e_j1.c

ecos实时嵌入式操作系统

//===========================================================================
//
//      e_j1.c
//
//      Part of the standard mathematical function library
//
//===========================================================================
//####ECOSGPLCOPYRIGHTBEGIN####
// -------------------------------------------
// This file is part of eCos, the Embedded Configurable Operating System.
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc.
//
// eCos is free software; you can redistribute it and/or modify it under
// the terms of the GNU General Public License as published by the Free
// Software Foundation; either version 2 or (at your option) any later version.
//
// eCos is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or
// FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
// for more details.
//
// You should have received a copy of the GNU General Public License along
// with eCos; if not, write to the Free Software Foundation, Inc.,
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
//
// As a special exception, if other files instantiate templates or use macros
// or inline functions from this file, or you compile this file and link it
// with other works to produce a work based on this file, this file does not
// by itself cause the resulting work to be covered by the GNU General Public
// License. However the source code for this file must still be made available
// in accordance with section (3) of the GNU General Public License.
//
// This exception does not invalidate any other reasons why a work based on
// this file might be covered by the GNU General Public License.
//
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc.
// at http://sources.redhat.com/ecos/ecos-license/
// -------------------------------------------
//####ECOSGPLCOPYRIGHTEND####
//===========================================================================
//#####DESCRIPTIONBEGIN####
//
// Author(s):   jlarmour
// Contributors:  jlarmour
// Date:        1998-02-13
// Purpose:     
// Description: 
// Usage:       
//
//####DESCRIPTIONEND####
//
//===========================================================================

// CONFIGURATION

#include <pkgconf/libm.h>   // Configuration header

// Include the Math library?
#ifdef CYGPKG_LIBM     

// Derived from code with the following copyright


/* @(#)e_j1.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/* __ieee754_j1(x), __ieee754_y1(x)
 * Bessel function of the first and second kinds of order zero.
 * Method -- j1(x):
 *      1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
 *      2. Reduce x to |x| since j1(x)=-j1(-x),  and
 *         for x in (0,2)
 *              j1(x) = x/2 + x*z*R0/S0,  where z = x*x;
 *         (precision:  |j1/x - 1/2 - R0/S0 |<2**-61.51 )
 *         for x in (2,inf)
 *              j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
 *              y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
 *         where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
 *         as follow:
 *              cos(x1) =  cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
 *                      =  1/sqrt(2) * (sin(x) - cos(x))
 *              sin(x1) =  sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
 *                      = -1/sqrt(2) * (sin(x) + cos(x))
 *         (To avoid cancellation, use
 *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
 *          to compute the worse one.)
 *         
 *      3 Special cases
 *              j1(nan)= nan
 *              j1(0) = 0
 *              j1(inf) = 0
 *              
 * Method -- y1(x):
 *      1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN 
 *      2. For x<2.
 *         Since 
 *              y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
 *         therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
 *         We use the following function to approximate y1,
 *              y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
 *         where for x in [0,2] (abs err less than 2**-65.89)
 *              U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
 *              V(z) = 1  + v0[0]*z + ... + v0[4]*z^5
 *         Note: For tiny x, 1/x dominate y1 and hence
 *              y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
 *      3. For x>=2.
 *              y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
 *         where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
 *         by method mentioned above.
 */

#include "mathincl/fdlibm.h"

static double pone(double), qone(double);

static const double 
huge    = 1e300,
one     = 1.0,
invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
        /* R0/S0 on [0,2] */
r00  = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
r01  =  1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
r02  = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
r03  =  4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
s01  =  1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
s02  =  1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
s03  =  1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
s04  =  5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
s05  =  1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */

static double zero    = 0.0;

        double __ieee754_j1(double x) 
{
        double z, s,c,ss,cc,r,u,v,y;
        int hx,ix;

        hx = CYG_LIBM_HI(x);
        ix = hx&0x7fffffff;
        if(ix>=0x7ff00000) return one/x;
        y = fabs(x);
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
                s = sin(y);
                c = cos(y);
                ss = -s-c;
                cc = s-c;
                if(ix<0x7fe00000) {  /* make sure y+y not overflow */
                    z = cos(y+y);
                    if ((s*c)>zero) cc = z/ss;
                    else            ss = z/cc;
                }
        /*
         * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
         * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
         */
                if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y);
                else {
                    u = pone(y); v = qone(y);
                    z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
                }
                if(hx<0) return -z;
                else     return  z;
        }
        if(ix<0x3e400000) {     /* |x|<2**-27 */
            if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
        }
        z = x*x;
        r =  z*(r00+z*(r01+z*(r02+z*r03)));
        s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
        r *= x;
        return(x*0.5+r/s);
}

static const double U0[5] = {
 -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
  5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
 -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
  2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
 -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
};
static const double V0[5] = {
  1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
  2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
  1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
  6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
  1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
};

        double __ieee754_y1(double x) 
{
        double z, s,c,ss,cc,u,v;
        int hx,ix,lx;

        hx = CYG_LIBM_HI(x);
        ix = 0x7fffffff&hx;
        lx = CYG_LIBM_LO(x);
    /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
        if(ix>=0x7ff00000) return  one/(x+x*x); 
        if((ix|lx)==0) return -one/zero;
        if(hx<0) return zero/zero;
        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
                s = sin(x);
                c = cos(x);
                ss = -s-c;
                cc = s-c;
                if(ix<0x7fe00000) {  /* make sure x+x not overflow */
                    z = cos(x+x);
                    if ((s*c)>zero) cc = z/ss;