//
// ********************************************************************
// * 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 *
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// * work make any representation or warranty, express or implied, *
// * regarding this software system or assume any liability for its *
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// * *
// * This code implementation is the result of the scientific and *
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// ********************************************************************
//
// 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 .
*/
// --------------------------------------------------------------------
#ifndef G4Log_hh
#define G4Log_hh 1
#ifdef WIN32
# define G4Log std::log
#else
# include "G4Types.hh"
# include "G4IEEE754.hh"
# include
# include
// 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::infinity();
if(original_x < G4LogConsts::LOG_LOWER_LIMIT) // THIS IS NAN!
res = -std::numeric_limits::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::infinity();
if(original_x < G4LogConsts::LOGF_LOWER_LIMIT)
res = -std::numeric_limits::quiet_NaN();
return res;
}
#endif /* WIN32 */
#endif /* LOG_H_ */