From 5f976068e2223060cfae3ff83dc8f748bc6b32a9 Mon Sep 17 00:00:00 2001
From: Jonas Rembser <jonas.rembser@cern.ch>
Date: Fri, 27 Feb 2026 01:29:17 +0100
Subject: [PATCH 1/2] [Math] Add custom derivative for `digamma` function

The `digamma` function is important because it's the derivative of the
log of the gamma function, which is widely used in likelihood fits
because it appears in the Poisson distribution. If we want analytical
Hessians, we also need to provide the analytical derivative of the
digamma function, which is the trigamma function. Fortunately, we can
find it in the GNU scientific library:

https://www.gnu.org/software/gsl/doc/html/specfunc.html#trigamma-function
---
 math/mathcore/inc/Math/CladDerivator.h    | 17 +++++++++--------
 math/mathmore/inc/Math/SpecFuncMathMore.h |  1 +
 math/mathmore/src/SpecFuncMathMore.cxx    |  5 +++++
 3 files changed, 15 insertions(+), 8 deletions(-)

diff --git a/math/mathcore/inc/Math/CladDerivator.h b/math/mathcore/inc/Math/CladDerivator.h
index 1c33e7cd3f1ca..b57722bb86242 100644
--- a/math/mathcore/inc/Math/CladDerivator.h
+++ b/math/mathcore/inc/Math/CladDerivator.h
@@ -34,8 +34,7 @@
 
 #include <stdexcept>
 
-namespace clad {
-namespace custom_derivatives {
+namespace clad::custom_derivatives {
 namespace TMath {
 template <typename T>
 ValueAndPushforward<T, T> Abs_pushforward(T x, T d_x)
@@ -222,8 +221,7 @@ ValueAndPushforward<Double_t, Double_t> Ln10_pushforward()
 #endif
 } // namespace TMath
 
-namespace ROOT {
-namespace Math {
+namespace ROOT::Math {
 
 inline void landau_pdf_pullback(double x, double xi, double x0, double d_out, double *d_x, double *d_xi, double *d_x0)
 {
@@ -1092,13 +1090,16 @@ inline void inc_gamma_c_pullback(double a, double x, double _d_y, double *_d_a,
    }
 }
 
+inline ValueAndPushforward<double, double> digamma_pushforward(double x, double d_x)
+{
+   return {::ROOT::Math::digamma(x), ::ROOT::Math::trigamma(x) * d_x};
+}
+
 #endif // R__HAS_MATHMORE
 
-} // namespace Math
-} // namespace ROOT
+} // namespace ROOT::Math
 
-} // namespace custom_derivatives
-} // namespace clad
+} // namespace clad::custom_derivatives
 
 // Forward declare BLAS functions.
 extern "C" void sgemm_(const char *transa, const char *transb, const int *m, const int *n, const int *k,
diff --git a/math/mathmore/inc/Math/SpecFuncMathMore.h b/math/mathmore/inc/Math/SpecFuncMathMore.h
index 564729efbb39f..897c637ac53bd 100644
--- a/math/mathmore/inc/Math/SpecFuncMathMore.h
+++ b/math/mathmore/inc/Math/SpecFuncMathMore.h
@@ -874,6 +874,7 @@ namespace Math {
    double wigner_9j(int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf, int two_jg, int two_jh, int two_ji);
 
    double digamma(double x);
+   double trigamma(double x);
 
 
 } // namespace Math
diff --git a/math/mathmore/src/SpecFuncMathMore.cxx b/math/mathmore/src/SpecFuncMathMore.cxx
index 73ed6c98149fe..8d29b10cca3d2 100644
--- a/math/mathmore/src/SpecFuncMathMore.cxx
+++ b/math/mathmore/src/SpecFuncMathMore.cxx
@@ -482,5 +482,10 @@ double digamma(double x)
    return gsl_sf_psi(x);
 }
 
+double trigamma(double x)
+{
+   return gsl_sf_psi_1(x);
+}
+
 } // namespace Math
 } // namespace ROOT

From cdd7d1700c8431bcc373ffe545939b7dcb959c83 Mon Sep 17 00:00:00 2001
From: Jonas Rembser <jonas.rembser@cern.ch>
Date: Fri, 27 Feb 2026 01:32:55 +0100
Subject: [PATCH 2/2] [Math] Remove unneeded code from CladDerivator.h

---
 math/mathcore/inc/Math/CladDerivator.h | 14 --------------
 1 file changed, 14 deletions(-)

diff --git a/math/mathcore/inc/Math/CladDerivator.h b/math/mathcore/inc/Math/CladDerivator.h
index b57722bb86242..1d5cdcf2f9a60 100644
--- a/math/mathcore/inc/Math/CladDerivator.h
+++ b/math/mathcore/inc/Math/CladDerivator.h
@@ -205,20 +205,6 @@ ValueAndPushforward<T, T> TanH_pushforward(T x, T d_x)
    return {::TMath::TanH(x), (1. / ::TMath::Sq(::TMath::CosH(x))) * d_x};
 }
 
-#ifdef WIN32
-// Additional custom derivatives that can be removed
-// after Issue #12108 in ROOT is resolved
-// constexpr is removed
-ValueAndPushforward<Double_t, Double_t> Pi_pushforward()
-{
-   return {3.1415926535897931, 0.};
-}
-// constexpr is removed
-ValueAndPushforward<Double_t, Double_t> Ln10_pushforward()
-{
-   return {2.3025850929940459, 0.};
-}
-#endif
 } // namespace TMath
 
 namespace ROOT::Math {