common/Q/jnl.c

25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER START
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * The contents of this file are subject to the terms of the
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Common Development and Distribution License (the "License").
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You may not use this file except in compliance with the License.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * or http://www.opensolaris.org/os/licensing.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * See the License for the specific language governing permissions
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * and limitations under the License.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER END
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
ddc0e0b53c661f6e439e3b7072b3ef353eadb4afRichard Lowe#pragma weak __jnl = jnl
ddc0e0b53c661f6e439e3b7072b3ef353eadb4afRichard Lowe#pragma weak __ynl = ynl
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * floating point Bessel's function of the 1st and 2nd kind
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * of order n: jn(n,x),yn(n,x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Special cases:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Note 2. About jn(n,x), yn(n,x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  For n=0, j0(x) is called,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  for n=1, j1(x) is called,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  for n<x, forward recursion us used starting
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  from values of j0(x) and j1(x).
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  for n>x, a continued fraction approximation to
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  j(n,x)/j(n-1,x) is evaluated and then backward
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  recursion is used starting from a supposed value
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  for j(n,x). The resulting value of j(0,x) is
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  compared with the actual value to correct the
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  supposed value of j(n,x).
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  yn(n,x) is similar in all respects, except
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  that forward recursion is used for all
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *  values of n>1.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "libm.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "longdouble.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include <float.h>  /* LDBL_MAX */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define GENERIC long double
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisstatic const GENERIC
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisinvsqrtpi = 5.641895835477562869480794515607725858441e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtistwo  = 2.0L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtiszero = 0.0L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisone  = 1.0L;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr JasiukajtisGENERIC
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisjnl(n, x) int n; GENERIC x; {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    int i, sgn;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    GENERIC a, b, temp, z, w;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    /*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis     * J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis     * Thus, J(-n,x) = J(n,-x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis     */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (n < 0) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        n = -n;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        x = -x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (n == 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (j0l(x));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (n == 1)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (j1l(x));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (x != x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (x+x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if ((n&1) == 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        sgn = 0;            /* even n */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        sgn = signbitl(x);  /* old n  */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    x = fabsl(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (x == zero || !finitel(x)) b = zero;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    else if ((GENERIC)n <= x) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                    /*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                     * Safe to use
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                     * J(n+1,x)=2n/x *J(n,x)-J(n-1,x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                     */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (x > 1.0e91L) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                /*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 * x >> n**2
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *  Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *   Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *   Let s=sin(x), c=cos(x),
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *  xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *     n    sin(xn)*sqt2    cos(xn)*sqt2
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *  ----------------------------------
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *     0     s-c         c+s
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *     1    -s-c        -c+s
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *     2    -s+c        -c-s
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *     3     s+c         c-s
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        switch (n&3) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            case 0: temp =  cosl(x)+sinl(x); break;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            case 1: temp = -cosl(x)+sinl(x); break;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            case 2: temp = -cosl(x)-sinl(x); break;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            case 3: temp =  cosl(x)-sinl(x); break;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        b = invsqrtpi*temp/sqrtl(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            a = j0l(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            b = j1l(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            for (i = 1; i < n; i++) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            temp = b;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            b = b*((GENERIC)(i+i)/x) - a; /* avoid underflow */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            a = temp;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (x < 1e-17L) {   /* use J(n,x) = 1/n!*(x/2)^n */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        b = powl(0.5L*x, (GENERIC)n);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (b != zero) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            for (a = one, i = 1; i <= n; i++) a *= (GENERIC)i;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            b = b/a;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        /* use backward recurrence */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        /*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *          x      x^2      x^2
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *          2n  - 2(n+1) - 2(n+2)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *          1      1        1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *  (for large x)   =  ----  ------   ------   .....
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *          2n   2(n+1)   2(n+2)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *          -- - ------ - ------ -
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *           x     x         x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * Let w = 2n/x and h=2/x, then the above quotient
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * is equal to the continued fraction:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *          1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *  = -----------------------
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *             1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *     w - -----------------
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *            1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *          w+h - ---------
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *             w+2h - ...
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * To determine how many terms needed, let
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * Q(0) = w, Q(1) = w(w+h) - 1,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * When Q(k) > 1e4  good for single
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * When Q(k) > 1e9  good for double
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * When Q(k) > 1e17 good for quaduple
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        /* determin k */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        GENERIC t, v;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        double q0, q1, h, tmp; int k, m;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        w  = (n+n)/(double)x; h = 2.0/(double)x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        q0 = w;  z = w+h; q1 = w*z - 1.0; k = 1;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        while (q1 < 1.0e17) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            k += 1; z += h;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            tmp = z*q1 - q0;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            q0 = q1;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            q1 = tmp;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        m = n+n;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        for (t = zero, i = 2*(n+k); i >= m; i -= 2) t = one/(i/x-t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        a = t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        b = one;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                /*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 * hence, if n*(log(2n/x)) > ...
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *  single 8.8722839355e+01
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *  double 7.09782712893383973096e+02
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *  long double 1.1356523406294143949491931077970765006170e+04
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *  then recurrent value may overflow and the result is
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 *  likely underflow to zero
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        tmp = n;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        v = two/x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        tmp = tmp*logl(fabsl(v*tmp));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (tmp < 1.1356523406294143949491931077970765e+04L) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                for (i = n-1; i > 0; i--) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                temp = b;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                b = ((i+i)/x)*b - a;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                a = temp;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                for (i = n-1; i > 0; i--) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                temp = b;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                b = ((i+i)/x)*b - a;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                a = temp;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            if (b > 1e1000L) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                            a /= b;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                            t /= b;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                            b  = 1.0;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            b = (t*j0l(x)/b);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (sgn == 1)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (-b);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (b);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis}
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr JasiukajtisGENERIC ynl(n, x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisint n; GENERIC x; {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    int i;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    int sign;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    GENERIC a, b, temp;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (x != x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (x+x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (x <= zero) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (x == zero)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            return (-one/zero);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            return (zero/zero);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    sign = 1;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (n < 0) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        n = -n;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if ((n&1) == 1) sign = -1;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (n == 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (y0l(x));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (n == 1)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (sign*y1l(x));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (!finitel(x))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (zero);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (x > 1.0e91L) {  /* x >> n**2
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                    Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                    Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                    Let s = sin(x), c = cos(x),
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                    xn = x-(2n+1)*pi/4, sqt2 = sqrt(2), then
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                       n    sin(xn)*sqt2    cos(xn)*sqt2
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                    ----------------------------------
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                       0     s-c         c+s
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                       1    -s-c        -c+s
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                       2    -s+c        -c-s
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                       3     s+c         c-s
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        switch (n&3) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            case 0: temp =  sinl(x)-cosl(x); break;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            case 1: temp = -sinl(x)-cosl(x); break;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            case 2: temp = -sinl(x)+cosl(x); break;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            case 3: temp =  sinl(x)+cosl(x); break;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        b = invsqrtpi*temp/sqrtl(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        a = y0l(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        b = y1l(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        /*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * fix 1262058 and take care of non-default rounding
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        for (i = 1; i < n; i++) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            temp = b;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            b *= (GENERIC) (i + i) / x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            if (b <= -LDBL_MAX)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                break;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            b -= a;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            a = temp;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (sign > 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (b);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        return (-b);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis}