/*
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* 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
#ifdef __STDC__
double __kernel_cos(double x, double y)
#else
double __kernel_cos(x, y)
double x,y;
#endif
{
int ix;
if(((int)x)==0) return one; /* generate inexact */
}
z = x*x;
return one - (0.5*z - (z*r - x*y));
else {
qx = 0.28125;
} else {
}
return a - (hz - (z*r-x*y));
}
}