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+/*************************************************************************
+ *
+ * $RCSfile: mcvmath.cxx,v $
+ *
+ * $Revision: 1.1.1.1 $
+ *
+ * last change: $Author: hr $ $Date: 2000-09-18 16:58:58 $
+ *
+ * The Contents of this file are made available subject to the terms of
+ * either of the following licenses
+ *
+ * - GNU Lesser General Public License Version 2.1
+ * - Sun Industry Standards Source License Version 1.1
+ *
+ * Sun Microsystems Inc., October, 2000
+ *
+ * GNU Lesser General Public License Version 2.1
+ * =============================================
+ * Copyright 2000 by Sun Microsystems, Inc.
+ * 901 San Antonio Road, Palo Alto, CA 94303, USA
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License version 2.1, as published by the Free Software Foundation.
+ *
+ * This library 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
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston,
+ * MA 02111-1307 USA
+ *
+ *
+ * Sun Industry Standards Source License Version 1.1
+ * =================================================
+ * The contents of this file are subject to the Sun Industry Standards
+ * Source License Version 1.1 (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.openoffice.org/license.html.
+ *
+ * Software provided under this License is provided on an "AS IS" basis,
+ * WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING,
+ * WITHOUT LIMITATION, WARRANTIES THAT THE SOFTWARE IS FREE OF DEFECTS,
+ * MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE, OR NON-INFRINGING.
+ * See the License for the specific provisions governing your rights and
+ * obligations concerning the Software.
+ *
+ * The Initial Developer of the Original Code is: Sun Microsystems, Inc.
+ *
+ * Copyright: 2000 by Sun Microsystems, Inc.
+ *
+ * All Rights Reserved.
+ *
+ * Contributor(s): _______________________________________
+ *
+ *
+ ************************************************************************/
+
+#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
+|*
+**************************************************************************/
+
+USHORT ImpSqrt( ULONG nRadi )
+{
+ register ULONG inf = 1;
+ register ULONG sup = nRadi;
+ register USHORT 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 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( USHORT 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 USHORT ImpATanx2( const Fix& rX, const Fix& rY )
+{
+ USHORT phi0 = 0; // result angel higher part
+ USHORT 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);
+ BOOL Small = 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=TRUE;
+ }
+ }
+ }
+
+ return phi0+phi;
+}
+
+/**************************************************************************
+|*
+|* ImpATan2()
+|*
+|* Beschreibung ATAN-Funktion fuer FixPoint-Berechnungen
+|* Ersterstellung SH 01.07.93
+|* Letzte Aenderung SH 01.07.93
+|*
+**************************************************************************/
+
+USHORT ImpATan2( const short x, const short y )
+{
+ Fix rRad = ImpSqrt(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, USHORT& rPhi )
+{
+ rRad = Fix( ImpSqrt( 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 USHORT Phi, short& rX, short& rY )
+{
+ FixCpx fc = ImpExPI( Phi ); // calculate sin() & cos()
+ fc.GetReal().MultBig( rR );
+ rX = long( fc.GetReal() );
+ fc.GetImag().MultBig( rR );
+ rY = long( fc.GetImag() );
+}
+
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