2fe8fb192f
There is important information about booting non-ack images in docs/UPDATING. ack/aout-format images can't be built any more, and booting clang/ELF-format ones is a little different. Updating to the new boot monitor is recommended. Changes in this commit: . drop boot monitor -> allowing dropping ack support . facility to copy ELF boot files to /boot so that old boot monitor can still boot fairly easily, see UPDATING . no more ack-format libraries -> single-case libraries . some cleanup of OBJECT_FMT, COMPILER_TYPE, etc cases . drop several ack toolchain commands, but not all support commands (e.g. aal is gone but acksize is not yet). . a few libc files moved to netbsd libc dir . new /bin/date as minix date used code in libc/ . test compile fix . harmonize includes . /usr/lib is no longer special: without ack, /usr/lib plays no kind of special bootstrapping role any more and bootstrapping is done exclusively through packages, so releases depend even less on the state of the machine making them now. . rename nbsd_lib* to lib* . reduce mtree
312 lines
8.8 KiB
C
312 lines
8.8 KiB
C
/* $NetBSD: n_jn.c,v 1.6 2003/08/07 16:44:51 agc Exp $ */
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/*-
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* Copyright (c) 1992, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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#if 0
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static char sccsid[] = "@(#)jn.c 8.2 (Berkeley) 11/30/93";
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#endif
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#endif /* not lint */
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/*
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* 16 December 1992
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* Minor modifications by Peter McIlroy to adapt non-IEEE architecture.
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*/
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/*
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* ====================================================
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* Copyright (C) 1992 by Sun Microsystems, Inc.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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* ******************* WARNING ********************
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* This is an alpha version of SunPro's FDLIBM (Freely
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* Distributable Math Library) for IEEE double precision
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* arithmetic. FDLIBM is a basic math library written
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* in C that runs on machines that conform to IEEE
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* Standard 754/854. This alpha version is distributed
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* for testing purpose. Those who use this software
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* should report any bugs to
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*
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* fdlibm-comments@sunpro.eng.sun.com
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*
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* -- K.C. Ng, Oct 12, 1992
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* ************************************************
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*/
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/*
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* jn(int n, double x), yn(int n, double x)
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* floating point Bessel's function of the 1st and 2nd kind
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* of order n
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*
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* Special cases:
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* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
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* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
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* Note 2. About jn(n,x), yn(n,x)
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* For n=0, j0(x) is called,
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* for n=1, j1(x) is called,
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* for n<x, forward recursion us used starting
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* from values of j0(x) and j1(x).
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* for n>x, a continued fraction approximation to
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* j(n,x)/j(n-1,x) is evaluated and then backward
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* recursion is used starting from a supposed value
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* for j(n,x). The resulting value of j(0,x) is
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* compared with the actual value to correct the
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* supposed value of j(n,x).
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*
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* yn(n,x) is similar in all respects, except
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* that forward recursion is used for all
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* values of n>1.
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*
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*/
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#include "mathimpl.h"
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#include <float.h>
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#include <errno.h>
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#if defined(__vax__) || defined(tahoe)
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#define _IEEE 0
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#else
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#define _IEEE 1
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#define infnan(x) (0.0)
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#endif
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static const double
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invsqrtpi= 5.641895835477562869480794515607725858441e-0001,
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two = 2.0,
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zero = 0.0,
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one = 1.0;
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double
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jn(int n, double x)
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{
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int i, sgn;
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double a, b, temp;
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double z, w;
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/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
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* Thus, J(-n,x) = J(n,-x)
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*/
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/* if J(n,NaN) is NaN */
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if (_IEEE && isnan(x)) return x+x;
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if (n<0){
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n = -n;
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x = -x;
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}
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if (n==0) return(j0(x));
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if (n==1) return(j1(x));
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sgn = (n&1)&(x < zero); /* even n -- 0, odd n -- sign(x) */
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x = fabs(x);
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if (x == 0 || !finite (x)) /* if x is 0 or inf */
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b = zero;
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else if ((double) n <= x) {
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/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
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if (_IEEE && x >= 8.148143905337944345e+090) {
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/* x >= 2**302 */
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/* (x >> n**2)
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* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
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* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
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* Let s=sin(x), c=cos(x),
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* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
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*
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* n sin(xn)*sqt2 cos(xn)*sqt2
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* ----------------------------------
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* 0 s-c c+s
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* 1 -s-c -c+s
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* 2 -s+c -c-s
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* 3 s+c c-s
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*/
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switch(n&3) {
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case 0: temp = cos(x)+sin(x); break;
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case 1: temp = -cos(x)+sin(x); break;
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case 2: temp = -cos(x)-sin(x); break;
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case 3: temp = cos(x)-sin(x); break;
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}
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b = invsqrtpi*temp/sqrt(x);
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} else {
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a = j0(x);
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b = j1(x);
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for(i=1;i<n;i++){
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temp = b;
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b = b*((double)(i+i)/x) - a; /* avoid underflow */
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a = temp;
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}
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}
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} else {
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if (x < 1.86264514923095703125e-009) { /* x < 2**-29 */
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/* x is tiny, return the first Taylor expansion of J(n,x)
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* J(n,x) = 1/n!*(x/2)^n - ...
