ComputeFunctions.cxx

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/*
 * Project: RooFit
 * Authors:
 *   Emmanouil Michalainas, CERN, Summer 2019
 *
 * Copyright (c) 2021, CERN
 *
 * Redistribution and use in source and binary forms,
 * with or without modification, are permitted according to the terms
 * listed in LICENSE (http://roofit.sourceforge.net/license.txt)
 */
 
/**
\file ComputeFunctions.cxx
\ingroup Roobatchcompute
 
This file contains vectorizable computation functions for PDFs and other Roofit objects.
The same source file can also be compiled with nvcc. All functions have a single `Batches`
object as an argument passed by value, which contains all the information necessary for the
computation. In case of cuda computations, the loops have a step (stride) the size of the grid
which allows for reusing the same code as the cpu implementations, easier debugging and in terms
of performance, maximum memory coalescing. For more details, see
https://developer.nvidia.com/blog/cuda-pro-tip-write-flexible-kernels-grid-stride-loops/
**/
 
#include "RooBatchCompute.h"
#include "RooVDTHeaders.h"
#include "Batches.h"
 
#include <TMath.h>
 
#include <complex>
 
#include "faddeeva_impl.h"
 
#ifdef __CUDACC__
#define BEGIN blockDim.x *blockIdx.x + threadIdx.x
#define STEP blockDim.x *gridDim.x
#else
#define BEGIN 0
#define STEP 1
#endif // #ifdef __CUDACC__
 
namespace RooBatchCompute {
namespace RF_ARCH {
 
__rooglobal__ void computeAddPdf(BatchesHandle batches)
{
   const int nPdfs = batches.getNExtraArgs();
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = batches.extraArg(0) * batches[0][i];
   for (int pdf = 1; pdf < nPdfs; pdf++)
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
         batches._output[i] += batches.extraArg(pdf) * batches[pdf][i];
}
 
__rooglobal__ void computeArgusBG(BatchesHandle batches)
{
   Batch m = batches[0], m0 = batches[1], c = batches[2], p = batches[3];
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double t = m[i] / m0[i];
      const double u = 1 - t * t;
      batches._output[i] = c[i] * u + p[i] * fast_log(u);
   }
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      if (m[i] >= m0[i])
         batches._output[i] = 0.0;
      else
         batches._output[i] = m[i] * fast_exp(batches._output[i]);
   }
}
 
__rooglobal__ void computeBernstein(BatchesHandle batches)
{
   const int nCoef = batches.getNExtraArgs() - 2;
   const int degree = nCoef - 1;
   const double xmin = batches.extraArg(nCoef);
   const double xmax = batches.extraArg(nCoef + 1);
   Batch xData = batches[0];
 
   // apply binomial coefficient in-place so we don't have to allocate new memory
   double binomial = 1.0;
   for (int k = 0; k < nCoef; k++) {
      batches.setExtraArg(k, batches.extraArg(k) * binomial);
      binomial = (binomial * (degree - k)) / (k + 1);
   }
 
   if (STEP == 1) {
      double X[bufferSize], _1_X[bufferSize], powX[bufferSize], pow_1_X[bufferSize];
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
         powX[i] = pow_1_X[i] = 1.0;
         X[i] = (xData[i] - xmin) / (xmax - xmin);
         _1_X[i] = 1 - X[i];
         batches._output[i] = 0.0;
      }
 
      // raising 1-x to the power of degree
      for (int k = 2; k <= degree; k += 2)
         for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
            pow_1_X[i] *= _1_X[i] * _1_X[i];
 
      if (degree % 2 == 1)
         for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
            pow_1_X[i] *= _1_X[i];
 
      // inverting 1-x ---> 1/(1-x)
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
         _1_X[i] = 1 / _1_X[i];
 
      for (int k = 0; k < nCoef; k++)
         for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
            batches._output[i] += batches.extraArg(k) * powX[i] * pow_1_X[i];
 
