#include "FEATURE/uwin"
#if !_UWIN || _lib_lgamma
void _STUB_lgamma(){}
#else
/*-
* 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
static char sccsid[] = "@(#)lgamma.c 8.2 (Berkeley) 11/30/93";
#endif /* not lint */
/*
* Coded by Peter McIlroy, Nov 1992;
*
* The financial support of UUNET Communications Services is greatfully
* acknowledged.
*/
#define gamma ______gamma
#define lgamma ______lgamma
#include <math.h>
#include <errno.h>
#include "mathimpl.h"
#undef gamma
#undef lgamma
/* Log gamma function.
* Error: x > 0 error < 1.3ulp.
* x > 4, error < 1ulp.
* x > 9, error < .6ulp.
* x < 0, all bets are off. (When G(x) ~ 1, log(G(x)) ~ 0)
* Method:
* x > 6:
* Use the asymptotic expansion (Stirling's Formula)
* 0 < x < 6:
* Use gamma(x+1) = x*gamma(x) for argument reduction.
* Use rational approximation in
* the range 1.2, 2.5
* Two approximations are used, one centered at the
* minimum to ensure monotonicity; one centered at 2
* to maintain small relative error.
* x < 0:
* Use the reflection formula,
* G(1-x)G(x) = PI/sin(PI*x)
* Special values:
* non-positive integer returns +Inf.
* NaN returns NaN
*/
static int endian;
#if defined(vax) || defined(tahoe)
#define _IEEE 0
/* double and float have same size exponent field */
#define TRUNC(x) x = (double) (float) (x)
#else
#define _IEEE 1
#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000
#define infnan(x) 0.0
#endif
static double small_lgam(double);
static double large_lgam(double);
static double neg_lgam(double);
static double zero = 0.0, one = 1.0;
int signgam;
#define UNDERFL (1e-1020 * 1e-1020)
#define LEFT (1.0 - (x0 + .25))
#define RIGHT (x0 - .218)
/*
* Constants for approximation in [1.244,1.712]
*/
#define x0 0.461632144968362356785
#define x0_lo -.000000000000000015522348162858676890521
#define a0_hi -0.12148629128932952880859
#define a0_lo .0000000007534799204229502
#define r0 -2.771227512955130520e-002
#define r1 -2.980729795228150847e-001
#define r2 -3.257411333183093394e-001
#define r3 -1.126814387531706041e-001
#define r4 -1.129130057170225562e-002
#define r5 -2.259650588213369095e-005
#define s0 1.714457160001714442e+000
#define s1 2.786469504618194648e+000
#define s2 1.564546365519179805e+000
#define s3 3.485846389981109850e-001
#define s4 2.467759345363656348e-002
/*
* Constants for approximation in [1.71, 2.5]
*/
#define a1_hi 4.227843350984671344505727574870e-01
#define a1_lo 4.670126436531227189e-18
#define p0 3.224670334241133695662995251041e-01
#define p1 3.569659696950364669021382724168e-01
#define p2 1.342918716072560025853732668111e-01
#define p3 1.950702176409779831089963408886e-02
#define p4 8.546740251667538090796227834289e-04
#define q0 1.000000000000000444089209850062e+00
#define q1 1.315850076960161985084596381057e+00
#define q2 6.274644311862156431658377186977e-01
#define q3 1.304706631926259297049597307705e-01
#define q4 1.102815279606722369265536798366e-02
#define q5 2.512690594856678929537585620579e-04
#define q6 -1.003597548112371003358107325598e-06
/*
* Stirling's Formula, adjusted for equal-ripple. x in [6,Inf].
