diff --git a/include/boost/decimal/detail/div_impl.hpp b/include/boost/decimal/detail/div_impl.hpp
index 6c49b8e6..c10514af 100644
--- a/include/boost/decimal/detail/div_impl.hpp
+++ b/include/boost/decimal/detail/div_impl.hpp
@@ -88,8 +88,9 @@ constexpr auto d128_generic_div_impl(const T& lhs, const T& rhs, T& q) noexcept
         const auto digit_delta {sig_dig - std::numeric_limits<detail::uint128>::digits10};
         res_sig /= detail::uint256_t(pow10(detail::uint128(digit_delta)));
         res_exp += digit_delta;
+        BOOST_DECIMAL_ASSERT(res_sig.high == 0);
     }
-    else if (res_sig == UINT64_C(0))
+    else if (res_sig.low == UINT64_C(0))
     {
         sign = false;
     }
diff --git a/include/boost/decimal/detail/integer_search_trees.hpp b/include/boost/decimal/detail/integer_search_trees.hpp
index a8a319d8..23d2139d 100644
--- a/include/boost/decimal/detail/integer_search_trees.hpp
+++ b/include/boost/decimal/detail/integer_search_trees.hpp
@@ -203,20 +203,36 @@ constexpr int num_digits(const uint256_t& x) noexcept
         return num_digits(x.low);
     }
 
-    // 10^77
-    auto current_power_of_10 {uint256_t{uint128{UINT64_C(15930919111324522770), UINT64_C(5327493063679123134)}, uint128{UINT64_C(12292710897160462336), UINT64_C(0)}}};
+    // Use the most significant bit position to approximate log10
+    // log10(x) ≈ log2(x) / log2(10) ≈ log2(x) / 3.32
 
-    for (int i = 78; i > 0; --i)
+    int msb {};
+    // Check high part of high (most significant 64 bits of 256-bit number)
+    if (x.high.high != 0)
     {
-        if (x >= current_power_of_10)
-        {
-            return i;
-        }
+        msb = 192 + (64 - countl_zero(x.high.high));
+    }
+    // Check low part of high (bits 128-191 of 256-bit number)
+    else if (x.high.low != 0)
+    {
+        msb = 128 + (64 - countl_zero(x.high.low));
+    }
 
-        current_power_of_10 /= UINT64_C(10);
+    // Approximate log10 using log2
+    const auto estimated_digits {(msb * 1000) / 3322 + 1}; // 1000/3322 approxeq 1/log2(10)
+
+    // Check if our estimate is correct or needs adjustment
+    if (x >= impl::emulated_256_pow10[estimated_digits])
+    {
+        // Check to make sure we don't exceed the maximum value
+        return estimated_digits != 78 ? estimated_digits + 1 : estimated_digits;
+    }
+    else if (estimated_digits > 1 && x < impl::emulated_256_pow10[estimated_digits - 1])
+    {
+        return estimated_digits - 1;
     }
 
-    return 1;
+    return estimated_digits;
 }
 
 #ifdef _MSC_VER