            // calculating next power for x and 1-x
            powX[i] *= X[i];
            pow_1_X[i] *= _1_X[i];
         }
   } else
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
         batches._output[i] = 0.0;
         const double X = (xData[i] - xmin) / (xmax - xmin);
         double powX = 1.0, pow_1_X = 1.0;
         for (int k = 1; k <= degree; k++)
            pow_1_X *= 1 - X;
         const double _1_X = 1 / (1 - X);
         for (int k = 0; k < nCoef; k++) {
            batches._output[i] += batches.extraArg(k) * powX * pow_1_X;
            powX *= X;
            pow_1_X *= _1_X;
         }
      }
 
   // reset extraArgs values so we don't mutate the Batches object
   binomial = 1.0;
   for (int k = 0; k < nCoef; k++) {
      batches.setExtraArg(k, batches.extraArg(k) / binomial);
      binomial = (binomial * (degree - k)) / (k + 1);
   }
}
 
__rooglobal__ void computeBifurGauss(BatchesHandle batches)
{
   Batch X = batches[0], M = batches[1], SL = batches[2], SR = batches[3];
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      double arg = X[i] - M[i];
      if (arg < 0)
         arg /= SL[i];
      else
         arg /= SR[i];
      batches._output[i] = fast_exp(-0.5 * arg * arg);
   }
}
 
__rooglobal__ void computeBreitWigner(BatchesHandle batches)
{
   Batch X = batches[0], M = batches[1], W = batches[2];
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double arg = X[i] - M[i];
      batches._output[i] = 1 / (arg * arg + 0.25 * W[i] * W[i]);
   }
}
 
__rooglobal__ void computeBukin(BatchesHandle batches)
{
   Batch X = batches[0], XP = batches[1], SP = batches[2], XI = batches[3], R1 = batches[4], R2 = batches[5];
   const double r3 = log(2.0);
   const double r6 = exp(-6.0);
   const double r7 = 2 * sqrt(2 * log(2.0));
 
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double r1 = XI[i] * fast_isqrt(XI[i] * XI[i] + 1);
      const double r4 = 1 / fast_isqrt(XI[i] * XI[i] + 1);
      const double hp = 1 / (SP[i] * r7);
      const double x1 = XP[i] + 0.5 * SP[i] * r7 * (r1 - 1);
      const double x2 = XP[i] + 0.5 * SP[i] * r7 * (r1 + 1);
 
      double r5 = 1.0;
      if (XI[i] > r6 || XI[i] < -r6)
         r5 = XI[i] / fast_log(r4 + XI[i]);
 
      double factor = 1, y = X[i] - x1, Yp = XP[i] - x1, yi = r4 - XI[i], rho = R1[i];
      if (X[i] >= x2) {
         factor = -1;
         y = X[i] - x2;
         Yp = XP[i] - x2;
         yi = r4 + XI[i];
         rho = R2[i];
      }
 
      batches._output[i] = rho * y * y / Yp / Yp - r3 + factor * 4 * r3 * y * hp * r5 * r4 / yi / yi;
      if (X[i] >= x1 && X[i] < x2) {
         batches._output[i] =
            fast_log(1 + 4 * XI[i] * r4 * (X[i] - XP[i]) * hp) / fast_log(1 + 2 * XI[i] * (XI[i] - r4));
         batches._output[i] *= -batches._output[i] * r3;
      }
      if (X[i] >= x1 && X[i] < x2 && XI[i] < r6 && XI[i] > -r6)
         batches._output[i] = -4 * r3 * (X[i] - XP[i]) * (X[i] - XP[i]) * hp * hp;
   }
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = fast_exp(batches._output[i]);
}
 
__rooglobal__ void computeCBShape(BatchesHandle batches)
{
   Batch M = batches[0], M0 = batches[1], S = batches[2], A = batches[3], N = batches[4];
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double t = (M[i] - M0[i]) / S[i];
      if ((A[i] > 0 && t >= -A[i]) || (A[i] < 0 && -t >= A[i]))
         batches._output[i] = -0.5 * t * t;
      else {
         batches._output[i] = N[i] / (N[i] - A[i] * A[i] - A[i] * t);
         batches._output[i] = fast_log(batches._output[i]);
         batches._output[i] *= N[i];
         batches._output[i] -= 0.5 * A[i] * A[i];
      }
   }
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = fast_exp(batches._output[i]);
}
 
__rooglobal__ void computeChebychev(BatchesHandle batches)
{
   Batch xData = batches[0];
   const int nCoef = batches.getNExtraArgs() - 2;
   const double xmin = batches.extraArg(nCoef);
   const double xmax = batches.extraArg(nCoef + 1);
 
   if (STEP == 1) {
      double prev[bufferSize][2], X[bufferSize];
 
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
         // set a0-->prev[i][0] and a1-->prev[i][1]
         // and x tranfsformed to range[-1..1]-->X[i]
         prev[i][0] = batches._output[i] = 1.0;
         prev[i][1] = X[i] = 2 * (xData[i] - 0.5 * (xmax + xmin)) / (xmax - xmin);
      }
      for (int k = 0; k < nCoef; k++)
         for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
            batches._output[i] += prev[i][1] * batches.extraArg(k);
 
            // compute next order
            const double next = 2 * X[i] * prev[i][1] - prev[i][0];
            prev[i][0] = prev[i][1];
            prev[i][1] = next;
         }
   } else
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
         double prev0 = 1.0, prev1 = 2 * (xData[i] - 0.5 * (xmax + xmin)) / (xmax - xmin), X = prev1;
         batches._output[i] = 1.0;
         for (int k = 0; k < nCoef; k++) {
            batches._output[i] += prev1 * batches.extraArg(k);
 
            // compute next order
            const double next = 2 * X * prev1 - prev0;
            prev0 = prev1;
            prev1 = next;
         }
      }
}
 
__rooglobal__ void computeChiSquare(BatchesHandle batches)
{
   Batch X = batches[0];
   const double ndof = batches.extraArg(0);
   const double gamma = 1 / std::tgamma(ndof / 2.0);
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = gamma;
 
   constexpr double ln2 = 0.693147180559945309417232121458;
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      double arg = (ndof - 2) * fast_log(X[i]) - X[i] - ndof * ln2;
      batches._output[i] *= fast_exp(0.5 * arg);
   }
}
 
__rooglobal__ void computeDstD0BG(BatchesHandle batches)
{
   Batch DM = batches[0], DM0 = batches[1], C = batches[2], A = batches[3], B = batches[4];
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double ratio = DM[i] / DM0[i];
      const double arg1 = (DM0[i] - DM[i]) / C[i];
      const double arg2 = A[i] * fast_log(ratio);
      batches._output[i] = (1 - fast_exp(arg1)) * fast_exp(arg2) + B[i] * (ratio - 1);
   }
 
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      if (batches._output[i] < 0)
         batches._output[i] = 0;
}
 
__rooglobal__ void computeExponential(BatchesHandle batches)
{
   Batch x = batches[0], c = batches[1];
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = fast_exp(x[i] * c[i]);
}
 
__rooglobal__ void computeGamma(BatchesHandle batches)
{
   Batch X = batches[0], G = batches[1], B = batches[2], M = batches[3];
   double gamma = -std::lgamma(G[0]);
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      if (X[i] == M[i])
         batches._output[i] = (G[i] == 1.0) / B[i];
      else if (G.isItVector())
         batches._output[i] = -std::lgamma(G[i]);
      else
         batches._output[i] = gamma;
 
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      if (X[i] != M[i]) {
         const double invBeta = 1 / B[i];
         double arg = (X[i] - M[i]) * invBeta;
         batches._output[i] -= arg;
         arg = fast_log(arg);
         batches._output[i] += arg * (G[i] - 1);
         batches._output[i] = fast_exp(batches._output[i]);
         batches._output[i] *= invBeta;
      }
}
 
__rooglobal__ void computeGaussian(BatchesHandle batches)
{
   auto x = batches[0], mean = batches[1], sigma = batches[2];
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double arg = x[i] - mean[i];
      const double halfBySigmaSq = -0.5 / (sigma[i] * sigma[i]);
      batches._output[i] = fast_exp(arg * arg * halfBySigmaSq);
   }
}
 
__rooglobal__ void computeNegativeLogarithms(BatchesHandle batches)
{
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = -fast_log(batches[0][i]);
   // Multiply by weights if they exist
   if (batches.extraArg(0))
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
         batches._output[i] *= batches[1][i];
}
 
__rooglobal__ void computeJohnson(BatchesHandle batches)
{
   Batch mass = batches[0], mu = batches[1], lambda = batches[2], gamma = batches[3], delta = batches[4];
   const double sqrtTwoPi = std::sqrt(TMath::TwoPi());
   const double massThreshold = batches.extraArg(0);
 
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double arg = (mass[i] - mu[i]) / lambda[i];
#ifdef R__HAS_VDT
      const double asinh_arg = fast_log(arg + 1 / fast_isqrt(arg * arg + 1));
#else
      const double asinh_arg = asinh(arg);
#endif
      const double expo = gamma[i] + delta[i] * asinh_arg;
      const double result =
         delta[i] * fast_exp(-0.5 * expo * expo) * fast_isqrt(1. + arg * arg) / (sqrtTwoPi * lambda[i]);
 
      const double passThrough = mass[i] >= massThreshold;
      batches._output[i] = result * passThrough;
   }
}
 
/* Actual computation of Landau(x,mean,sigma) in a vectorization-friendly way
 * Code copied from function landau_pdf (math/mathcore/src/PdfFuncMathCore.cxx)
 * and rewritten to enable vectorization.
 */
__rooglobal__ void computeLandau(BatchesHandle batches)
{
   auto case0 = [](double x) {
      const double a1[3] = {0.04166666667, -0.01996527778, 0.02709538966};
      const double u = fast_exp(x + 1.0);
      return 0.3989422803 * fast_exp(-1 / u - 0.5 * (x + 1)) * (1 + (a1[0] + (a1[1] + a1[2] * u) * u) * u);
   };
   auto case1 = [](double x) {
      constexpr double p1[5] = {0.4259894875, -0.1249762550, 0.03984243700, -0.006298287635, 0.001511162253};
      constexpr double q1[5] = {1.0, -0.3388260629, 0.09594393323, -0.01608042283, 0.003778942063};
      const double u = fast_exp(-x - 1);
      return fast_exp(-u - 0.5 * (x + 1)) * (p1[0] + (p1[1] + (p1[2] + (p1[3] + p1[4] * x) * x) * x) * x) /
             (q1[0] + (q1[1] + (q1[2] + (q1[3] + q1[4] * x) * x) * x) * x);
   };
   auto case2 = [](double x) {
      constexpr double p2[5] = {0.1788541609, 0.1173957403, 0.01488850518, -0.001394989411, 0.0001283617211};
      constexpr double q2[5] = {1.0, 0.7428795082, 0.3153932961, 0.06694219548, 0.008790609714};
      return (p2[0] + (p2[1] + (p2[2] + (p2[3] + p2[4] * x) * x) * x) * x) /
             (q2[0] + (q2[1] + (q2[2] + (q2[3] + q2[4] * x) * x) * x) * x);
   };
   auto case3 = [](double x) {
      constexpr double p3[5] = {0.1788544503, 0.09359161662, 0.006325387654, 0.00006611667319, -0.000002031049101};
      constexpr double q3[5] = {1.0, 0.6097809921, 0.2560616665, 0.04746722384, 0.006957301675};
      return (p3[0] + (p3[1] + (p3[2] + (p3[3] + p3[4] * x) * x) * x) * x) /
             (q3[0] + (q3[1] + (q3[2] + (q3[3] + q3[4] * x) * x) * x) * x);
   };
   auto case4 = [](double x) {
      constexpr double p4[5] = {0.9874054407, 118.6723273, 849.2794360, -743.7792444, 427.0262186};
      constexpr double q4[5] = {1.0, 106.8615961, 337.6496214, 2016.712389, 1597.063511};
      const double u = 1 / x;
      return u * u * (p4[0] + (p4[1] + (p4[2] + (p4[3] + p4[4] * u) * u) * u) * u) /
             (q4[0] + (q4[1] + (q4[2] + (q4[3] + q4[4] * u) * u) * u) * u);
   };
   auto case5 = [](double x) {
      constexpr double p5[5] = {1.003675074, 167.5702434, 4789.711289, 21217.86767, -22324.94910};
      constexpr double q5[5] = {1.0, 156.9424537, 3745.310488, 9834.698876, 66924.28357};
      const double u = 1 / x;
      return u * u * (p5[0] + (p5[1] + (p5[2] + (p5[3] + p5[4] * u) * u) * u) * u) /
             (q5[0] + (q5[1] + (q5[2] + (q5[3] + q5[4] * u) * u) * u) * u);
   };
   auto case6 = [](double x) {
      constexpr double p6[5] = {1.000827619, 664.9143136, 62972.92665, 475554.6998, -5743609.109};
      constexpr double q6[5] = {1.0, 651.4101098, 56974.73333, 165917.4725, -2815759.939};
      const double u = 1 / x;
      return u * u * (p6[0] + (p6[1] + (p6[2] + (p6[3] + p6[4] * u) * u) * u) * u) /
             (q6[0] + (q6[1] + (q6[2] + (q6[3] + q6[4] * u) * u) * u) * u);
   };
   auto case7 = [](double x) {
      const double a2[2] = {-1.845568670, -4.284640743};
      const double u = 1 / (x - x * fast_log(x) / (x + 1));
      return u * u * (1 + (a2[0] + a2[1] * u) * u);
   };
 
   Batch X = batches[0], M = batches[1], S = batches[2];
 
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = (X[i] - M[i]) / S[i];
 
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      if (S[i] <= 0.0)
         batches._output[i] = 0;
      else if (batches._output[i] < -5.5)
         batches._output[i] = case0(batches._output[i]);
      else if (batches._output[i] < -1.0)
         batches._output[i] = case1(batches._output[i]);
      else if (batches._output[i] < 1.0)
         batches._output[i] = case2(batches._output[i]);
      else if (batches._output[i] < 5.0)
         batches._output[i] = case3(batches._output[i]);
      else if (batches._output[i] < 12.0)
         batches._output[i] = case4(batches._output[i]);
      else if (batches._output[i] < 50.0)
         batches._output[i] = case5(batches._output[i]);
      else if (batches._output[i] < 300.)
         batches._output[i] = case6(batches._output[i]);
      else
         batches._output[i] = case7(batches._output[i]);
}
 
__rooglobal__ void computeLognormal(BatchesHandle batches)
{
   Batch X = batches[0], M0 = batches[1], K = batches[2];
   const double rootOf2pi = 2.506628274631000502415765284811;
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      double lnxOverM0 = fast_log(X[i] / M0[i]);
      double lnk = fast_log(K[i]);
      if (lnk < 0)
         lnk = -lnk;
      double arg = lnxOverM0 / lnk;
      arg *= -0.5 * arg;
      batches._output[i] = fast_exp(arg) / (X[i] * lnk * rootOf2pi);
   }
}
 
/* TMath::ASinH(x) needs to be replaced with ln( x + sqrt(x^2+1))
 * argasinh -> the argument of TMath::ASinH()
 * argln -> the argument of the logarithm that replaces AsinH
 * asinh -> the value that the function evaluates to
 *
 * ln is the logarithm that was solely present in the initial
 * formula, that is before the asinh replacement
 */
__rooglobal__ void computeNovosibirsk(BatchesHandle batches)
{
   Batch X = batches[0], P = batches[1], W = batches[2], T = batches[3];
   constexpr double xi = 2.3548200450309494; // 2 Sqrt( Ln(4) )
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      double argasinh = 0.5 * xi * T[i];
      double argln = argasinh + 1 / fast_isqrt(argasinh * argasinh + 1);
      double asinh = fast_log(argln);
 
      double argln2 = 1 - (X[i] - P[i]) * T[i] / W[i];
      double ln = fast_log(argln2);
      batches._output[i] = ln / asinh;
      batches._output[i] *= -0.125 * xi * xi * batches._output[i];
      batches._output[i] -= 2.0 / xi / xi * asinh * asinh;
   }
 
   // faster if you exponentiate in a seperate loop (dark magic!)
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = fast_exp(batches._output[i]);
}
 
__rooglobal__ void computePoisson(BatchesHandle batches)
{
   Batch x = batches[0], mean = batches[1];
   bool protectNegative = batches.extraArg(0);
   bool noRounding = batches.extraArg(1);
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double x_i = noRounding ? x[i] : floor(x[i]);
      batches._output[i] = std::lgamma(x_i + 1.);
   }
 
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double x_i = noRounding ? x[i] : floor(x[i]);
      const double logMean = fast_log(mean[i]);
      const double logPoisson = x_i * logMean - mean[i] - batches._output[i];
      batches._output[i] = fast_exp(logPoisson);
 
