[treeplayer] Fix precision loss in TTree::Scan for 64-bit integers

The `"lld"` column format passed without an embedded size (e.g. via
`"colsize=N col=lld"`) was not recognized as a `"long long"` modifier in
**TTreeFormula::PrintValue**, so 64-bit integer branches (e.g.
`ULong64_t`) were evaluated as double and rounded above 2^53.

This commit fixes a off-by-one problem in the length-modifier detection
to address the issue, adding also a regression test.

Closes #7844.

🤖 Done with the help of [Claude Code](https://claude.com/claude-code) (Claude Opus 4.8)

(cherry picked from commit 7cea10c)

Author: guitargeek

tree/treeplayer/src/TTreeFormula.cxx

@@ -5052,12 +5052,12 @@ char *TTreeFormula::PrintValue(Int_t mode, Int_t instance, const char *decform)
             Ssiz_t len = strlen(decform);
             Char_t outputSizeLevel = 1;
             char *expo = nullptr;
-            if (len>2) {
+            if (len > 1) {
                switch (decform[len-2]) {
                   case 'l':
                   case 'L': {
                      outputSizeLevel = 2;
-                     if (len>3 && tolower(decform[len-3])=='l') {
+                     if (len > 2 && tolower(decform[len - 3]) == 'l') {
                         outputSizeLevel = 3;
                      }
                      break;

tree/treeplayer/test/regressions.cxx

@@ -19,6 +19,7 @@
 
 #include "gtest/gtest.h"
 
+#include <limits>
 #include <string>
 #include <vector>
 #include <fstream>
@@ -668,3 +669,78 @@ TEST(TTreeScan, TTreeGetBranchOfFriendTChain)
          throw std::runtime_error("Could not retrieve TTreePlayer from main tree!");
    }
 }
+
+// https://github.com/root-project/root/issues/7844
+// TTree::Scan() used to lose precision when printing 64-bit integer branches
+// (e.g. ULong64_t): the "lld" column format, when given without an embedded
+// column size (i.e. via "colsize=N col=lld"), was not recognized as a
+// "long long" modifier because of an off-by-one in the length-modifier
+// detection in TTreeFormula::PrintValue. As a consequence the value was
+// evaluated and printed as a double, rounding anything above 2^53.
+TEST(TTreeScan, ULong64Precision)
+{
+   // The "long long" Scan/Draw column format is evaluated through `long double`
+   // (see TTreeFormula::PrintValue), so exact 64-bit integer output is only
+   // possible where `long double` has more mantissa bits than `double`. That is
+   // the case on x86-64 (80-bit, 64-bit mantissa) but not, e.g., on macOS ARM
+   // where `long double` is just a 64-bit `double` (53-bit mantissa). Skip the
+   // exactness check there, since the value genuinely cannot be represented.
+   if (std::numeric_limits<long double>::digits <= std::numeric_limits<double>::digits)
+      GTEST_SKIP() << "long double is not wider than double here; the 64-bit value "
+                      "is genuinely unrepresentable and exactness cannot be checked";
+
+   // 1617047019150033926 needs 61 bits, so it cannot be represented exactly
+   // by a double (53-bit mantissa).
+   constexpr ULong64_t value{1617047019150033926ULL};
+
+   constexpr const char *treeName{"tree_7844"};
+   ROOT::TestSupport::FileRaii fileGuard{"tree_7844.root"};
+   {
+      std::unique_ptr<TFile> file{TFile::Open(fileGuard.GetPath().c_str(), "recreate")};
+      auto tree = std::make_unique<TTree>(treeName, treeName);
+
+      ULong64_t x = value;
+      tree->Branch("x", &x, "x/l");
+      tree->Fill();
+      file->Write();
+   }
+
+   std::unique_ptr<TFile> file{TFile::Open(fileGuard.GetPath().c_str())};
+   auto tree = file->Get<TTree>(treeName);
+
+   auto *treePlayer = static_cast<TTreePlayer *>(tree->GetPlayer());
+   ASSERT_TRUE(treePlayer) << "Could not retrieve TTreePlayer from main tree!";
+
+   ROOT::TestSupport::FileRaii redirectFile{"tree_7844_regression_redirect.txt"};
+   // SetScanFileName() stores the raw pointer, so keep the path string alive.
+   const std::string redirectPath{redirectFile.GetPath()};
+   treePlayer->SetScanRedirect(true);
+   treePlayer->SetScanFileName(redirectPath.c_str());
+
+   // Run a Scan with the given option string into the redirect file and return
+   // its contents.
+   auto scanToString = [&](const char *option) {
+      tree->Scan("x:x-1617047019150033925:x-1617047019150033000", "", option);
+      std::ifstream redirectStream(redirectPath.c_str());
+      std::stringstream redirectOutput;
+      redirectOutput << redirectStream.rdbuf();
+      return redirectOutput.str();
+   };
+
+   const static std::string expectedScanOut{
+      R"Scan(************************************************************************************
+*    Row   *                     x * x-1617047019150033925 * x-1617047019150033000 *
+************************************************************************************
+*        0 *   1617047019150033926 *                     1 *                   926 *
+************************************************************************************
+)Scan"};
+
+   // The "long long" column format must print the exact 64-bit value, as well as
+   // the exact result of integer arithmetic with large constants. The column size
+   // can either be given separately via "colsize=" (so the format passed to
+   // TTreeFormula::PrintValue is just "lld") or be embedded in the format token
+   // itself ("21lld"). Only the former triggered the off-by-one in the
+   // length-modifier detection, but both must yield the exact output.
+   EXPECT_EQ(scanToString("colsize=21 col=lld:lld:lld"), expectedScanOut);
+   EXPECT_EQ(scanToString("col=21lld:21lld:21lld"), expectedScanOut);
+}