[BP][6.40][tree,hist] do not silently hide sqrt of negative value in T(Tree)Formula

README/ReleaseNotes/v640/index.md

@@ -217,6 +217,16 @@ This change affects the following classes:  `TFile`, `TMapFile`, `TMemFile`, `TD
 
 ### TTree
 
+#### Behavior change since 6.40.06: `sqrt()` of negative arguments in TTreeFormula now returns NaN
+
+Since its introduction in 1995, the formula engine used by `TTree::Draw()`, `TTree::Scan()` and `TTreeFormula`
+silently evaluated `sqrt(x)` as `sqrt(abs(x))` for negative arguments (or as `0` in the optimized evaluation path
+of the legacy `ROOT::v5::TFormula`). This could produce silently wrong results, e.g. in selections involving
+`sqrt` of an expression that can become negative. `sqrt()` now returns NaN for negative arguments, consistent
+with `TMath::Sqrt()`, the standard C `sqrt()`, and the modern `TFormula` used by `TF1`.
+Note that in a selection, a NaN evaluates as `false`, so entries where the `sqrt` argument is negative now fail
+the cut instead of being selected based on `sqrt(abs(x))`.
+
 ### RNTuple
 
 - A new API to create "active entry tokens" was added to the `RNTupleReader`. Active entry tokens that are used prevent cache eviction of the entries at hand.

hist/hist/src/TFormula_v5.cxx

@@ -2764,7 +2764,7 @@ Double_t TFormula::EvalParOld(const Double_t *x, const Double_t *uparams)
          case kfmod : pos--; tab[pos-1] = fmod(tab[pos-1],tab[pos]); continue;
          case kpow  : pos--; tab[pos-1] = TMath::Power(tab[pos-1],tab[pos]); continue;
          case ksq   : tab[pos-1] = tab[pos-1]*tab[pos-1]; continue;
-         case ksqrt : tab[pos-1] = TMath::Sqrt(TMath::Abs(tab[pos-1])); continue;
+         case ksqrt : tab[pos-1] = TMath::Sqrt(tab[pos-1]); continue;
 
          case kstrstr : strpos -= 2; pos-=2; pos++;
                         if (strstr(stringStack[strpos],stringStack[strpos+1])) tab[pos-1]=1;

tree/treeplayer/src/TTreeFormula.cxx

@@ -4259,7 +4259,7 @@ T TTreeFormula::EvalInstance(Int_t instance, const char *stringStackArg[])
             case kfmod : pos--; tab[pos-1] = fmod_local(tab[pos-1],tab[pos]); continue;
             case kpow  : pos--; tab[pos-1] = TMath::Power(tab[pos-1],tab[pos]); continue;
             case ksq   : tab[pos-1] = tab[pos-1]*tab[pos-1]; continue;
-            case ksqrt : tab[pos-1] = TMath::Sqrt(TMath::Abs(tab[pos-1])); continue;
+            case ksqrt : tab[pos-1] = TMath::Sqrt(tab[pos-1]); continue;
 
             case kstrstr : pos2 -= 2; pos++;if (strstr(stringStack[pos2],stringStack[pos2+1])) tab[pos-1]=1;
                                             else tab[pos-1]=0;

tree/treeplayer/test/regressions.cxx

@@ -744,3 +744,21 @@ TEST(TTreeScan, ULong64Precision)
    EXPECT_EQ(scanToString("colsize=21 col=lld:lld:lld"), expectedScanOut);
    EXPECT_EQ(scanToString("col=21lld:21lld:21lld"), expectedScanOut);
 }
+
+// https://github.com/root-project/root/issues/22755
+// sqrt() of a negative argument used to evaluate to sqrt(abs(x)) instead of NaN
+TEST(TTreeFormulaRegressions, SqrtOfNegative)
+{
+   TTree t("t", "t");
+   int x = 0;
+   t.Branch("x", &x, "x/I");
+   t.Fill();
+   t.GetEntry(0);
+
+   TTreeFormula tf("tf", "sqrt(-4.0)", &t);
+   EXPECT_TRUE(std::isnan(tf.EvalInstance()));
+   TTreeFormula tf2("tf2", "sqrt(x - 4)", &t);
+   EXPECT_TRUE(std::isnan(tf2.EvalInstance()));
+   TTreeFormula tf3("tf3", "sqrt(x + 9)", &t);
+   EXPECT_FLOAT_EQ(tf3.EvalInstance(), 3.);
+}