 * Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
52 * Math Software, vol 16. no 4, pp 378-400, Dec 1990).
53 *
54 * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
55 * where F = j/128 for j an integer in [0, 128].
56 *
57 * log(2^m) = log2_hi*m + log2_tail*m
58 * since m is an integer, the dominant term is exact.
59 * m has at most 10 digits (for subnormal numbers),
60 * and log2_hi has 11 trailing zero bits.
61 *
62 * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
63 * logF_hi[] + 512 is exact.
64 *
65 * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
66 * the leading term is calculated to extra precision in two
67 * parts, the larger of which adds exactly to the dominant
68 * m and F terms.
69 * There are two cases:
70 * 1. when m, j are non-zero (m | j), use absolute
71 * precision for the leading term.
72 * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
73 * In this case, use a relative precision of 24 bits.
74 * (This is done differently in the original paper)
75 *
76 * Special cases:
77 * 0 return signalling -Inf
78 * neg return signalling NaN
79 * +Inf return +Inf
80 */
81
82 #if defined(vax) || defined(tahoe)
83 #define _IEEE 0
84 #define TRUNC(x) x = (double) (float) (x)
85 #else
86 #define _IEEE 1
87 #define endian (((*(int *) &one)) ? 1 : 0)
88 #define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000
89 #define infnan(x) 0.0
90 #endif
91
92 #define N 128
93
94 /* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
95 * Used for generation of extend precision logarithms.
96 * The constant 35184372088832 is 2^45, so the divide is exact.
97 * It ensures correct reading of logF_head, even for inaccurate
98 * decimal-to-binary conversion routines. (Everybody gets the
99 * right answer for integers less than 2^53.)
100 * Values for log(F) were generated using error < 10^-57 absolute
101 * with the bc -l package.
102 */
103 static double A1 = .08333333333333178827;
104 static double A2 = .01250000000377174923;
105 static double A3 = .002232139987919447809;
106 static double A4 = .0004348877777076145742;
107
108 static double logF_head[N+1] = {
109 0.,
110 .007782140442060381246,
111 .015504186535963526694,
112 .023167059281547608406,
113 .030771658666765233647,
114 .038318864302141264488,
115 .045809536031242714670,
116 .053244514518837604555,
117 .060624621816486978786,
118 .067950661908525944454,
119 .075223421237524235039,
120 .082443669210988446138,
121 .089612158689760690322,
122 .096729626458454731618,
123 .103796793681567578460,
124 .110814366340264314203,
125 .117783035656430001836,
126 .124703478501032805070,
127 .131576357788617315236,
128 .138402322859292326029,
129 .145182009844575077295,
130 .151916042025732167530,
131 .158605030176659056451,
132 .165249572895390883786,
133 .171850256926518341060,
134 .178407657472689606947,
135 .184922338493834104156,
136 .191394852999565046047,
137 .197825743329758552135,
138 .204215541428766300668,
139 .210564769107350002741,
140 .216873938300523150246,
141 .223143551314024080056,
142 .229374101064877322642,
143 .235566071312860003672,
144 .241719936886966024758,
145 .247836163904594286577,
146 .253915209980732470285,
147 .259957524436686071567,
148 .265963548496984003577,
149 .271933715484010463114,
150 .277868451003087102435,
151 .283768173130738432519,
152 .289633292582948342896,
153 .295464212893421063199,
154 .301261330578199704177,
155 .307025035294827830512,
156 .312755710004239517729,
157 .318453731118097493890,
158 .324119468654316733591,
159 .329753286372579168528,
160 .335355541920762334484,
161 .340926586970454081892,
162 .346466767346100823488,
163 .351976423156884266063,
164 .357455888922231679316,
165 .362905493689140712376,
166 .368325561158599157352,
167 .373716409793814818840,
168 .379078352934811846353,
169 .384411698910298582632,
170 .389716751140440464951,
171 .394993808240542421117,
172 .400243164127459749579,
173 .405465108107819105498,
174 .410659924985338875558,
175 .415827895143593195825,
176 .420969294644237379543,
177 .426084395310681429691,
178 .431173464818130014464,
179 .436236766774527495726,
180 .441274560805140936281,
181 .446287102628048160113,
182 .451274644139630254358,
183 .456237433481874177232,
184 .461175715122408291790,
185 .466089729924533457960,
186 .470979715219073113985,
187 .475845904869856894947,
188 .480688529345570714212,
189 .485507815781602403149,
190 .490303988045525329653,
191 .495077266798034543171,
192 .499827869556611403822,
193 .504556010751912253908,
194 .509261901790523552335,
