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 //
 // ********************************************************************
 // * License and Disclaimer                                           *
 // *                                                                  *
 // * The  Geant4 software  is  copyright of the Copyright Holders  of *
 // * the Geant4 Collaboration.  It is provided  under  the terms  and *
 // * conditions of the Geant4 Software License,  included in the file *
 // * LICENSE and available at  http://cern.ch/geant4/license .  These *
 // * include a list of copyright holders.                             *
 // *                                                                  *
 // * Neither the authors of this software system, nor their employing *
 // * institutes,nor the agencies providing financial support for this *
 // * work  make  any representation or  warranty, express or implied, *
 // * regarding  this  software system or assume any liability for its *
 // * use.  Please see the license in the file  LICENSE  and URL above *
 // * for the full disclaimer and the limitation of liability.         *
 // *                                                                  *
 // * This  code  implementation is the result of  the  scientific and *
 // * technical work of the GEANT4 collaboration.                      *
 // * By using,  copying,  modifying or  distributing the software (or *
 // * any work based  on the software)  you  agree  to acknowledge its *
 // * use  in  resulting  scientific  publications,  and indicate your *
 // * acceptance of all terms of the Geant4 Software license.          *
 // ********************************************************************
 //
 // G4Log
 //
 // Class description:
 //
 // 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/
 // Code and algorithms for G4Exp have been extracted and adapted for Geant4
 // from the original implementation in the VDT mathematical library
 // (https://svnweb.cern.ch/trac/vdt), version 0.3.7.
 
 // Original implementation 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 G4Log_hh
 #define G4Log_hh 1
 
 #ifdef WIN32
 
 #  define G4Log std::log
 
 #else
 
 #  include "G4Types.hh"
 #  include "G4IEEE754.hh"
 #  include <cstdint>
 #  include <limits>
 
 // local namespace for the constants/functions which are necessary only here
 //
 namespace G4LogConsts
 {
   const G4double LOG_UPPER_LIMIT = 1e307;
   const G4double LOG_LOWER_LIMIT = 0;
 
   const G4double SQRTH  = 0.70710678118654752440;
   const G4float MAXNUMF = 3.4028234663852885981170418348451692544e38f;
 
   inline G4double get_log_px(const G4double x)
   {
     const G4double PX1log = 1.01875663804580931796E-4;
     const G4double PX2log = 4.97494994976747001425E-1;
     const G4double PX3log = 4.70579119878881725854E0;
     const G4double PX4log = 1.44989225341610930846E1;
     const G4double PX5log = 1.79368678507819816313E1;
     const G4double PX6log = 7.70838733755885391666E0;
 
     G4double 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 G4double get_log_qx(const G4double x)
   {
     const G4double QX1log = 1.12873587189167450590E1;
     const G4double QX2log = 4.52279145837532221105E1;
     const G4double QX3log = 8.29875266912776603211E1;
     const G4double QX4log = 7.11544750618563894466E1;
     const G4double QX5log = 2.31251620126765340583E1;
 
     G4double qx = x;
     qx += QX1log;
     qx *= x;
     qx += QX2log;
     qx *= x;
     qx += QX3log;
     qx *= x;
     qx += QX4log;
     qx *= x;
     qx += QX5log;
     return qx;
   }
 
   //----------------------------------------------------------------------------
   /// Like frexp but vectorising and the exponent is a double.
   inline G4double getMantExponent(const G4double x, G4double& fe)
   {
     uint64_t n = G4IEEE754::dp2uint64(x);
 
     // Shift to the right up to the beginning of the exponent.
     // Then with a mask, cut off the sign bit
     uint64_t le = (n >> 52);
 
     // chop the head of the number: an int contains more than 11 bits (32)
     int32_t e =
       (int32_t)le;  // This is important since sums on uint64_t do not vectorise
     fe = e - 1023;
 
