diff --git a/Number_types/include/CGAL/Number_types/internal/Exact_type_selector.h b/Number_types/include/CGAL/Number_types/internal/Exact_type_selector.h
index 745d1d93433..772200e7b72 100644
--- a/Number_types/include/CGAL/Number_types/internal/Exact_type_selector.h
+++ b/Number_types/include/CGAL/Number_types/internal/Exact_type_selector.h
@@ -23,8 +23,8 @@
 #include <CGAL/MP_Float.h>
 #include <CGAL/Quotient.h>
 
-#include <CGAL/boost_mp.h>
-#  include <CGAL/cpp_float.h>
+#include <CGAL/cpp_float.h>
+
 #ifdef CGAL_USE_GMP
 #  include <CGAL/Gmpz.h>
 #  include <CGAL/Gmpq.h>
diff --git a/Number_types/include/CGAL/boost_mp_type.h b/Number_types/include/CGAL/boost_mp_type.h
index 731364b43c7..1c038ad3390 100644
--- a/Number_types/include/CGAL/boost_mp_type.h
+++ b/Number_types/include/CGAL/boost_mp_type.h
@@ -20,8 +20,18 @@
 // easy solution.
 // MSVC had trouble with versions <= 1.69:
 // https://github.com/boostorg/multiprecision/issues/98
+//
+// Disable also on Windows 32 bits
+// because CGAL/cpp_float.h assumes _BitScanForward64 is available
+// See https://learn.microsoft.com/en-us/cpp/intrinsics/bitscanforward-bitscanforward64
+//
+// Disable also with PowerPC processors, with Boost<1.80 because of that bug:
+// https://github.com/boostorg/multiprecision/pull/421
+//
 #if !defined CGAL_DO_NOT_USE_BOOST_MP && \
-    (!defined _MSC_VER || BOOST_VERSION >= 107000)
+    (!defined _MSC_VER || BOOST_VERSION >= 107000) && \
+    (!defined _WIN32 || defined _WIN64) && \
+    (BOOST_VERSION >= 108000 || (!defined _ARCH_PPC && !defined _ARCH_PPC64))
 #define CGAL_USE_BOOST_MP 1
 
 #include <CGAL/Quotient.h>