fixedmath.h

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/**
 * \file fixedmath.h
 * \author Wei Yongming <[e-mail]>
 * \date 2002/01/12
 * 
 *  This file includes fixed point and three-dimension math routines.
 *
 \verbatim
    Copyright (C) 1998-2002 Wei Yongming.
    Copyright (C) 2002-2004 Feynman Software.

    This file is part of MiniGUI, a compact cross-platform Graphics 
    User Interface (GUI) support system for real-time embedded systems.

    This program 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 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY 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 this program; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

 \endverbatim
 */

/*
 * $Id: fixedmath.h,v 1.20 2004/06/26 08:41:44 weiym Exp $
 *
 *             MiniGUI for Linux/uClinux, eCos, uC/OS-II, and VxWorks version 1.6.x
 *             Copyright (C) 1998-2002 Wei Yongming.
 *             Copyright (C) 2002-2004 Feynman Software.
 *
 *             Fix point math routins come from Allegro
 *             By Shawn Hargreaves and others.
 *             So thank for their great work and good license.
 *
 *             "Allegro is a gift-software" 
 *
 *         ______   ___    ___
 *        /\  _  \ /\_ \  /\_ \
 *        \ \ \L\ \\//\ \ \//\ \      __     __   _ __   ___
 *         \ \  __ \ \ \ \  \ \ \   /'__`\ /'_ `\/\`'__\/ __`\
 *          \ \ \/\ \ \_\ \_ \_\ \_/\  __//\ \L\ \ \ \//\ \L\ \
 *           \ \_\ \_\/\____\/\____\ \____\ \____ \ \_\\ \____/
 *            \/_/\/_/\/____/\/____/\/____/\/___L\ \/_/ \/___/
 *                                           /\____/
 *                                           \_/__/
 *
 */

#ifndef _MGUI_FIXED_MATH_H
#define _MGUI_FIXED_MATH_H

#include <errno.h>
#include <math.h>

/* Set up for C function definitions, even when using C++ */
#ifdef __cplusplus
extern "C" {
#endif

#ifdef _FIXED_MATH

    /**
     * \addtogroup fns Functions
     * @{
     */

    /**
     * \addtogroup global_fns Global/general functions
     * @{
     */

    /**
     * \defgroup fixed_math_fns Fixed point math functions
     * 
     * You know that the float point mathematics routines are very
     * expensive. If you do not want precision mathematics result, 
     * you can use fixed point. MiniGUI uses a double word (32-bit)
     * integer to represent a fixed point ranged from -32767.0 to 
     * 32767.0, and defines some fixed point mathematics routines for 
     * your application. Some GDI functions need fixed point 
     * math routines, like \a Arc.
     *
     * Example 1:
     * 
     * \include fixed_point.c
     *
     * Example 2:
     * 
     * \include fixedpoint.c
     * @{
     */

/**
 * \fn fixed fsqrt (fixed x)
 * \brief Returns the non-negative square root of a fixed point value.
 *
 * This function returns the non-negative square root of \a x.
 * It fails and sets errno to EDOM, if x is negative.
 *
 * \sa fhypot
 */
fixed fsqrt (fixed x);

/**
 * \fn fixed fhypot (fixed x, fixed y)
 * \brief Returns the Euclidean distance from the origin.
 * 
 * The function returns the \a sqrt(x*x+y*y). This is the length of 
 * the hypotenuse of a right-angle triangle with sides of length \a x and \a y, 
 * or the distance of the point \a (x,y) from the origin.
 *
 * \sa fsqrt
 */
fixed fhypot (fixed x, fixed y);

/**
 * \fn fixed fatan (fixed x)
 * \brief Calculates the arc tangent of a fixed point value.
 *
 * This function calculates the arc tangent of \a x; that is the value 
 * whose tangent is \a x.
 *
 * \return Returns the arc tangent in radians and the value is 
 *         mathematically defined to be between -PI/2 and PI/2 (inclusive).
 *
 * \sa fatan2
 */
fixed fatan (fixed x);