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*/
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if (n > 33) /* underflow */
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b = zero;
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else {
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temp = x*0.5; b = temp;
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for (a=one,i=2;i<=n;i++) {
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a *= (double)i; /* a = n! */
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b *= temp; /* b = (x/2)^n */
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}
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b = b/a;
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}
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} else {
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/* use backward recurrence */
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/* x x^2 x^2
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* J(n,x)/J(n-1,x) = ---- ------ ------ .....
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* 2n - 2(n+1) - 2(n+2)
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*
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* 1 1 1
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* (for large x) = ---- ------ ------ .....
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* 2n 2(n+1) 2(n+2)
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* -- - ------ - ------ -
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* x x x
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*
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* Let w = 2n/x and h=2/x, then the above quotient
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* is equal to the continued fraction:
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* 1
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* = -----------------------
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* 1
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* w - -----------------
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* 1
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* w+h - ---------
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* w+2h - ...
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*
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* To determine how many terms needed, let
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* Q(0) = w, Q(1) = w(w+h) - 1,
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* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
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* When Q(k) > 1e4 good for single
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* When Q(k) > 1e9 good for double
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* When Q(k) > 1e17 good for quadruple
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*/
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/* determine k */
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double t,v;
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double q0,q1,h,tmp; int k,m;
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w = (n+n)/(double)x; h = 2.0/(double)x;
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q0 = w; z = w+h; q1 = w*z - 1.0; k=1;
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while (q1<1.0e9) {
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k += 1; z += h;
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tmp = z*q1 - q0;
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q0 = q1;
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q1 = tmp;
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}
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m = n+n;
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for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
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a = t;
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b = one;
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/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
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* Hence, if n*(log(2n/x)) > ...
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* single 8.8722839355e+01
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* double 7.09782712893383973096e+02
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* long double 1.1356523406294143949491931077970765006170e+04
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* then recurrent value may overflow and the result will
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* likely underflow to zero
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*/
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tmp = n;
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v = two/x;
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tmp = tmp*log(fabs(v*tmp));
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for (i=n-1;i>0;i--){
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temp = b;
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b = ((i+i)/x)*b - a;
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a = temp;
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/* scale b to avoid spurious overflow */
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# if defined(__vax__) || defined(tahoe)
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# define BMAX 1e13
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# else
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# define BMAX 1e100
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# endif /* defined(__vax__) || defined(tahoe) */
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if (b > BMAX) {
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a /= b;
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t /= b;
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b = one;
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}
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}
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b = (t*j0(x)/b);
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}
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}
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return ((sgn == 1) ? -b : b);
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}
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double
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yn(int n, double x)
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{
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int i, sign;
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double a, b, temp;
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/* Y(n,NaN), Y(n, x < 0) is NaN */
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if (x <= 0 || (_IEEE && x != x))
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if (_IEEE && x < 0) return zero/zero;
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else if (x < 0) return (infnan(EDOM));
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else if (_IEEE) return -one/zero;
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else return(infnan(-ERANGE));
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else if (!finite(x)) return(0);
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sign = 1;
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if (n<0){
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n = -n;
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sign = 1 - ((n&1)<<2);
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}
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if (n == 0) return(y0(x));
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if (n == 1) return(sign*y1(x));
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if(_IEEE && x >= 8.148143905337944345e+090) { /* x > 2**302 */
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/* (x >> n**2)
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* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
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* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
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* Let s=sin(x), c=cos(x),
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* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
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*
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* n sin(xn)*sqt2 cos(xn)*sqt2
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* ----------------------------------
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* 0 s-c c+s
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* 1 -s-c -c+s
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* 2 -s+c -c-s
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* 3 s+c c-s
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*/
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switch (n&3) {
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case 0: temp = sin(x)-cos(x); break;
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case 1: temp = -sin(x)-cos(x); break;
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case 2: temp = -sin(x)+cos(x); break;
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case 3: temp = sin(x)+cos(x); break;
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}
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b = invsqrtpi*temp/sqrt(x);
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} else {
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a = y0(x);
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b = y1(x);
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/* quit if b is -inf */
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for (i = 1; i < n && !finite(b); i++){
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temp = b;
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b = ((double)(i+i)/x)*b - a;
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a = temp;
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}
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}
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if (!_IEEE && !finite(b))
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return (infnan(-sign * ERANGE));
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return ((sign > 0) ? b : -b);
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}
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