*/
#define lns2pi .418938533204672741780329736405
#define pb0 8.33333333333333148296162562474e-02
#define pb1 -2.77777777774548123579378966497e-03
#define pb2 7.93650778754435631476282786423e-04
#define pb3 -5.95235082566672847950717262222e-04
#define pb4 8.41428560346653702135821806252e-04
#define pb5 -1.89773526463879200348872089421e-03
#define pb6 5.69394463439411649408050664078e-03
#define pb7 -1.44705562421428915453880392761e-02
extern __pure double lgamma(double x)
{
double r;
signgam = 1;
endian = ((*(int *) &one)) ? 1 : 0;
if (!finite(x))
if (_IEEE)
return (x+x);
else return (infnan(EDOM));
if (x > 6 + RIGHT) {
r = large_lgam(x);
return (r);
} else if (x > 1e-16)
return (small_lgam(x));
else if (x > -1e-16) {
if (x < 0)
signgam = -1, x = -x;
return (-log(x));
} else
return (neg_lgam(x));
}
static double
large_lgam(double x)
{
double z, p, x1;
struct Double t, u, v;
u = __log__D(x);
u.a -= 1.0;
if (x > 1e15) {
v.a = x - 0.5;
TRUNC(v.a);
v.b = (x - v.a) - 0.5;
t.a = u.a*v.a;
t.b = x*u.b + v.b*u.a;
if (_IEEE == 0 && !finite(t.a))
return(infnan(ERANGE));
return(t.a + t.b);
}
x1 = 1./x;
z = x1*x1;
p = pb0+z*(pb1+z*(pb2+z*(pb3+z*(pb4+z*(pb5+z*(pb6+z*pb7))))));
/* error in approximation = 2.8e-19 */
p = p*x1; /* error < 2.3e-18 absolute */
/* 0 < p < 1/64 (at x = 5.5) */
v.a = x = x - 0.5;
TRUNC(v.a); /* truncate v.a to 26 bits. */
v.b = x - v.a;
t.a = v.a*u.a; /* t = (x-.5)*(log(x)-1) */
t.b = v.b*u.a + x*u.b;
t.b += p; t.b += lns2pi; /* return t + lns2pi + p */
return (t.a + t.b);
}
static double
small_lgam(double x)
{
int x_int;
double y, z, t, r = 0, p, q, hi, lo;
struct Double rr;
x_int = (int)(x + .5);
y = x - x_int;
if (x_int <= 2 && y > RIGHT) {
t = y - x0;
y--; x_int++;
goto CONTINUE;
} else if (y < -LEFT) {
t = y +(1.0-x0);
CONTINUE:
z = t - x0_lo;
p = r0+z*(r1+z*(r2+z*(r3+z*(r4+z*r5))));
q = s0+z*(s1+z*(s2+z*(s3+z*s4)));
r = t*(z*(p/q) - x0_lo);
t = .5*t*t;
z = 1.0;
switch (x_int) {
case 6: z = (y + 5);
case 5: z *= (y + 4);
case 4: z *= (y + 3);
case 3: z *= (y + 2);
rr = __log__D(z);
rr.b += a0_lo; rr.a += a0_hi;
return(((r+rr.b)+t+rr.a));
case 2: return(((r+a0_lo)+t)+a0_hi);
case 0: r -= log1p(x);
default: rr = __log__D(x);
rr.a -= a0_hi; rr.b -= a0_lo;
return(((r - rr.b) + t) - rr.a);
}
} else {
p = p0+y*(p1+y*(p2+y*(p3+y*p4)));
q = q0+y*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*q6)))));
p = p*(y/q);
t = (double)(float) y;
z = y-t;
hi = (double)(float) (p+a1_hi);
lo = a1_hi - hi; lo += p; lo += a1_lo;
r = lo*y + z*hi; /* q + r = y*(a0+p/q) */
q = hi*t;
z = 1.0;
switch (x_int) {
case 6: z = (y + 5);
case 5: z *= (y + 4);
case 4: z *= (y + 3);
case 3: z *= (y + 2);
rr = __log__D(z);
r += rr.b; r += q;
return(rr.a + r);
case 2: return (q+ r);
case 0: rr = __log__D(x);
r -= rr.b; r -= log1p(x);
r += q; r-= rr.a;
return(r);
default: rr = __log__D(x);
r -= rr.b;
q -= rr.a;
return (r+q);
}
}
}
static double
neg_lgam(double x)
{
int xi;
double y, z, one = 1.0, zero = 0.0;
extern double gamma();
/* avoid destructive cancellation as much as possible */
if (x > -170) {
xi = (int)x;
if (xi == x)
if (_IEEE)
return(one/zero);
else
return(infnan(ERANGE));
y = gamma(x);
if (y < 0)
y = -y, signgam = -1;
return (log(y));
}
z = floor(x + .5);
if (z == x) { /* convention: G(-(integer)) -> +Inf */
if (_IEEE)
return (one/zero);
else
return (infnan(ERANGE));
}
y = .5*ceil(x);
if (y == ceil(y))
signgam = -1;
x = -x;
z = fabs(x + z); /* 0 < z <= .5 */
if (z < .25)
z = sin(M_PI*z);
else
z = cos(M_PI*(0.5-z));
z = log(M_PI/(z*x));
y = large_lgam(x);
return (z - y);
}
#endif