/*

 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.

 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

 *

 * This code is free software; you can redistribute it and/or modify it

 * under the terms of the GNU General Public License version 2 only, as

 * published by the Free Software Foundation.  Oracle designates this

 * particular file as subject to the "Classpath" exception as provided

 * by Oracle in the LICENSE file that accompanied this code.

 *

 * This code 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

 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

 *

 * You should have received a copy of the GNU General Public License version

 * 2 along with this work; if not, write to the Free Software Foundation,

 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

 *

 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

 * or visit www.oracle.com if you need additional information or have any

 * questions.

 */

/*

 * __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 "fdlibm.h"

#ifdef __STDC__

static const double

#else

static double

#endif

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 */

#ifdef __STDC__

        double __kernel_cos(double x, double y)

#else

        double __kernel_cos(x, y)

        double x,y;

#endif

{

        double a,hz,z,r,qx;

        int ix;

        ix = __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 {

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

                __LO(qx) = 0;

            }

            hz = 0.5*z-qx;

            a  = one-qx;

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

        }

}