/****************************************************************************
 *
 * $Source: /usr/local/cvsroot/gccsdk/unixlib/source/math/k_cos.c,v $
 * $Date: 2001/01/29 15:10:19 $
 * $Revision: 1.2 $
 * $State: Exp $
 * $Author: admin $
 *
 ***************************************************************************/

#ifdef EMBED_RCSID
static const char rcs_id[] = "$Id: k_cos.c,v 1.2 2001/01/29 15:10:19 admin Exp $";
#endif

/* @(#)k_cos.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, 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 <math.h>
#include <unixlib/math.h>
#include <unixlib/types.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;
  __int32_t ix;
  GET_HIGH_WORD (ix, x);
  ix &= 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
	{
	  INSERT_WORDS (qx, ix - 0x00200000, 0);	/* x/4 */
	}
      hz = 0.5 * z - qx;
      a = one - qx;
      return a - (hz - (z * r - x * y));
    }
}
