2fe8fb192f
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
309 lines
8.2 KiB
C
309 lines
8.2 KiB
C
/* $NetBSD: n_lgamma.c,v 1.6 2006/11/24 21:15:54 wiz Exp $ */
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/*-
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* Copyright (c) 1992, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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#if 0
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static char sccsid[] = "@(#)lgamma.c 8.2 (Berkeley) 11/30/93";
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#endif
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#endif /* not lint */
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/*
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* Coded by Peter McIlroy, Nov 1992;
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*
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* The financial support of UUNET Communications Services is gratefully
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* acknowledged.
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*/
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#include <math.h>
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#include <errno.h>
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#include "mathimpl.h"
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/* Log gamma function.
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* Error: x > 0 error < 1.3ulp.
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* x > 4, error < 1ulp.
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* x > 9, error < .6ulp.
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* x < 0, all bets are off. (When G(x) ~ 1, log(G(x)) ~ 0)
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* Method:
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* x > 6:
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* Use the asymptotic expansion (Stirling's Formula)
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* 0 < x < 6:
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* Use gamma(x+1) = x*gamma(x) for argument reduction.
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* Use rational approximation in
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* the range 1.2, 2.5
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* Two approximations are used, one centered at the
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* minimum to ensure monotonicity; one centered at 2
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* to maintain small relative error.
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* x < 0:
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* Use the reflection formula,
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* G(1-x)G(x) = PI/sin(PI*x)
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* Special values:
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* non-positive integer returns +Inf.
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* NaN returns NaN
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*/
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#if defined(__vax__) || defined(tahoe)
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#define _IEEE 0
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/* double and float have same size exponent field */
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#define TRUNC(x) x = (double) (float) (x)
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#else
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static int endian;
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#define _IEEE 1
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#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000
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#define infnan(x) 0.0
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#endif
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static double small_lgam(double);
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static double large_lgam(double);
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static double neg_lgam(double);
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static const double one = 1.0;
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int signgam;
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#define UNDERFL (1e-1020 * 1e-1020)
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#define LEFT (1.0 - (x0 + .25))
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#define RIGHT (x0 - .218)
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/*
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* Constants for approximation in [1.244,1.712]
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*/
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#define x0 0.461632144968362356785
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#define x0_lo -.000000000000000015522348162858676890521
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#define a0_hi -0.12148629128932952880859
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#define a0_lo .0000000007534799204229502
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#define r0 -2.771227512955130520e-002
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#define r1 -2.980729795228150847e-001
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#define r2 -3.257411333183093394e-001
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#define r3 -1.126814387531706041e-001
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#define r4 -1.129130057170225562e-002
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#define r5 -2.259650588213369095e-005
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#define s0 1.714457160001714442e+000
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#define s1 2.786469504618194648e+000
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#define s2 1.564546365519179805e+000
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#define s3 3.485846389981109850e-001
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#define s4 2.467759345363656348e-002
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/*
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* Constants for approximation in [1.71, 2.5]
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*/
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#define a1_hi 4.227843350984671344505727574870e-01
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#define a1_lo 4.670126436531227189e-18
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#define p0 3.224670334241133695662995251041e-01
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#define p1 3.569659696950364669021382724168e-01
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#define p2 1.342918716072560025853732668111e-01
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#define p3 1.950702176409779831089963408886e-02
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#define p4 8.546740251667538090796227834289e-04
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#define q0 1.000000000000000444089209850062e+00
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#define q1 1.315850076960161985084596381057e+00
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#define q2 6.274644311862156431658377186977e-01
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#define q3 1.304706631926259297049597307705e-01
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#define q4 1.102815279606722369265536798366e-02
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#define q5 2.512690594856678929537585620579e-04
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#define q6 -1.003597548112371003358107325598e-06
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/*
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* Stirling's Formula, adjusted for equal-ripple. x in [6,Inf].
