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/*
* atan.h
* The basic idea is to exploit Pade polynomials.
* A lot of ideas were inspired by the cephes math library (by Stephen L. Moshier
* moshier@na-net.ornl.gov) as well as actual code.
* The Cephes library can be found here: http://www.netlib.org/cephes/
*
* Created on: Jun 23, 2012
* Author: Danilo Piparo, Thomas Hauth, Vincenzo Innocente
*/
/*
* VDT is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser Public License as published by
* the Free Software Foundation, either version 3 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 Lesser Public License for more details.
*
* You should have received a copy of the GNU Lesser Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef ATAN_H_
#define ATAN_H_
#include "vdtcore_common.h"
namespace vdt{
namespace details{
const double T3PO8 = 2.41421356237309504880;
const double MOREBITSO2 = MOREBITS * 0.5;
inline double get_atan_px(const double x2){
const double PX1atan = -8.750608600031904122785E-1;
const double PX2atan = -1.615753718733365076637E1;
const double PX3atan = -7.500855792314704667340E1;
const double PX4atan = -1.228866684490136173410E2;
const double PX5atan = -6.485021904942025371773E1;
double px = PX1atan;
px *= x2;
px += PX2atan;
px *= x2;
px += PX3atan;
px *= x2;
px += PX4atan;
px *= x2;
px += PX5atan;
return px;
}
inline double get_atan_qx(const double x2){
const double QX1atan = 2.485846490142306297962E1;
const double QX2atan = 1.650270098316988542046E2;
const double QX3atan = 4.328810604912902668951E2;
const double QX4atan = 4.853903996359136964868E2;
const double QX5atan = 1.945506571482613964425E2;
double qx=x2;
qx += QX1atan;
qx *=x2;
qx += QX2atan;
qx *=x2;
qx += QX3atan;
qx *=x2;
qx += QX4atan;
qx *=x2;
qx += QX5atan;
return qx;
}
}
/// Fast Atan implementation double precision
inline double fast_atan(double x){
/* make argument positive and save the sign */
const uint64_t sign_mask = details::getSignMask(x);
x=std::fabs(x);
/* range reduction */
const double originalx=x;
double y = details::PIO4;
double factor = details::MOREBITSO2;
x = (x-1.0) / (x+1.0);
if( originalx > details::T3PO8 ) {
y = details::PIO2;
factor = details::MOREBITS;
x = -1.0 / originalx ;
}
if ( originalx <= 0.66 ) {
y = 0.;
factor = 0.;
x = originalx;
}
const double x2 = x * x;
const double px = details::get_atan_px(x2);
const double qx = details::get_atan_qx(x2);
//double res = y +x * x2 * px / qx + x +factor;
const double poq=px / qx;
double res = x * x2 * poq + x;
res+=y;
res+=factor;
return details::dpORuint64(res,sign_mask);
}
//------------------------------------------------------------------------------
/// Fast Atan implementation single precision
inline float fast_atanf( float xx ) {
const uint32_t sign_mask = details::getSignMask(xx);
float x= std::fabs(xx);
const float x0=x;
float y=0.0f;
/* range reduction */
if( x0 > 0.4142135623730950f ){ // * tan pi/8
x = (x0-1.0f)/(x0+1.0f);
y = details::PIO4F;
}
if( x0 > 2.414213562373095f ){ // tan 3pi/8
x = -( 1.0f/x0 );
y = details::PIO2F;
}
const float x2 = x * x;
y +=
((( 8.05374449538e-2f * x2
- 1.38776856032E-1f) * x2
+ 1.99777106478E-1f) * x2
- 3.33329491539E-1f) * x2 * x
+ x;
return details::spORuint32(y,sign_mask);
}
//------------------------------------------------------------------------------
// Vector signatures
void atanv(const uint32_t size, double const * __restrict__ iarray, double* __restrict__ oarray);
void fast_atanv(const uint32_t size, double const * __restrict__ iarray, double* __restrict__ oarray);
void atanfv(const uint32_t size, float const * __restrict__ iarray, float* __restrict__ oarray);
void fast_atanfv(const uint32_t size, float const * __restrict__ iarray, float* __restrict__ oarray);
}// end of vdt
#endif // end of atan
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