Using `#pragma clad checkpoint loop` to optimize gradients breaks `clad::hessian()`

[guitargeek]

This is the only blocker before we can start using Clad-generated Hessians in RooFit.

Reproducer as a ROOT macro:

// Gaussian.C

// auto-generated test macro
#include <RooFit/Detail/MathFuncs.h>
#include <Math/CladDerivator.h>

double roo_codegen_0(double *params, double const *obs, double const *xlArr)
{
   constexpr double inf = std::numeric_limits<double>::infinity();
   double RooNLLVarNewWeightSum = 0.0;
   double RooNLLVarNewResult = 0.0;
   const double t1 = (params[0] + params[1]);
   const double t3 = 1.5;
   double t2[]{params[2], t3};
   const double t4 = RooFit::Detail::MathFuncs::product(t2, 2);
   const double t6 = RooFit::Detail::MathFuncs::gaussianIntegral(-10, 10, t1, t4);
#pragma clad checkpoint loop
   for (int loopIdx1 = 0; loopIdx1 < obs[1]; loopIdx1++) {
      const double t5 = RooFit::Detail::MathFuncs::gaussian(obs[static_cast<int>(obs[0]) + loopIdx1], t1, t4);
      const double t7 = t5 / t6;
      RooNLLVarNewResult += RooFit::Detail::MathFuncs::nll(t7, obs[static_cast<int>(obs[2]) + loopIdx1], 0, 0);
   }
   return RooNLLVarNewResult;
}

#pragma clad ON
void gradient_request()
{
   clad::gradient(roo_codegen_0, "params");
   clad::hessian(roo_codegen_0, "params[0:2]");
}
#pragma clad OFF
// clang-format off

std::vector<double> parametersVec = {
    0, 1, 3
};

std::vector<double> observablesVec = {
    6, 54, 60, 54, 114, 54, -9.1, -8.1, -5.7, -5.5, 
    -5.3, -4.9, -4.5, -4.3, -3.9, -3.7, -3.5, -3.1, -2.9, -2.5, 
    -2.3, -1.7, -1.5, -1.3, -1.1, -0.9, -0.7, -0.5, -0.3, -0.1, 
    0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.9, 2.1, 
    2.3, 2.7, 3.1, 3.7, 4.5, 4.7, 4.9, 5.1, 5.5, 6.1, 
    6.3, 6.5, 7.1, 7.3, 7.7, 7.9, 8.9, 9.1, 9.3, 9.9, 
    1, 1, 1, 1, 1, 2, 3, 3, 1, 1, 
    1, 2, 1, 1, 3, 2, 1, 1, 3, 3, 
    3, 2, 3, 3, 3, 2, 2, 4, 3, 4, 
    1, 1, 1, 2, 3, 2, 2, 1, 2, 1, 
    1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 
    1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 
    3, 3, 1, 1, 1, 2, 1, 1, 3, 2, 
    1, 1, 3, 3, 3, 2, 3, 3, 3, 2, 
    2, 4, 3, 4, 1, 1, 1, 2, 3, 2, 
    2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 
    2, 2, 1, 2, 1, 2, 1, 1
};

std::vector<double> auxConstantsVec = {
};

// clang-format on

// To run as a ROOT macro
void Gaussian()
{
   auto func = [&](std::span<double> params) {
      return roo_codegen_0(params.data(), observablesVec.data(), auxConstantsVec.data());
   };
   auto grad = [&](std::span<double> params, std::span<double> out) {
      return roo_codegen_0_grad_0(parametersVec.data(), observablesVec.data(), auxConstantsVec.data(), out.data());
   };

   auto hess = [&](std::span<double> params, std::span<double> out) {
      return roo_codegen_0_hessian_0(parametersVec.data(), observablesVec.data(), auxConstantsVec.data(), out.data());
   };

   std::vector<double> gradientVec(parametersVec.size());
   std::vector<double> hessianVec(parametersVec.size() * parametersVec.size());

   grad(parametersVec, gradientVec);
   hess(parametersVec, hessianVec);

   auto numDiff = [&](int i) {
      const double eps = 1e-6;
      std::vector<double> p{parametersVec};
      p[i] = parametersVec[i] - eps;
      double funcValDown = func(p);
      p[i] = parametersVec[i] + eps;
      double funcValUp = func(p);
      return (funcValUp - funcValDown) / (2 * eps);
   };

   for (std::size_t i = 0; i < parametersVec.size(); ++i) {
      std::cout << i << ":" << std::endl;
      std::cout << "  numr : " << numDiff(i) << std::endl;
      std::cout << "  clad : " << gradientVec[i] << std::endl;
   }

   std::cout << std::endl;

   auto n = parametersVec.size();

   for (std::size_t i = 0; i < n; ++i) {
      for (std::size_t j = 0; j < n; ++j) {
          std::cout << hessianVec[i + n *j] << "   ";
      }
      std::cout << std::endl;
   }
}

Error message:

In file included from input_line_8:1:
/home/rembserj/Gaussian.C:15:25: error: '#pragma clad checkpoint loop' is only allowed before a loop
#pragma clad checkpoint loop
                        ^
/home/rembserj/Gaussian.C:15:25: error: '#pragma clad checkpoint loop' is only allowed before a loop
/home/rembserj/Gaussian.C:15:25: error: '#pragma clad checkpoint loop' is only allowed before a loop
/home/rembserj/Gaussian.C:15:25: error: '#pragma clad checkpoint loop' is only allowed before a loop
warning: attempted differentiation of function 'digamma' without definition and no suitable overload was found in namespace 'custom_derivatives'
note: falling back to numerical differentiation for 'digamma' since no suitable overload was found and clad could not derive it; to disable this feature, compile your programs with -DCLAD_NO_NUM_DIFF
warning: attempted differentiation of function 'digamma' without definition and no suitable overload was found in namespace 'custom_derivatives'
note: falling back to numerical differentiation for 'digamma' since no suitable overload was found and clad could not derive it; to disable this feature, compile your programs with -DCLAD_NO_NUM_DIFF

[fatfat123-arch]

Hello, I opened a PR for this: #1756.

The workflows for the fork PR are still awaiting approval, so some CI/codecov checks are pending. Could a maintainer approve or rerun them when possible? Thank you!