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//===========================================================================
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//
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// k_cos.c
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//
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// Part of the standard mathematical function library
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//
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//===========================================================================
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// ####ECOSGPLCOPYRIGHTBEGIN####
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// -------------------------------------------
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// This file is part of eCos, the Embedded Configurable Operating System.
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// Copyright (C) 1998, 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
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//
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// eCos is free software; you can redistribute it and/or modify it under
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// the terms of the GNU General Public License as published by the Free
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// Software Foundation; either version 2 or (at your option) any later
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// version.
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//
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// eCos is distributed in the hope that it will be useful, but WITHOUT
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// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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// for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with eCos; if not, write to the Free Software Foundation, Inc.,
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// 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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//
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// As a special exception, if other files instantiate templates or use
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// macros or inline functions from this file, or you compile this file
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// and link it with other works to produce a work based on this file,
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// this file does not by itself cause the resulting work to be covered by
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// the GNU General Public License. However the source code for this file
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// must still be made available in accordance with section (3) of the GNU
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// General Public License v2.
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//
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// This exception does not invalidate any other reasons why a work based
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// on this file might be covered by the GNU General Public License.
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// -------------------------------------------
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// ####ECOSGPLCOPYRIGHTEND####
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//===========================================================================
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//#####DESCRIPTIONBEGIN####
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//
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// Author(s): jlarmour
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// Contributors: jlarmour
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// Date: 1998-02-13
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// Purpose:
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// Description:
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// Usage:
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//
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//####DESCRIPTIONEND####
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//
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//===========================================================================
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// CONFIGURATION
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#include <pkgconf/libm.h> // Configuration header
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// Include the Math library?
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#ifdef CYGPKG_LIBM
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// Derived from code with the following copyright
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/* @(#)k_cos.c 1.3 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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* __kernel_cos( x, y )
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* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
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* Input x is assumed to be bounded by ~pi/4 in magnitude.
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* Input y is the tail of x.
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*
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* Algorithm
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* 1. Since cos(-x) = cos(x), we need only to consider positive x.
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* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
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* 3. cos(x) is approximated by a polynomial of degree 14 on
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* [0,pi/4]
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* 4 14
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* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
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* where the remez error is
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*
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* | 2 4 6 8 10 12 14 | -58
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* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
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* | |
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*
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* 4 6 8 10 12 14
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* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
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* cos(x) = 1 - x*x/2 + r
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* since cos(x+y) ~ cos(x) - sin(x)*y
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* ~ cos(x) - x*y,
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* a correction term is necessary in cos(x) and hence
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* cos(x+y) = 1 - (x*x/2 - (r - x*y))
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* For better accuracy when x > 0.3, let qx = |x|/4 with
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* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
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* Then
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* cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
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* Note that 1-qx and (x*x/2-qx) is EXACT here, and the
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* magnitude of the latter is at least a quarter of x*x/2,
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* thus, reducing the rounding error in the subtraction.
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*/
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#include "mathincl/fdlibm.h"
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static const double
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
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C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
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C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
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C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
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C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
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C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
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double __kernel_cos(double x, double y)
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{
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double a,hz,z,r,qx;
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int ix;
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ix = CYG_LIBM_HI(x)&0x7fffffff; /* ix = |x|'s high word*/
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if(ix<0x3e400000) { /* if x < 2**27 */
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if(((int)x)==0) return one; /* generate inexact */
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}
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z = x*x;
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r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
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if(ix < 0x3FD33333) /* if |x| < 0.3 */
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return one - (0.5*z - (z*r - x*y));
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else {
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if(ix > 0x3fe90000) { /* x > 0.78125 */
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qx = 0.28125;
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} else {
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CYG_LIBM_HI(qx) = ix-0x00200000; /* x/4 */
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CYG_LIBM_LO(qx) = 0;
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}
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hz = 0.5*z-qx;
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a = one-qx;
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return a - (hz - (z*r-x*y));
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}
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}
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#endif // ifdef CYGPKG_LIBM
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// EOF k_cos.c
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