minix/lib/libm/noieee_src/n_log.c
Ben Gras 2fe8fb192f Full switch to clang/ELF. Drop ack. Simplify.
There is important information about booting non-ack images in
docs/UPDATING. ack/aout-format images can't be built any more, and
booting clang/ELF-format ones is a little different. Updating to the
new boot monitor is recommended.

Changes in this commit:

	. drop boot monitor -> allowing dropping ack support
	. facility to copy ELF boot files to /boot so that old boot monitor
	  can still boot fairly easily, see UPDATING
	. no more ack-format libraries -> single-case libraries
	. some cleanup of OBJECT_FMT, COMPILER_TYPE, etc cases
	. drop several ack toolchain commands, but not all support
	  commands (e.g. aal is gone but acksize is not yet).
	. a few libc files moved to netbsd libc dir
	. new /bin/date as minix date used code in libc/
	. test compile fix
	. harmonize includes
	. /usr/lib is no longer special: without ack, /usr/lib plays no
	  kind of special bootstrapping role any more and bootstrapping
	  is done exclusively through packages, so releases depend even
	  less on the state of the machine making them now.
	. rename nbsd_lib* to lib*
	. reduce mtree
2012-02-14 14:52:02 +01:00

491 lines
14 KiB
C

/* $NetBSD: n_log.c,v 1.7 2008/03/20 16:41:26 mhitch Exp $ */
/*
* Copyright (c) 1992, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#ifndef lint
#if 0
static char sccsid[] = "@(#)log.c 8.2 (Berkeley) 11/30/93";
#endif
#endif /* not lint */
#include "../src/namespace.h"
#include <math.h>
#include <errno.h>
#include "mathimpl.h"
#ifdef __weak_alias
__weak_alias(log, _log);
__weak_alias(logf, _logf);
#endif
/* Table-driven natural logarithm.
*
* This code was derived, with minor modifications, from:
* Peter Tang, "Table-Driven Implementation of the
* Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
* Math Software, vol 16. no 4, pp 378-400, Dec 1990).
*
* Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
* where F = j/128 for j an integer in [0, 128].
*
* log(2^m) = log2_hi*m + log2_tail*m
* since m is an integer, the dominant term is exact.
* m has at most 10 digits (for subnormal numbers),
* and log2_hi has 11 trailing zero bits.
*
* log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
* logF_hi[] + 512 is exact.
*
* log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
* the leading term is calculated to extra precision in two
* parts, the larger of which adds exactly to the dominant
* m and F terms.
* There are two cases:
* 1. when m, j are non-zero (m | j), use absolute
* precision for the leading term.
* 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
* In this case, use a relative precision of 24 bits.
* (This is done differently in the original paper)
*
* Special cases:
* 0 return signalling -Inf
* neg return signalling NaN
* +Inf return +Inf
*/
#if defined(__vax__) || defined(tahoe)
#define _IEEE 0
#define TRUNC(x) x = (double) (float) (x)
#else
#define _IEEE 1
#define endian (((*(int *) &one)) ? 1 : 0)
#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000
#define infnan(x) 0.0
#endif
#define N 128
/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
* Used for generation of extend precision logarithms.
* The constant 35184372088832 is 2^45, so the divide is exact.
* It ensures correct reading of logF_head, even for inaccurate
* decimal-to-binary conversion routines. (Everybody gets the
* right answer for integers less than 2^53.)
* Values for log(F) were generated using error < 10^-57 absolute
* with the bc -l package.
