/**
 * @(#) $RCSfile: TrigonometryTable.as,v $ $Revision: 1.5 $ $Date: 2003/02/13 17:59:03 $
 *
 * Copyright 2003 Orgdot AS. All Rights Reserved.
 * http://dev.swfit.com
 *
 * 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.
 */

/**
 * This will generate a table of trigonometric values for Flash4 and place those
 * values into level 0 of the movie.
 *
 * @author      Olaf Havnes
 * @version     $Revision: 1.5 $ $Date: 2003/02/13 17:59:03 $
 * @since       SWFIT1.0
 */


/**
 * We split the unit circle in NUM_DEG degrees (and store that value).
 */

/:DEG_MULT = 4;
/:NUM_DEG = 360 * /:DEG_MULT;
/:MATH_PI = 3.141592654;

s_0 = 0;
c_0 = 1;


// s_1 = Math.sin (( MATH_PI * 2) / NUM_DEG);
// c_1 = Math.cos (( MATH_PI * 2) / NUM_DEG);
s_1 = 0.00436331;
c_1 = 0.99999;

s = s_1 * 2;
i = 0;

// Store the values in _level0.
/:SIN_0 = s_0;
/:COS_0 = c_0;

/:SIN_1 = s_1;
/:COS_1 = c_1;


/**
 * We iterate over the double angle formulas - see EOF for notes.
 */

i = 2;
while (i < /:NUM_DEG)
{
    s_2 = s_0 + s * c_1;
    c_2 = c_0 - s * s_1;

    s_0 = s_1;
    c_0 = c_1;

    s_1 = s_2;
    c_1 = c_2;

    // Store the values in _level0.
    set ( "/:SIN_" add i, s_2 );
    set ( "/:COS_" add i, c_2 );

    i++;
}

/**
 * Create an inverse table for the first quadrant - saturated with values, some 
 * will overwrite previous values, but the important thing is to fill all steps.
 * We're slightly off on this one, so don't navigate a battle ship by this code.
 */
 
i = 0;
while (i < /:NUM_DEG / /:DEG_MULT)
{
    sin = eval ("/:SIN_" add i);
    cos = eval ("/:COS_" add i);
    s00 = int (100.0 * sin);
    c00 = int (100.0 * cos);
    angle = i / DEG_MULT;

    set ("/:ASIN_" add s00, angle);
    set ("/:ACOS_" add c00, angle);

    i++;
}


/**
 * FRACTIONAL TRIGONOMETRY WITH nSHIFTEES:
 * 
 * This algorithm is adapted from a java applet I made - in flash4 there is of course 
 * no point in using bitshifts...
 *
 * I will define 1 nShiftee is as asin (2^(-n)) ~= 2^(-n) Radians. This relation 
 * will of course be more correct the larger n is, as sin(x)/x approaches 1 when
 * x approaches 0.
 * 
 * We have that:
 * 
 * sin (A+B) = sin (A) * cos (B) + cos (A) * sin (B)
 * cos (A+B) = cos (A) * cos (B) - sin (A) * sin (B)
 * 
 * sin (2*B) = 2 * sin (B) * cos (B)
 * cos (2*B) = cos^2 (B) - sin^2 (B)
 * 
 * ==>
 * 
 * sin (A+2*B) = sin (A) * cos (2*B) + cos (A) * sin (2*B) = sin (A) * ( cos^2 (B) - sin^2 (B) ) + cos (A) * 2 * sin (B) * cos (B)
 * cos (A+2*B) = cos (A) * cos (2*B) - sin (A) * sin (2*B) = cos (A) * ( cos^2 (B) - sin^2 (B) ) - sin (A) * 2 * sin (B) * cos (B)
 * 
 * ==>
 * 
 * sin (A+2*B) = sin (A) * ( 1 - 2 * sin^2 (B) ) + cos (A) * 2 * sin (B) * cos (B)
 * cos (A+2*B) = cos (A) * ( 1 - 2 * sin^2 (B) ) - sin (A) * 2 * sin (B) * cos (B)
 * 
 * ==>
 * 
 * sin (A+2*B) = sin (A) + 2 * sin (B) * cos (A+B)
 * cos (A+2*B) = cos (A) - 2 * sin (B) * sin (A+B)
 * 
 * 
 * We introduce the nShiftee into the equation:
 * If B = 1 nShiftee = asin (2^(-n)), then sin (B) = 2^(-n)
 * 
 * A0 = A + 0*B
 * A1 = A + 1*B
 * A2 = A + 2*B
 * ...
 * Ai = A + i*B
 * 
 * 
 * in general:
 * 
 * sin (Ai) = sin (Ai-2) + cos (Ai-1) * 2^(1-n)
 * cos (Ai) = cos (Ai-2) - sin (Ai-1) * 2^(1-n)
 * 
 **/