195 .513945751101346104405,
196 .518607764208354637958,
197 .523248143765158602036,
198 .527867089620485785417,
199 .532464798869114019908,
200 .537041465897345915436,
201 .541597282432121573947,
202 .546132437597407260909,
203 .550647117952394182793,
204 .555141507540611200965,
205 .559615787935399566777,
206 .564070138285387656651,
207 .568504735352689749561,
208 .572919753562018740922,
209 .577315365035246941260,
210 .581691739635061821900,
211 .586049045003164792433,
212 .590387446602107957005,
213 .594707107746216934174,
214 .599008189645246602594,
215 .603290851438941899687,
216 .607555250224322662688,
217 .611801541106615331955,
218 .616029877215623855590,
219 .620240409751204424537,
220 .624433288012369303032,
221 .628608659422752680256,
222 .632766669570628437213,
223 .636907462236194987781,
224 .641031179420679109171,
225 .645137961373620782978,
226 .649227946625615004450,
227 .653301272011958644725,
228 .657358072709030238911,
229 .661398482245203922502,
230 .665422632544505177065,
231 .669430653942981734871,
232 .673422675212350441142,
233 .677398823590920073911,
234 .681359224807238206267,
235 .685304003098281100392,
236 .689233281238557538017,
237 .693147180560117703862
238 };
239
240 static double logF_tail[N+1] = {
241 0.,
242 -.00000000000000543229938420049,
243 .00000000000000172745674997061,
244 -.00000000000001323017818229233,
245 -.00000000000001154527628289872,
246 -.00000000000000466529469958300,
247 .00000000000005148849572685810,
248 -.00000000000002532168943117445,
249 -.00000000000005213620639136504,
250 -.00000000000001819506003016881,
251 .00000000000006329065958724544,
252 .00000000000008614512936087814,
253 -.00000000000007355770219435028,
254 .00000000000009638067658552277,
255 .00000000000007598636597194141,
256 .00000000000002579999128306990,
257 -.00000000000004654729747598444,
258 -.00000000000007556920687451336,
259 .00000000000010195735223708472,
260 -.00000000000017319034406422306,
261 -.00000000000007718001336828098,
262 .00000000000010980754099855238,
263 -.00000000000002047235780046195,
264 -.00000000000008372091099235912,
265 .00000000000014088127937111135,
266 .00000000000012869017157588257,
267 .00000000000017788850778198106,
268 .00000000000006440856150696891,
269 .00000000000016132822667240822,
270 -.00000000000007540916511956188,
271 -.00000000000000036507188831790,
272 .00000000000009120937249914984,
273 .00000000000018567570959796010,
274 -.00000000000003149265065191483,
275 -.00000000000009309459495196889,
276 .00000000000017914338601329117,
277 -.00000000000001302979717330866,
278 .00000000000023097385217586939,
279 .00000000000023999540484211737,
280 .00000000000015393776174455408,
281 -.00000000000036870428315837678,
282 .00000000000036920375082080089,
283 -.00000000000009383417223663699,
284 .00000000000009433398189512690,
285 .00000000000041481318704258568,
286 -.00000000000003792316480209314,
287 .00000000000008403156304792424,
288 -.00000000000034262934348285429,
289 .00000000000043712191957429145,
290 -.00000000000010475750058776541,
291 -.00000000000011118671389559323,
292 .00000000000037549577257259853,
293 .00000000000013912841212197565,
294 .00000000000010775743037572640,
295 .00000000000029391859187648000,
296 -.00000000000042790509060060774,
297 .00000000000022774076114039555,
298 .00000000000010849569622967912,
299 -.00000000000023073801945705758,
300 .00000000000015761203773969435,
301 .00000000000003345710269544082,
302 -.00000000000041525158063436123,
303 .00000000000032655698896907146,
304 -.00000000000044704265010452446,
305 .00000000000034527647952039772,
306 -.00000000000007048962392109746,
307 .00000000000011776978751369214,
308 -.00000000000010774341461609578,
309 .00000000000021863343293215910,
310 .00000000000024132639491333131,
311 .00000000000039057462209830700,
312 -.00000000000026570679203560751,
313 .00000000000037135141919592021,
314 -.00000000000017166921336082431,
315 -.00000000000028658285157914353,
316 -.00000000000023812542263446809,
317 .00000000000006576659768580062,
318 -.00000000000028210143846181267,
319 .00000000000010701931762114254,
320 .00000000000018119346366441110,
321 .00000000000009840465278232627,
322 -.00000000000033149150282752542,
323 -.00000000000018302857356041668,
324 -.00000000000016207400156744949,
325 .00000000000048303314949553201,
326 -.00000000000071560553172382115,
327 .00000000000088821239518571855,
328 -.00000000000030900580513238244,
329 -.00000000000061076551972851496,
330 .00000000000035659969663347830,
