AOO410/main/svtools/source/dialogs/mcvmath.cxx

/**************************************************************
 * 
 * Licensed to the Apache Software Foundation (ASF) under one
 * or more contributor license agreements.  See the NOTICE file
 * distributed with this work for additional information
 * regarding copyright ownership.  The ASF licenses this file
 * to you under the Apache License, Version 2.0 (the
 * "License"); you may not use this file except in compliance
 * with the License.  You may obtain a copy of the License at
 * 
 *   http://www.apache.org/licenses/LICENSE-2.0
 * 
 * Unless required by applicable law or agreed to in writing,
 * software distributed under the License is distributed on an
 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 * KIND, either express or implied.  See the License for the
 * specific language governing permissions and limitations
 * under the License.
 * 
 *************************************************************/



// MARKER(update_precomp.py): autogen include statement, do not remove
#include "precompiled_svtools.hxx"

#include <mcvmath.hxx>

// ---------------------------------------------------------------------
// die folgenden Tabellen enthalten     sin(phi) * 2**14
// fuer phi= 360Grad*2**-32 bis 360 Grad
// def. fuer x: phi=360Grad * 2**(x-16)
//           d.h. x =  16 -> 360 Grad
//                x = -16 -> (2**-16) * 360 Grad
//         x:         -16 ... 0 ... 15
//x=    0,     1,     2,     3,     4,     5,     6,      7,
//      8,     9,    10,    11,    12,    13,    14,     15

static const short CosTab[16] =
{
	16384, 16384, 16384, 16384, 16384, 16384, 16384,  16383,
	16379, 16364, 16305, 16069, 15137, 11585,     0, -16383
};
static const short SinTab[16]=
{
		2,     3,      6,    13,    25,     50,   101,  201,
	  402,   804,   1606,  3196,  6270,  11585, 16384,    0
};

/**************************************************************************
|*
|*    ImpMultBig2()
|*
|*    Beschreibung       Multiplikation fuer FixPoint-Berechnungen
|*    Ersterstellung     SH 01.07.93
|*    Letzte Aenderung   SH 01.07.93
|*
**************************************************************************/

//  first parameter should be the bigger one

Fix ImpMultBig2( const Fix& a, const Fix& b )
{
	Fix f;
	f.x = (((b.x+FIX_A2)>>FIX_P2)*a.x+FIX_A3)>>FIX_P3;
	return f;
}

/**************************************************************************
|*
|*    ImpMultBig2()
|*
|*    Beschreibung       Multiplikation fuer FixPoint-Berechnungen
|*    Ersterstellung     SH 01.07.93
|*    Letzte Aenderung   SH 01.07.93
|*
**************************************************************************/

//  first parameter should be the bigger one

FixCpx ImpMultBig2( const FixCpx& ra, const FixCpx& rb )
{
	Fix rr = ImpMultBig2(ra.r,rb.r)-ImpMultBig2(ra.i,rb.i);
	Fix ii = ImpMultBig2(ra.r,rb.i)+ImpMultBig2(ra.i,rb.r);
	return FixCpx( rr,ii );
}

/**************************************************************************
|*
|*    ImpSqrt()
|*
|*    Beschreibung       Wurzelfunktion fuer FixPoint-Berechnungen
|*    Ersterstellung     SH 01.07.93
|*    Letzte Aenderung   SH 01.07.93
|*
**************************************************************************/

sal_uInt16 ImpSqrt( sal_uLong nRadi )
{
	register sal_uLong  inf = 1;
	register sal_uLong  sup = nRadi;
	register sal_uLong sqr;

	if ( !nRadi )
		return 0;

	while ( (inf<<1) <= sup )
	{
		sup >>= 1;
		inf <<= 1;
	}
	sqr = (sup+inf) >> 1;               // Anfangswert der Iteration

	sqr = (nRadi/sqr + sqr) >> 1;       // 2 Newton-Iterationen reichen fuer
	sqr = (nRadi/sqr + sqr) >> 1;       // +- 1 Digit

	return sal::static_int_cast< sal_uInt16 >(sqr);
}

/**************************************************************************
|*
|*    ImpExPI()
|*
|*    Beschreibung       EXPI-Funktion fuer FixPoint-Berechnungen
|*    Ersterstellung     SH 01.07.93
|*    Letzte Aenderung   SH 01.07.93
|*
**************************************************************************/

