1 files changed, 352 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/C/j1.c b/usr/src/lib/libm/common/C/j1.c
new file mode 100644
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+++ b/usr/src/lib/libm/common/C/j1.c
@@ -0,0 +1,352 @@
+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+
+/*
+ * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
+ */
+/*
+ * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
+ * Use is subject to license terms.
+ */
+
+/*
+ * floating point Bessel's function of the first and second kinds
+ * of order zero: j1(x),y1(x);
+ *
+ * Special cases:
+ *	y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
+ *	y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
+ */
+
+#pragma weak j1 = __j1
+#pragma weak y1 = __y1
+
+#include "libm.h"
+#include "libm_synonyms.h"
+#include "libm_protos.h"
+#include <math.h>
+#include <values.h>
+
+#define	GENERIC double
+static const GENERIC
+zero    = 0.0,
+small	= 1.0e-5,
+tiny 	= 1.0e-20,
+one	= 1.0,
+invsqrtpi = 5.641895835477562869480794515607725858441e-0001,
+tpi	= 0.636619772367581343075535053490057448;
+
+static GENERIC pone(GENERIC), qone(GENERIC);
+static const GENERIC r0[4] = {
+	-6.250000000000002203053200981413218949548e-0002,
+	1.600998455640072901321605101981501263762e-0003,
+	-1.963888815948313758552511884390162864930e-0005,
+	8.263917341093549759781339713418201620998e-0008,
+};
+static const GENERIC s0[7] = {
+	1.0e0,
+	1.605069137643004242395356851797873766927e-0002,
+	1.149454623251299996428500249509098499383e-0004,
+	3.849701673735260970379681807910852327825e-0007,
+};
+static const GENERIC r1[12] = {
+	4.999999999999999995517408894340485471724e-0001,
+	-6.003825028120475684835384519945468075423e-0002,
+	2.301719899263321828388344461995355419832e-0003,
+	-4.208494869238892934859525221654040304068e-0005,
+	4.377745135188837783031540029700282443388e-0007,
+	-2.854106755678624335145364226735677754179e-0009,
+	1.234002865443952024332943901323798413689e-0011,
+	-3.645498437039791058951273508838177134310e-0014,
+	7.404320596071797459925377103787837414422e-0017,
+	-1.009457448277522275262808398517024439084e-0019,
+	8.520158355824819796968771418801019930585e-0023,
+	-3.458159926081163274483854614601091361424e-0026,
+};
+static const GENERIC s1[5] = {
+	1.0e0,
+	4.923499437590484879081138588998986303306e-0003,
+	1.054389489212184156499666953501976688452e-0005,
+	1.180768373106166527048240364872043816050e-0008,
+	5.942665743476099355323245707680648588540e-0012,
+};
+
+GENERIC
+j1(GENERIC x) {
+	GENERIC z, d, s, c, ss, cc, r;
+	int i, sgn;
+
+	if (!finite(x))
+		return (one/x);
+	sgn = signbit(x);
+	x = fabs(x);
+	if (x > 8.00) {
+		s = sin(x);
+		c = cos(x);
+	/*
+	 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0))
+	 * where x0 = x-3pi/4
+	 * 	Better formula:
+	 *		cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+	 *			=  1/sqrt(2) * (sin(x) - cos(x))
+	 *		sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+	 *			= -1/sqrt(2) * (cos(x) + sin(x))
+	 * To avoid cancellation, use
+	 *		sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+	 * to compute the worse one.
