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//===========================================================================

//

//      k_cos.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

/* @(#)k_cos.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.

 * ====================================================

 */

/*

 * __kernel_cos( x,  y )

 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164

 * Input x is assumed to be bounded by ~pi/4 in magnitude.

 * Input y is the tail of x.

 *

 * Algorithm

 *      1. Since cos(-x) = cos(x), we need only to consider positive x.

 *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.

 *      3. cos(x) is approximated by a polynomial of degree 14 on

 *         [0,pi/4]

 *                                       4            14

 *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x

 *         where the remez error is

 *

 *      |              2     4     6     8     10    12     14 |     -58

 *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2

 *      |                                                      |

 *

 *                     4     6     8     10    12     14

 *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then

 *             cos(x) = 1 - x*x/2 + r

 *         since cos(x+y) ~ cos(x) - sin(x)*y

 *                        ~ cos(x) - x*y,

 *         a correction term is necessary in cos(x) and hence

 *              cos(x+y) = 1 - (x*x/2 - (r - x*y))

 *         For better accuracy when x > 0.3, let qx = |x|/4 with

 *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.

 *         Then

 *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).

 *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the

 *         magnitude of the latter is at least a quarter of x*x/2,

 *         thus, reducing the rounding error in the subtraction.

 */

#include "mathincl/fdlibm.h"

static const double

one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */

C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */

C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */

C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */

C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */

C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */

C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */

        double __kernel_cos(double x, double y)

{

        double a,hz,z,r,qx;

        int ix;

        ix = CYG_LIBM_HI(x)&0x7fffffff; /* ix = |x|'s high word*/

        if(ix<0x3e400000) {                     /* if x < 2**27 */

            if(((int)x)==0) return one;         /* generate inexact */

        }

        z  = x*x;

        r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));

        if(ix < 0x3FD33333)                     /* if |x| < 0.3 */

            return one - (0.5*z - (z*r - x*y));

        else {

            if(ix > 0x3fe90000) {               /* x > 0.78125 */

                qx = 0.28125;

            } else {

                CYG_LIBM_HI(qx) = ix-0x00200000;        /* x/4 */

                CYG_LIBM_LO(qx) = 0;

            }

            hz = 0.5*z-qx;

            a  = one-qx;

            return a - (hz - (z*r-x*y));

        }

}

#endif // ifdef CYGPKG_LIBM     

// EOF k_cos.c