331 .00000000000035782396591276383,
332 -.00000000000046226087001544578,
333 .00000000000062279762917225156,
334 .00000000000072838947272065741,
335 .00000000000026809646615211673,
336 -.00000000000010960825046059278,
337 .00000000000002311949383800537,
338 -.00000000000058469058005299247,
339 -.00000000000002103748251144494,
340 -.00000000000023323182945587408,
341 -.00000000000042333694288141916,
342 -.00000000000043933937969737844,
343 .00000000000041341647073835565,
344 .00000000000006841763641591466,
345 .00000000000047585534004430641,
346 .00000000000083679678674757695,
347 -.00000000000085763734646658640,
348 .00000000000021913281229340092,
349 -.00000000000062242842536431148,
350 -.00000000000010983594325438430,
351 .00000000000065310431377633651,
352 -.00000000000047580199021710769,
353 -.00000000000037854251265457040,
354 .00000000000040939233218678664,
355 .00000000000087424383914858291,
356 .00000000000025218188456842882,
357 -.00000000000003608131360422557,
358 -.00000000000050518555924280902,
359 .00000000000078699403323355317,
360 -.00000000000067020876961949060,
361 .00000000000016108575753932458,
362 .00000000000058527188436251509,
363 -.00000000000035246757297904791,
364 -.00000000000018372084495629058,
365 .00000000000088606689813494916,
366 .00000000000066486268071468700,
367 .00000000000063831615170646519,
368 .00000000000025144230728376072,
369 -.00000000000017239444525614834
370 };
371
372 #if !_lib_log
373
374 extern double
375 #ifdef _ANSI_SOURCE
log(double x)376 log(double x)
377 #else
378 log(x) double x;
379 #endif
380 {
381 int m, j;
382 double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0;
383 volatile double u1;
384
385 /* Catch special cases */
386 if (x <= 0)
387 if (_IEEE && x == zero) /* log(0) = -Inf */
388 return (-one/zero);
389 else if (_IEEE) /* log(neg) = NaN */
390 return (zero/zero);
391 else if (x == zero) /* NOT REACHED IF _IEEE */
392 return (infnan(-ERANGE));
393 else
394 return (infnan(EDOM));
395 else if (!finite(x))
396 if (_IEEE) /* x = NaN, Inf */
397 return (x+x);
398 else
399 return (infnan(ERANGE));
400
401 /* Argument reduction: 1 <= g < 2; x/2^m = g; */
402 /* y = F*(1 + f/F) for |f| <= 2^-8 */
403
404 m = logb(x);
405 g = ldexp(x, -m);
406 if (_IEEE && m == -1022) {
407 j = logb(g), m += j;
408 g = ldexp(g, -j);
409 }
410 j = N*(g-1) + .5;
411 F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */
412 f = g - F;
413
414 /* Approximate expansion for log(1+f/F) ~= u + q */
415 g = 1/(2*F+f);
416 u = 2*f*g;
417 v = u*u;
418 q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
419
420 /* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8,
421 * u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits.
422 * It also adds exactly to |m*log2_hi + log_F_head[j] | < 750
423 */
424 if (m | j)
425 u1 = u + 513, u1 -= 513;
426
427 /* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero;
428 * u1 = u to 24 bits.
429 */
430 else
431 u1 = u, TRUNC(u1);
432 u2 = (2.0*(f - F*u1) - u1*f) * g;
433 /* u1 + u2 = 2f/(2F+f) to extra precision. */
434
435 /* log(x) = log(2^m*F*(1+f/F)) = */
436 /* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */
437 /* (exact) + (tiny) */
438
439 u1 += m*logF_head[N] + logF_head[j]; /* exact */
440 u2 = (u2 + logF_tail[j]) + q; /* tiny */
441 u2 += logF_tail[N]*m;
442 return (u1 + u2);
443 }
444
445 #endif
446
447 /*
448 * Extra precision variant, returning struct {double a, b;};
449 * log(x) = a+b to 63 bits, with a is rounded to 26 bits.
450 */
451 struct Double
452 #ifdef _ANSI_SOURCE
__log__D(double x)453 __log__D(double x)
454 #else
455 __log__D(x) double x;
456 #endif
457 {
458 int m, j;
459 double F, f, g, q, u, v, u2, one = 1.0;
460 volatile double u1;
461 struct Double r;
462
463 /* Argument reduction: 1 <= g < 2; x/2^m = g; */
464 /* y = F*(1 + f/F) for |f| <= 2^-8 */
465
466 m = (int)logb(x);
467 g = ldexp(x, -m);
468 if (_IEEE && m == -1022) {
469 j = (int)logb(g), m += j;
470 g = ldexp(g, -j);
471 }
472 j = (int)(N*(g-1) + .5);
473 F = (1.0/N) * j + 1;
474 f = g - F;
475
476 g = 1/(2*F+f);
477 u = 2*f*g;
478 v = u*u;
479 q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
480 if (m | j)
481 u1 = u + 513, u1 -= 513;
482 else
483 u1 = u, TRUNC(u1);
484 u2 = (2.0*(f - F*u1) - u1*f) * g;
485
486 u1 += m*logF_head[N] + logF_head[j];
487
488 u2 += logF_tail[j]; u2 += q;
489 u2 += logF_tail[N]*m;
490 r.a = u1 + u2; /* Only difference is here */
491 TRUNC(r.a);
492 r.b = (u1 - r.a) + u2;
493 return (r);
494 }
495
496 #endif
497