/**
 * \fn fixed fatan2 (fixed y, fixed x)
 * \brief Calclulates the arc tangent of two fixed point variables.
 *
 *  This function calculates the arc tangent of the two variables \a x and \a y.
 *  It is similar to calculating the arc tangent of \a y / \a x, except that 
 *  the signs of both arguments are used to determine the quadrant of the result.
 *
 * \return Returns the result in radians, which is between -PI and PI (inclusive).
 *
 * \sa fatan
 */
fixed fatan2 (fixed y, fixed x);

extern fixed _cos_tbl[];
extern fixed _tan_tbl[];
extern fixed _acos_tbl[];

/************************** inline fixed point math functions *****************/
/* ftofix and fixtof are used in generic C versions of fmul and fdiv */

/**
 * \fn fixed ftofix (double x)
 * \brief Converts a float point value to a fixed point value.
 *
 * This function converts the specified float point value \a x to 
 * a fixed point value.
 *
 * \note The float point should be ranged from -32767.0 to 32767.0.
 * If it runs out of the range, this function sets \a errno to \a ERANGE.
 *
 * \sa fixtof
 */
static inline fixed ftofix (double x)
{ 
   if (x > 32767.0) {
      errno = ERANGE;
      return 0x7FFFFFFF;
   }

   if (x < -32767.0) {
      errno = ERANGE;
      return -0x7FFFFFFF;
   }

   return (long)(x * 65536.0 + (x < 0 ? -0.5 : 0.5)); 
}

/**
 * \fn double fixtof (fixed x)
 * \brief Converts a fixed point value to a float point value.
 *
 * This function converts the specified fixed point value \a x to 
 * a float point value.
 *
 * \sa ftofix
 */
static inline double fixtof (fixed x)
{ 
   return (double)x / 65536.0; 
}


/**
 * \fn fixed fadd (fixed x, fixed y)
 * \brief Returns the sum of two fixed point values.
 *
 * This function adds two fixed point values \a x and \a y, and
 * returns the sum.
 *
 * \param x x,y: Two addends.
 * \param y x,y: Two addends.
 * \return The sum. If the result runs out of range of fixed point, this function
 *         sets \a errno to \a ERANGE.
 *
 * \sa fsub
 */
static inline fixed fadd (fixed x, fixed y)
{
   fixed result = x + y;

   if (result >= 0) {
      if ((x < 0) && (y < 0)) {
	 errno = ERANGE;
	 return -0x7FFFFFFF;
      }
      else
	 return result;
   }
   else {
      if ((x > 0) && (y > 0)) {
	 errno = ERANGE;
	 return 0x7FFFFFFF;
      }
      else
	 return result;
   }
}

/**
 * \fn fixed fsub (fixed x, fixed y)
 * \brief Subtract a fixed point value from another.
 *
 * This function subtracts the fixed point values \a y from the fixed point value \a x,
 * and returns the difference.
 *
 * \param x The minuend.
 * \param y The subtrahend.
 * \return The difference. If the result runs out of range of fixed point, this function
 *         sets \a errno to \a ERANGE.
 *
 * \sa fadd
 */
static inline fixed fsub (fixed x, fixed y)
{
   fixed result = x - y;

   if (result >= 0) {
      if ((x < 0) && (y > 0)) {
	 errno = ERANGE;
	 return -0x7FFFFFFF;
      }
      else
	 return result;
   }
   else {
      if ((x > 0) && (y < 0)) {
	 errno = ERANGE;
	 return 0x7FFFFFFF;
      }
      else
	 return result;
   }
}

/**
 * \fn fixed fmul (fixed x, fixed y)
 * \brief Returns the product of two fixed point values.
 * 
 * This function returns the product of two fixed point values \a x and \a y.
 *
 * \param x The faciend.
 * \param y The multiplicato.
 * \return The prodcut. If the result runs out of range of fixed point, this function
 *         sets \a errno to \a ERANGE.
 * 
 * \sa fdiv
 */
static inline fixed fmul (fixed x, fixed y)
{
   return ftofix(fixtof(x) * fixtof(y));
}

/**
 * \fn fixed fdiv (fixed x, fixed y)
 * \brief Returns the quotient of two fixed point values.
 * 
 * This function returns the quotient of two fixed point values \a x and \a y.
 *
 * \param x The dividend.
 * \param y The divisor.
 * \return The quotient. If the result runs out of range of fixed point, this function
 *         sets \a errno to \a ERANGE.
 * 
 * \sa fmul
 */
static inline fixed fdiv (fixed x, fixed y)
{
   if (y == 0) {
      errno = ERANGE;