log.h

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/*
 * log.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 LOG_H_
#define LOG_H_

#include "vdtcore_common.h"
#include <limits>

namespace vdt{

// local namespace for the constants/functions which are necessary only here
namespace details{

const double LOG_UPPER_LIMIT = 1e307;
const double LOG_LOWER_LIMIT = 0;

const double SQRTH = 0.70710678118654752440;

inline double get_log_px(const double x){
   const double PX1log = 1.01875663804580931796E-4;
   const double PX2log = 4.97494994976747001425E-1;
   const double PX3log = 4.70579119878881725854E0;
   const double PX4log = 1.44989225341610930846E1;
   const double PX5log = 1.79368678507819816313E1;
   const double PX6log = 7.70838733755885391666E0;

   double px = PX1log;
   px *= x;
   px += PX2log;
   px *= x;
   px += PX3log;
   px *= x;
   px += PX4log;
   px *= x;
   px += PX5log;
   px *= x;
   px += PX6log;
   return px;

}

inline double get_log_qx(const double x){
   const double QX1log = 1.12873587189167450590E1;
   const double QX2log = 4.52279145837532221105E1;
   const double QX3log = 8.29875266912776603211E1;
   const double QX4log = 7.11544750618563894466E1;
   const double QX5log = 2.31251620126765340583E1;

   double qx = x;
   qx += QX1log;
   qx *=x;
   qx += QX2log;
   qx *=x;
   qx += QX3log;
   qx *=x;
   qx += QX4log;
   qx *=x;
   qx += QX5log;
   return qx;
}

}

// Log double precision --------------------------------------------------------
inline double fast_log(double x){

   const double original_x = x;

   /* separate mantissa from exponent */
   double fe;
   x = details::getMantExponent(x,fe);

   // blending
   x > details::SQRTH? fe+=1. : x+=x ;
   x -= 1.0;

   /* rational form */
   double px =  details::get_log_px(x);

   //for the final formula
   const double x2 = x*x;
   px *= x;
   px *= x2;

   const double qx = details::get_log_qx(x);

   double res = px / qx ;

   res -= fe * 2.121944400546905827679e-4;
   res -= 0.5 * x2  ;

   res = x + res;
   res += fe * 0.693359375;

   if (original_x > details::LOG_UPPER_LIMIT)
      res = std::numeric_limits<double>::infinity();
   if (original_x < details::LOG_LOWER_LIMIT) // THIS IS NAN!
      res =  - std::numeric_limits<double>::quiet_NaN();

   return res;

}

// Log single precision --------------------------------------------------------



namespace details{

const float LOGF_UPPER_LIMIT = MAXNUMF;
const float LOGF_LOWER_LIMIT = 0;

const float PX1logf = 7.0376836292E-2f;
const float PX2logf   = -1.1514610310E-1f;
const float PX3logf   = 1.1676998740E-1f;
const float PX4logf   = -1.2420140846E-1f;
const float PX5logf   = 1.4249322787E-1f;
const float PX6logf   = -1.6668057665E-1f;
const float PX7logf   = 2.0000714765E-1f;
const float PX8logf   = -2.4999993993E-1f;
const float PX9logf   = 3.3333331174E-1f;

inline float get_log_poly(const float x){
   float y = x*PX1logf;
   y += PX2logf;
   y *= x;
   y += PX3logf;
   y *= x;
   y += PX4logf;
   y *= x;
   y += PX5logf;
   y *= x;
   y += PX6logf;
   y *= x;
   y += PX7logf;
   y *= x;
   y += PX8logf;
   y *= x;
   y += PX9logf;
   return y;
}

const float SQRTHF = 0.707106781186547524f;

}

// Log single precision --------------------------------------------------------
inline float fast_logf( float x ) {

   const float original_x = x;

   float fe;
   x = details::getMantExponentf( x, fe);

   x > details::SQRTHF? fe+=1.f : x+=x ;
   x -= 1.0f;

   const float x2 = x*x;

   float res = details::get_log_poly(x);
   res *= x2*x;

   res += -2.12194440e-4f * fe;
   res +=  -0.5f * x2;

   res= x + res;

   res += 0.693359375f * fe;

   if (original_x > details::LOGF_UPPER_LIMIT)
      res = std::numeric_limits<float>::infinity();
   if (original_x < details::LOGF_LOWER_LIMIT)
      res = -std::numeric_limits<float>::quiet_NaN();

   return res;
}


//------------------------------------------------------------------------------

// void logv(const uint32_t size, double const * __restrict__ iarray, double* __restrict__ oarray);
// void fast_logv(const uint32_t size, double const * __restrict__ iarray, double* __restrict__ oarray);
// void logfv(const uint32_t size, float const * __restrict__ iarray, float* __restrict__ oarray);
// void fast_logfv(const uint32_t size, float const * __restrict__ iarray, float* __restrict__ oarray);

} //vdt namespace

#endif /* LOG_H_ */