1#include "FEATURE/uwin"
2
3#if !_UWIN || _lib_lgamma
4
5void _STUB_lgamma(){}
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
39static char sccsid[] = "@(#)lgamma.c	8.2 (Berkeley) 11/30/93";
40#endif /* not lint */
41
42/*
43 * Coded by Peter McIlroy, Nov 1992;
44 *
45 * The financial support of UUNET Communications Services is greatfully
46 * acknowledged.
47 */
48
49#define gamma	______gamma
50#define lgamma	______lgamma
51
52#include <math.h>
53#include <errno.h>
54#include "mathimpl.h"
55
56#undef	gamma
57#undef	lgamma
58
59/* Log gamma function.
60 * Error:  x > 0 error < 1.3ulp.
61 *	   x > 4, error < 1ulp.
62 *	   x > 9, error < .6ulp.
63 * 	   x < 0, all bets are off. (When G(x) ~ 1, log(G(x)) ~ 0)
64 * Method:
65 *	x > 6:
66 *		Use the asymptotic expansion (Stirling's Formula)
67 *	0 < x < 6:
68 *		Use gamma(x+1) = x*gamma(x) for argument reduction.
69 *		Use rational approximation in
70 *		the range 1.2, 2.5
71 *		Two approximations are used, one centered at the
72 *		minimum to ensure monotonicity; one centered at 2
73 *		to maintain small relative error.
74 *	x < 0:
75 *		Use the reflection formula,
76 *		G(1-x)G(x) = PI/sin(PI*x)
77 * Special values:
78 *	non-positive integer	returns +Inf.
79 *	NaN			returns NaN
80*/
81static int endian;
82#if defined(vax) || defined(tahoe)
83#define _IEEE		0
84/* double and float have same size exponent field */
85#define TRUNC(x)	x = (double) (float) (x)
86#else
87#define _IEEE		1
88#define TRUNC(x)	*(((int *) &x) + endian) &= 0xf8000000
89#define infnan(x)	0.0
90#endif
91
92static double small_lgam(double);
93static double large_lgam(double);
94static double neg_lgam(double);
95static double zero = 0.0, one = 1.0;
96int signgam;
97
98#define UNDERFL (1e-1020 * 1e-1020)
99
100#define LEFT	(1.0 - (x0 + .25))
101#define RIGHT	(x0 - .218)
102/*
103 * Constants for approximation in [1.244,1.712]
104*/
105#define x0	0.461632144968362356785
106#define x0_lo	-.000000000000000015522348162858676890521
107#define a0_hi	-0.12148629128932952880859
108#define a0_lo	.0000000007534799204229502
109#define r0	-2.771227512955130520e-002
110#define r1	-2.980729795228150847e-001
111#define r2	-3.257411333183093394e-001
112#define r3	-1.126814387531706041e-001
113#define r4	-1.129130057170225562e-002
114#define r5	-2.259650588213369095e-005
115#define s0	 1.714457160001714442e+000
116#define s1	 2.786469504618194648e+000
117#define s2	 1.564546365519179805e+000
118#define s3	 3.485846389981109850e-001
119#define s4	 2.467759345363656348e-002
120/*
121 * Constants for approximation in [1.71, 2.5]
122*/
123#define a1_hi	4.227843350984671344505727574870e-01
124#define a1_lo	4.670126436531227189e-18
125#define p0	3.224670334241133695662995251041e-01
126#define p1	3.569659696950364669021382724168e-01
127#define p2	1.342918716072560025853732668111e-01
128#define p3	1.950702176409779831089963408886e-02
129#define p4	8.546740251667538090796227834289e-04
130#define q0	1.000000000000000444089209850062e+00
131#define q1	1.315850076960161985084596381057e+00
132#define q2	6.274644311862156431658377186977e-01
133#define q3	1.304706631926259297049597307705e-01
134#define q4	1.102815279606722369265536798366e-02
135#define q5	2.512690594856678929537585620579e-04
136#define q6	-1.003597548112371003358107325598e-06
137/*
138 * Stirling's Formula, adjusted for equal-ripple. x in [6,Inf].