      // Cosmetics
      if (x_i < 0)
         batches._output[i] = 0;
      else if (x_i == 0)
         batches._output[i] = 1 / fast_exp(mean[i]);
 
      if (protectNegative && mean[i] < 0)
         batches._output[i] = 1.E-3;
   }
}
 
__rooglobal__ void computePolynomial(BatchesHandle batches)
{
   Batch X = batches[0];
   const int nCoef = batches.getNExtraArgs() - 1;
   const int lowestOrder = batches.extraArg(nCoef);
   if (nCoef == 0) {
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
         batches._output[i] = (lowestOrder > 0.0);
      return;
   } else
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
         batches._output[i] = batches.extraArg(nCoef - 1);
 
   /* Indexes are in range 0..nCoef-1 but coefList[nCoef-1]
    * has already been processed. In order to traverse the list,
    * with step of 2 we have to start at index nCoef-3 and use
    * coefList[k+1] and coefList[k]
    */
   for (int k = nCoef - 3; k >= 0; k -= 2)
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
         batches._output[i] = X[i] * (batches._output[i] * X[i] + batches.extraArg(k + 1)) + batches.extraArg(k);
 
   // If nCoef is even, then the coefList[0] didn't get processed
   if (nCoef % 2 == 0)
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
         batches._output[i] = batches._output[i] * X[i] + batches.extraArg(0);
 
   // Increase the order of the polynomial, first by myltiplying with X[i]^2
   if (lowestOrder != 0) {
      for (int k = 2; k <= lowestOrder; k += 2)
         for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
            batches._output[i] *= X[i] * X[i];
 
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
         if (lowestOrder % 2 == 1)
            batches._output[i] *= X[i];
         batches._output[i] += 1.0;
      }
   }
}
 
__rooglobal__ void computeProdPdf(BatchesHandle batches)
{
   const int nPdfs = batches.extraArg(0);
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = 1.;
   for (int pdf = 0; pdf < nPdfs; pdf++)
      for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
         batches._output[i] *= batches[pdf][i];
}
 
__rooglobal__ void computeRatio(BatchesHandle batches)
{
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      batches._output[i] = batches[0][i] / batches[1][i];
}
 
__rooglobal__ void computeVoigtian(BatchesHandle batches)
{
   Batch X = batches[0], M = batches[1], W = batches[2], S = batches[3];
   const double invSqrt2 = 0.707106781186547524400844362105;
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP) {
      const double arg = (X[i] - M[i]) * (X[i] - M[i]);
      if (S[i] == 0.0 && W[i] == 0.0)
         batches._output[i] = 1.0;
      else if (S[i] == 0.0)
         batches._output[i] = 1 / (arg + 0.25 * W[i] * W[i]);
      else if (W[i] == 0.0)
         batches._output[i] = fast_exp(-0.5 * arg / (S[i] * S[i]));
      else
         batches._output[i] = invSqrt2 / S[i];
   }
 
   for (size_t i = BEGIN; i < batches.getNEvents(); i += STEP)
      if (S[i] != 0.0 && W[i] != 0.0) {
         if (batches._output[i] < 0)
            batches._output[i] = -batches._output[i];
         const double factor = W[i] > 0.0 ? 0.5 : -0.5;
         std::complex<double> z(batches._output[i] * (X[i] - M[i]), factor * batches._output[i] * W[i]);
         batches._output[i] *= faddeeva_impl::faddeeva(z).real();
      }
}
 
/// Returns a std::vector of pointers to the compute functions in this file.
std::vector<void (*)(BatchesHandle)> getFunctions()
{
   return {computeAddPdf,
           computeArgusBG,
           computeBernstein,
           computeBifurGauss,
           computeBreitWigner,
           computeBukin,
           computeCBShape,
           computeChebychev,
           computeChiSquare,
           computeDstD0BG,
           computeExponential,
           computeGamma,
           computeGaussian,
           computeJohnson,
           computeLandau,
           computeLognormal,
           computeNegativeLogarithms,
           computeNovosibirsk,
           computePoisson,
           computePolynomial,
           computeProdPdf,
           computeRatio,
           computeVoigtian};
}
} // End namespace RF_ARCH
} // End namespace RooBatchCompute