*/
static const double A1 = .08333333333333178827;
static const double A2 = .01250000000377174923;
static const double A3 = .002232139987919447809;
static const double A4 = .0004348877777076145742;
static const double logF_head[N+1] = {
0.,
.007782140442060381246,
.015504186535963526694,
.023167059281547608406,
.030771658666765233647,
.038318864302141264488,
.045809536031242714670,
.053244514518837604555,
.060624621816486978786,
.067950661908525944454,
.075223421237524235039,
.082443669210988446138,
.089612158689760690322,
.096729626458454731618,
.103796793681567578460,
.110814366340264314203,
.117783035656430001836,
.124703478501032805070,
.131576357788617315236,
.138402322859292326029,
.145182009844575077295,
.151916042025732167530,
.158605030176659056451,
.165249572895390883786,
.171850256926518341060,
.178407657472689606947,
.184922338493834104156,
.191394852999565046047,
.197825743329758552135,
.204215541428766300668,
.210564769107350002741,
.216873938300523150246,
.223143551314024080056,
.229374101064877322642,
.235566071312860003672,
.241719936886966024758,
.247836163904594286577,
.253915209980732470285,
.259957524436686071567,
.265963548496984003577,
.271933715484010463114,
.277868451003087102435,
.283768173130738432519,
.289633292582948342896,
.295464212893421063199,
.301261330578199704177,
.307025035294827830512,
.312755710004239517729,
.318453731118097493890,
.324119468654316733591,
.329753286372579168528,
.335355541920762334484,
.340926586970454081892,
.346466767346100823488,
.351976423156884266063,
.357455888922231679316,
.362905493689140712376,
.368325561158599157352,
.373716409793814818840,
.379078352934811846353,
.384411698910298582632,
.389716751140440464951,
.394993808240542421117,
.400243164127459749579,
.405465108107819105498,
.410659924985338875558,
.415827895143593195825,
.420969294644237379543,
.426084395310681429691,
.431173464818130014464,
.436236766774527495726,
.441274560805140936281,
.446287102628048160113,
.451274644139630254358,
.456237433481874177232,
.461175715122408291790,
.466089729924533457960,
.470979715219073113985,
.475845904869856894947,
.480688529345570714212,
.485507815781602403149,
.490303988045525329653,
.495077266798034543171,
.499827869556611403822,
.504556010751912253908,
.509261901790523552335,
.513945751101346104405,
.518607764208354637958,
.523248143765158602036,
.527867089620485785417,
.532464798869114019908,
.537041465897345915436,
.541597282432121573947,
.546132437597407260909,
.550647117952394182793,
.555141507540611200965,
.559615787935399566777,
.564070138285387656651,
.568504735352689749561,
.572919753562018740922,
.577315365035246941260,
.581691739635061821900,
.586049045003164792433,
.590387446602107957005,
.594707107746216934174,
.599008189645246602594,
.603290851438941899687,
.607555250224322662688,
.611801541106615331955,
.616029877215623855590,
.620240409751204424537,
.624433288012369303032,
.628608659422752680256,
.632766669570628437213,
.636907462236194987781,
.641031179420679109171,
.645137961373620782978,
.649227946625615004450,
.653301272011958644725,
.657358072709030238911,
.661398482245203922502,
.665422632544505177065,
.669430653942981734871,
.673422675212350441142,
.677398823590920073911,
.681359224807238206267,
.685304003098281100392,
.689233281238557538017,
.693147180560117703862
};
static const double logF_tail[N+1] = {
0.,
-.00000000000000543229938420049,
.00000000000000172745674997061,
-.00000000000001323017818229233,
-.00000000000001154527628289872,
-.00000000000000466529469958300,
.00000000000005148849572685810,
-.00000000000002532168943117445,
-.00000000000005213620639136504,
-.00000000000001819506003016881,
.00000000000006329065958724544,
.00000000000008614512936087814,
-.00000000000007355770219435028,
.00000000000009638067658552277,
.00000000000007598636597194141,
.00000000000002579999128306990,
-.00000000000004654729747598444,
-.00000000000007556920687451336,
.00000000000010195735223708472,
-.00000000000017319034406422306,
-.00000000000007718001336828098,
.00000000000010980754099855238,
-.00000000000002047235780046195,
-.00000000000008372091099235912,
.00000000000014088127937111135,
.00000000000012869017157588257,
.00000000000017788850778198106,
.00000000000006440856150696891,
.00000000000016132822667240822,
-.00000000000007540916511956188,
-.00000000000000036507188831790,
.00000000000009120937249914984,
.00000000000018567570959796010,
-.00000000000003149265065191483,
-.00000000000009309459495196889,
.00000000000017914338601329117,
-.00000000000001302979717330866,
.00000000000023097385217586939,
.00000000000023999540484211737,
.00000000000015393776174455408,
-.00000000000036870428315837678,
.00000000000036920375082080089,
-.00000000000009383417223663699,
.00000000000009433398189512690,
.00000000000041481318704258568,
-.00000000000003792316480209314,
.00000000000008403156304792424,
-.00000000000034262934348285429,
.00000000000043712191957429145,
-.00000000000010475750058776541,
-.00000000000011118671389559323,