+	 */
+		if (x > 8.9e307) {	/* x+x may overflow */
+			ss = -s-c;
+			cc =  s-c;
+		} else if (signbit(s) != signbit(c)) {
+			cc = s - c;
+			ss = cos(x+x)/cc;
+		} else {
+			ss = -s-c;
+			cc = cos(x+x)/ss;
+		}
+	/*
+	 * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss)
+	 * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc)
+	 */
+		if (x > 1.0e40)
+		    d = (invsqrtpi*cc)/sqrt(x);
+		else
+			d =  invsqrtpi*(pone(x)*cc-qone(x)*ss)/sqrt(x);
+
+		if (x > X_TLOSS) {
+		    if (sgn != 0) { d = -d; x = -x; }
+			return (_SVID_libm_err(x, d, 36));
+		} else
+		    if (sgn == 0)
+				return (d);
+			else
+				return (-d);
+	}
+	if (x <= small) {
+		if (x <= tiny)
+			d = 0.5*x;
+		else
+			d =  x*(0.5-x*x*0.125);
+		if (sgn == 0)
+			return (d);
+		else
+			return (-d);
+	}
+	z = x*x;
+	if (x < 1.28) {
+	    r = r0[3];
+	    s = s0[3];
+	    for (i = 2; i >= 0; i--) {
+		r = r*z + r0[i];
+		s = s*z + s0[i];
+	    }
+	    d = x*0.5+x*(z*(r/s));
+	} else {
+	    r = r1[11];
+	    for (i = 10; i >= 0; i--) r = r*z + r1[i];
+	    s = s1[0]+z*(s1[1]+z*(s1[2]+z*(s1[3]+z*s1[4])));
+	    d = x*(r/s);
+	}
+	if (sgn == 0)
+		return (d);
+	else
+		return (-d);
+}
+
+static const GENERIC u0[4] = {
+	-1.960570906462389461018983259589655961560e-0001,
+	4.931824118350661953459180060007970291139e-0002,
+	-1.626975871565393656845930125424683008677e-0003,
+	1.359657517926394132692884168082224258360e-0005,
+};
+static const GENERIC v0[5] = {
+	1.0e0,
+	2.565807214838390835108224713630901653793e-0002,
+	3.374175208978404268650522752520906231508e-0004,
+	2.840368571306070719539936935220728843177e-0006,
+	1.396387402048998277638900944415752207592e-0008,
+};
+static const GENERIC u1[12] = {
+	-1.960570906462389473336339614647555351626e-0001,
+	5.336268030335074494231369159933012844735e-0002,
+	-2.684137504382748094149184541866332033280e-0003,
+	5.737671618979185736981543498580051903060e-0005,
+	-6.642696350686335339171171785557663224892e-0007,
+	4.692417922568160354012347591960362101664e-0009,
+	-2.161728635907789319335231338621412258355e-0011,
+	6.727353419738316107197644431844194668702e-0014,
+	-1.427502986803861372125234355906790573422e-0016,
+	2.020392498726806769468143219616642940371e-0019,
+	-1.761371948595104156753045457888272716340e-0022,
+	7.352828391941157905175042420249225115816e-0026,
+};
+static const GENERIC v1[5] = {
+	1.0e0,
+	5.029187436727947764916247076102283399442e-0003,
+	1.102693095808242775074856548927801750627e-0005,
+	1.268035774543174837829534603830227216291e-0008,
+	6.579416271766610825192542295821308730206e-0012,
+};
+
+
+GENERIC
+y1(GENERIC x) {
+	GENERIC z, d, s, c, ss, cc, u, v;
+	int i;
+
+	if (isnan(x))
+		return (x*x);	/* + -> * for Cheetah */
+	if (x <= zero) {
+		if (x == zero)
+		    /* return -one/zero;  */
+		    return (_SVID_libm_err(x, x, 10));
+		else
+		    /* return zero/zero; */
+		    return (_SVID_libm_err(x, x, 11));
+	}
+	if (x > 8.0) {
+		if (!finite(x))
+			return (zero);
+		s = sin(x);
+		c = cos(x);
+	/*
+	 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x0)-q1(x)*sin(x0))
+	 * where x0 = x-3pi/4
+	 * 	Better formula:
+	 *		cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+	 *			=  1/sqrt(2) * (sin(x) - cos(x))
+	 *		sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+	 *			= -1/sqrt(2) * (cos(x) + sin(x))
+	 * To avoid cancellation, use
+	 *		sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+	 * to compute the worse one.
