/************************************************************** * * 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 // --------------------------------------------------------------------- // 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<>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< 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() )); }