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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.          *
 // ********************************************************************
 //
 // G4Exp
 //
 // 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
 // Authors: 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 G4Exp_hh
 #define G4Exp_hh 1
 
 #ifdef WIN32
 
 #  define G4Exp std::exp
 
 #else
 
 #  include "G4Types.hh"
 #  include "G4IEEE754.hh"
 #  include <cstdint>
 #  include <limits>
 
 namespace G4ExpConsts
 {
   const G4double EXP_LIMIT = 708;
 
   const G4double PX1exp = 1.26177193074810590878E-4;
   const G4double PX2exp = 3.02994407707441961300E-2;
   const G4double PX3exp = 9.99999999999999999910E-1;
   const G4double QX1exp = 3.00198505138664455042E-6;
   const G4double QX2exp = 2.52448340349684104192E-3;
   const G4double QX3exp = 2.27265548208155028766E-1;
   const G4double QX4exp = 2.00000000000000000009E0;
 
   const G4double LOG2E = 1.4426950408889634073599;  // 1/log(2)
 
   const G4float MAXLOGF = 88.72283905206835f;
   const G4float MINLOGF = -88.f;
 
   const G4float C1F = 0.693359375f;
   const G4float C2F = -2.12194440e-4f;
 
   const G4float PX1expf = 1.9875691500E-4f;
   const G4float PX2expf = 1.3981999507E-3f;
   const G4float PX3expf = 8.3334519073E-3f;
   const G4float PX4expf = 4.1665795894E-2f;
   const G4float PX5expf = 1.6666665459E-1f;
   const G4float PX6expf = 5.0000001201E-1f;
 
   const G4float LOG2EF = 1.44269504088896341f;
 
   //----------------------------------------------------------------------------
   /**
    * A vectorisable floor implementation, not only triggered by fast-math.
    * These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
    * compliant for argument -0.0
    **/
   inline G4double fpfloor(const G4double x)
   {
     // no problem since exp is defined between -708 and 708. Int is enough for
     // it!
     int32_t ret = int32_t(x);
     ret -= (G4IEEE754::sp2uint32(x) >> 31);
     return ret;
   }
 
   //----------------------------------------------------------------------------
   /**
    * A vectorisable floor implementation, not only triggered by fast-math.
    * These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
    * compliant for argument -0.0
    **/
   inline G4float fpfloor(const G4float x)
   {
     int32_t ret = int32_t(x);
     ret -= (G4IEEE754::sp2uint32(x) >> 31);
     return ret;
   }
 }  // namespace G4ExpConsts
 
 // Exp double precision --------------------------------------------------------
 
 /// Exponential Function double precision
 inline G4double G4Exp(G4double initial_x)
 {
   G4double x  = initial_x;
   G4double px = G4ExpConsts::fpfloor(G4ExpConsts::LOG2E * x + 0.5);
 
   const int32_t n = int32_t(px);
 
   x -= px * 6.93145751953125E-1;
   x -= px * 1.42860682030941723212E-6;
 
   const G4double xx = x * x;
 
   // px = x * P(x**2).
   px = G4ExpConsts::PX1exp;
   px *= xx;
   px += G4ExpConsts::PX2exp;
   px *= xx;
   px += G4ExpConsts::PX3exp;
   px *= x;
 
   // Evaluate Q(x**2).
   G4double qx = G4ExpConsts::QX1exp;
   qx *= xx;
   qx += G4ExpConsts::QX2exp;
   qx *= xx;
   qx += G4ExpConsts::QX3exp;
   qx *= xx;
   qx += G4ExpConsts::QX4exp;
 
   // e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
   x = px / (qx - px);
   x = 1.0 + 2.0 * x;
 
   // Build 2^n in double.
   x *= G4IEEE754::uint642dp((((uint64_t) n) + 1023) << 52);
 
   if(initial_x > G4ExpConsts::EXP_LIMIT)
     x = std::numeric_limits<G4double>::infinity();
   if(initial_x < -G4ExpConsts::EXP_LIMIT)
     x = 0.;
 
   return x;
 }
 
 // Exp single precision --------------------------------------------------------
 
 /// Exponential Function single precision
 inline G4float G4Expf(G4float initial_x)
 {
   G4float x = initial_x;
 
   G4float z =
     G4ExpConsts::fpfloor(G4ExpConsts::LOG2EF * x +
                          0.5f); /* std::floor() truncates toward -infinity. */
 
   x -= z * G4ExpConsts::C1F;
   x -= z * G4ExpConsts::C2F;
   const int32_t n = int32_t(z);
 
   const G4float x2 = x * x;
 
   z = x * G4ExpConsts::PX1expf;
   z += G4ExpConsts::PX2expf;
   z *= x;
   z += G4ExpConsts::PX3expf;
   z *= x;
   z += G4ExpConsts::PX4expf;
   z *= x;
   z += G4ExpConsts::PX5expf;
   z *= x;
   z += G4ExpConsts::PX6expf;
   z *= x2;
   z += x + 1.0f;
 
   /* multiply by power of 2 */
   z *= G4IEEE754::uint322sp((n + 0x7f) << 23);
 
   if(initial_x > G4ExpConsts::MAXLOGF)
     z = std::numeric_limits<G4float>::infinity();
   if(initial_x < G4ExpConsts::MINLOGF)
     z = 0.f;
 
   return z;
 }
 
 #endif /* WIN32 */
 
 #endif

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