+	 */
+		if (x > 8.9e307) {	/* x+x may overflow */
+			ss = -s-c;
+			cc =  s-c;
+		} else if (signbit(s) != signbit(c)) {
+			cc = s - c;
+			ss = cos(x+x)/cc;
+		} else {
+			ss = -s-c;
+			cc = cos(x+x)/ss;
+		}
+	/*
+	 * j1(x) = 1/sqrt(pi*x) * (P(1,x)*cc - Q(1,x)*ss)
+	 * y1(x) = 1/sqrt(pi*x) * (P(1,x)*ss + Q(1,x)*cc)
+	 */
+		if (x > 1.0e91)
+		    d =  (invsqrtpi*ss)/sqrt(x);
+		else
+			d = invsqrtpi*(pone(x)*ss+qone(x)*cc)/sqrt(x);
+
+		if (x > X_TLOSS)
+			return (_SVID_libm_err(x, d, 37));
+		else
+			return (d);
+	}
+		if (x <= tiny) {
+			return (-tpi/x);
+		}
+	z = x*x;
+	if (x < 1.28) {
+	    u = u0[3]; v = v0[3]+z*v0[4];
+	    for (i = 2; i >= 0; i--) {
+		u = u*z + u0[i];
+		v = v*z + v0[i];
+	    }
+	} else {
+	    for (u = u1[11], i = 10; i >= 0; i--) u = u*z+u1[i];
+	    v = v1[0]+z*(v1[1]+z*(v1[2]+z*(v1[3]+z*v1[4])));
+	}
+	return (x*(u/v) + tpi*(j1(x)*log(x)-one/x));
+}
+
+static const GENERIC pr0[6] = {
+	-.4435757816794127857114720794e7,
+	-.9942246505077641195658377899e7,
+	-.6603373248364939109255245434e7,
+	-.1523529351181137383255105722e7,
+	-.1098240554345934672737413139e6,
+	-.1611616644324610116477412898e4,
+};
+static const GENERIC ps0[6] = {
+	-.4435757816794127856828016962e7,
+	-.9934124389934585658967556309e7,
+	-.6585339479723087072826915069e7,
+	-.1511809506634160881644546358e7,
+	-.1072638599110382011903063867e6,
+	-.1455009440190496182453565068e4,
+};
+static const GENERIC huge    = 1.0e10;
+
+static GENERIC
+pone(GENERIC x) {
+	GENERIC s, r, t, z;
+	int i;
+		/* assume x > 8 */
+	if (x > huge)
+		return (one);
+
+	t = 8.0/x; z = t*t;
+	r = pr0[5]; s = ps0[5]+z;
+	for (i = 4; i >= 0; i--) {
+		r = z*r + pr0[i];
+		s = z*s + ps0[i];
+	}
+	return (r/s);
+}
+
+
+static const GENERIC qr0[6] = {
+	0.3322091340985722351859704442e5,
+	0.8514516067533570196555001171e5,
+	0.6617883658127083517939992166e5,
+	0.1849426287322386679652009819e5,
+	0.1706375429020768002061283546e4,
+	0.3526513384663603218592175580e2,
+};
+static const GENERIC qs0[6] = {
+	0.7087128194102874357377502472e6,
+	0.1819458042243997298924553839e7,
+	0.1419460669603720892855755253e7,
+	0.4002944358226697511708610813e6,
+	0.3789022974577220264142952256e5,
+	0.8638367769604990967475517183e3,
+};
+
+static GENERIC
+qone(GENERIC x) {
+	GENERIC s, r, t, z;
+	int i;
+	if (x > huge)
+		return (0.375/x);
+
+	t = 8.0/x; z = t*t;
+		/* assume x > 8 */
+	r = qr0[5]; s = qs0[5]+z;
+	for (i = 4; i >= 0; i--) {
+		r = z*r + qr0[i];
+		s = z*s + qs0[i];
+	}
+	return (t*(r/s));
+}