693 Opensource replacement of sunwlibm

Reviewed by: Igor Kozhukhov ikozhukhov@gmail.com
Reviewed by: Keith M Wesolowski <keith.wesolowski@joyent.com>
Reviewed by: Richard Lowe <richlowe@richlowe.net>
Approved by: Dan McDonald <danmcd@omniti.com>

1 files changed, 306 insertions, 0 deletions

diff --git a/usr/src/lib/libm/common/C/jn.c b/usr/src/lib/libm/common/C/jn.c
new file mode 100644
index 0000000000..b8d507dd59
--- /dev/null
+++ b/usr/src/lib/libm/common/C/jn.c
@@ -0,0 +1,306 @@
+/*
+ * 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.
+ */
+
+#pragma weak jn = __jn
+#pragma weak yn = __yn
+
+/*
+ * floating point Bessel's function of the 1st and 2nd kind
+ * of order n: jn(n,x),yn(n,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.
+ * Note 2. About jn(n,x), yn(n,x)
+ *	For n=0, j0(x) is called,
+ *	for n=1, j1(x) is called,
+ *	for n<x, forward recursion us used starting
+ *	from values of j0(x) and j1(x).
+ *	for n>x, a continued fraction approximation to
+ *	j(n,x)/j(n-1,x) is evaluated and then backward
+ *	recursion is used starting from a supposed value
+ *	for j(n,x). The resulting value of j(0,x) is
+ *	compared with the actual value to correct the
+ *	supposed value of j(n,x).
+ *
+ *	yn(n,x) is similar in all respects, except
+ *	that forward recursion is used for all
+ *	values of n>1.
+ *
+ */
+
+#include "libm.h"
+#include <float.h>	/* DBL_MIN */
+#include <values.h>	/* X_TLOSS */
+#include "xpg6.h"	/* __xpg6 */
+
+#define	GENERIC double
+
+static const GENERIC
+	invsqrtpi = 5.641895835477562869480794515607725858441e-0001,
+	two	= 2.0,
+	zero	= 0.0,
+	one	= 1.0;
+
+GENERIC
+jn(int n, GENERIC x) {
+	int i, sgn;
+	GENERIC a, b, temp = 0;
+	GENERIC z, w, ox, on;
+
+	/*
+	 * J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
+	 * Thus, J(-n,x) = J(n,-x)
+	 */
+	ox = x; on = (GENERIC)n;
+	if (n < 0) {
+		n = -n;
+		x = -x;
+	}
+	if (isnan(x))
+		return (x*x);	/* + -> * for Cheetah */
+	if (!((int) _lib_version == libm_ieee ||
+		(__xpg6 & _C99SUSv3_math_errexcept) != 0)) {
+	    if (fabs(x) > X_TLOSS)
+			return (_SVID_libm_err(on, ox, 38));
+	}
+	if (n == 0)
+		return (j0(x));
+	if (n == 1)
+		return (j1(x));
+	if ((n&1) == 0)
+		sgn = 0; 			/* even n */
+	else
+		sgn = signbit(x);	/* old n  */
+	x = fabs(x);
+	if (x == zero||!finite(x)) b = zero;
+	else if ((GENERIC)n <= x) {
+					/*
+					 * Safe to use
+					 *  J(n+1,x)=2n/x *J(n,x)-J(n-1,x)
+					 */
+	    if (x > 1.0e91) {
+				/*
+				 * x >> n**2
+				 *    Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+				 *   Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+				 *   Let s=sin(x), c=cos(x),
+				 *	xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+				 *
+				 *	   n	sin(xn)*sqt2	cos(xn)*sqt2
+				 *	----------------------------------
+				 *	   0	 s-c		 c+s
+				 *	   1	-s-c 		-c+s
+				 *	   2	-s+c		-c-s
+				 *	   3	 s+c		 c-s
+				 */
+		switch (n&3) {
+		    case 0: temp =  cos(x)+sin(x); break;
+		    case 1: temp = -cos(x)+sin(x); break;
+		    case 2: temp = -cos(x)-sin(x); break;
+		    case 3: temp =  cos(x)-sin(x); break;
+		}
+		b = invsqrtpi*temp/sqrt(x);
+	    } else {
+			a = j0(x);
+			b = j1(x);
+			for (i = 1; i < n; i++) {
+		    temp = b;
+		    b = b*((GENERIC)(i+i)/x) - a; /* avoid underflow */
+		    a = temp;
+			}
+	    }
+	} else {
+	    if (x < 1e-9) {	/* use J(n,x) = 1/n!*(x/2)^n */
+		b = pow(0.5*x, (GENERIC) n);
+		if (b != zero) {
+		    for (a = one, i = 1; i <= n; i++) a *= (GENERIC)i;
+		    b = b/a;
+		}
+	    } else {
+		/*
+		 * use backward recurrence
+		 * 			x	  x^2	  x^2
+		 *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