// e**(i*nPhi), Einheit nPhi: 2**16 == 360 Grad

FixCpx ImpExPI( sal_uInt16 nPhi )
{
	short i;
	FixCpx aIter(1L);                   // e**(0*i)
	FixCpx Mul;
	const char Sft=14-FIX_POST;

	for ( i = 15; i >= 0; i-- )
	{
		if ( (1L<<i) & nPhi )
		{
			Mul.r.x = CosTab[i]>>Sft;   // e**(i(phi1+phi2)) =
			Mul.i.x = SinTab[i]>>Sft;   // e**(i*phi1)) * e**(i*phi2))
			aIter  *= Mul;
		}
	}

	return aIter;
}

/**************************************************************************
|*
|*    ImpATanx2()
|*
|*    Beschreibung       ATANX2-Funktion fuer FixPoint-Berechnungen
|*    Ersterstellung     SH 01.07.93
|*    Letzte Aenderung   SH 01.07.93
|*
**************************************************************************/

// use for x*x+y*y==1 only

static sal_uInt16 ImpATanx2( const Fix& rX, const Fix& rY )
{
	sal_uInt16      phi0 = 0;           // result angel higher part
	sal_uInt16      phi = 0;            // dito lower part
	long        x = rX.x;
	long        y = rY.x;
	long        z;
	const char  Sft=14-FIX_POST;
	short       i;
	FixCpx      aTry;
	FixCpx      aInc;
	FixCpx      aIter(1L);
	sal_Bool        Small = sal_False;

	if ( (x==0) && (y==0) )
		return 0;

	if ( y < 0)
	{
		// reduce 3. to 1. quadrant (0..90 Degree)
		phi0 += 180L * 65536L / 360L;
		// turn 180 degree
		y    *= -1;
		x    *= -1;
	}

	if ( x < 0)
	{
		// 2. to 1. q.
		phi0 += 90L * 65536L / 360L;
		// turn 90 degree clockwise
		z = y;
		y = -x;
		x = z;
	}

	for ( i = 13; i >= 0; i-- )
	{
		aInc.r.x = CosTab[i]>>Sft; // e**(i(phi1+phi2)) =
		aInc.i.x = SinTab[i]>>Sft; // e**(i*phi1)) * e**(i*phi2))
		aTry     = aIter*aInc;

		if ( Small )
		{
			// is try ok
		   if ( aTry.r.x >= x )
		   {
				aIter =  aTry;
				phi   += (1<<i);
			}
		}
		else
		{
			// is try ok
			if ( aTry.i.x <= y )
			{
				aIter = aTry;
				phi  += (1<<i);

				if ( i > 11 )
					Small=sal_True;
			}
		}
	}

	return phi0+phi;
}

/**************************************************************************
|*
|*    ImpATan2()
|*
|*    Beschreibung       ATAN-Funktion fuer FixPoint-Berechnungen
|*    Ersterstellung     SH 01.07.93
|*    Letzte Aenderung   SH 01.07.93
|*
**************************************************************************/

sal_uInt16 ImpATan2( const short x, const short y )
{
	Fix rRad = ImpSqrt(sal_uLong(long(x)*x+long(y)*y));

	if ( !rRad.x )
		return 0;
	Fix fx = x;
	fx.DivBig( rRad );            // Normiere auf Einheitskreis
	Fix fy = y;
	fy.DivBig( rRad );

	return ImpATanx2( fx, fy );
}

/**************************************************************************
|*
|*    ImpCartToPolar()
|*
|*    Beschreibung       Koordinaaten-Wandlung
|*    Ersterstellung     SH 01.07.93
|*    Letzte Aenderung   SH 01.07.93
|*
**************************************************************************/

void ImpCartToPolar( const short x, const short y, Fix& rRad, sal_uInt16& rPhi )
{
	rRad = Fix( ImpSqrt( sal_uLong( long(x)*x+long(y)*y ) ) );

	if ( !rRad.x )
		rPhi=0;
	else
	{
		// Normiere auf Einheitskreis
		Fix fx = x;
		fx.DivBig(rRad);
		Fix fy = y;
		fy.DivBig(rRad);
		rPhi = ImpATanx2(fx, fy);
	}
}

/**************************************************************************
|*
|*    ImpPolarToCart()
|*
|*    Beschreibung       Koordinaaten-Wandlung
|*    Ersterstellung     SH 01.07.93
|*    Letzte Aenderung   SH 01.07.93
|*
**************************************************************************/

void ImpPolarToCart( const Fix& rR, const sal_uInt16 Phi, short& rX, short& rY )
{
	FixCpx fc = ImpExPI( Phi );  // calculate sin() & cos()
	fc.GetReal().MultBig( rR );
	rX = sal::static_int_cast< short >(long( fc.GetReal() ));
	fc.GetImag().MultBig( rR );
	rY = sal::static_int_cast< short >(long( fc.GetImag() ));
}