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/*************************************************************************
*
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* Copyright 2000, 2010 Oracle and/or its affiliates.
*
* OpenOffice.org - a multi-platform office productivity suite
*
* This file is part of OpenOffice.org.
*
* OpenOffice.org is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License version 3
* only, as published by the Free Software Foundation.
*
* OpenOffice.org 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 version 3 for more details
* (a copy is included in the LICENSE file that accompanied this code).
*
* You should have received a copy of the GNU Lesser General Public License
* version 3 along with OpenOffice.org. If not, see
* <http://www.openoffice.org/license.html>
* for a copy of the LGPLv3 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
|*
**************************************************************************/
USHORT ImpSqrt( ULONG nRadi )
{
register ULONG inf = 1;
register ULONG sup = nRadi;
register 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< USHORT >(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 = sal::static_int_cast< short >(long( fc.GetReal() ));
fc.GetImag().MultBig( rR );
rY = sal::static_int_cast< short >(long( fc.GetImag() ));
}
|