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*/
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#define lns2pi .418938533204672741780329736405
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#define pb0 8.33333333333333148296162562474e-02
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#define pb1 -2.77777777774548123579378966497e-03
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#define pb2 7.93650778754435631476282786423e-04
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#define pb3 -5.95235082566672847950717262222e-04
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#define pb4 8.41428560346653702135821806252e-04
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#define pb5 -1.89773526463879200348872089421e-03
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#define pb6 5.69394463439411649408050664078e-03
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#define pb7 -1.44705562421428915453880392761e-02
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__pure double
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lgamma(double x)
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{
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double r;
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signgam = 1;
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#if _IEEE
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endian = ((*(int *) &one)) ? 1 : 0;
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#endif
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if (!finite(x)) {
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if (_IEEE)
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return (x+x);
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else return (infnan(EDOM));
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}
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if (x > 6 + RIGHT) {
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r = large_lgam(x);
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return (r);
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} else if (x > 1e-16)
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return (small_lgam(x));
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else if (x > -1e-16) {
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if (x < 0)
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signgam = -1, x = -x;
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return (-log(x));
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} else
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return (neg_lgam(x));
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}
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static double
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large_lgam(double x)
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{
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double z, p, x1;
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struct Double t, u, v;
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u = __log__D(x);
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u.a -= 1.0;
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if (x > 1e15) {
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v.a = x - 0.5;
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TRUNC(v.a);
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v.b = (x - v.a) - 0.5;
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t.a = u.a*v.a;
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t.b = x*u.b + v.b*u.a;
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if (_IEEE == 0 && !finite(t.a))
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return(infnan(ERANGE));
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return(t.a + t.b);
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}
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x1 = 1./x;
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z = x1*x1;
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p = pb0+z*(pb1+z*(pb2+z*(pb3+z*(pb4+z*(pb5+z*(pb6+z*pb7))))));
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/* error in approximation = 2.8e-19 */
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p = p*x1; /* error < 2.3e-18 absolute */
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/* 0 < p < 1/64 (at x = 5.5) */
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v.a = x = x - 0.5;
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TRUNC(v.a); /* truncate v.a to 26 bits. */
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v.b = x - v.a;
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t.a = v.a*u.a; /* t = (x-.5)*(log(x)-1) */
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t.b = v.b*u.a + x*u.b;
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t.b += p; t.b += lns2pi; /* return t + lns2pi + p */
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return (t.a + t.b);
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}
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static double
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small_lgam(double x)
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{
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int x_int;
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double y, z, t, r = 0, p, q, hi, lo;
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struct Double rr;
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x_int = (x + .5);
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y = x - x_int;
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if (x_int <= 2 && y > RIGHT) {
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t = y - x0;
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y--; x_int++;
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goto CONTINUE;
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} else if (y < -LEFT) {
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t = y +(1.0-x0);
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CONTINUE:
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z = t - x0_lo;
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p = r0+z*(r1+z*(r2+z*(r3+z*(r4+z*r5))));
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q = s0+z*(s1+z*(s2+z*(s3+z*s4)));
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r = t*(z*(p/q) - x0_lo);
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t = .5*t*t;
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z = 1.0;
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switch (x_int) {
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case 6: z = (y + 5);
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case 5: z *= (y + 4);
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case 4: z *= (y + 3);
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case 3: z *= (y + 2);
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rr = __log__D(z);
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rr.b += a0_lo; rr.a += a0_hi;
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return(((r+rr.b)+t+rr.a));
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case 2: return(((r+a0_lo)+t)+a0_hi);
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case 0: r -= log1p(x);
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default: rr = __log__D(x);
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rr.a -= a0_hi; rr.b -= a0_lo;
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return(((r - rr.b) + t) - rr.a);
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}
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} else {
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p = p0+y*(p1+y*(p2+y*(p3+y*p4)));
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q = q0+y*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*q6)))));
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p = p*(y/q);
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t = (double)(float) y;
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z = y-t;
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hi = (double)(float) (p+a1_hi);
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lo = a1_hi - hi; lo += p; lo += a1_lo;
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r = lo*y + z*hi; /* q + r = y*(a0+p/q) */
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q = hi*t;
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z = 1.0;
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switch (x_int) {
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case 6: z = (y + 5);
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case 5: z *= (y + 4);
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case 4: z *= (y + 3);
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case 3: z *= (y + 2);
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rr = __log__D(z);
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r += rr.b; r += q;
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return(rr.a + r);
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case 2: return (q+ r);
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case 0: rr = __log__D(x);
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r -= rr.b; r -= log1p(x);
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r += q; r-= rr.a;
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return(r);
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default: rr = __log__D(x);
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r -= rr.b;
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q -= rr.a;
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return (r+q);
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}
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}
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}
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static double
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neg_lgam(double x)
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{
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int xi;
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double y, z, zero = 0.0;
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/* avoid destructive cancellation as much as possible */
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if (x > -170) {
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xi = x;
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if (xi == x) {
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if (_IEEE)
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return(one/zero);
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else
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return(infnan(ERANGE));
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}
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y = gamma(x);
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if (y < 0)
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y = -y, signgam = -1;
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return (log(y));
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}
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z = floor(x + .5);
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if (z == x) { /* convention: G(-(integer)) -> +Inf */
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if (_IEEE)
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return (one/zero);
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else
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return (infnan(ERANGE));
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}
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y = .5*ceil(x);
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if (y == ceil(y))
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signgam = -1;
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x = -x;
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z = fabs(x + z); /* 0 < z <= .5 */
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if (z < .25)
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z = sin(M_PI*z);
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else
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z = cos(M_PI*(0.5-z));
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z = log(M_PI/(z*x));
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y = large_lgam(x);
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return (z - y);
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}
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