/* origin: FreeBSD /usr/src/lib/msun/src/k_cos.c */
/*
 * ====================================================
 * 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.
 * ====================================================
 */
/*
 * __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, rearrange to
 *              cos(x+y) ~ w + (tmp + (r-x*y))
 *         where w = 1 - x*x/2 and tmp is a tiny correction term
 *         (1 - x*x/2 == w + tmp exactly in infinite precision).
 *         The exactness of w + tmp in infinite precision depends on w
 *         and tmp having the same precision as x.  If they have extra
 *         precision due to compiler bugs, then the extra precision is
 *         only good provided it is retained in all terms of the final
 *         expression for cos().  Retention happens in all cases tested
 *         under FreeBSD, so don't pessimize things by forcibly clipping
 *         any extra precision in w.
 */

#include "libm.h"

static const double 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 __cos(double x, double y) {
  double_t hz, z, r, w;

  z = x * x;
  w = z * z;
  r = z * (C1 + z * (C2 + z * C3)) + w * w * (C4 + z * (C5 + z * C6));
  hz = 0.5 * z;
  w = 1.0 - hz;
  return w + (((1.0 - w) - hz) + (z * r - x * y));
}