     // This puts to 11 zeroes the exponent
     n &= 0x800FFFFFFFFFFFFFULL;
     // build a mask which is 0.5, i.e. an exponent equal to 1022
     // which means *2, see the above +1.
     const uint64_t p05 = 0x3FE0000000000000ULL;  // dp2uint64(0.5);
     n |= p05;
 
     return G4IEEE754::uint642dp(n);
   }
 
   //----------------------------------------------------------------------------
   /// Like frexp but vectorising and the exponent is a float.
   inline G4float getMantExponentf(const G4float x, G4float& fe)
   {
     uint32_t n = G4IEEE754::sp2uint32(x);
     int32_t e  = (n >> 23) - 127;
     fe         = e;
 
     // fractional part
     const uint32_t p05f = 0x3f000000;  // //sp2uint32(0.5);
     n &= 0x807fffff;                   // ~0x7f800000;
     n |= p05f;
 
     return G4IEEE754::uint322sp(n);
   }
 }  // namespace G4LogConsts
 
 // Log double precision --------------------------------------------------------
 
 inline G4double G4Log(G4double x)
 {
   const G4double original_x = x;
 
   /* separate mantissa from exponent */
   G4double fe;
   x = G4LogConsts::getMantExponent(x, fe);
 
   // blending
   x > G4LogConsts::SQRTH ? fe += 1. : x += x;
   x -= 1.0;
 
   /* rational form */
   G4double px = G4LogConsts::get_log_px(x);
 
   // for the final formula
   const G4double x2 = x * x;
   px *= x;
   px *= x2;
 
   const G4double qx = G4LogConsts::get_log_qx(x);
 
   G4double res = px / qx;
 
   res -= fe * 2.121944400546905827679e-4;
   res -= 0.5 * x2;
 
   res = x + res;
   res += fe * 0.693359375;
 
   if(original_x > G4LogConsts::LOG_UPPER_LIMIT)
     res = std::numeric_limits<G4double>::infinity();
   if(original_x < G4LogConsts::LOG_LOWER_LIMIT)  // THIS IS NAN!
     res = -std::numeric_limits<G4double>::quiet_NaN();
 
   return res;
 }
 
 // Log single precision --------------------------------------------------------
 
 namespace G4LogConsts
 {
   const G4float LOGF_UPPER_LIMIT = MAXNUMF;
   const G4float LOGF_LOWER_LIMIT = 0;
 
   const G4float PX1logf = 7.0376836292E-2f;
   const G4float PX2logf = -1.1514610310E-1f;
   const G4float PX3logf = 1.1676998740E-1f;
   const G4float PX4logf = -1.2420140846E-1f;
   const G4float PX5logf = 1.4249322787E-1f;
   const G4float PX6logf = -1.6668057665E-1f;
   const G4float PX7logf = 2.0000714765E-1f;
   const G4float PX8logf = -2.4999993993E-1f;
   const G4float PX9logf = 3.3333331174E-1f;
 
   inline G4float get_log_poly(const G4float x)
   {
     G4float 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 G4float SQRTHF = 0.707106781186547524f;
 }  // namespace G4LogConsts
 
 // Log single precision --------------------------------------------------------
 
 inline G4float G4Logf(G4float x)
 {
   const G4float original_x = x;
 
   G4float fe;
   x = G4LogConsts::getMantExponentf(x, fe);
 
   x > G4LogConsts::SQRTHF ? fe += 1.f : x += x;
   x -= 1.0f;
 
   const G4float x2 = x * x;
 
   G4float res = G4LogConsts::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 > G4LogConsts::LOGF_UPPER_LIMIT)
     res = std::numeric_limits<G4float>::infinity();
   if(original_x < G4LogConsts::LOGF_LOWER_LIMIT)
     res = -std::numeric_limits<G4float>::quiet_NaN();
 
   return res;
 }
 
 #endif /* WIN32 */
 
 #endif /* LOG_H_ */

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