1 #include "FEATURE/uwin" 2 3 #if !_UWIN || _lib_lgamma 4 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-02 149 150 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 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 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 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