exp.h

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/*
 * exp.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 _VDT_EXP_
#define _VDT_EXP_

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

namespace vdt{

namespace details{

  const double EXP_LIMIT = 708;

  const double PX1exp = 1.26177193074810590878E-4;
  const double PX2exp = 3.02994407707441961300E-2;
  const double PX3exp = 9.99999999999999999910E-1;
  const double QX1exp = 3.00198505138664455042E-6;
  const double QX2exp = 2.52448340349684104192E-3;
  const double QX3exp = 2.27265548208155028766E-1;
  const double QX4exp = 2.00000000000000000009E0;

  const double LOG2E = 1.4426950408889634073599; // 1/log(2)

  const float MAXLOGF = 88.72283905206835f;
  const float MINLOGF = -88.f;

  const float C1F =   0.693359375f;
  const float C2F =  -2.12194440e-4f;

  const float PX1expf = 1.9875691500E-4f;
  const float PX2expf =1.3981999507E-3f;
  const float PX3expf =8.3334519073E-3f;
  const float PX4expf =4.1665795894E-2f;
  const float PX5expf =1.6666665459E-1f;
  const float PX6expf =5.0000001201E-1f;

  const float LOG2EF = 1.44269504088896341f;

}

// Exp double precision --------------------------------------------------------


/// Exponential Function double precision
inline double fast_exp(double initial_x){

    double x = initial_x;
    double px=details::fpfloor(details::LOG2E * x +0.5);

    const int32_t n = int32_t(px);

    x -= px * 6.93145751953125E-1;
    x -= px * 1.42860682030941723212E-6;

    const double xx = x * x;

    // px = x * P(x**2).
    px = details::PX1exp;
    px *= xx;
    px += details::PX2exp;
    px *= xx;
    px += details::PX3exp;
    px *= x;

    // Evaluate Q(x**2).
    double qx = details::QX1exp;
    qx *= xx;
    qx += details::QX2exp;
    qx *= xx;
    qx += details::QX3exp;
    qx *= xx;
    qx += details::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 *= details::uint642dp(( ((uint64_t)n) +1023)<<52);

    if (initial_x > details::EXP_LIMIT)
            x = std::numeric_limits<double>::infinity();
    if (initial_x < -details::EXP_LIMIT)
            x = 0.;

    return x;

}

// Exp single precision --------------------------------------------------------

/// Exponential Function single precision
inline float fast_expf(float initial_x) {

    float x = initial_x;

    float z = details::fpfloor( details::LOG2EF * x +0.5f ); /* floor() truncates toward -infinity. */

    x -= z * details::C1F;
    x -= z * details::C2F;
    const int32_t n = int32_t ( z );

    const float x2 = x * x;

    z = x*details::PX1expf;
    z += details::PX2expf;
    z *= x;
    z += details::PX3expf;
    z *= x;
    z += details::PX4expf;
    z *= x;
    z += details::PX5expf;
    z *= x;
    z += details::PX6expf;
    z *= x2;
    z += x + 1.0f;

    /* multiply by power of 2 */
    z *=  details::uint322sp((n+0x7f)<<23);

    if (initial_x > details::MAXLOGF) z=std::numeric_limits<float>::infinity();
    if (initial_x < details::MINLOGF) z=0.f;

    return z;

  }

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

// void expv(const uint32_t size, double const * __restrict__ iarray, double* __restrict__ oarray);
// void fast_expv(const uint32_t size, double const * __restrict__ iarray, double* __restrict__ oarray);
// void expfv(const uint32_t size, float const * __restrict__ iarray, float* __restrict__ oarray);
// void fast_expfv(const uint32_t size, float const * __restrict__ iarray, float* __restrict__ oarray);

} // end namespace vdt

#endif