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//===========================================================================
//
//      k_sin.c
//
//      Part of the standard mathematical function library
//
//===========================================================================
//####ECOSGPLCOPYRIGHTBEGIN####
// -------------------------------------------
// This file is part of eCos, the Embedded Configurable Operating System.
// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc.
//
// eCos is free software; you can redistribute it and/or modify it under
// the terms of the GNU General Public License as published by the Free
// Software Foundation; either version 2 or (at your option) any later version.
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or
// FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
// for more details.
//
// You should have received a copy of the GNU General Public License along
// with eCos; if not, write to the Free Software Foundation, Inc.,
// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
//
// As a special exception, if other files instantiate templates or use macros
// or inline functions from this file, or you compile this file and link it
// with other works to produce a work based on this file, this file does not
// by itself cause the resulting work to be covered by the GNU General Public
// License. However the source code for this file must still be made available
// in accordance with section (3) of the GNU General Public License.
//
// This exception does not invalidate any other reasons why a work based on
// this file might be covered by the GNU General Public License.
//
// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc.
// at http://sources.redhat.com/ecos/ecos-license/
// -------------------------------------------
//####ECOSGPLCOPYRIGHTEND####
//===========================================================================
//#####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