/****************************************************************************
 *
 * $Source: /usr/local/cvsroot/gccsdk/unixlib/source/math/k_sin.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_sin.c,v 1.2 2001/01/29 15:10:19 admin Exp $";
#endif

/* @(#)k_sin.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_sin( x, y, iy)
 * kernel sin function on [-pi/4, pi/4], 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. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
 *      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))
 */

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

static const double
  half = 5.00000000000000000000e-01,	/* 0x3FE00000, 0x00000000 */
  S1 = -1.66666666666666324348e-01,	/* 0xBFC55555, 0x55555549 */
  S2 = 8.33333333332248946124e-03,	/* 0x3F811111, 0x1110F8A6 */
  S3 = -1.98412698298579493134e-04,	/* 0xBF2A01A0, 0x19C161D5 */
  S4 = 2.75573137070700676789e-06,	/* 0x3EC71DE3, 0x57B1FE7D */
  S5 = -2.50507602534068634195e-08,	/* 0xBE5AE5E6, 0x8A2B9CEB */
  S6 = 1.58969099521155010221e-10;	/* 0x3DE5D93A, 0x5ACFD57C */

double
__kernel_sin (double x, double y, int iy)
{
  double z, r, v;
  __int32_t ix;
  GET_HIGH_WORD (ix, x);
  ix &= 0x7fffffff;		/* high word of x */
  if (ix < 0x3e400000)		/* |x| < 2**-27 */
    {
      if ((int) x == 0)
	return x;
    }				/* generate inexact */
  z = x * x;
  v = z * x;
  r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
  if (iy == 0)
    return x + v * (S1 + z * r);
  else
    return x - ((z * (half * y - v * r) - y) - v * S1);
}
