1 #include "FEATURE/uwin"
2
3 #if !_UWIN || _lib_lgamma
4
_STUB_lgamma()5 void _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
39 static 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 */
81 static 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
92 static double small_lgam(double);
93 static double large_lgam(double);
94 static double neg_lgam(double);
95 static double zero = 0.0, one = 1.0;
96 int 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
lgamma(double x)150 extern __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
175 static double
large_lgam(double x)176 large_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
208 static double
small_lgam(double x)209 small_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);
222 CONTINUE:
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
275 static double
neg_lgam(double x)276 neg_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