+		 *			2n  - 2(n+1) - 2(n+2)
+		 *
+		 * 			1	  1	    1
+		 *  (for large x)   =  ----  ------   ------   .....
+		 *			2n   2(n+1)   2(n+2)
+		 *			-- - ------ - ------ -
+		 *			 x	 x		 x
+		 *
+		 * Let w = 2n/x and h = 2/x, then the above quotient
+		 * is equal to the continued fraction:
+		 *		    1
+		 *	= -----------------------
+		 *			   1
+		 *	   w - -----------------
+		 *			  1
+		 * 			w+h - ---------
+		 *			   w+2h - ...
+		 *
+		 * To determine how many terms needed, let
+		 * Q(0) = w, Q(1) = w(w+h) - 1,
+		 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+		 * When Q(k) > 1e4	good for single
+		 * When Q(k) > 1e9	good for double
+		 * When Q(k) > 1e17	good for quaduple
+		 */
+	    /* determin k */
+		GENERIC t, v;
+		double q0, q1, h, tmp; int k, m;
+		w  = (n+n)/(double)x; h = 2.0/(double)x;
+		q0 = w;  z = w + h; q1 = w*z - 1.0; k = 1;
+		while (q1 < 1.0e9) {
+			k += 1; z += h;
+			tmp = z*q1 - q0;
+			q0 = q1;
+			q1 = tmp;
+		}
+		m = n+n;
+		for (t = zero, i = 2*(n+k); i >= m; i -= 2) t = one/(i/x-t);
+		a = t;
+		b = one;
+		/*
+		 * estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+		 *  hence, if n*(log(2n/x)) > ...
+		 *  single 8.8722839355e+01
+		 *  double 7.09782712893383973096e+02
+		 *  long double 1.1356523406294143949491931077970765006170e+04
+		 *  then recurrent value may overflow and the result is
+		 *  likely underflow to zero
+		 */
+		tmp = n;
+		v = two/x;
+		tmp = tmp*log(fabs(v*tmp));
+		if (tmp < 7.09782712893383973096e+02) {
+			    for (i = n-1; i > 0; i--) {
+				temp = b;
+				b = ((i+i)/x)*b - a;
+			    a = temp;
+				}
+		} else {
+				for (i = n-1; i > 0; i--) {
+				    temp = b;
+				    b = ((i+i)/x)*b - a;
+				    a = temp;
+					if (b > 1e100) {
+						a /= b;
+						t /= b;
+						b  = 1.0;
+					}
+				}
+		}
+			b = (t*j0(x)/b);
+	    }
+	}
+	if (sgn == 1)
+		return (-b);
+	else
+		return (b);
+}
+
+GENERIC
+yn(int n, GENERIC x) {
+	int i;
+	int sign;
+	GENERIC a, b, temp = 0, ox, on;
+
+	ox = x; on = (GENERIC)n;
+	if (isnan(x))
+		return (x*x);	/* + -> * for Cheetah */
+	if (x <= zero) {
+		if (x == zero) {
+			/* return -one/zero; */
+			return (_SVID_libm_err((GENERIC)n, x, 12));
+		} else {
+			/* return zero/zero; */
+			return (_SVID_libm_err((GENERIC)n, x, 13));
+		}
+	}
+	if (!((int) _lib_version == libm_ieee ||
+		(__xpg6 & _C99SUSv3_math_errexcept) != 0)) {
+	    if (x > X_TLOSS)
+			return (_SVID_libm_err(on, ox, 39));
+	}
+	sign = 1;
+	if (n < 0) {
+		n = -n;
+		if ((n&1) == 1) sign = -1;
+	}
+	if (n == 0)
+		return (y0(x));
+	if (n == 1)
+		return (sign*y1(x));
+	if (!finite(x))
+		return (zero);
+
+	if (x > 1.0e91) {
+				/*
+				 * x >> n**2
+				 *  Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+				 *  Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+				 *  Let s = sin(x), c = cos(x),
+				 *  xn = x-(2n+1)*pi/4, sqt2 = sqrt(2), then
+				 *
+				 *    n	sin(xn)*sqt2	cos(xn)*sqt2
+				 *	----------------------------------
+				 *	 0	 s-c		 c+s
+				 *	 1	-s-c 		-c+s
+				 *	 2	-s+c		-c-s
+				 *	 3	 s+c		 c-s
+				 */
+		switch (n&3) {
+		    case 0: temp =  sin(x)-cos(x); break;
+		    case 1: temp = -sin(x)-cos(x); break;
+		    case 2: temp = -sin(x)+cos(x); break;
+		    case 3: temp =  sin(x)+cos(x); break;
+		}
+		b = invsqrtpi*temp/sqrt(x);
+	} else {
+		a = y0(x);
+		b = y1(x);
+		/*
+		 * fix 1262058 and take care of non-default rounding
+		 */
+		for (i = 1; i < n; i++) {
+			temp = b;
+			b *= (GENERIC) (i + i) / x;
+			if (b <= -DBL_MAX)
+				break;
+			b -= a;
+			a = temp;
+		}
+	}
+	if (sign > 0)
+		return (b);
+	else
+		return (-b);
+}