//===========================================================================
//
//      k_sin.c
//
//      Part of the standard mathematical function library
//
//===========================================================================
//####COPYRIGHTBEGIN####
//
// -------------------------------------------
// The contents of this file are subject to the Cygnus eCos Public License
// Version 1.0 (the "License"); you may not use this file except in
// compliance with the License.  You may obtain a copy of the License at
// http://sourceware.cygnus.com/ecos
// 
// Software distributed under the License is distributed on an "AS IS"
// basis, WITHOUT WARRANTY OF ANY KIND, either express or implied.  See the
// License for the specific language governing rights and limitations under
// the License.
// 
// The Original Code is eCos - Embedded Cygnus Operating System, released
// September 30, 1998.
// 
// The Initial Developer of the Original Code is Cygnus.  Portions created
// by Cygnus are Copyright (C) 1998,1999 Cygnus Solutions.  All Rights Reserved.
// -------------------------------------------
//
//####COPYRIGHTEND####
//===========================================================================
//#####DESCRIPTIONBEGIN####
//
// Author(s):   jlarmour
// Contributors:  jlarmour
// Date:        1998-02-13
// Purpose:     
// Description: 
// Usage:       
//
//####DESCRIPTIONEND####
//
//===========================================================================

// CONFIGURATION

#include <pkgconf/libm.h>   // Configuration header

// Include the Math library?
#ifdef CYGPKG_LIBM     

// Derived from code with the following copyright


/* @(#)k_sin.c 1.3 95/01/18 */
/*
 * ====================================================
 * 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.
 * ====================================================
 */

/* __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 "mathincl/fdlibm.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;
        int ix;
        ix = CYG_LIBM_HI(x)&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);
}

#endif // ifdef CYGPKG_LIBM     

// EOF k_sin.c