.00000000000037549577257259853,
.00000000000013912841212197565,
.00000000000010775743037572640,
.00000000000029391859187648000,
-.00000000000042790509060060774,
.00000000000022774076114039555,
.00000000000010849569622967912,
-.00000000000023073801945705758,
.00000000000015761203773969435,
.00000000000003345710269544082,
-.00000000000041525158063436123,
.00000000000032655698896907146,
-.00000000000044704265010452446,
.00000000000034527647952039772,
-.00000000000007048962392109746,
.00000000000011776978751369214,
-.00000000000010774341461609578,
.00000000000021863343293215910,
.00000000000024132639491333131,
.00000000000039057462209830700,
-.00000000000026570679203560751,
.00000000000037135141919592021,
-.00000000000017166921336082431,
-.00000000000028658285157914353,
-.00000000000023812542263446809,
.00000000000006576659768580062,
-.00000000000028210143846181267,
.00000000000010701931762114254,
.00000000000018119346366441110,
.00000000000009840465278232627,
-.00000000000033149150282752542,
-.00000000000018302857356041668,
-.00000000000016207400156744949,
.00000000000048303314949553201,
-.00000000000071560553172382115,
.00000000000088821239518571855,
-.00000000000030900580513238244,
-.00000000000061076551972851496,
.00000000000035659969663347830,
.00000000000035782396591276383,
-.00000000000046226087001544578,
.00000000000062279762917225156,
.00000000000072838947272065741,
.00000000000026809646615211673,
-.00000000000010960825046059278,
.00000000000002311949383800537,
-.00000000000058469058005299247,
-.00000000000002103748251144494,
-.00000000000023323182945587408,
-.00000000000042333694288141916,
-.00000000000043933937969737844,
.00000000000041341647073835565,
.00000000000006841763641591466,
.00000000000047585534004430641,
.00000000000083679678674757695,
-.00000000000085763734646658640,
.00000000000021913281229340092,
-.00000000000062242842536431148,
-.00000000000010983594325438430,
.00000000000065310431377633651,
-.00000000000047580199021710769,
-.00000000000037854251265457040,
.00000000000040939233218678664,
.00000000000087424383914858291,
.00000000000025218188456842882,
-.00000000000003608131360422557,
-.00000000000050518555924280902,
.00000000000078699403323355317,
-.00000000000067020876961949060,
.00000000000016108575753932458,
.00000000000058527188436251509,
-.00000000000035246757297904791,
-.00000000000018372084495629058,
.00000000000088606689813494916,
.00000000000066486268071468700,
.00000000000063831615170646519,
.00000000000025144230728376072,
-.00000000000017239444525614834
};
double
log(double x)
{
int m, j;
double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0;
volatile double u1;
/* Catch special cases */
if (x <= 0) {
if (_IEEE && x == zero) /* log(0) = -Inf */
return (-one/zero);
else if (_IEEE) /* log(neg) = NaN */
return (zero/zero);
else if (x == zero) /* NOT REACHED IF _IEEE */
return (infnan(-ERANGE));
else
return (infnan(EDOM));
} else if (!finite(x)) {
if (_IEEE) /* x = NaN, Inf */
return (x+x);
else
return (infnan(ERANGE));
}
/* Argument reduction: 1 <= g < 2; x/2^m = g; */
/* y = F*(1 + f/F) for |f| <= 2^-8 */
m = logb(x);
g = ldexp(x, -m);
if (_IEEE && m == -1022) {
j = logb(g), m += j;
g = ldexp(g, -j);
}
j = N*(g-1) + .5;
F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */
f = g - F;
/* Approximate expansion for log(1+f/F) ~= u + q */
g = 1/(2*F+f);
u = 2*f*g;
v = u*u;
q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
/* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8,
* u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits.
* It also adds exactly to |m*log2_hi + log_F_head[j] | < 750
*/
if (m | j)
u1 = u + 513, u1 -= 513;
/* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero;
* u1 = u to 24 bits.
*/
else
u1 = u, TRUNC(u1);
u2 = (2.0*(f - F*u1) - u1*f) * g;
/* u1 + u2 = 2f/(2F+f) to extra precision. */
/* log(x) = log(2^m*F*(1+f/F)) = */
/* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */
/* (exact) + (tiny) */
u1 += m*logF_head[N] + logF_head[j]; /* exact */
u2 = (u2 + logF_tail[j]) + q; /* tiny */
u2 += logF_tail[N]*m;
return (u1 + u2);
}
/*
* Extra precision variant, returning struct {double a, b;};
* log(x) = a+b to 63 bits, with a is rounded to 26 bits.
*/
struct Double
__log__D(double x)
{
int m, j;
double F, f, g, q, u, v, u2;
volatile double u1;
struct Double r;
/* Argument reduction: 1 <= g < 2; x/2^m = g; */
/* y = F*(1 + f/F) for |f| <= 2^-8 */
m = logb(x);
g = ldexp(x, -m);
if (_IEEE && m == -1022) {
j = logb(g), m += j;
g = ldexp(g, -j);
}
j = N*(g-1) + .5;
F = (1.0/N) * j + 1;
f = g - F;
g = 1/(2*F+f);
u = 2*f*g;
v = u*u;
q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
if (m | j)
u1 = u + 513, u1 -= 513;
else
u1 = u, TRUNC(u1);
u2 = (2.0*(f - F*u1) - u1*f) * g;
u1 += m*logF_head[N] + logF_head[j];
u2 += logF_tail[j]; u2 += q;
u2 += logF_tail[N]*m;
r.a = u1 + u2; /* Only difference is here */
TRUNC(r.a);
r.b = (u1 - r.a) + u2;
return (r);
}
float
logf(float x)
{
return(log((double)x));
}