1 files changed, 307 insertions, 0 deletions
diff --git a/lib/libm/common_source/lgamma.c b/lib/libm/common_source/lgamma.c
new file mode 100644
index 0000000..b5cb49f
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+++ b/lib/libm/common_source/lgamma.c
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+/*-
+ * 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. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *	This product includes software developed by the University of
+ *	California, Berkeley and its contributors.
+ * 4. 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.
+ */
+
+#include <math.h>
+#include <errno.h>
+
+#include "mathimpl.h"
+
+/* 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
+
+__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;
+	int i;
+	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 = (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 = 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);
+}