/****************************************************************************
 * libs/libc/math/__sin.c
 *
 * Ported to NuttX from FreeBSD by Alan Carvalho de Assis:
 *
 *   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.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 * 3. Neither the name NuttX nor the names of its contributors may be
 *    used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
 * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
 * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *
 ****************************************************************************/

/* __sin( x, y, iy)
 *
 * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
 * Input y is the tail of x.
 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
 *
 * Algorithm
 *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
 *      2. Callers must return sin(-0) = -0 without calling here since our
 *         odd polynomial is not evaluated in a way that preserves -0.
 *         Callers may do the optimization sin(x) ~ x for tiny x.
 *      3. sin(x) is approximated by a polynomial of degree 13 on
 *         [0,pi/4]
 *                               3            13
 *              sin(x) ~ x + S1*x + ... + S6*x
 *         where
 *
 *      |sin(x)         2     4     6     8     10     12  |     -58
 *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
 *      |  x                                               |
 *
 *      4. sin(x+y) = sin(x) + sin'(x')*y
 *                  ~ sin(x) + (1-x*x/2)*y
 *         For better accuracy, let
 *                   3      2      2      2      2
 *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
 *         then                   3    2
 *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
 */

/****************************************************************************
 * Included Files
 ****************************************************************************/

#include <nuttx/config.h>
#include <nuttx/compiler.h>

#include <sys/types.h>
#include <math.h>

#ifdef CONFIG_HAVE_DOUBLE

/****************************************************************************
 * Private Data
 ****************************************************************************/

static const double g_s1  = -1.66666666666666324348e-01; /* 0xbfc55555, 0x55555549 */
static const double g_s2  =  8.33333333332248946124e-03; /* 0x3f811111, 0x1110f8a6 */
static const double g_s3  = -1.98412698298579493134e-04; /* 0xbf2a01a0, 0x19c161d5 */
static const double g_s4  =  2.75573137070700676789e-06; /* 0x3ec71de3, 0x57b1fe7d */
static const double g_s5  = -2.50507602534068634195e-08; /* 0xbe5ae5e6, 0x8a2b9ceb */
static const double g_s6  =  1.58969099521155010221e-10; /* 0x3de5d93a, 0x5acfd57c */

/****************************************************************************
 * Public Functions
 ****************************************************************************/

double __sin(double x, double y, int iy)
{
  double z;
  double r;
  double v;
  double w;

  z = x * x;
  w = z * z;
  r = g_s2 + z * (g_s3 + z * g_s4) + z * w * (g_s5 + z * g_s6);
  v = z * x;

  if (iy == 0)
    {
      return x + v * (g_s1 + z * r);
    }
  else
    {
      return x - ((z * (0.5 * y - v * r) - y) - v * g_s1);
    }
}
#endif