139*/
140#define lns2pi	.418938533204672741780329736405
141#define pb0	 8.33333333333333148296162562474e-02
142#define pb1	-2.77777777774548123579378966497e-03
143#define pb2	 7.93650778754435631476282786423e-04
144#define pb3	-5.95235082566672847950717262222e-04
145#define pb4	 8.41428560346653702135821806252e-04
146#define pb5	-1.89773526463879200348872089421e-03
147#define pb6	 5.69394463439411649408050664078e-03
148#define pb7	-1.44705562421428915453880392761e-02
149
150extern __pure double lgamma(double x)
151{
152	double r;
153
154	signgam = 1;
155	endian = ((*(int *) &one)) ? 1 : 0;
156
157	if (!finite(x))
158		if (_IEEE)
159			return (x+x);
160		else return (infnan(EDOM));
161
162	if (x > 6 + RIGHT) {
163		r = large_lgam(x);
164		return (r);
165	} else if (x > 1e-16)
166		return (small_lgam(x));
167	else if (x > -1e-16) {
168		if (x < 0)
169			signgam = -1, x = -x;
170		return (-log(x));
171	} else
172		return (neg_lgam(x));
173}
174
175static double
176large_lgam(double x)
177{
178	double z, p, x1;
179	struct Double t, u, v;
180	u = __log__D(x);
181	u.a -= 1.0;
182	if (x > 1e15) {
183		v.a = x - 0.5;
184		TRUNC(v.a);
185		v.b = (x - v.a) - 0.5;
186		t.a = u.a*v.a;
187		t.b = x*u.b + v.b*u.a;
188		if (_IEEE == 0 && !finite(t.a))
189			return(infnan(ERANGE));
190		return(t.a + t.b);
191	}
192	x1 = 1./x;
193	z = x1*x1;
194	p = pb0+z*(pb1+z*(pb2+z*(pb3+z*(pb4+z*(pb5+z*(pb6+z*pb7))))));
195					/* error in approximation = 2.8e-19 */
196
197	p = p*x1;			/* error < 2.3e-18 absolute */
198					/* 0 < p < 1/64 (at x = 5.5) */
199	v.a = x = x - 0.5;
200	TRUNC(v.a);			/* truncate v.a to 26 bits. */
201	v.b = x - v.a;
202	t.a = v.a*u.a;			/* t = (x-.5)*(log(x)-1) */
203	t.b = v.b*u.a + x*u.b;
204	t.b += p; t.b += lns2pi;	/* return t + lns2pi + p */
205	return (t.a + t.b);
206}
207
208static double
209small_lgam(double x)
210{
211	int x_int;
212	double y, z, t, r = 0, p, q, hi, lo;
213	struct Double rr;
214	x_int = (int)(x + .5);
215	y = x - x_int;
216	if (x_int <= 2 && y > RIGHT) {
217		t = y - x0;
218		y--; x_int++;
219		goto CONTINUE;
220	} else if (y < -LEFT) {
221		t = y +(1.0-x0);
222CONTINUE:
223		z = t - x0_lo;
224		p = r0+z*(r1+z*(r2+z*(r3+z*(r4+z*r5))));
225		q = s0+z*(s1+z*(s2+z*(s3+z*s4)));
226		r = t*(z*(p/q) - x0_lo);
227		t = .5*t*t;
228		z = 1.0;
229		switch (x_int) {
230		case 6:	z  = (y + 5);
231		case 5:	z *= (y + 4);
232		case 4:	z *= (y + 3);
233		case 3:	z *= (y + 2);
234			rr = __log__D(z);
235			rr.b += a0_lo; rr.a += a0_hi;
236			return(((r+rr.b)+t+rr.a));
237		case 2: return(((r+a0_lo)+t)+a0_hi);
238		case 0: r -= log1p(x);
239		default: rr = __log__D(x);
240			rr.a -= a0_hi; rr.b -= a0_lo;
241			return(((r - rr.b) + t) - rr.a);
242		}
243	} else {
244		p = p0+y*(p1+y*(p2+y*(p3+y*p4)));
245		q = q0+y*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*q6)))));
246		p = p*(y/q);
247		t = (double)(float) y;
248		z = y-t;
249		hi = (double)(float) (p+a1_hi);
250		lo = a1_hi - hi; lo += p; lo += a1_lo;
251		r = lo*y + z*hi;	/* q + r = y*(a0+p/q) */
252		q = hi*t;
253		z = 1.0;
254		switch (x_int) {
255		case 6:	z  = (y + 5);
256		case 5:	z *= (y + 4);
257		case 4:	z *= (y + 3);
258		case 3:	z *= (y + 2);
259			rr = __log__D(z);
260			r += rr.b; r += q;
261			return(rr.a + r);
262		case 2:	return (q+ r);
263		case 0: rr = __log__D(x);
264			r -= rr.b; r -= log1p(x);
265			r += q; r-= rr.a;
266			return(r);
267		default: rr = __log__D(x);
268			r -= rr.b;
269			q -= rr.a;
270			return (r+q);
271		}
272	}
273}
274
275static double
276neg_lgam(double x)
277{
278	int xi;
279	double y, z, one = 1.0, zero = 0.0;
280	extern double gamma();
281
282	/* avoid destructive cancellation as much as possible */
283	if (x > -170) {
284		xi = (int)x;
285		if (xi == x)
286			if (_IEEE)
287				return(one/zero);
288			else
289				return(infnan(ERANGE));
290		y = gamma(x);
291		if (y < 0)
292			y = -y, signgam = -1;
293		return (log(y));
294	}
295	z = floor(x + .5);
296	if (z == x) {		/* convention: G(-(integer)) -> +Inf */
297		if (_IEEE)
298			return (one/zero);
299		else
300			return (infnan(ERANGE));
301	}
302	y = .5*ceil(x);
303	if (y == ceil(y))
304		signgam = -1;
305	x = -x;
306	z = fabs(x + z);	/* 0 < z <= .5 */
307	if (z < .25)
308		z = sin(M_PI*z);
309	else
310		z = cos(M_PI*(0.5-z));
311	z = log(M_PI/(z*x));
312	y = large_lgam(x);
313	return (z - y);
314}
315
316#endif
317